UNIVERSITÉ DU QUÉBEC À MONTRÉAL
TROIS ESSAIS SUR LA SANTÉ, LA CONSOMMATION ET LES OUTILS DE
DÉCUMULATION
THÈSE
PRÉSENTÉE
COMME EXIGENCE PARTIELLE
DU DOCTORAT EN ÉCONOMIQUE
PAR
ISMAËL CHOINIÈRE CRÈVECOEUR
SEPTEMBRE 2020
UNIVERSITÉ DU QUÉBEC À MONTRÉAL
THREE ESSAYS ON HEALTH, CONSUMPTION AND DECUMULATION
TOOLS
THESIS
PRESENTED
AS PARTIAL REQUIREMENT
OF DOCTORAL OF PHILOSOPHY IN ECONOMICS
BY
ISMAËL CHOINIÈRE CRÈVECOEUR
SEPTEMBER 2020
REMERCIEMENTS
La réalisation de mon doctorat aura été un moment exigeant et marquant de mon
parcours académique et professionnel. L’expérience aura toutefois été des plus val-
orisante et jamais je n’aurais pu accomplir un tel exploit sans le soutien infaillible
de nombreuses personnes qui m’ont encouragé durant ces 5 dernières années.
Je tiens tout d’abord à remercier mes directeurs de recherche, les professeurs Raquel
Fonseca et Pierre-Carl Michaud. Merci pour votre confiance, pour votre générosité
et pour les nombreuses opportunités que vous m’avez offertes. Je n’aurais jamais
entrepris une telle aventure sans votre optimisme quant à mes chances de réussir.
J’aimerais également remercier la Chaire de recherche sur les enjeux économiques
intergénérationnels (CREEI), l’Institut sur la retraite et l’épargne (IRE), le Réseau
canadien des Centres de données de recherche (RCCDR), de même que le Cen-
tre interuniversitaire québécois de statistiques sociales (CIQSS), pour vos appuis
financiers, pour l’accès aux données nécessaires à la réalisation de cette thèse et pour
m’avoir donné l’opportunité de participer à de nombreux projets parallèles.
Finalement, je voudrais remercier ma femme, Mèlina, pour son support et sa patience
durant ces années exigeantes.
Enfin, je souhaite dédier cette thèse à ma fille Marilou, qui réussit toujours à m’émerveiller
et à égayer mes journées, même les plus difficiles.
TABLE DES MATIÈRES
LISTE DES FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
LISTE DES TABLEAUX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
RÉSUMÉ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
CHAPITRE I INCOME VOLATILITY, HEALTH AND WELL-BEING . . . 6
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Data and Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.1 Sample Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.2 Health and Well-Being Outcomes . . . . . . . . . . . . . . . . . . 11
1.2.3 Retrospective Component of LISA . . . . . . . . . . . . . . . . . 13
1.2.4 Covariates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.3 Econometric Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.3.1 Estimating Variances of Transitory and Permanent Shocks . . . . 16
1.3.2 Estimating Impacts of Income Volatility on Health and Well-Being 20
1.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.4.1 General Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.4.2 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
CHAPITRE II CONSUMPTION AND HEALTH IN OLD AGE . . . . . . . 35
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
v
2.2 Theoretical Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.3.1 Sample Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.3.2 Definition of Spending Variables . . . . . . . . . . . . . . . . . . . 48
2.3.3 Health Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.3.4 Net Wealth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.3.5 Other Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.3.6 Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.4 Empirical Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
CHAPITRE III LOW DEMAND FOR REVERSE MORTGAGES IN CA-
NADA : PRICE OR PREFERENCES ? . . . . . . . . . . . . . . . . . . . . . 72
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.2 What Should the Price of a Reverse Mortgage Be? . . . . . . . . . . . . 77
3.2.1 Computation of the Reverse Mortgage Insurance Premium . . . . 78
3.2.2 House Price Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 80
3.3 Canadian Home Income Plan . . . . . . . . . . . . . . . . . . . . . . . . 82
3.3.1 Actuarially Fair Mortgage Insurance Premium in Canada . . . . . 85
3.4 Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.4.1 Survival Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.4.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.4.3 Relative Fairness . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.5 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3.5.1 Knowledge and Intention of Buying . . . . . . . . . . . . . . . . . 102
vi
3.5.2 Empirical Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
APPENDIX A INCOME VOLATILITY, HEALTH AND WELL-BEING . . 116
A.1 Health Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
A.2 Information Window on Income . . . . . . . . . . . . . . . . . . . . . . . 117
APPENDIX B CONSUMPTION AND HEALTH IN OLD AGE . . . . . . . 119
APPENDIX C REVERSE MORTGAGE . . . . . . . . . . . . . . . . . . . . 121
C.1 Regression Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
C.2 Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
LISTE DES FIGURES
Figure Page
1.1 Distribition of health and well-being outcomes . . . . . . . . . . . . . 14
1.2 Mental health issues . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1 HRS and CAMS Timing . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.1 MLS Home Price Index for the cities of Vancouver, Toronto and
Montreal, from 2005 to 2018 . . . . . . . . . . . . . . . . . . . . . . . 81
3.2 Comparative statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
A.1 Information Window on Income . . . . . . . . . . . . . . . . . . . . . 118
LISTE DES TABLEAUX
Tableau Page
1.1 Sample selection - LISA database . . . . . . . . . . . . . . . . . . . . 11
1.2 Variances of permanent and transitory components of income . . . . 19
1.3 Estimates of the variances of permanent and transitory components
of income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.4 Effect of income volatility on health and well-being . . . . . . . . . . 26
1.5 Effect of income volatility on mental health issues . . . . . . . . . . . 28
1.6 Robustness tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.1 Sample selection from CAMS and HRS . . . . . . . . . . . . . . . . . 47
2.2 Nondurable spending categories . . . . . . . . . . . . . . . . . . . . . 49
2.3 ADL & IADL joint probabilities . . . . . . . . . . . . . . . . . . . . . 50
2.4 Net wealth categories . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.5 Expectations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.6 Effect on Expectations . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.7 Effect on Aggregates . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2.8 Effect on composition of spending . . . . . . . . . . . . . . . . . . . . 63
2.9 Decomposition of spending categories change . . . . . . . . . . . . . . 65
2.10 Effect on composition of net wealth . . . . . . . . . . . . . . . . . . . 67
2.11 Housing wealth dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 68
ix
3.1 House price dynamic . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.2 Maximum loan-to-value . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.3 Actuarially fair rates . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.4 Sample Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.5 Expected remaining years of life . . . . . . . . . . . . . . . . . . . . . 97
3.6 Relative Fairness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.7 Knowledge of reverse mortgages . . . . . . . . . . . . . . . . . . . . . 104
3.8 Subjective expectation of house price growth over the next 5 years . . 105
3.9 Probability of buying a reverse mortgage within the next year . . . . 106
3.10 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
3.11 Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
B.1 Spending category and variable names across waves . . . . . . . . . . 120
C.1 Results using objective life tables . . . . . . . . . . . . . . . . . . . . 122
C.2 Results using prospective life tables . . . . . . . . . . . . . . . . . . . 123
C.3 Results using subjective life tables . . . . . . . . . . . . . . . . . . . . 124
LISTE DES ABRÉVIATIONS, DES SIGLES ET DES ACRONYMES
AVQ Activités de la vie quotidienne
ADL Activity of daily living
AIVQ Activités instrumentales de la vie quotidienne
CAMS Consumption and Activities Mail Survey
CCHS Canadian Community Health Survey
CHIP Canadian Home Income Plan
CMA Cencus metropolitan area
CREA Canadian Real Estate Association
FHA Federal Housing Administration
IADL Instrumental activity of daily living
GDP Gross domestic product
HRS Health and Retirement Study
IRA Individual retirement accounts
LISA Longitudinal and International Study of Adults
MIP Mortgage insurance premium
NNEG No-negative equity guarantee
OLS Ordinary least squares
SDF Single family dwelling
SES Socio-economics status
UK United Kingdom
U.S. United States
RÉSUMÉ
Cette thèse est composée de trois chapitres portant sur la santé, la consommation et
les outils de décumulation d’épargne.
Un premier chapitre porte sur l’effet d’une volatilité soutenue du revenu durant la
vie active sur la santé et le bien-être à un âge plus avancé. Bien qu’il y ait de plus
en plus de preuves que des chocs de revenus importants, par exemple sous la forme
d’une perte d’emploi, peuvent avoir un impact sur la santé et la mortalité, il existe
peu d’études sur la relation potentielle entre la volatilité soutenue du revenu et la
santé, indépendamment du niveau de revenu. Ce chapitre exploite de riches données
d’enquête sur la santé et le bien-être de Canadiens d’un âge avancé, ainsi que leurs
dossiers fiscaux, pour déterminer si une relation existe entre la santé et le bien-être
d’une part, et la volatilité du revenu propre à chaque individu de l’autre, décomposant
la volatilité en composantes permanente et transitoire. En tenant compte du revenu
moyen durant la vie active, nous avons constaté qu’une augmentation d’une unité
de la variance de la composante permanente du revenu (log) vécu au cours de la vie
professionnelle était associée à une probabilité plus faible d’être en excellente (-23,9
%) ou en très bonne (-13,3 %) santé, d’être satisfait de la vie (-34,9 %), et implique
une augmentation de 1,1 problème de santé mentale supplémentaire. Nous avons
trouvé des résultats semblables, quoique plus faibles, pour la composante transitoire
du revenu. Ces résultats ont des implications potentiellement importantes pour les
politiques publiques, ainsi que pour la compréhension de la relation entre le marché
du travail et la santé de la population.
Un deuxième chapitre étudie comment les dépenses et la composition des dépenses
changent en raison de l’incidence de limitations dans les activités de la vie quoti-
dienne (AVQ). En combinant les données longitudinales du Consumption and Acti-
vities Mail Survey (CAMS) et du Health and Retirement Study (HRS), nous avons
construit un test visant à identifier dans quelle mesure l’utilité marginale des dé-
penses dépend de la santé dans un contexte intertemporel. Une dépendance positive
à l’égard de l’état de santé signifie qu’un dollar dépensé a plus de valeur lorsqu’on
est en bonne santé. Nous avons constaté que l’utilité marginale des dépenses totales
xii
et non durables augmente avec l’incidence de limitations dans les activités instru-
mentales de la vie quotidienne (AIVQ), entraînant ainsi une dépendance négative.
Étant donné que certaines assurances protègent contre les difficultés financières en
cas de mauvaise santé, ce résultat implique que ces assurances ont plus de valeur que
celle prévue en utilisant le cadre standard. D’un autre côté, l’utilité marginale des
dépenses totales n’a pas changé en raison de l’incidence de limitations des AVQ, ce
qui suggère l’absence de dépendance à l’égard de l’état de santé à la suite de tels
chocs. Suite à l’incidence de limitations AIVQ, nous avons observé un remaniement
dans les catégories de dépenses et dans les catégories d’actifs, en réaffectant les actifs
résidentiels vers des actifs financiers. Ce dernier résultat suggère que les propriétaires
utilisent la valeur nette de leur maison comme un outil d’assurance.
Un troisième chapitre étudie les déterminants de la faible demande d’hypothèques in-
versées au Canada. La caractéristique principale qui différencie une hypothèque inver-
sée d’une marge de crédit hypothécaire est la no-negative equity guarantee (NNEG).
Cette caractéristique assure que, au moment de repayer le prêt, l’emprunteur n’aura
qu’à payer le minimum entre la valeur de revente de la maison et le solde du prêt.
Dans ce chapitre, nous utilisons un modèle de tarification pour calculer les primes
d’assurances hypothécaires permettant de couvrir les pertes reliées à la NNEG. Étant
donné les prêts actuellement accordés dans le marché canadien, nous trouvons que
les primes actuarielles justes sont approximativement de zéro, ce qui implique que
la NNEG est inexistante dans le marché canadien. Nous avons aussi construit une
enquête de type stated-choice experiment, où des répondants canadiens étaient invi-
tés à évaluer divers produits de prêt hypothécaire inversé. En utilisant une variation
exogène des taux d’intérêt et de la taille des prêts présentés lors de l’enquête, nous
avons utilisé ces évaluations pour calculer l’élasticité de la demande au Canada et
pour identifier les autres facteurs qui peuvent expliquer la faible demande. Nos ré-
sultats montrent que plus de la moitié des Canadiens admissibles n’ont même pas
de connaissances de base sur les prêts hypothécaires inversés. De plus, les Canadiens
admissibles ne semblent pas comprendre comment tirer parti de la NNEG. Enfin, la
demande canadienne en prêts hypothécaires inversés est inélastique, mais elle devient
élastique avec un meilleur niveau de connaissance du produit. Par conséquent, une
combinaison d’ajustement des prix et d’éducation sur les hypothèques inversées pour-
rait être un bon moyen d’élargir la taille du marché canadien et pourrait représenter
une solution gagnant-gagnant pour les prêteurs et les emprunteurs.
Mots clés : Volatilité du revenu, santé, bien-être, Canada, consommation, cycle de
vie, assurance, richesse, hypothèques inversées, demande du marché de l’habitation.
ABSTRACT
This thesis consists of three chapters on health, consumption and decumulation tools.
The first chapter looks at the effect of sustained income volatility during a person’s
working life on their health and well-being at a later age. While there is mount-
ing evidence that large income shocks—e.g., a job loss—may impact health and
mortality, little evidence exists on the potential relationship between sustained in-
come volatility, keeping average lifetime income constant, and health. This chapter
exploits rich survey data on the near-elderly in Canada paired with their adminis-
trative tax records to investigate whether a relationship exists between health and
well-being, on the one hand, and individual-specific volatility of income on the other,
decomposing volatility into permanent and transitory components. Controlling for
average lifetime income, we found that a one unit increase in the variance of the
permanent component of (log) income experienced over the working life is associated
with a lower probability of being in excellent (-23.9%) or very good (-13.3%) health,
of being satisfied with life (-34.9%), and implies the onset of 1.1 additional mental
health issues. Similar results, albeit smaller in size, were found for the transitory
component of income. The implications of these results are potentially important for
public policy, as well as for understanding the relationship between the labor market
and population health.
The second chapter investigates how spending and the composition of spending
change as a result of the onset of limitations in activities of daily living (ADL) and
limitations in instrumental activities of daily living (IADL). Combining longitudinal
data from the Consumption and Activities Mail Survey (CAMS) and the Health
and Retirement Study (HRS), we constructed a test aimed to identify the presence
of health state dependence of the marginal utility of spending in an intertemporal
context. A positive health state dependence of the marginal utility of spending is
when a dollar spent is more valuable when in good health. We found evidence that
the marginal utility of total and non-durable spending increased with the onset of
instrumental activities of daily living (IADL) limitations, hence resulting in negative
state dependence. Given that insurance protects against financial hardship while in
poor health, this result implies that insurance is more valuable than expected using
xiv
the standard framework. On the other hand, the marginal utility of total spending
didn’t change as a result of the onset of ADL limitations, suggesting the absence of
state dependence as a result of such shocks. We also found evidence of some reshuff-
ling across spending categories and wealth portfolio by reallocating housing wealth
to financial wealth with the occurrence of IADL limitations. This last result suggests
that homeowners use their home equity as an insurance tool.
A third chapter examines the determinants of weak demand for reverse mortgages in
Canada. One of the main features that differentiate reverse mortgages from a more
traditional home equity line of credit is the no-negative equity guarantee (NNEG).
This feature ensures that, at the time of repaying the loan, the borrower only has
to repay the minimum between the resale value of the house and the value of the
loan. In this chapter, we use a pricing model to calculate mortgage insurance premi-
ums charged to cover the losses related to the NNEG. Given the size of the loans
that are granted in the Canadian market, we find that actuarially fair premiums
are approximately zero, which implies that the NNEG is a missing feature in the
Canadian market. We then constructed a stated-choice experiment where Canadian
respondents were asked to evaluate various reverse mortgage products. By using
exogenous variations of the interest rates and the size of the loans from the survey
design, we used these stated-choice evaluations to compute the demand elasticity
of reverse mortgages in Canada and to look at other factors that could explain low
demand. Our results show that more than half of eligible Canadians do not even
have basic knowledge about reverse mortgages. Also, eligible Canadians do not seem
to understand how to take advantage of the NNEG. Finally, Canadian demand for
reverse mortgages is inelastic, but becomes elastic with a better level of knowledge
of the product. As a result, a combination of price adjustment and education on
reverse mortgages could be a good way to expand the size of the Canadian market
and could represent a win-win solution for both lenders and borrowers.
Keywords: Income volatility, health, well-being, Canada, consumption, life-cycle,
insurance, wealth, mortgages, housing demand.
INTRODUCTION
La qualité de l’environnement dans lequel les ménages retraités évoluent est déter-
minée par plusieurs facteurs. Un facteur important est la quantité et la qualité des
ressources disponibles pour financer la consommation une fois à la retraite. Un autre
facteur important est l’état de santé dans lequel les ménages vivront tout au long de
leur retraite.
Les gouvernements et les ménages ont la responsabilité partagée de prévoir des
ressources suffisantes qui seront destinées à financer la consommation de ces derniers
tout au long de leur retraite. Par conséquent, la majorité des ménages participent
au marché du travail et épargnent une fraction de leur revenu dans le but de financer
leur retraite. Durant leur vie active, la taille et la stabilité de leur revenu ont le po-
tentiel d’affecter leur niveau de santé actuel et, du même coup, de déterminer celui
qu’ils auront une fois à la retraite.
En plus d’avoir le potentiel d’entraîner des coûts financiers, un mauvais état de santé
peut influencer la capacité d’exercer certaines activités et d’apprécier certains biens
consommés. Puisqu’il est généralement observé que l’état de santé se détériore avec
les années, celui espéré à la retraite doit être considéré pour bien évaluer quels seront
les besoins de consommation une fois à cette étape. L’état de santé qu’on aura à la
retraite est toutefois difficile à prévoir. Par conséquent, certaines assurances offrent
une protection contre les difficultés financières en cas de mauvaise santé. Pour bien
évaluer ses besoins en assurance, il est donc important de bien comprendre si un
2
dollar dépensé a plus ou moins de valeur lorsqu’on est en bonne santé. Le niveau
de protection nécessaire sera donc influencé par la complémentarité entre la santé et
l’utilité marginale de la consommation.
Une autre problématique à laquelle font face certains ménages retraités est liée à
l’accessibilité des ressources qu’ils ont accumulées. Alors qu’une partie des ressources
accumulées est composée d’actifs financiers liquides, une autre consiste souvent en
actifs moins liquides, tels qu’une résidence principale. La résidence principale est
généralement l’actif le plus important possédé par les ménages retraités. Par con-
séquent, certains d’entre eux pourraient souhaiter accéder à une partie de la valeur
nette de celle-ci pour financer leurs dépenses courantes. Une manière de toucher
la valeur de la résidence principale est de la vendre pour ensuite devenir locataire
ou en acheter une moins dispendieuse. Puisque certains ménages sont réticents à
quitter leur résidence pour un logement plus petit une fois à la retraite, on observe
l’émergence de nouveaux produits financiers qui permettent d’obtenir une portion
de la valeur de la résidence tout en y demeurant.
Dans l’objectif de contribuer à la réflexion sur ces sujets, cette thèse est composée de
trois chapitres portant sur la santé, la consommation et les outils de décumulation.
Un premier chapitre porte sur l’effet d’une volatilité soutenue du revenu durant la
vie active sur la santé et le bien-être à un âge plus avancé. Bien qu’il y ait de plus
en plus de preuves que des chocs de revenus importants, par exemple sous la forme
d’une perte d’emploi, peuvent avoir un impact sur la santé et la mortalité, il existe
peu d’études sur la relation potentielle entre la volatilité soutenue du revenu et la
santé, indépendamment du niveau de revenu. Ce chapitre exploite de riches données
d’enquête sur la santé et le bien-être de Canadiens d’un âge avancé, ainsi que leurs
dossiers fiscaux, pour déterminer si une relation existe entre la santé et le bien-être
3
d’une part, et la volatilité du revenu propre à chaque individu de l’autre, décomposant
la volatilité en composantes permanente et transitoire. En tenant compte du revenu
moyen durant la vie active, nous avons constaté qu’une augmentation d’une unité
de la variance de la composante permanente du revenu (log) vécu au cours de la vie
professionnelle était associée à une probabilité plus faible d’être en excellente (-23,9
%) ou en très bonne (-13,3 %) santé, d’être satisfait de la vie (-34,9 %), et implique
une augmentation de 1,1 problème de santé mentale supplémentaire. Nous avons
trouvé des résultats semblables, quoique plus faibles, pour la composante transitoire
du revenu. Ces résultats ont des implications potentiellement importantes pour les
politiques publiques, ainsi que pour la compréhension de la relation entre le marché
du travail et la santé de la population.
Un deuxième chapitre étudie comment les dépenses et la composition des dépenses
changent en raison de l’incidence de limitations dans les activités de la vie quotidienne
(AVQ). En combinant les données longitudinales du Consumption and Activities Mail
Survey (CAMS) et du Health and Retirement Study (HRS), nous avons construit un
test visant à identifier dans quelle mesure l’utilité marginale des dépenses dépend de
la santé dans un contexte intertemporel. Une dépendance positive à l’égard de l’état
de santé signifie qu’un dollar dépensé a plus de valeur lorsqu’on est en bonne santé.
Nous avons constaté que l’utilité marginale des dépenses totales et non durables
augmente avec l’incidence de limitations dans les activités instrumentales de la vie
quotidienne (AIVQ), entraînant ainsi une dépendance négative. Étant donné que
certaines assurances protègent contre les difficultés financières en cas de mauvaise
santé, ce résultat implique que ces assurances ont plus de valeur que celle prévue
en utilisant le cadre standard. D’un autre côté, l’utilité marginale des dépenses to-
tales n’a pas changé en raison de l’incidence de limitations des AVQ, ce qui suggère
4
l’absence de dépendance à l’égard de l’état de santé à la suite de tels chocs. Suite à
l’incidence de limitations AIVQ, nous avons observé un remaniement dans les caté-
gories de dépenses et dans les catégories d’actifs, en réaffectant les actifs résidentiels
vers des actifs financiers. Ce dernier résultat suggère que les propriétaires utilisent
la valeur nette de leur maison comme un outil d’assurance.
Un troisième chapitre étudie les déterminants de la faible demande d’hypothèques
inversées au Canada. La caractéristique principale qui différencie une hypothèque
inversée d’une marge de crédit hypothécaire est la no-negative equity guarantee
(NNEG). Cette caractéristique assure que, au moment de repayer le prêt, l’emprunteur
n’aura qu’à payer le minimum entre la valeur de revente de la maison et le solde
du prêt. Dans ce chapitre, nous utilisons un modèle de tarification pour calculer
les primes d’assurances hypothécaires permettant de couvrir les pertes reliées à la
NNEG. Étant donné les prêts actuellement accordés dans le marché canadien, nous
trouvons que les primes actuarielles justes sont approximativement de zéro, ce qui
implique que la NNEG est inexistante dans le marché canadien. Nous avons aussi
construit une enquête de type stated-choice experiment, où des répondants canadiens
étaient invités à évaluer divers produits de prêt hypothécaire inversé. En utilisant
une variation exogène des taux d’intérêt et de la taille des prêts présentés lors de
l’enquête, nous avons utilisé ces évaluations pour calculer l’élasticité de la demande
au Canada et pour identifier les autres facteurs qui peuvent expliquer la faible de-
mande. Nos résultats montrent que plus de la moitié des Canadiens admissibles
n’ont même pas de connaissances de base sur les prêts hypothécaires inversés. De
plus, les Canadiens admissibles ne semblent pas comprendre comment tirer parti
de la NNEG. Enfin, la demande canadienne en prêts hypothécaires inversés est in-
élastique, mais elle devient élastique avec un meilleur niveau de connaissance du
5
produit. Par conséquent, une combinaison d’ajustement des prix et d’éducation sur
les hypothèques inversées pourrait être un bon moyen d’élargir la taille du marché
canadien et pourrait représenter une solution gagnant-gagnant pour les prêteurs et
les emprunteurs.
CHAPITRE I
INCOME VOLATILITY, HEALTH AND WELL-BEING
Abstract
While there is mounting evidence that large income shocks—e.g., a job loss—may im-
pact health and mortality, little research exists on the potential relationship between
sustained income volatility, keeping average lifetime income constant, and health.
This chapter exploits rich survey data on the near-elderly in Canada paired with
their administrative tax records to investigate whether a relationship exists between
health and well-being, on the one hand, and individual specific volatility of income on
the other, decomposing volatility into permanent and transitory components. Con-
trolling for average lifetime income, we found that a one unit increase in the variance
of the permanent component of (log) income experienced over the working life is
associated with a lower probability of being in “excellent” (-23.9%) or “very good”
(-13.3%) health, of being satisfied with life (-34.9%), and implied the onset of 1.1
additional mental health issues. Similar results, albeit smaller in size, were found
for the transitory component of income. These results have potentially important
implications for public policy, as well as for understanding the relationship between
the labor market and population health.
Keywords: Income volatility, health, well-being, Canada.
Note: A version of this study co-authored with Amélie Adeline, Raquel Fonseca and Pierre-
Carl Michaud is published in the IZA discussion papers and is available at the following address:
https://www.iza.org/en/publications/dp/12823/income-volatility-health-and-well-being
7
1.1 Introduction
Over time and space, a strong correlation has been documented between socio-
economic status (SES), in particular income, and health (Winkleby et al., 1992;
Smith, 1999; Case et al., 2002; Deaton, 2008). Understanding the sources of this
SES gradient in health has been at the forefront of the research agenda in health
economics for the last decades. As documented by Smith (2007), the gradient ex-
pands over the working years to fade once individuals reach retirement. Hence, some
of its origins may stem from experience on the labor market.
There is mounting evidence that labor market shocks, such as job loss, may impact
health, sometimes later in life. In the United States, Strully (2009), Sullivan &
Von Wachter (2009), Michaud et al. (2016), and Schaller & Stevens (2015) all found
a negative effect of job loss on health and well-being outcomes. For example, Sullivan
& Von Wachter (2009) showed that there was a 10 to 15% increase in mortality rates
for displaced workers 20 years after the job displacement when compared to other
workers. A link between job loss and biomarkers has been found by Michaud et al.
(2016), who used the Health and Retirement Study. General well-being also appeared
to suffer after events such as unemployment (Winkelmann & Winkelmann, 1998).
Yet, Smith (2007) found modest evidence that dynamics in income predict health
events during the working life. While using noisy measures of income from survey
data could explain this weak result, it is also possible that the impact of labor market
turmoil may take time to materialize. In fact, some biological theories emphasize
the potential negative health effects of the cumulative toll from stress related to
shocks in various domains of life, including the labor market (Seeman et al., 1997).
This cumulative toll has often been referred to as the allostatic load. Just like any
8
machinery, the human body experiences more rapid wear and tear when its capacity
to adapt is challenged repeatedly.
The theory of allostatic load would predict that workers with higher volatility may
experience more stress, and therefore carry a larger allostatic load, which could lead
to adverse health effects later in life. While the theory is plausible and could explain
why the gradient expands over the working years, we know of no empirical test
looking for associations between volatility over workers’ careers and their health at
older ages.
In this paper, we investigate whether a correlation exists between the income volat-
ility (both permanent and transitory) experienced over the working life and health
and well-being after age 50. Permanent income volatility depends on factors that
affect income permanently, such as a loss of transfers or an event implying a per-
manent work stoppage, while transitory income volatility depends on factors such
as the economic cycle or a temporary drop in wages due to, for example, group or
individual layoffs, or business closures. We used health and well-being information
from the 2012, 2014 and 2016 waves of the Longitudinal and International Study
of Adults (LISA) for respondents over the age of 50, and we estimated individual
level income volatility measures by applying the methodology developed by Carroll
& Samwick (1997) on Canadian administrative tax records associated with each re-
spondent between 1982 and 2015 (34 years). We then related the two in a regression
framework which controlled for various confounders and, importantly, for lifetime
average income.
Our results support the view that volatility over the life cycle is associated with
worse health and well-being. Controlling for the average level of income during the
9
working life, we found evidence that permanent and transitory income volatility are
negatively associated with health and well-being. Indeed, a one unit increase in the
variance of the permanent component of income experienced over the working life
was associated with a decrease in the probabilities of being in “excellent” or “very
good” health by 23.9% and 13.3%, respectively; a decrease in the probability of being
satisfied with life by 34.9%; and implied the onset of 1.1 additional mental health
issues. Moreover, a one unit increase in the variance of the transitory component of
income was associated with a decrease in the probabilities of being in “excellent” or
“very good” health by 5.74% and 3.20%, respectively; a decrease in the probability of
being satisfied with life by 11.95%; and implied the onset of 0.42 additional mental
health issues. One particular threat to our identification strategy was that health
shocks during the working life caused volatility in income. In order to control for
this issue, we showed that results were very similar whether or not we excluded those
who may have received disability benefits during the 34 years covered by the data.
Our analysis is structured as follows. Section 1.2 details the two databases used to
carry out the analysis and gives some descriptive statistics. Section 1.3 presents the
method used to compute measures of volatility, as well as the econometric analysis.
In section 1.4, we give an interpretation of our results. Section 1.5 concludes the
chapter.
1.2 Data and Descriptive Statistics
To conduct our analysis, we used the Longitudinal and International Study of Adults
(LISA), a multi-topic and unique database of microdata on health, life satisfaction,
education, employment, income, and family of individuals from Canada. Since 2012,
10
LISA has been asking questions to a sample of households throughout Canada, these
households being re-interviewed every 2 years in the panel.
We also used the retrospective component of the LISA database based on adminis-
trative data sources. Indeed, LISA is linked to the “T1 Family File” corresponding to
annual tax records for census families and individuals
1
and gives access to individu-
als’ income history, to information on whether individuals are eligible to and used
different tax credits, and to their marital status, between 1982 and 2015.
1.2.1 Sample Selection
To properly identify the relationship between income volatility and health and well-
being, we focused on a population of men aged 50 to 75 in 2012, 2014 and 2016,
since this corresponds to a period in which health generally begins to deteriorate.
We focused our analysis on individuals who were surveyed at least once in the three
waves of this survey. When they had been interviewed more than once, we focused
on their answers from the most recent wave.
To estimate income volatility, we focused on income history of these respondents
while they were between 30 and 55 years of age between 1982 and 2015. We restricted
our sample to respondents aged 30 to 55 since such an age range corresponds to a
working-age period in which individuals are no longer in school and are not yet
retired. We chose to work on a male population as men are less likely to voluntarily
leave the labor force due, for example, to childbearing, which could also have health
consequences. Since information on income history from 1982 to 2015 is available,
1
These data give information on demographic characteristics and income, collected from
income tax returns submitted to the Canada Revenue Agency (CRA).
11
we excluded respondents who were over 75 years old in 2012, 2014 and 2016 to ensure
sufficient information concerning income history. Indeed, the older the individuals
considered in the 2012–2016 sample, the less information we had to compute income
variances, given that the latter were computed during the working age (from 30 to
55 years old).
2
Table 1.1 gives details about the different sample restrictions. We ended up with a
sample of 5,134 respondents over the three waves.
Table 1.1: Sample selection - LISA database
(1) Total individuals 27,712
(2) Men 13,434
(3) 50-75 years old 5,416
(4) Available information on current income in tax records 5,134
Note: Starting from the original LISA sample (1), we restricted the sample to men
(2), and then selected only respondents aged between 50 and 75 (3). We also dropped
respondents for whom we had missing information on their annual income between
1982 and 2015 (4).
1.2.2 Health and Well-Being Outcomes
We now define the different health and well-being variables: self-perceived health
status, life satisfaction and mental health.
2
For instance, an individual who is 86 years old in 2012 in the well-being sample was 55
years old in 1982, such that we only have a single observation to compute their income variances
given the selection criteria (income variances computed during the working age). The white part of
Table A.1 in the appendix section A represents the information set for respondents aged between
50 and 75 years old in 2012 (final health and well-being sample), which can be used to compute
variances of income (the latter being computed during the working age).
12
Self-perceived health status assesses the general perceived health of an individual.
Respondents were asked: “Would you say your health in general is. . . ” and they had
to choose between five answers: “excellent,” “very good,” “good,” “fair” or “poor”.
Self-perceived health status is an important subjective predictor of an individual’s
health since it combines different elements that an individual knows about their own
health and integrates factors which are not always considered by health professionals,
such as their beliefs and attitudes towards health commodities (Benitez-Silva et al.
(2004)).
We also considered an indicator on individuals’ satisfaction with their life to invest-
igate well-being. Individuals were asked to rate their feelings about life in general,
from “very unsatisfied” (0) to “very satisfied” (10). We created a dummy variable
equal to one when the individual rated their feeling about life from 7 to 10 or, in
other words, when the individual seems satisfied with their life in general.
3
Moreover, LISA asked individuals a set of ten questions on their feelings concerning
their mental health, such as “In the last month, how often did you feel anxious”
or, “In the last month, how often did you feel sad/depressed,” to which individuals
responded with “never,” “rarely,” “sometimes,” “most of the time,” or “all the time”
(see Appendix section A.1 for further details). We created a dummy variable equal to
one when individuals responded “sometimes,” “most of the time” or “all the time.” The
categories were grouped this way in order to capture the chronicity of these mental
health problems. Then, we created a variable which added up each issue reported by
an individual. Thus, we considered this variable as a sum of these different problems,
which ranges from 0 to 10.
3
Using the score without transformation results found are similar and available upon request.
13
Figure 1.1 presents descriptive statistics on the different outcome variables. A major-
ity of respondents rated their self-assessed health as “good” or “very good”. Over 80%
of them rated their life satisfaction at a level of 7 or above, meaning that the major-
ity of individuals seemed satisfied with their life. Finally, about 40% of individuals
reported having had at least one mental health issue in the previous month.
Figure 1.2 presents the distribution of specific mental health issues used to construct
our mental health index. About 24% and 17% of the respondents reported feeling
tired out for no good reason, and restless or unable to stand still, respectively. Close
to 16% of the respondents declared feeling nervous. More than 10% reported feeling
either depressed or that everything was an effort. Finally, around 5% revealed feeling
desperate, worthless, so nervous that nothing could calm them down, so restless that
they could not stand still, or so depressed that nothing could cheer them up.
1.2.3 Retrospective Component of LISA
To measure income volatility, we used the variance of residual income. To decompose
the variance of income into permanent and transitory dimensions, we used inform-
ation obtained in the retrospective component of the data from 1982 to 2015. We
focused on total family income before taxes, which includes the taxfiler’s income
from taxable as well as nontaxable sources. Using family income instead of personal
income gives more information about the financial situation of the respondents, be-
cause it allows us to account for the insurance effects between household members.
4
4
Using the personal income of the respondents might be misleading due to an overestimation
of the variances of income whenever a respondent has an unstable income situation and lives with
someone who might have a stable financial situation. On the other hand, we might underestimate
the variances of income when considering an individual who has a stable income situation but lives
with someone who is financially unstable. There is, however, a limit to this approach. Indeed, faced
14
Figure 1.1: Distribition of health and well-being outcomes
0 10 20 30 40
%
Excellent Very Good Good Fair Poor
Self-Assessed Health
0 20 40 60 80
%
Unsatisfied Satisfied
Life Satisfaction
0 20 40 60
%
0 1 2 3 4 5 6 7 8 9 10
Mental Health Issues
Income was then deflated using the Consumer price index with 2013 as the base year.
Some individuals reported having a very low income, which might be equal to zero
sometimes. However, individuals could apply for a welfare aid program representing
a few thousand dollars a year. Moreover, individuals reporting zero income may have
worked abroad during that period. To address this concern, we excluded individuals
who reported an income of $0. Then, for the other incomes below $11,000, we im-
with the high income volatility of a member of a household, a spouse may have to work more to
compensate for it. Our approach therefore does not capture this source of volatility, which could
have an effect on the respondent’s health and well-being.
15
Figure 1.2: Mental health issues
0 5 10 15 20 25
%
Tired
Restless
Nervous
Effort
Depressed
So restless
Desperate
Worthless
So depressed
So nervous
Note: Tired refers to “tired out for no good reason.” So nervous refers to “so nervous
that nothing could calm down.” Restless refers to “restless or unable to stand still.”
So restless refers to “so restless that they could not stand still.” Depressed refers to
“sad/depressed.” So depressed refers to “so depressed that nothing could cheer them
up.” Effort refers to “everything was an effort.” Worthless refers to “the feeling of
being good-for-nothing.”
posed the latter to take this upper limit as a minimum.
5
Finally, for individuals who
claimed to be retired, we excluded their income observations in the years following
the year they retired.
5
We chose this amount since it corresponds to the 2013 non-refundable tax credit, also
known as the personal amount, and adjusted annually to allow for inflation.
16
1.2.4 Covariates
We also used a set of covariates when estimating effects of permanent and transitory
income risk on health and well-being. As a result, we included categories for age and
education, civil status, number of children, whether or not they were born in Canada
and, in order to capture regional effects, dummies for provinces of Canada.
6
1.3 Econometric Analysis
First, we present the methodology used to estimate the variances of the permanent
and transitory components of income in order to identify the income volatility exper-
ienced by each respondent during their working life. Next, we detail the methodology
used to analyze the association between income volatility on the one hand and health
and well-being on the other.
1.3.1 Estimating Variances of Transitory and Permanent Shocks
The estimation of the variances of permanent and transitory shocks follows the meth-
odology proposed by Carroll & Samwick (1997). Two steps are involved.
7
First, we
are interested in residual income volatility once predictable changes in income are
accounted for. Hence, the predictable growth needs to be removed from the income
6
Descriptive statistics on these variables are not included here, but are available upon
request.
7
Meghir & Pistaferri (2004) also used this method to investigate dynamics of the variance
of income and the associated observable and unobservable heterogeneity using an ARCH process
on the Panel Study of Income Dynamics. They looked at the impact of income shocks early in life
on earnings determination.
17
process. In a second step, we computed a specific time series estimation of the vari-
ance of transitory and permanent components which come from unexpected events
for each respondent.
Our approach to estimate income volatility differs from Carroll & Samwick (1997) in
two ways. First, we used administrative data which comes from income tax returns in
Canada, while they used U.S. survey data from the Panel Study of Income Dynamics.
The advantage of administrative data is that it reduces the potential for measurement
errors, which bias income volatility (Bound et al. (2001) explained that measurement
errors might be prevalent in survey data). Second, our observation window and
selected sample gave access to up to 26 observations per respondent, while Carroll
& Samwick (1997) only used 7 observations per individual.
8
We modeled log income, log y
it
, as the product of a predictable component, p
it
, a
permanent shock (random walk), η
it
, and a transitory component,
it
, which is iid
with variance σ
2
i,
(individual specific). We denote (log) income as:
log y
it
= p
it
+ η
it
+
it
(1.1)
The predictable component is given by p
it
= x
it
γ. We allowed for heterogeneity
between respondents growth path by allowing γ to vary by province (Atlantic, Que-
bec, Ontario, Prairies and British Columbia) and level of education (less than high
school and high school, college, university). We included in x
it
a quadratic age and
8
Indeed, we had access to information on respondents aged between 30 and 55 between 1982
and 2015, while Carroll & Samwick (1997) had access to data only from 1982 to 1987.
18
marital status (single or couple). In order to have robust results, we also controlled
for health status in a robustness test since it can affect the ability to work, and
thus income. To do so, we included in x
it
a dummy if the respondent receives a tax
benefit for being disabled.
9
We thus created a binary variable equal to one when an
individual stated having received this help.
10
Denoting ν
it
= η
it
+
it
, we first netted
out the predictable component by estimating γ by ordinary least squares (OLS) from
log y
it
= x
it
γ + ν
it
(for each province and education group pair). We then obtained
the residuals ˆν
it
from this regression. These residuals were used in the second step.
We modeled the permanent component of income as a random walk, η
it
= η
i,t−1
+ ζ
it
where ζ
it
is iid with variance σ
2
iζ
. We then defined the difference in residuals between
d years as:
r
id
= ˆν
it+d
− ˆν
it
(1.2)
= η
it+d
+
it+d
− η
it
−
it
, (1.3)
Recursively substituting we obtained:
r
id
= (ζ
it+1
+ ζ
it+2
+ ... + ζ
it+d
) +
it+d
−
it
(1.4)
which is a function of d permanent shocks and 2 transitory shocks. The variance of
9
The variable is defined as follows: “A taxfiler may claim a preset disability amount if he
or she was severely physically or mentally impaired in the tax year, and the impairment noticeably
restricted the taxfiler’s activities of daily living.”
10
Available since 1982, this disability indicator is only used in order to compute the variances
of income because it allows the purging of the variances from health effects. As a result, when using
these variances, we try to ensure the exogeneity of the latter in the health and well-being estimates.
However, mental health factors that do not lead to benefits could have a significant influence on
the variance.
19
equation (1.4) is given by:
r
2
id
= V ar(r
id
) = dσ
2
iζ
+ 2σ
2
i
(1.5)
For each respondent, we constructed the set of all possible r
2
id
(for each pairwise
combination of residuals), which is a function of d and the constant 2, to estimate
σ
2
iζ
and σ
2
i
.
11
The latter are obtained by running, for each individual i, a regression
of r
2
id
on d, and 2, a constant term for all d. We allowed for serial correlation in
it
, in the form of a moving average of order 2 process, by exploiting only pairwise
comparisons of order d > 2.
12
Table 1.2 shows means across respondents of the variances of permanent and trans-
itory components. We see that estimated variances of the permanent component of
income were quite low, with an average of 0.0261, while variances of the transitory
component of income were higher, with an average of 0.0994.
13
Table 1.2: Variances of permanent and transitory components of income
Permanent Transitory
Mean 0.0261 0.0994
Standard deviation 0.0841 0.2996
11
Indeed, equation 1.5 corresponds to d times the variance of the permanent component of
income and 2 times the variance of the transitory component of income.
12
As discussed by Carroll & Samwick (1997), studies in the literature do not find evidence of
household income process with transitory component of order greater than M A(2) (see MaCurdy
(1982), Abowd & Card (1989) and Moffitt & Gottschalk (2011)).
13
The fact that the average variance of the permanent component of income was smaller
than the transitory one does not indicate that the former contributes less to the total variance.
Given that permanent shock is a random walk, the variance of a permanent shock T periods ahead
is T σ
2
i,ζ
.
20
Table 1.3 shows OLS estimates of these variances on the different covariates used
in the health and well-being estimates, i.e. (i) the logarithm of the average income
when individuals are between 30 and 55 years old, (ii) the birth year of individuals,
(iii) their marital status between 2012 and 2016, (iv) their level of education, (v) the
province in which they live, (vi) whether or not they were born in Canada, and (vii)
the number of children they have. On the one hand, results suggest that variances
of the permanent component of income are positively and significantly correlated
with the birth year, the level of education and the number of children. On the other
hand, a positive relationship is found with the province and the fact of being born in
Canada for the variances of the transitory component of income. As a result, living
in British Columbia relatively to the Atlantic provinces was significantly correlated
with a higher variance of both permanent and transitory components of income.
On the contrary, being born in Canada was negatively related to the variance of the
permanent component of income. Moreover, the variance of the transitory component
of income was negatively correlated to the marital status and the number of children.
Finally, the average level of income was negatively related to the variances of both
permanent and transitory components.
1.3.2 Estimating Impacts of Income Volatility on Health and Well-Being
We used these estimates to investigate the association of permanent and transitory
income volatility occurring during the working life (from 30 to 55 years of age) on
self-perceived health status, life satisfaction and mental health in older age (from 50
to 75 years of age, from 2012 to 2016). We estimated the following equation:
21
Table 1.3: Estimates of the variances of permanent and transitory components of
income
Income volatility
Permanent Transitory
log y
i
-0.0045 *** -0.0499 ***
(0.0017) (0.0052)
1940-1944 -0.0028 0.0042
(0.0056) (0.0170)
1945-1949 0.0011 0.0017
(0.0051) (0.0156)
1950-1954 -0.0032 0.0145
(0.0050) (0.0153)
1955-1959 -0.0027 0.0195
(0.0050) (0.0151)
1960-1964 0.0040 0.0020
(0.0050) (0.0153)
1965-1969 0.0114 ** -0.0248
(0.0058) (0.0177)
Marital status -0.0027 -0.0212 ***
(0.0024) (0.0074)
High School -0.0028 -0.0009
(0.0024) (0.0073)
College -0.0021 0.0047
(0.0028) (0.0084)
University 0.0083 *** 0.0097
(0.0028) (0.0087)
Quebec 0.0031 0.0006
(0.0024) (0.0073)
Ontario 0.0018 0.0236 ***
(0.0025) (0.0076)
Prairies 0.0062 *** 0.0117
(0.0024) (0.0072)
British Columbia 0.0054 * 0.0284 ***
(0.0030) (0.0090)
Born in Canada -0.0391 *** 0.0442 ***
(0.0022) (0.0067)
Number of children 0.0024 ** -0.0067 **
(0.0010) (0.0030)
cons 0.0710 *** 0.2607 ***
(0.0084) (0.0256)
N 4,890 4,890
Note: Standard errors in parentheses. ***: statistically significant at 1%; **: stat-
istically significant at 5%; *: statistically significant at 10%.
22
h
i
= β
0
+ β
1
ˆσ
2
iζ
+ β
2
ˆσ
2
i
+ β
3
log y
i
+ X
i
Γ + u
i
(1.6)
where h
i
corresponds to the health or well-being outcome of individual i; σ
2
iζ
cor-
responds to the variance of the permanent component of income; σ
2
i
corresponds to
the variance of the transitory component of income; log y
i
is the logarithmic trans-
formation of average income of the household i when the individual was between 30
and 55 years old; X
i
stands for control variables (socio-demographic characteristics
of individual i) and u
i
is an error term assumed to be normally distributed.
Concerning self-assessed health, it corresponds to a qualitative dependent variable.
We observed an indicator of the category such that the observed variable was equal
to 1, 2, 3, 4 or 5 for “excellent,” “very good,” “good,” “fair” or “poor,” respectively.
Thus, we estimated the following equation with an ordered probit model:
h
∗
i
= β
0
+ β
1
ˆσ
2
ζ,i
+ β
2
ˆσ
2
,i
+ β
3
log y
i
+ X
i
Γ + u
i
(1.7)
where h
∗
i
is a latent variable which underlies self-reported health status.
Next, we investigated a more general definition of well-being with life satisfaction.For
this outcome, we estimated equation 1.7 with a probit, where h
∗
i
is a latent variable
which underlies life satisfaction.
Finally, the LISA database contains detailed information on mental health such that
we investigated the impact of income risk on a sum of mental health issues using an
OLS model.
We studied the impact of income risk on a broad range of health and well-being
23
outcomes to get a relatively complete picture of the relationship between income
volatility during a working-age period and the health and well-being of individuals
aged 50 and older. For each outcome, we ran two specifications where covariates were
added one by one: (1) only variances of the permanent and transitory components
of income; (2) plus logarithm of the average income between 30 and 55 years of
age
14
, and demographic variables (groups of age, being in a relationship, categories
of education, dummies for provinces of Canada, number of children and a dummy
equal to one when the individual was born in Canada)
15
.
1.4 Results
1.4.1 General Results
We focused on the impact of income volatility on three outcomes: self-assessed health,
life satisfaction and mental health. In Table 1.4, we reported strong associations of
both transitory and permanent components of income with our outcomes. Column
(1) represents the estimates without the covariates and the logarithmic transforma-
tion of the average income and covariates. Results across columns were very similar,
such that we focused our analyses on the last column.
The variance of the permanent component of income had a global negative association
with the different outcomes studied (see coefficients of ˆσ
2
ζ
in column (2) of Table 1.4).
Indeed, a one unit increase in the variance of the permanent component of income
14
Estimates controlling for the square of the logarithm of average income were implemented
as a robustness check. Results were very similar and are available upon request.
15
The regressions do not take into account the fact that the volatility variables are generated
regressors.
24
experienced over the working life decreased the probability of being in “excellent” or
“very good” health by 23.86% and 13.31%, respectively, and decreased the probability
of being satisfied with life by 34.95%. Furthermore, our estimates suggest that the
variance of the permanent component of income was associated with a change of the
onset of 1.1 additional mental health issues. More specifically, the variance of the
permanent component of income had a negative association with “feeling so nervous
that nothing could calm them down,” “depressed” and “worthless” (see coefficients ˆσ
2
ζ
in Table 1.5).
Moreover, the variance of the transitory component of income had a global negative
association with each outcome (see the coefficients of ˆσ
2
in column (2) of Table 1.4).
For all these outcomes, the associations were smaller than the associations of the
variance of the permanent component of income. Indeed, a one unit increase in the
variance of the transitory component of income was associated with a decrease of
the probability of being in “excellent” or “very good” health of 5.74% and 3.20%,
respectively, and with a decrease of the probability of being satisfied with life of
11.95%. Concerning mental health, a one unit increase in the variance of the trans-
itory component of income was associated with an increase of 0.42 in the number
of mental health issues. More specifically, we investigated this last relationship by
studying the association of these variances with each mental health outcome (see
Table 1.5). According to these results, the negative relationship between the mental
health indicator and the variance of the transitory component of income came from
the following mental health issues: “feeling nervous,” “so nervous that nothing could
calm them down” and “depressed”. Particularly, a one unit increase in the variance
of the transitory component of income was associated with an increase of around 7%
in the probability of reporting being nervous or depressed. In other words, events
25
such as a job loss, group or individual layoffs, or business closures, have negative
associations with mental health issues.
Finally, in the second column of Table 1.4, we investigated the association of the
logarithmic transformation of the average income while the individuals were between
30 and 55 years old. Indeed, we focused on income volatility, such that we should
also control for the average income level in order to capture the real impact of the
variances of income. For each outcome, results suggested a positive association of
average income with health and well-being. Indeed, looking at self-assessed health,
a 1% increase of the average income during the working life was associated with an
increase in the probability of reporting being in “excellent” or “very good” health of
8.17% and 4.56%, respectively. For life satisfaction, a 1% increase of the average
income during the working life was associated with an increase in the probability of
being satisfied with life of 8.16%. For mental health, a 1% increase of the average
income during the working life was associated with a decrease of 0.51 mental health
issues. Moreover, focusing on each mental health outcome (Table 1.5), we see that
a 1% increase of the average income during the working life was associated with a
significant decrease of the probability of the onset of each mental health issue.
26
Table 1.4: Effect of income volatility on health and well-being
(1) (2)
Self-assessed health ˆσ
2
ζ
Excellent -0.2703*** -0.2386***
(0.0774) (0.0787)
Very good -0.1518*** -0.1331***
(0.0435) (0.0440)
Good 0.1810*** 0.1592***
(0.0519) (0.0526)
Fair 0.1472*** 0.1317***
(0.0423) (0.0436)
Poor 0.0940*** 0.0808***
(0.0273) (0.0270)
ˆσ
2
Excellent -0.1237** -0.0574**
(0.0262) (0.0258)
Very good -0.0695** -0.0320**
(0.0148) (0.0144)
Good 0.0828** 0.0383**
(0.0176) (0.0172)
Fair 0.0673** 0.0317**
(0.0144) (0.0143)
Poor 0.0430** 0.0194**
(0.0094) (0.0088)
ln(Income) Excellent 0.0817***
(0.0082)
Very good 0.0456***
(0.0047)
Good -0.0546***
(0.0055)
Fair -0.0451***
(0.0047)
Poor -0.0277***
(0.0032)
N 4,890 4,890
Covariates Demographic No Yes
Note: ˆσ
2
ζ
refers to the variance of the permanent component of income, while ˆσ
2
refers to that of transitory component of income. Marginal effects are reported, with
standard errors in parentheses. ***: statistically significant at 1%; **: statistic-
ally significant at 5%; *: statistically significant at 10%. Demographic variables are
categories of age and education, marital status, number of children, being born in
Canada and categories for provinces. Self-assessed health is clustered at the respond-
ent level.
27
Table 1.4 (continued): Effect of income volatility on health and well-being
(1) (2)
Life satisfaction ˆσ
2
ζ
-0.6000*** -0.3495***
(0.0977) (0.1008)
ˆσ
2
-0.2288*** -0.1195***
(0.0326) (0.0331)
ln(Income) 0.0816***
(0.0108)
N 4,153 4,153
Number of mental health issues ˆσ
2
ζ
1.6115*** 1.0985*
(0.5715) (0.5950)
ˆσ
2
0.8895*** 0.4213**
(0.1936) (0.1951)
ln(Income) -0.5094***
(0.0606)
N 4,143 4,143
Covariates Demographic No Yes
28
Table 1.5: Effect of income volatility on mental health issues
Tired Nervous So nervous Desperate Restless So restless Depressed So depressed Effort Worthless
ˆσ
2
ζ
0.0329 0.1441 0.0829* 0.0933 0.1220 -0.0393 0.2376** 0.0489 0.1381 0.1397**
(0.1433) (0.1141) (0.0459) (0.0676) (0.1282) (0.0884) (0.0944) (0.0562) (0.1086) (0.0618)
ˆσ
2
0.0416 0.0741** 0.0370*** 0.0185 0.0509 -0.0023 0.0758** 0.0024 0.0495 0.0327
(0.0458) (0.0367) (0.0143) (0.0232) (0.0393) (0.0266) (0.0309) (0.0194) (0.0345) (0.0203)
ln(Income) -0.0997*** -0.0421*** -0.0166*** -0.0470*** -0.0234* -0.0351*** -0.0378*** -0.0238*** -0.0883*** -0.0455***
(0.0140) (0.0117) (0.0051) (0.0072) (0.0124) (0.0081) (0.0100) (0.0059) (0.0108) (0.0067)
N 4,142 4,142 4,142 4,142 4,142 4,142 4,142 4,142 4,142 4,142
Covariates: Demographic Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
Note: ˆσ
2
ζ
refers to the variance of the permanent component of income, while ˆσ
2
refer to the one of the transit-
ory component of income. Marginal effects are reported, with standard errors in parentheses. ***: statistically
significant at 1%; **: statistically significant at 5%; *: statistically significant at 10%. Demographic variables
are categories of age and education, marital status, number of children, being born in Canada and categories
for provinces.
29
1.4.2 Robustness
We investigated the association of income volatility on health and well-being out-
comes using two additional sub-samples in order to extend the validity of our results
(see columns (2) and (3) of Table 1.6) .
The first robustness test performed used the variances for which we controlled for
the disability benefits an individual may have received. The idea was to correct
for health shocks during the working life which may cause volatility in income. In
column (2) of Table 1.6, results for the variances of both permanent and transitory
components of income were very similar to the baseline estimates (column (1)).
For instance, a one unit increase in the variance of the permanent component of
income is associated with a 23.59% decrease in the probability of reporting being
in “excellent” health (compared to a 23.86% decrease in the baseline results), a 35%
decrease in the probability of reporting being satisfied with life (compared to a 34.95%
decrease in the baseline results), and an increase of 1.13 of the onset of mental
health issues (compared to 1.1 in the baseline results, i.e., column (1)). As a result,
when disability was used to compute income variances, we purged the latter from
health effects and came closer to measures of the variances which were orthogonal
to health shocks. Results were very similar to the baseline ones. One possibility
is that volatility of income was caused by changes in household composition. The
second robustness test performed considered a sample with a control over the number
of different relationships that an individual had (column (3)). When the variances
of the permanent and transitory components of income were estimated, even if a
person reported being in a relationship for two consecutive years, this individual
may have been in a relationship with different people who earned different annual
30
incomes. We thus controlled for the different relationships in order to capture such
effects. Results for all outcomes were qualitatively similar (and even smaller in
magnitude for the permanent component of income) when compared to the baseline
estimates (column (1)). The variance of the permanent component of income had a
negative association with probability of being in “excellent” or “very good” health, of
reporting being satisfied with life, and increased the number of mental health issues.
Specifically, a one unit increase in the latter was associated with a 23.19% decrease
in the probability of reporting being in “excellent” health, a 34.67% decrease in the
probability of reporting being satisfied with life, and an increase of the number of
mental health issues by 1.07. Similarly, results for the variance of the transitory
component of income were qualitatively similar to the baseline results.
31
Table 1.6: Robustness tests
(1) (2) (3)
Self assessed health ˆσ
2
ζ
Excellent -0.2386*** -0.2359*** -0.2319***
(0.0787) (0.0788) (0.0813)
Very good -0.1331*** -0.1316*** -0.1287***
(0.0440) (0.0440) (0.0452)
Good 0.1592*** 0.1575*** 0.1581***
(0.0526) (0.0526) (0.0554)
Fair 0.1317*** 0.1302*** 0.1266***
(0.0436) (0.0436) (0.0445)
Poor 0.0808*** 0.0799*** 0.0760***
(0.0270) (0.0270) (0.0270)
ˆσ
2
Excellent -0.0574** -0.0584** -0.0634**
(0.0258) (0.0257) (0.0272)
Very good -0.0320** -0.0326** -0.0352**
(0.0144) (0.0144) (0.0151)
Good 0.0383** 0.0390** 0.0432**
(0.0172) (0.0172) (0.0185)
Fair 0.0317** 0.0322** 0.0346**
(0.0143) (0.0142) (0.0149)
Poor 0.0194** 0.0198** 0.0208**
(0.0088) (0.0088) (0.0090)
ln(Income) Excellent 0.0817*** 0.0817*** 0.0807***
(0.0082) (0.0082) (0.0086)
Very good 0.0456*** 0.0456*** 0.0448***
(0.0047) (0.0047) (0.0049)
Good -0.0546*** -0.0545*** -0.0550***
(0.0055) (0.0055) (0.0059)
Fair -0.0451*** -0.0451*** -0.0440***
(0.0047) (0.0047) (0.0049)
Poor -0.0277*** -0.0277*** -0.0265***
(0.0032) (0.0032) (0.0032)
N 4,890 4,889 4,678
Covariates Demographic Yes Yes Yes
Note: Marginal effects are reported. Standard errors in parentheses. ***: statistic-
ally significant at 1%; **: statistically significant at 5%; *: statistically significant
at 10%. Demographic variables are categories of age and education, marital status,
number of children, being born in Canada and categories for provinces. Self-assessed
health is clustered at the respondent level. (1) corresponds to the baseline results.
(2) uses the variances for which we control for the disability benefits an individual
may have received. (3) considers a sample with a control over the number of different
relationships that an individual had.
32
Table 1.6 (continued): Robustness tests
(1) (2) (3)
Life satisfaction ˆσ
2
ζ
-0.3495*** -0.3500*** -0.3467***
(0.1008) (0.1009) (0.1010)
ˆσ
2
-0.1195*** -0.1223*** -0.1186***
(0.0331) (0.0329) (0.0343)
ln(Income) 0.0816*** 0.0814*** 0.0782***
(0.0108) (0.0108) (0.0110)
N 4,153 4,153 3,987
Number of mental health issues ˆσ
2
ζ
1.0985* 1.1289* 1.0676**
(0.5950) (0.5955) (0.932)
ˆσ
2
0.4213** 0.4375** 0.5731**
(0.1951) (0.1946) (0.305)
ln(Income) -0.5094*** -0.5083*** -0.3396***
(0.0606) (0.0606) (0.073)
N 4,143 4,142 3,979
Covariates Demographic Yes Yes Yes
1.5 Conclusion
In this paper, we tested the hypothesis that income volatility is associated with worse
health outcomes and well-being. Using the Longitudinal and International Study of
33
Adults (LISA) and its associated retrospective component for administrative data
that follows Canadians, we investigated whether a relationship exists between health
and well-being, on the one hand, and individual-specific volatility of income on the
other, decomposing volatility into permanent and transitory components.
Our results suggest that permanent and transitory income volatility are associated
with a deterioration of health and well-being, which is consistent with the theory
of allostatic load (Seeman et al. (1997)). A one unit increase in the variance of the
permanent component of income experienced over the working life is associated with
a decrease in the probability of being in “excellent” or “very good” health of 23.86%
and 13.31%, respectively, a decrease in the probability of being satisfied with life
of 34.95%, and is associated with the onset of 1.1 additional mental health issues.
Moreover, a one unit increase in the variance of the transitory component of income
is associated with a decrease of the probability of being in “excellent” and “very
good” health of 5.74% and 3.20%, respectively, a decrease in the probability of being
satisfied with life of 11.95%, and an increase of 0.42 in the number of mental health
issues. These results were robust to the inclusion of controls for disability during
the working life, an attempt to account for reverse causality. They also held if we
controlled for the composition of the household. In other words, this association was
not due to changes in household composition over the life cycle.
Establishing causality between income volatility and health outcomes is a difficult
endeavor. Despite our best efforts to control for other lifetime factors, including
disability, it is possible that causality runs the other way: individuals who are more
fragile in terms of both physical and mental health sustain more income shocks. Our
results are, however, consistent with a mounting body of work which shows that labor
market shocks have a causal impact on health outcomes (Strully (2009); Sullivan
34
& Von Wachter (2009); Michaud et al. (2016); Schaller & Stevens (2015)). Finally,
understanding this potential relationship has important implications for social policy.
For example, if causal, this relationship would imply that social insurance improves
health at older ages. Furthermore, it emphasizes that health policy may target
both lower income individuals and individuals who have significant variation in their
incomes.
CHAPITRE II
CONSUMPTION AND HEALTH IN OLD AGE
Abstract
We investigate how spending and the composition of spending change as a result
of the onset of limitations in activities of daily living (ADL) and limitations in
instrumental activities of daily living (IADL). Combining longitudinal data from the
Consumption and Activities Mail Survey (CAMS) and the Health and Retirement
Study (HRS), we constructed a test aimed at identifying the presence of health
state dependence of the marginal utility of spending in an intertemporal context. A
positive health state dependence of the marginal utility of spending is when a dollar
spent is more valuable when in good health. We find evidence that the marginal
utility of total and nondurable spending increase with the onset of IADL limitations,
hence resulting in negative state dependence. Given that insurance protects against
financial hardship when in poor health, this result implies that insurance is more
valuable than expected using the standard framework. On the other hand, the
marginal utility of total spending doesn’t change as a result of the onset of ADL
limitations, suggesting the absence of state dependence as a result of such shocks.
We also find evidence of some reshuffling across spending categories and wealth
portfolios by reallocating housing wealth to financial wealth with the onset of IADL
limitations. This last result suggests that homeowners use their home equity as an
insurance tool.
Keywords: Consumption, health, life cycle, insurance, wealth.
Note: This study is co-authored with Michael Hurd, Pierre-Carl Michaud and Susann Rohwedder.
36
2.1 Introduction
A long-standing question in the study of consumption and the demand for insur-
ance is whether consumption is less valuable when a person’s health is poor than
when it is good. Given that insurance protects against financial hardship when in
poor health, evidence of a lower marginal utility of consumption in that state would
imply that insurance is less valuable than expected using the standard framework.
This would help explain several puzzles, such as the low take-up of long-term care
insurance (Brown & Finkelstein, 2011). It would also help explain why consumption
declines with age, with implications for the estimation of preferences and for retire-
ment preparation, as households who expect their health to decline faster would not
need to save as much for retirement (Skinner, 2007; Hurd & Rohwedder, 2011).
The first studies that looked at this question aimed to estimate measures of com-
pensating variation for varying health risk (e.g., job injury) using hypothetical survey
questions. Conclusions from studies assessing the state dependence of utility using
this method are mixed. Evans & Viscusi (1991) found no difference, while Sloan
et al. (1998) and Viscusi & Evans (1990) found positive state dependence (marginal
utility is larger in good health). Although this method had the advantage of directly
eliciting the type of trade-offs informative to answer the question, the risks involved
were narrowly defined (multiple sclerosis or exposure to chemicals) and the questions
were hypothetical, raising questions about external validity and generalizability.
Other studies directly estimated the state dependence of the marginal utility of
consumption on health using structural life cycle models on panel data containing
information on wealth (savings). An early example is Lillard & Weiss (1997), who
found negative state dependence (marginal utility is larger in poor health) using data
37
from the Retirement History Survey. DeNardi et al. (2010) also found negative state
dependence using data from AHEAD cohorts in the Health and Retirement Study
although not statistically significant. Scholz & Seshadri (2010) found positive state
dependence when modeling both health and consumption as joint choices. Scholz &
Seshadri (2016) found a positive state-dependence effect using spending data from
the Consumption and Activities Mailout Survey and using self-reported health from
the Health and Retirement Study. Not surprisingly, results from structural models
hinged on the specification of preferences and, perhaps more importantly, on how
health impacts budget constraints, since wealth data is used to estimate preferences.
Furthermore, the health measure is often self-reported health, which may encompass
many dimensions of health. An important question is to assess whether the depend-
ence may differ across health dimensions. In particular, measures of limitations with
activities of daily living are important as benefits from long-term care insurance may
be conditioned on such measures of health (for example in Canada). An alternative
is to look at subjective well-being. Finkelstein et al. (2013) used life satisfaction data
to directly infer how the slope of the utility function depends on health. Their results
support positive state dependence. Since the authors did not observe consumption,
they investigated instead how life satisfaction was related to measures of permanent
income.
As argued by Finkelstein et al. (2009), a promising avenue is to use spending tra-
jectories in panels and investigate how these trajectories vary across individuals with
different health statuses. In this chapter, we use panel data on detailed spending of
Health and Retirement Study (HRS) respondents collected as part of the Consump-
tion and Activities Mailout Survey (CAMS) covering a period of 16 years (9 waves).
The use of detailed information on the composition of expenditures distinguishes our
38
paper from others who have studied the issue. Because spending data is collected in
the off years of the survey, we also have access to the wealth of information contained
in the Health and Retirement Study regarding changes in health as well as in other
characteristics. We used limitations in activities of daily living (bathing, eating,
dressing, walking across a room and getting out of bed) and instrumental activities
of daily living (using the phone, taking medication and handling money) as meas-
ures of health. Activities of daily living (ADL) represent activities that people do in
the morning to prepare themselves to start the day, while instrumental activities of
daily living (IADL) represent activities that people do once the day has started. The
ability to do IADLs is not fundamental to functioning but helps to be self-sufficient.
The availability of subjective expectations on survival, bequests and nursing home
entry allows us to investigate mechanisms behind the change in spending following
changes in health.
Controlling for the change in the subjective probability of survival associated with the
health shocks, our results suggest that the increase in total and nondurable spending
following the onset of IADL limitations is related to an increase in the marginal
utility of total spending, hence resulting in negative state dependence. However, the
absence of variation in total spending following the onset of ADL limitations suggests
the absence of a state dependence related to this dimension of health. Moreover, we
found a reshuffling in the spending shares assigned to transportation, donations and
gifts, and health spending following the onset of IADL limitations. Although there
was no significant evidence of a drawdown in total net wealth, IADL limitations led
to a reshuffling in the wealth portfolio by reallocating housing wealth in financial
wealth. This last result suggests that homeowners use their home equity as an
insurance tool.
39
The chapter is structured as follows. In section 2.2, we show how theory leads to
predictions on how changes in health are related to changes in spending. In section
2.3, we provide a description of the data and a definition of variables. Section 2.4
proposes an empirical strategy in order to formally test for state dependence of utility.
Finally, section 2.5 presents results while section 2.6 concludes.
2.2 Theoretical Framework
We consider a simple life cycle problem of allocating consumption across the life
cycle with uncertainty in health and mortality. Consumption can be allocated among
J consumption items which include health spending. We denote the consumption
vector at age t as c
t
= (c
1,t
, ..., c
J,t
). The utility from consumption is:
u(c
t
, h
t
) =
J
X
j=1
δ
j
(h
t
)
c
1−σ
j
jt
1 − σ
j
, (2.1)
with σ
j
> 0 and where h
t
represents health measured from bad to good. The function
u() allows the marginal utility of each spending item to be different as a function
of health. We say that a good is a complement to health if
∂
2
u(c
t
,h
t
)
∂c
jt
∂h
t
> 0, and a
substitute if
∂
2
u(c
t
,h
t
)
∂c
jt
∂h
t
< 0. It follows that the complementarity between health and
consumption of a good will depend on the value of
∂δ
j
(h
t
)
∂h
t
. Given a total spending
budget m
t
1
and using within period preferences, the intraperiod allocation problem
is simply to allocate m
t
between each consumption item by solving :
1
We assumed prices were constant over time and therefore we did not distinguish between
consumption and expenditures in what follows.
40
max
{c
j,t
}
J
j=1
J
X
j=1
δ
j
(h
t
)
c
1−σ
j
jt
1 − σ
j
(2.2)
under intraperiod budget constraints:
X
j
c
j,t
= m
t
. (2.3)
The solution is such that :
∂u(c
t
, h
t
)
∂c
j,t
=
∂u(c
t
, h
t
)
∂c
k,t
, ∀j, k (2.4)
and the budget constraint holds. From our explicit formulation, we have:
δ
j
(h
t
)c
−σ
j
jt
= δ
k
(h
t
)c
−σ
k
kt
, ∀j, k
⇒ c
kt
= c
σ
j
σ
k
jt
δ
k
(h
t
)
δ
j
(h
t
)
1
σ
k
, ∀j, k. (2.5)
Substituting in the intratemporal budget constraint, we have:
41
m
t
= c
σ
j
σ
1
jt
δ
1
(h
t
)
δ
j
(h
t
)
1
σ
1
+ ... + c
σ
j
σ
J
jt
δ
J
(h
t
)
δ
j
(h
t
)
1
σ
J
, ∀j
⇒ m
t
=
J
X
k=1
c
σ
j
σ
k
jt
δ
k
(h
t
)
δ
j
(h
t
)
1
σ
k
, ∀j (2.6)
The solution to this problem then yields a conditional optimal allocation for each
consumption item as a function of total budget and health c
∗
j,t
(m
t
, h
t
) that satisfies
equation (2.6). When σ
j
6= σ
k
, the Engel curves are nonlinear, so the share of m
t
allocated to the consumption of item j, that we express as α
j
(m
t
, h
t
), is a function
of the total budget as well as of the health status. When σ
j
= σ
k
= σ, ∀j, k, the
Engel curves are linear, so the share α
j
(h
t
) =
δ
j
(h
t
)
1
σ
P
J
k=1
δ
k
(h
t
)
1
σ
of m
t
allocated to the
consumption of item j is a function of h
t
and is independent of m
t
.
Replacing the solution for each consumption item c
∗
j,t
(m
t
, h
t
) as a function of total
spending into the utility function, we obtain the indirect utility function v(m
t
, h
t
). As
an example, we can take the special case where σ
j
= σ
k
= σ, ∀j, k and c
∗
j,t
(m
t
, h
t
) =
m
t
δ
j
(h
t
)
1
σ
P
J
k=1
δ
k
(h
t
)
1
σ
. By substituting this solution in the indirect utility function, we get:
v(m
t
, h
t
) =
J
X
j=1
δ
j
(h
t
)
m
t
δ
j
(h
t
)
1
σ
P
J
k=1
δ
k
(h
t
)
1
σ
1−σ
1 − σ
42
⇒ v(m
t
, h
t
) =
m
1−σ
t
1 − σ
1
h
P
J
k=1
δ
k
(h
t
)
1
σ
i
1−σ
J
X
j=1
δ
j
(h
t
)
1−σ
σ
+1
⇒ v(m
t
, h
t
) =
m
1−σ
t
1 − σ
1
h
P
J
k=1
δ
k
(h
t
)
1
σ
i
1−σ
J
X
j=1
δ
j
(h
t
)
1
σ
.
Knowing that
P
J
j=1
δ
j
(h
t
) =
P
J
k=1
δ
k
(h
t
), we then have:
⇒ v(m
t
, h
t
) =
m
1−σ
t
1 − σ
"
J
X
k=1
δ
k
(h
t
)
1
σ
#
σ
⇒ v(m
t
, h
t
) = δ(h
t
)
m
1−σ
t
1 − σ
, (2.7)
where δ(h
t
) =
h
P
J
k=1
δ
k
(h
t
)
1
σ
i
σ
. We then see that this solution corresponds to the
formulation of the utility of consumption used by DeNardi et al. (2010).
The choice of m
t
is governed by the intertemporal allocation problem. We say
that total spending is a complement to health if
∂
2
v(m
t
,h
t
)
∂m
t
∂h
t
> 0, and a substitute
if
∂
2
v(m
t
,h
t
)
∂m
t
∂h
t
< 0. The dynamic budget constraint is given by:
43
w
t+1
= R(w
t
+ y
t
− m
t
) (2.8)
where w
t
denotes wealth, y
t
income, R the gross return and m
t
=
P
j
c
j,t
total
expenditures. The agent has a discount factor β. He faces risk in terms of health
(and mortality). Let p
m
(h
t
, t) be the probability of dying next year and p
h
(h
t+1
|h
t
, t)
the probability of health status in the year t+1 as a function of current health h
t
. We
assume that there is no bequest motive, a hypothesis that we will validate empirically
in a subsequent section. Hence, the intertemporal choice of m
t
is given by:
V (w
t
, h
t
) = max
m
t
v(m
t
, h
t
) + β(1 − p
m
(h
t
, t))
X
h
V (w
t+1
, h
t+1
= h)p
h
(h
t+1
= h|h
t
, t), (2.9)
subject to the law of motion for wealth w
t+1
= R(w
t
+ y
t
− m
t
). If the borrowing
constraint is not binding, the solution for the path of m is governed by the Euler
equation:
v
0
(m
t
, h
t
) = Rβ(1 − p
m
(h
t
, t))
X
h
v
0
(m
t+1
, h
t+1
= h)p
h
(h
t+1
= h|h
t
, t) (2.10)
and the lifetime budget constraint. Upon finding a solution for m
∗
t
(w
t
, h
t
), we can
obtain a solution for each spending item by solving:
44
∂v(m
∗
t
(w
t
, h
t
), h
t
)
∂c
j,t
=
∂v(m
∗
t
(w
t
, h
t
), h
t
)
∂c
k,t
, ∀j, k (2.11)
under intratemporal budget constraints
P
j
c
j,t
= m
∗
t
(w
t
, h
t
). This solution leads us
to a set of optimal consumption items c
∗
t
= {c
∗
j
(w
t
, h
t
)}
J
j=1
.
To analyze how health changes affect the marginal utility of consumption items, it
is useful to express the solution of this intraperiod problem as α
j
(h
t
, m
∗
t
(w
t
, h
t
)) =
c
∗
j
(w
t
,h
t
)
m
∗
t
(w
t
,h
t
)
. Hence, the solution can be decomposed in two terms:
c
∗
j
(w
t
, h
t
) = α
j
(h
t
, m
∗
t
(w
t
, h
t
))m
∗
t
(w
t
, h
t
). (2.12)
A change in health can have three different effects on consumption items. Taking
the total derivative with respect to h, we get:
∂c
∗
j
(w
t
, h
t
)
∂h
t
=
∂α
j
(h
t
, m
∗
t
)
∂h
t
+
∂α
j
(h
t
, m
∗
t
)
∂m
t
∂m
∗
t
∂h
t
m
∗
t
+ α
j
(h
t
, m
∗
t
)
∂m
∗
t
(w
t
, h
t
)
∂h
t
.(2.13)
The first term is the pure state-dependence effect on the marginal utility of spending
in category j. Other things held constant, it captures the nature of the relationship
between the marginal utility of each consumption item and health. For example,
consumption of some goods may be less pleasurable when in worse health, while it
may be more necessary to consume other goods when in poor health. The second is
an income effect on the composition of spending: the induced effect of a change in
45
total spending on within period allocation. For example, if the shock shortens the
life horizon and therefore current consumption rises, spending on goods which are
more elastic to income will increase relative to other goods. If Engel curves are linear
(shares are constant with income or total spending), this term vanishes. Finally, the
last term is the life-cycle effect on total spending which affects spending of category
j even if shares do not vary with h
t
. As shown above, this effect is both related to
the change in the probability of dying and to the change in marginal utility of total
expenditures.
The formulation above makes it clear that aggregate spending may fall or increase
with a change in health. It can also remain roughly constant despite considerable
complementarity or substitutability within particular consumption items. Import-
antly, unconditional changes in aggregate spending as a function of health do not
isolate state dependence unless one can control for the income and life-cycle effects.
2.3 Data
2.3.1 Sample Selection
Our primary data source is the Consumption and Activities Mailout Study (CAMS)
which is an off-wave component of the Health and Retirement Study (HRS). Starting
in 2001, a sub-sample of the 2,000 HRS core respondents takes part in a paper survey
aimed at measuring spending at the household level. Details on the design of the
survey can be found in Hurd et al. (2014). Of the original 5,000 questionnaires sent
in 2001, 77% were completed. Respondents were then followed over time for up to
9 waves. Additional sub-samples were included in 2005 and 2011 to take the Early
Baby Boomer and the new Mid Baby Boomer cohorts into account, which were
46
recruited for the HRS the year before. In this paper, we used waves 2 (2003) to 9
(2017) of the survey. We dropped the 2001 wave because of differences in spending
categories. We used the survey weights provided with CAMS. Measures of health
and other variables needed for the analysis were obtained by merging information
from the adjacent waves of the HRS.
We focused on single respondents, using marital status at the time of CAMS inter-
views. Decision-making at the household level involves several complexities which
make it more difficult to isolate the effect of health on the marginal utility of consump-
tion (e.g., risk sharing, bargaining). Furthermore, most of the literature focusing on
consumption and saving of older individuals focuses on singles. For the most part,
these are widows and widowers. We also restricted the age range from 65 to 95 years
old. Prior to age 65, more respondents were working. Furthermore, the eligibility age
for universal health insurance coverage is 65 (Medicare), which reduces heterogeneity
in medical expenditure risk exposure. We focused on respondents aged less than 95
for sample size considerations and because a large fraction of respondents above this
age resided in nursing homes and were likely to have limited control over their spend-
ing. We also dropped respondents between the ages of 65 and 95 who were in nursing
homes, as the reliability of their expenditure data was limited due to the fact that
nursing homes provide services which have considerable consumption value but are
not recorded in CAMS. We also dropped observations with zero total expenditures
or too many missing spending categories (we kept those with more than 20 out of
32 categories). Finally, using information on time use, we dropped respondents who
reported having worked at least one hour. In Table 2.1, we provide details on the
consequences of these various sample restrictions. The final sample includes 6,926
observations from approximately 850 respondents per wave.
47
Table 2.1: Sample selection from CAMS and HRS
Observations
CAMS wave 2 3004
CAMS wave 3 3598
CAMS wave 4 3446
CAMS wave 5 3301
CAMS wave 6 4094
CAMS wave 7 3799
CAMS wave 8 3454
CAMS wave 9 3241
CAMS total 27937
Age: 65-94 17495
Single 10702
Not in nursing home 8450
Nondurable spending > 0 8435
Doesn’t work 6926
Final sample:
Wave 2 862
Wave 3 1023
Wave 4 885
Wave 5 825
Wave 6 853
Wave 7 865
Wave 8 819
Wave 9 794
Total 6926
Note: Sample selection from CAMS and HRS: Starting from the original CAMS
sample, we restricted to age 65–95 and selected only single respondents. We also
dropped those in nursing homes, those with zero expenditures and those who worked.
48
2.3.2 Definition of Spending Variables
The CAMS questionnaire covers 32 spending items. In what follows, we focus on
total and nondurable spending. Total spending is composed of durable (refrigerator,
washer, dishwasher, television and computer) and nondurable spending. Out of those
nondurable spending items, we constructed 9 categories: housing, transportation,
utilities, donations (and gifts), food (both at home and eating out), leisure, household
supplies, clothing and health (insurance, drugs, services and supplies). The mapping
for each wave of original spending categories to the ones used here is presented in
Table B.1 in the appendix.
For missing items, imputations were used. Hurd & Rohwedder (2006) reported no
statistically significant pattern of missing responses across socio-economic groups.
Over 54% of respondents had complete records over the 32 items, another 26% only
had one or two items missing. Overall, 90% had more than 26 items with nonmissing
records. The highest category with missing information was rent, but core interview
responses from HRS allowed to determine that most were homeowners. Overall,
mean imputations were used for remaining observations. Respondents were allowed
to report several nondurable items on a weekly, monthly and annual basis. All
responses were transformed into an annual measure covering the last 12 months.
To account for changes in price levels, we used the general consumer price index
to transform all monetary amounts in 2017 dollars. Given the relatively short time
span, we did not adjust for changes in relative prices across consumption items.
Table 2.2 reports the distribution of spending across different items. On average
households in our sample spend $27,809 on nondurables in a year. Housing, food
and health and the three largest items, household spending close to $6,765 per year on
49
housing, on average, $4,556 on food and $4,141 on health. Transportation, utilities
and donations (and gifts) are the next highest spending categories. Not surprisingly,
the distribution of most spending items is skewed, with medians generally lower than
means.
Table 2.2: Nondurable spending categories
Variables obs % share mean p10 p25 p50 p75 p90
Housing 6857 24.3% 6764 1089 2489 4609 8262 13188
Transport 6857 10.3% 2728 0 762 2133 3607 6037
Utilities 6857 15.7% 3640 888 2065 3323 4642 6168
Gifts 6857 6.9% 2443 0 100 708 2259 5595
Food 6857 17.7% 4555 931 2005 3495 5814 8864
Leisure 6857 3.4% 1119 0 0 315 1247 2936
HH supplies and services 6857 4.5% 1249 79 252 627 1438 2777
Clothing 6857 2.1% 559 0 71 274 653 1262
Health 6857 15.2% 4141 466 1351 3040 5292 8428
Nondurable 6857 100.0% 27808 10672 15523 23327 33684 48334
Note: This table reports statistics on nondurable spending categories over the previ-
ous 12 months. p10 and p90 refer to the 10th and the 90th percentile, respectively.
Weighted using CAMS weights.
2.3.3 Health Measures
Measures of health were obtained from HRS core interviews. As opposed to health
conditions such as cancer, which if treated does not reflect physical and cognitive
incapacity, we created proxies of health states by constructing measures of disability
using limitations on activities of daily living (ADL; bathing, eating, dressing, walking
across a room and getting out of bed) and instrumental activities of daily living
(IADL; using the phone, taking medication and handling money). ADLs represent
activities that people do in the morning to prepare themselves to start the day, while
50
IADLs represent activities that people do once the day has started. The ability to
do IADLs is not fundamental to functioning but helps to be self-sufficient. ADL and
IADL limitations are most likely to impact the enjoyment of consumption. Table 2.3
presents the joint probabilities of having ADL and IADL limitations. In 73% of the
observations in our sample, respondents do not have any of these limitations. It is
also most common to have only one of these kinds of limitations, ADL limitations
being the most frequent.
Table 2.3: ADL & IADL joint probabilities
IADL
0 1 2 3+
ADL
0 0.7336 0.0351 0.0040 0.0017
1 0.0956 0.0111 0.0036 0.0019
2 0.0402 0.0089 0.0026 0.0022
3+ 0.0312 0.0150 0.0071 0.0061
Note: This table reports the joint distribution of limitations in activities of daily
living and instrumental activities of daily living. N = 6,926. Weighted using CAMS
weights. ADL refers to limitations in activities of daily living (bathing, eating,
dressing, walking across a room and getting out of bed). IADL refers to limitations
in instrumental activities of daily living (using a telephone, taking medication and
handling money).
2.3.4 Net Wealth
The HRS also has extensive information on each respondent’s balance sheet. We
constructed a measure of household net wealth from the core interview prior the
CAMS interview. This measure accounted for all sources of assets minus debt. Assets
were composed of checking accounts, certificates of deposit, stocks, bonds, housing
51
(primary and other real estate), transportation, and individual retirement accounts
(IRAs), while debts were composed of mortgages (primary and other), home loans
and other debts (credit cards, etc.). Net household wealth was the difference between
assets and debt. We focused on the main categories composing net wealth: financial
wealth, housing wealth, transportation wealth and real estate. Descriptive statistics
of these categories can be seen in Table 2.4.
Table 2.4: Net wealth categories
Variables obs % share mean p10 p25 p50 p75 p90
Net financial 6926 34.2% 119637 -500 50 10000 84700 302000
Net housing 6926 38.0% 100512 0 0 55000 150000 250000
Transport 6926 9.3% 7206 0 0 3000 10000 20000
Real estate 6926 2.5% 22831 0 0 0 0 0
Net wealth 6926 100.0% 312850.9 20 16000 111000 346550 764700
This table reports statistics on the distribution of each wealth category as well as
totals. Net financial refers to the net financial wealth, net housing refers to the net
housing wealth and transport refers to transportation wealth. p10 and p90 refers to
the 10th and the 90th percentile, respectively. Weighted using CAMS weights.
On average, households in our sample had $312,850 in net wealth. Financial and
housing wealth were the two largest sources of wealth, with $119,637 of financial
wealth on average and $100,512 of housing wealth. Transportation assets and real
estate followed with an average of $7,206 and $22,831, respectively. Not surprisingly,
the distribution of wealth categories was skewed with medians generally lower than
means.
52
2.3.5 Other Variables
For our subsequent analysis, we constructed additional variables. In our model,
health status is a determinant of mortality risk. As shown by the Euler equation
(2.10), mortality risk is a key element determining the consumption path. Indeed,
Hurd (1989) and Salm (2010a) found that consumption choices were sensible to
change in mortality risk. So, this change in probability could affect the path of
spending change by increasing the future expected spending. Changes in health could
also affect the probability of needing services like nursing home in the subsequent
years and affect the expectation of leaving a bequest.
To understand the mechanisms explaining the spending path, we used variables meas-
uring these different types of expectations. First, the HRS core asked respondents
about their probability of living another 10 years. Second, the HRS core contained
several questions on intentions of leaving a bequest. We used the probability that
the respondent would leave an inheritance of more than $10,000. Finally, we used a
question from the core interview where they asked respondents about their chances
of entering a nursing home in the next 5 years. Descriptive statistics on these ex-
pectations by age group are provided in Table 2.5.
We also constructed a measure of household net income from the core interview
preceding the CAMS interview (as the reference period coincides with CAMS). This
measure accounted for all the sources of income of the household.
53
Table 2.5: Expectations
Age Bequest > 10k Nursing home < 5 years Survive 10 years
65-69 57.12 11.64 47.61
70-74 57.94 13.86 51.52
75-79 61.40 16.21 44.79
80-84 61.95 21.58 36.18
85-89 62.36 24.18 30.13
90-94 58.82 25.23 25.70
Total 59.78 17.63 42.88
Note: This table presents the average probability for different kinds of expectations
by 5-year age groups. Bequest > 10k refers to the subjective probability of leaving a
bequest over $10,000. Nursing home < 5 yrs refers to the subjective probability of
entering a nursing home in the next 5 years. Survive 10 yrs refers to the subjective
probability of living another 10 years. Weighted using CAMS weights.
2.3.6 Timing
In order to merge CAMS information with HRS survey waves, we needed to overcome
one important difficulty. CAMS surveys are done in the survey year between two
HRS survey years and measure consumption on an annual basis. On the other hand,
health is measured contemporaneously in HRS interviews. In particular, while we
used answers to questions about ADL limitations, if an HRS respondent answered
not having limitations in one wave and having some in the next one, we do not know
whether or not the respondent had limitations at the time of the CAMS interview.
We tried a number of ad hoc rules to assign health status to CAMS interviews, such
as assigning to the closest interview. However, the match is far from perfect and
results are very sensitive to the exact matching procedure. Instead, we constructed
54
a sample for which the baseline CAMS measurement of spending is surrounded by
HRS waves in which the respondent did not report limitations. We then used the
occurrence of limitations after these two waves and the subsequent measurement of
spending in CAMS for inference. Hence, we constructed change in total spending as:
∆log(m
i,t
) = log(m
i,t
) − log(m
i,t−4
) (2.14)
and two binary variables indicating if there was an increase in the number of ADL
and IADL limitations conditional to having had no limitations the previous 2 waves:
∆h
i,t−1
= I(h
i,t−1
> h
i,t−k
, h
i,t−k
= 0), (2.15)
with h
i,t
∈ {ADL
i,t
, IADL
i,t
} and k ∈ {3, 5}. Fixing the health baseline to zero
limitations allowed us to capture a cleaner effect of the onset of a limitation on
spending. We give a schematic representation of the sample design in Figure 2.1.
Take the CAMS interview in 2007, which we refer to as period t. We know that
the HRS report of health in the 2006 interview is prior to the measurement of con-
sumption. The treatment is given by the onset of limitations in year 2006. In order
to obtain an uncontaminated measure of baseline spending, we look at the sample
of respondents who reported no limitations in the 2004 and 2002 interviews. In the
case of that sample, we have baseline spending measured in the 2003 CAMS inter-
view. Since we did not use the first wave of CAMS and our data runs until 2017, we
55
Figure 2.1: HRS and CAMS Timing
Note: We present an example of health change, wealth change and spending change
timing between HRS and CAMS data for the 2002 to 2007 waves.
56
have potential differences in spending (2007-2003, 2009-2005, 2011-2007, 2013-2009,
2015-2011 and 2017-2013).
We also computed variables on change in total wealth. Since we are interested in
the wealth endowment of individuals prior to spending measurements, we computed
wealth changes between t − 5 and t − 1 :
∆w
i,t
= w
i,t−1
− w
i,t−5
. (2.16)
We finally computed variables on change in expectations. Since the expectations and
health measures both come from the HRS core and that measured the expectations
at the moment of the interview, we computed expectations change between t − 1 and
t − 3:
∆p
i,t
= p
i,t−1
− p
i,t−3
(2.17)
where p
i,t
∈ {Survival
t
, NursingHome
t
, Bequest
t
}. We then had the change in
expectations that could be related with the onset of our two types of limitations.
2.4 Empirical Strategy
This section presents empirical strategy in order to formally test for state dependence
of utility. For this purpose, we present different econometric specifications to estimate
57
the effect of the onset of ADL and IADL limitations on different outcomes.
To account for factors which may explain spending changes with changes in health
leading to worse health, we considered a median regression specification on aggreg-
ates, where the outcome quantities are defined as the differences between log of
spending, ∆log(m
i,t
) = log(m
i,j,t
) − log(m
i,j,t−4
):
∆log(m
i,t
) = x
i
β + γ
A
ADL
i,t−1
+ γ
I
IADL
i,t−1
+ ∆˜p
survival
i,t−1
+ λ
t
.
We used the same strategy for the log change of net wealth. x
i
is a vector of demo-
graphic variables controlling for age, gender, race and ethnicity. x
i
also controls for
baseline socio-economic status (SES) using log of income, log of net wealth and educa-
tion level at t−5. To capture a state dependence effect, we also controlled for the life
cycle effect coming from the change in survival using ∆˜p
survival
i,t−1
= p
survival
i,t−1
− p
survival
i,t−5
,
which is the change in the probability of surviving another 10 years between the
health measurements. We accounted for the panel nature of the data by using stand-
ard errors which accounted for clustering at the respondent level.
Next, we used a tobit with random effects on change in expectation of leaving a
bequest and of entering a nursing home, and on subjective survival probability. The
reason we use a tobit is that the possible share and expectation changes depend on the
initial expectation of each individual. The outcome is the difference in expectations:
p
i,t−1
− p
i,t−3
. We controlled for the same demographic and SES variables as before.
For spending categories, we also considered a tobit with random effects. The outcome
was the difference in the share of each item: α
i,t
− α
i,t−4
. We finally did the same
58
for share change in composition of net wealth. We then had a different left and right
censoring for each observation. The left censoring limit for share was set as −α
i,t−4
for respondent i, and the right censoring limit was set as 1 − α
i,t−4
. We can then
formulate the method as:
∆α
∗
it
= βx
it
+ γ
A
ADL
i,t−1
+ γ
I
IADL
i,t−1
+ v
i
+ u
it
,
with ∆α
it
=
−α
i,t−4
if ∆α
∗
it
< −α
i,t−4
, ∀i
∆α
∗
it
if − α
i,t−4
≤ ∆α
∗
it
≤ 1 − α
i,t−4
, ∀i
1 − α
i,t−4
if ∆α
∗
it
> 1 − α
i,t−4
, ∀i
The estimation with random effect at the respondent level is another way to take
the panel nature of the data into account and leads to efficiency gains.
2.5 Results
This section presents results on the effect of the onset of ADL and IADL limitations
on different outcomes.
A. Effects on Expectations
We first analyzed the effect of onset of ADL and IADL limitations on expectations
that had the potential to play an important role in the Euler equation. Table 2.6
reports coefficients of tobit regressions with random effects on the subjective prob-
59
ability of leaving a bequest over $10,000, entering a nursing home in the next 5 years
and surviving the next 10 years.
Table 2.6: Effect on Expectations
Bequest > 10k Nursing home < 5 years Survive 10 years
ADL -0.638 2.110 -2.168
(4.407) (2.633) (2.348)
IADL -4.703 2.828 -11.694 ***
(7.398) (4.206) (3.871)
σ
ν
13.46 0.00 0.00
σ
u
59.03 35.45 33.71
Observations 3087 2672 2862
Individuals 1344 1153 1269
Note: This table presents a tobit with random effect estimations where the outcome
is changes in expectations over 4 years. For each respondent i, the left censoring
limit was set as −p
i,t−4
and the right censoring limit was set as 1 − p
i,t−4
, where
p
i,t−4
was the expectation 4 years before. Bequest > 10k refers to the change in the
subjective probability of leaving a bequest over $10,000. Nursing home < 5 yrs refers
to the change in the subjective probability of entering a nursing home in the next 5
years. Survive 10 yrs refers to change in the subjective probability of living another
10 years. ADL refers to the onset of limitations in activities of daily living (bathing,
eating, dressing, walking across a room and getting out of bed), conditional to not
having had any limitation 4 years before. IADL refers to the onset of limitations
in instrumental activities of daily living (using a telephone, taking medication and
handling money), conditional to not having had any limitation 4 years before. σ
µ
refers to the panel-level standard deviation. σ
u
refers to the standard deviation of
u
it
.
First of all, none of these limitations had any significant effect on the probability of
leaving a bequest superior to $10,000 and entering a nursing home in the next 5 years.
These results justify the absence of these expectations in our theoretical framework.
60
On the other hand, IADL limitations had a negative and significant effect on the
subjective probability of surviving another 10 years, decreasing this probability by
around 12 percentage points. The effect of ADL limitations on survival was not
significant and close to zero. This result shows that the subjective probability of
surviving is a key element of our theoretical framework and must be taken into
account to identify the health state dependence effect of total spending.
Indeed, the Euler equation presented in the theoretical framework tells us that a
decrease in the probability of survival due to a change in health state requires a
reduction in the ratio between the marginal utility of total expenditure at time t
relative to the expected marginal utility of total expenditures at t + 1. Equation
(2.18) shows that a decrease in the probability of survival causes a wealth effect that
increases the budget for the remaining years of life, allowing an increase in total
spending at the present time.
v
0
(m
t
, h
t
)
P
h
v
0
(m
t+1
, h
t+1
= h)p
h
(h
t+1
= h|h
t
, t)
| {z }
∆
−
= Rβ (1 − p
m
(h
t
, t))
| {z }
∆
−
. (2.18)
An increase in expenditure will decrease the value of v
0
(m
t
, h
t
), thus allowing the
equality of Euler’s equation to be respected. However, an increase in total spending
could also be the result of a negative health state dependence effect, which would
mean that the marginal utility of spending is higher when we are in bad health. All
these elements must be taken into account when we try to identify the health state
dependence of the marginal utility of total spending.
61
B. Effects on Aggregates
Next, we analyzed the health state dependence of the marginal utility of total spend-
ing. We identified the health state dependence effect by estimating how spending
and net wealth change following the onset of ADL and IADL limitations, controlling
for the life cycle effect coming from the change in subjective survival. Table 2.7
reports coefficient of median regressions of ADLs, IADLs and the change in survival
for all these aggregates.
Table 2.7: Effect on Aggregates
Total spending Non-durable Net wealth
ADL -0.0068 -0.0140 -0.0786
(0.0280) (0.0268) (0.0499)
IADL 0.0937 * 0.0953 ** 0.0481
(0.0489) (0.0442) (0.0776)
Survive 10 years -0.0001 -0.0001 0.0003
(0.0003) (0.0003) (0.0005)
Observations 2530 2530 2677
R-Squared 0.010 0.010 0.009
Note: This table presents median regressions where outcome is the change in log of
aggregates over 4 years. Estimates were corrected for clustering at individual level.
ADL refers to the onset of limitations in activities of daily living (bathing, eating,
dressing, walking across a room and getting out of bed), conditional to not having had
any limitation 4 years before. IADL refers to the onset of limitations in instrumental
activities of daily living (using a telephone, taking medication and handling money),
conditional to not having had any limitation 4 years before. Survive 10 years refers
to the change in the subjective probability of living another 10 years.
Results showed that total and nondurable spending changes were the only aggregates
62
significantly affected by the onset of IADL limitations. The onset of IADL limita-
tions significantly increased total and nondurable spending by almost 10% at the
median. There was no significant effect of the onset of ADL limitations on any of
the aggregates. Furthermore, none of these limitations had a statistically significant
effect on total net wealth. Finally, the effect of the change in the subjective prob-
ability of surviving another 10 years on these aggregates was very close to zero and
not significant.
These results suggest that the onset of IADL limitations increase the marginal utility
of total and nondurable spending. This result is consistent with those of Lillard &
Weiss (1997) and DeNardi et al. (2010). On the other hand, the onset of ADL limit-
ations did not seem to affect the marginal utility of total and nondurable spending.
C. Effects on Spending Shares
The onset of ADL and IADL limitations can have a specific effect on the marginal
utility of each spending item. These effects can go in opposite directions. Even if
there is an absence of change in total spending following the onset of ADL limitations,
there may still be an effect on spending items that compensate each other and lead
to a simple reshuffling of spending categories. Thus, it is important to investigate
how ADL and IADL limitations affect spending items separately.
The theoretical framework shows that changes in spending categories following the
onset of a limitation are in part explained by the change of their respective shares.
The change in spending share, expressed by
∂α
j
(h
t
,m
∗
t
)
∂h
+
∂α
j
(h
t
,m
∗
)
∂m
∂m
∗
∂h
, is composed
of a pure state dependence effect and an income effect. Tobit regressions on shares of
spending categories allow us to capture the combination of these two effects. Results
63
are reported in Table 2.8.
Table 2.8: Effect on composition of spending
Housing Transport Utilities HH services Health Gifts Food Leisure Clothing
ADL 0.001 -0.006 -0.008 -0.005 0.009 -0.014 0.003 -0.003 -0.005
(0.011) (0.008) (0.007) (0.004) (0.008) (0.008) (0.009) (0.005) (0.003)
IADL -0.004 -0.027 ** 0.007 -0.002 0.036 *** -0.025 ** 0.001 -0.007 -0.003
(0.018) (0.012) (0.011) (0.007) (0.013) (0.013) (0.014) (0.007) (0.005)
σ
ν
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
σ
u
0.173 0.111 0.109 0.066 0.131 0.119 0.133 0.065 0.043
Observations 2922 2922 2922 2922 2922 2922 2922 2922 2922
Individuals 1250 1250 1250 1250 1250 1250 1250 1250 1250
Note: This table presents a tobit with random effects estimations where outcomes
are changes in consumption shares over 4 years. For each respondent i, the left
censoring limit was set as −α
i,t−4
and the right censoring limit was set as 1 − α
i,t−4
,
where α
i,t−4
was the share 4 years before. ADL refers to the onset of limitations in
activities of daily living (bathing, eating, dressing, walking across a room and getting
out of bed), conditional to not having had any limitation 4 years before. IADL
refers to the onset of limitations in instrumental activities of daily living (using a
telephone, taking medication and handling money), conditional to not having had
any limitation 4 years before. σ
µ
refers to the panel-level standard deviation. σ
u
refers to the standard deviation of u
it
.
These results suggest that only the onset of IADL limitations has a significant effect
on the composition of spending. Indeed, there was a significant reallocation from
transportation and gifts spending to health spending, with an increase of 3.6 per-
centage points of the share of health spending. On the other hand, the effect of ADL
limitations on composition of spending is very close to zero and nonsignificant.
Based on equation (2.13), Table 2.9 presents the expenditure variations,
∂c
∗
j
(w
t
,h
t
)
∂h
t
,
64
of each spending category following the occurrence of ADL and IADL limitations,
as well as the decomposition of these variations in terms of a combination of state
dependence effect and income effect on the one hand, and in terms of life cycle effect
on the other.
The values of
∂m
∗
(w
t
,h
t
)
∂h
t
are based on the results presented in Table 2.7 for nondurable
spending. The values of
∂α
j
(h
t
,m
∗
t
)
∂h
t
+
∂α
j
(h
t
,m
∗
t
)
∂m
t
∂m
∗
t
∂h
t
are based on the results presen-
ted in Table 2.8. The value of m
t
= $23, 531 is the median value of nondurable
spending at the baseline and α
j
(h
t
, m
∗
t
) is the share of total spending allocated to
spending category j at the baseline.
We first analyzed the decomposition of change of transportation and gift spending
following the onset of IADL limitations. While the life cycle effect put upward pres-
sure on transportation and gifts spending, the combination of the state dependence
effect and the income effect was much more important, leading to a decrease in trans-
portation and gifts spending. For health spending, both effects led to an increase in
health spending, but the combination of the state dependence effect and the income
effect was much more important.
65
Table 2.9: Decomposition of spending categories change
Total change = State-dependence & income + Life-cycle
IADL
Housing $440 -$98 $538
Transport -$356 -$628 $272
Utilities $500 $169 $331
HH services $55 -$36 $91
Health $1,148 $838 $310
Gifts -$414 -$590 $176
Food $413 $30 $384
Leisure -$77 -$170 $93
Clothing -$18 -$67 $49
ADL
Housing -$55 $25 -$79
Transport -$178 -$138 -$40
Utilities -$241 -$192 -$49
HH Services -$124 -$111 -$13
Health $160 $206 -$46
Gifts -$359 -$334 -$26
Food $20 $77 -$57
Leisure -$73 -$59 -$14
Clothing -$120 -$113 -$7
Note: This table presents the expenditure variations,
∂c
∗
j
(w
t
,h
t
)
∂h
t
, of each spending cat-
egory following the onset of ADL and IADL limitations, as well as the decomposition
of these variations in terms of a combination of state dependence effect and income
effect one hand, and in terms of life cycle effect on the other. ADL refers to the
onset of limitations in activities of daily living (bathing, eating, dressing, walking
across a room and getting out of bed), conditional to not having had any limitation
4 years before. IADL refers to the onset of limitations in instrumental activities of
daily living (using a telephone, taking medication and handling money), conditional
to not having had any limitation 4 years before.
66
D. Effects on Wealth Shares
Next, we looked at the dynamic behind total net wealth by analyzing the wealth
portfolio choices. Table 2.10 shows that there was a significant reallocation from
housing wealth to financial wealth with the onset of IADL limitations. The share of
housing wealth decreased by 12.1 percentage points while the share of financial wealth
increased by 10.7 percentage points. There are two channels that can explain this
phenomenon. First, it is possible that a person with an IADL limitation no longer
has the capacity to take care of their house. Another channel can be a reallocation
from non-liquid to liquid wealth given that an increase in health spending caused by
the onset of IADL limitations also announce an increase in the probability of future
health spending. In this case, home equity could be a substitute for insurance, such
as health insurance or long-term insurance (Davidoff (2009a) and Davidoff (2010)).
Moreover, the onset of ADL limitations significantly decreases the share of housing
wealth by 5.3 percentage points.
Table 2.11 gives us more details about what is happening. The first column presents
marginal effects of logistic regressions where the dependent variable is a dummy
variable indicating if the respondents have moved since the base year. The second
column presents marginal effects of logistic regressions where the dependent variable
is a dummy variable indicating if the respondents became renters or not, conditional
to having been a homeowner in the base year. We see that the onset of ADL and
IADL limitations significantly increased the likelihood of moving from the current
house by 3.2% and 5.3%, respectively. Also, the onset of IADL limitations signi-
ficantly increased the likelihood of becoming renters by 6.5%. The onset of ADL
limitations also increased the likelihood of becoming renters, but not significantly.
67
Table 2.10: Effect on composition of net wealth
Financial Housing Transport
ADL 0.011 -0.053 ** -0.017
(0.026) (0.026) (0.017)
IADL 0.107 *** -0.121 *** -0.024
(0.040) (0.041) (0.026)
σ
ν
0.000 0.189 0.090
σ
u
0.375 0.311 0.215
Observations 2740 2740 2740
Individuals 1226 1226 1226
Note: This table presents a tobit with random effect estimations where the outcome
is changes in share of net wealth over 4 years. For each respondent i, the left censoring
limit was set as −α
i,t−4
and the right censoring limit was set as 1 − α
i,t−4
, where
α
i,t−4
was the share 4 years before. ADL refers to the onset of limitations in activities
of daily living (bathing, eating, dressing, walking across a room and getting out of
bed), conditional to not having had any limitation 4 years before. IADL refers to
the onset of limitations in instrumental activities of daily living (using a telephone,
taking medication and handling money), conditional to not having had any limitation
4 years before. σ
µ
refers to the panel-level standard deviation. σ
u
refers to the
standard deviation of u
it
.
68
Table 2.11: Housing wealth dynamics
Moved Rent home House value Mortgage
Logit Logit OLS OLS
ADL 0.032 ** 0.024 -0.273 -0.002
(0.016) (0.018) (0.250) (0.282)
IADL 0.053 ** 0.065 *** -0.697 * 0.373
(0.022) (0.022) (0.395) (0.329)
Observations 3324 2148 2481 2481
R2 0.017 0.025 0.010 0.016
Note: Moved means that the household has moved since the base year. Rent home
means that the household rents their home in the current wave, conditional to hav-
ing been a homeowner in the base year. House value and Mortgage refer to the
log change in the composition of net housing wealth, conditional to having been a
homeowner in the base year. ADL refers to the onset of limitations in activities
of daily living (bathing, eating, dressing, walking across a room and getting out of
bed), conditional to not having had any limitation 4 years before. IADL refers to the
onset of limitations in instrumental activities of daily living (using a telephone, tak-
ing medication and handling money), conditional to not having had any limitation
4 years before.
69
The third and the fourth columns show results of OLS regressions on the house value
and mortgage balance, conditional to having been a homeowner in the base year. The
onset of IADL limitations had a significant and negative effect on the house value,
decreasing it by 69.7%. Finally, there was not any significant effect of these onsets on
the mortgage balance. These results suggest that, if there is need for liquid wealth
following the onset of IADL limitations, respondents do not see loans based on their
home equity as an instrument to finance health spending and they are more likely
to sell their house and buy a smaller one or become renters.
2.6 Conclusion
We investigated how spending and the composition of spending change as a result of
the onset of ADL and IADL limitations. Using the longitudinal data from CAMS and
HRS, we constructed a test aimed to identify the presence of health state dependence
of the marginal utility of spending in an intertemporal context.
Our results suggest that total and nondurable spending increase in response to the
onset of an IADL limitation. Since we were controlling for the change in survival,
this result suggests a negative health state dependence of the marginal utility of total
and nondurable spending related to this health dimension. There is also evidence
of spending reallocation from transportation and gifts spending to health spending.
This reallocation is mostly related to the combination of a state dependence effect
and an income effect following the onset of an IADL limitation. None of these
limitations affect the subjective probabilities of entering a nursing home. However,
the subjective probability of surviving another 10 years decreases with the onset of
IADL limitations. Finally, there was no evidence of overall effect on net wealth, but
70
evidence of a shift from housing wealth to financial wealth. This shift is explained by
the fact that, following the onset of IADL limitations, homeowners sell their house
and buy a smaller one or become renters.
These results have important implications for two key policy questions. The first is
knowing why more households are not buying long-term care insurance. Our results
suggest that home equity might be used as a substitute to health and long-term
care insurance. The substitution for a health insurance is more likely since health
spending increases with the onset of IADL limitations, and the onset of ADL and
IADL limitations does not affect the subjective likelihood of using the services of a
nursing home.
The second important policy question concerns the degree to which households are
prepared for retirement. Given that the likelihood of poor health increases with age,
our results suggest that optimal savings for retirement may be higher than often
calculated because the decline in health and its effect on the marginal utility of
consumption are not taken into account. Incorporating this mechanism in life cycle
models and estimating such models from longitudinal spending data is an important
next step to better understand the insurance and savings needs of the near-elderly in
the future. For example, this would allow us to separate the state dependence effect
and the income effect according to the impact of the ADL and IADL limitations for
each of the expenditure categories
Finally, our estimates suggest that the onset of IADL limitations is not related to a
decrease of net wealth. However, there still is a puzzle behind the wealth reallocation
from housing wealth to financial wealth with the onset of IADL limitations. This
pattern might be related to the limitation itself, affecting the capability of caring
71
for and using these kinds of assets. It might also be related to the need for more
liquid wealth given the increase in expected future health spending with the onset
of IADL limitations. Even if they wished to stay a few more years in their house,
that need for liquid wealth might force people to sell it. An interesting extension
could be to analyze how financial products such as reverse mortgages could help
liquid-constrained households keep their house if they so desired.
CHAPITRE III
LOW DEMAND FOR REVERSE MORTGAGES IN CANADA : PRICE OR
PREFERENCES ?
Abstract
One of the main features that differentiate reverse mortgages from a more traditional
home equity line of credit is the no-negative equity guarantee (NNEG). This feature
ensures that, at the time of repaying the loan, the borrower only has to repay the
minimum between the resale value of the house and the value of the loan. In this
chapter, we used a pricing model to calculate mortgage insurance premiums charged
to cover the losses related to the NNEG. Given the size of the loans that are granted
in the Canadian market, we find that actuarially fair premiums are approximately
zero, which implies that the NNEG is a missing feature in the Canadian market. We
then constructed a stated-choice experiment in which Canadian respondents were
asked to evaluate various reverse mortgage products. By using exogenous variation
of the interest rates and the size of the loans from the survey design, we used these
stated-choice evaluations to compute the demand elasticity of reverse mortgages in
Canada and to look at other factors that could explain low demand. Our results
showed that more than half of eligible Canadians do not even have a basic knowledge
of reverse mortgages. Also, eligible Canadians do not seem to understand how to
take advantage of the NNEG. Finally, Canadian demand for reverse mortgages is
inelastic, but becomes elastic with a better level of knowledge on the product. As a
result, a combination of price adjustment and education on reverse mortgages could
be a good way to expand the size of the Canadian market.
Keywords: Mortgages, Housing Demand.
Note: This study is co-authored with Pierre-Carl Michaud.
73
3.1 Introduction
Housing is a major component of household wealth in retirement. The primary
residence accounts for approximately 33% of the median wealth accumulated by
Canadian households
1
. In retirement, owning a house provides a service flow with
a shadow price equal to the price of renting a similar location. In addition, home
equity acts as insurance against financial risks due to disability risk, since the house is
typically sold when individuals enter a nursing home (Davidoff, 2009b, 2010). Given
that housing is illiquid, many households are house rich and cash poor, which limits
their capacity of extracting home equity to finance consumption in their old age.
Downsizing a house is a direct way of extracting home equity. Yet, Venti and Wise
(2004) show that the elderly are reluctant to move to smaller houses or become
renters. An indirect way of downsizing a house is by reducing or eliminating main-
tenance, which implies higher consumption against a lower resale value (Davidoff,
2006). However, Davidoff (2006) shows that this is an ineffective way of downsizing,
because the amount of extra money that can be spent while letting the house depre-
ciate is lower than the appreciation that could have been obtained by maintaining
it. Borrowing against home equity while remaining in the house is becoming a pop-
ular alternative. For those who qualify, home equity lines of credit allow borrowing
against equity, but expose owners to the risk that the loan accumulated will end
up being greater than the value of the house. Furthermore, qualification for these
loans is restricted among the elderly, because of their limited repayment capacity.
An emerging alternative is reverse mortgages.
1
https://www150.statcan.gc.ca/n1/daily-quotidien/171207/dq171207b-eng.htm
74
A reverse mortgage is a financial product that allows a homeowner to convert a
portion of the current net value of his principal residence into cash. Unlike many
other mortgage products, the borrower is not obligated to make payments before
moving out, selling or dying. In addition, the borrower’s estimate is insured against
the risk that the loan is worth more than the house when it is sold. This is called
the no-negative equity guarantee (NNEG) of the reverse mortgage. This feature
means that the borrower’s longevity risk, as well as the risk of a drop in house
prices, is transferred to the lender. A reverse mortgage will typically command a
higher borrowing rate because of that guarantee. That premium will also depend on
whether or not lenders are insured against losses. In the United States, the Federal
Housing Administration (FHA) provides that insurance. In Canada, these reverse
mortgages are not insured. In North America, the market for reverse mortgage
purchases is tiny. In 2014, only 2.11% of Canadian households reported planning to
obtain a reverse mortgage as a source of income upon retirement (Gouvernement du
Canada, 2014). The average borrowing rate for reverse mortgages is roughly two
percentage points above the rate charged on home equity lines of credit.
One reason why this market is tiny is that reverse mortgages are mispriced. Several
attempts have been made to estimate the fair price of a reverse mortgage (Wang
et al., 2011; Yang, 2011; Huang et al., 2011; Shao et al., 2015). In this chapter, we
first use a pricing model to calculate actuarially fair mortgage insurance premiums
charged to cover losses related to the NNEG in Canada. We consider survival risk
given the borrower’s characteristics as well as the risk of downward variation of the
Canadian houses market. Given the size of loans granted in the Canadian market,
we found that actuarially fair mortgage insurance premiums are approximately zero.
This result shows that lenders do not take any risk by offering the NNEG, making
75
it a missing feature in the Canadian market.
Another reason for the small size of this market is the preferences and resources of
the clients (demand side). Reverse mortgages are particularly useful for those who
are house rich and cash poor. This means that potential market size is limited. Since
the supply of reverse mortgages is relatively new in some Canadian provinces, the
low demand could also be explained by a lack of knowledge about reverse mortgages.
Moreover, households with a large bequest motive could have a lower demand for
reverse mortgages. Retirees who expect to receive care from their family may also
have a lower demand, as they face fewer financial risks. Furthermore, government
programs that effectively provide insurance against financial risk may dampen de-
mand. Finally, they may be very price sensitive, which may explain low demand to
the extent that the price is high. Nakajuma & Telyukova (2017) studied the effect of
some of these factors on the demand for reverse mortgages in the United States. Us-
ing a lifecycle model, they found that bequest motive and uncertainty about health
and expenses are factors that account for low demand. To understand what role
these factors play in Canada, we constructed a stated-choice experiment in which
Canadian respondents were asked to evaluate various reverse mortgage products.
These products are composed of a proportion of the equity of the house that can be
borrowed and an interest rate. Using exogenous variation in interest rates (price)
and in the amount of the loan from the survey design, these stated choices were used
to look at factors that explain low demand and to compute the demand elasticity
of the Canadian market. Our results showed that more than half of eligible Ca-
nadians (55.48%) do not even have a basic knowledge of reverse mortgages. Also,
Canadians do not seem to understand how to take advantage of the no-negative
equity guarantee, since the stated demand increased significantly with the subjective
76
expectation of house price growth. Expecting that their family would take care of
them financially if needed, or would take up the responsibility of taking care of them
if they had important limitations in activities of daily living (ADL), did not have
any significant effect on the stated demand. Those who thought that their home is
an asset that must be sold only in the case of financial hardship had a significantly
higher demand, making reverse mortgages an interesting product for those with a
high level of attachment to their home. Although our results suggested an overall
inelastic Canadians market (0.81), the demand goes from highly inelastic (0.51) to
elastic (1.18) with a better knowledge of this product. As a result, a combination of
price adjustment and education on reverse mortgages could be a good way to expand
the size of the Canadian market, in addition to increasing profits.
The chapter is divided as follows. Section 3.2 presents a pricing framework used to
compute actuarially fair mortgage insurance premiums to cover losses related to the
NNEG. In the section 3.3, we describe the structure of the reverse mortgage supply
in Canada and compare the actuarially fair mortgage insurance premium with the
actual premiums charged on the market. Section 3.4 presents an overview of a survey
of 3,000 Canadians with the objective of measuring their level of knowledge about
reverse mortgages, and also of presenting the stated-choice experiment that measures
their intention of buying different reverse mortgage products. Section 3.5 provides
a descriptive analysis of the Canadian knowledge and estimates of the Canadian
demand models, while section 3.6 concludes.
77
3.2 What Should the Price of a Reverse Mortgage Be?
There is a vast literature of studies on the pricing of reverse mortgages (Li et al.,
2010; Chen et al., 2010; Cho et al., 2013; Alai et al., 2014; Shao et al., 2015). The
loaner is exposed to a multitude of risks, since the no-negative equity guarantee gives
the assurance to the borrower that the amount of debt will never exceed the resale
value of the house. Therefore, a mortgage insurance premium must be charged to
cover the losses associated to these risks. The main risks considered in the recent
literature are the longevity risk, the risk of downward variation in house prices and
the risk of interest rate (Li et al., 2010; Chen et al., 2010; Cho et al., 2013; Alai et al.,
2014; Shao et al., 2015).
The modeling of these risks has been done in several ways. Some have modeled
the house price dynamic by using a nationwide house price index for the United
States (Chen et al., 2010) and for the UK (Li et al., 2010). Others, like Cho et al.
(2013), consider this risk using data at the city level. More recently, Shao et al.
(2015) modeled the house price dynamic using Australian data on individual prop-
erty transactions. They used a Vector Auto-Regression model to account for the
correlation between the house price growth and other components, such as GDP
growth rate and the yield of short-term bonds. The longevity risk has also been
taken into account in different ways. While the majority of papers have considered
a deterministic model for mortality improvement from one cohort to another, other
papers, like Shao et al. (2015) ), consider both deterministic and stochastic models.
Finally, the risk of interest rate is generally modeled using the yield of short-term
bonds and is estimated in the Vector Auto-Regression model (Li et al., 2010; Chen
et al., 2010; Cho et al., 2013; Alai et al., 2014; Shao et al., 2015).
78
In this section, we present a pricing framework used to compute actuarially fair
mortgage insurance premiums to cover losses related to the no-negative equity guar-
antee in Canada. We use a simplified version of the models suggested by Chen et al.
(2010), Shao et al. (2015), Li et al. (2010) and Alai et al. (2014) ), only considering
the longevity risk and the risk of downward variation in house prices. We estim-
ated the house price risk using a simple autoregressive model instead of a vector
autoregression model as used in many studies (Li et al., 2010; Shao et al., 2015; Cho
et al., 2013; Alai et al., 2014). To do so, we used Canadian historical data on the
price of housing. This data set gave us detailed information on the average price of
different types of dwelling for the principal Canadian cities, allowing heterogeneity
in price growth and volatility (more details are provided in section 3.2.2). Finally, we
modeled the longevity risk considering a deterministic mortality improvement from
one cohort to another (more details are provided in sections 3.3.1 and 3.4.1).
3.2.1 Computation of the Reverse Mortgage Insurance Premium
Let γ be the loan-to-value ratio of the equity of the house H
a
, borrowed by an
individual of age a. The initial value of the loan, L
a
, is then given by L
a
= γH
a
.
The value of the loan at a + t is given by:
L
a+t
= L
a
(1 + r
LC
+ π)
t
, (3.1)
where r
LC
represents the rate of a home equity line of credit that we consider constant
over time, π represents a mortgage insurance premium to cover losses related to the
79
NNEG, and r
RM
= r
LC
+ π represents the interest rate of the loan. Let H
a+t
be
the resale value of the house if the borrower leaves or dies at the t period. The
no-negative equity guarantee ensures that the amount recovered by the lender at the
time of the sale of the house is:
min{L
a+t
, (1 − c)H
a+t
}, (3.2)
where c is a transaction cost calibrated at 5%
2
of the selling price. The loss by the
lender is then defined as:
max{L
a+t
− (1 − c)H
a+t
, 0}. (3.3)
The expected present value of future losses related to the NNEG is given by:
NNEG(a, π, γ) = E
H
T
X
t=1
q
a,a+t
max(L
a+t
− (1 − c)H
a+t
, 0)
(1 + i)
t
!
, (3.4)
where i is the discount rate of 3.8%
3
and q
a+t
is the conditional probability of dying
2
According to Sun Life Financial, the transaction costs in Canada are around 3% and 7%.
3
We define the discount rate as i = β
c
t+1
c
t
σ
. We calibrate
c
t+1
c
t
at 4%, which represent
the FRED average annual nominal consumption growth between 2005 and 2017. β is a discount
factor calibrated at 0.96 and σ is a CRRA utility calibrated at 2.
80
at age a + t for someone of age a at t = 0. The expected present value of the
accumulated mortgage insurance premium is given by:
MIP(a, π, γ) = π(a, γ)E
H
T
X
t=1
s
a,a+t
L
a+t
(1 + i)
t
!
, (3.5)
where s
a,a+t
is the conditional probability to survive at age a + t for someone aged
a at t = 0. Finally, the actuarial fair mortgage insurance premium π(a, γ) is such as
NNEG(a, π, γ) = MIP(a, π, γ).
3.2.2 House Price Dynamics
We calibrated the house price dynamics using the MLS Home Price Index from
the Canadian Real Estate Association (CREA), which provides information on the
price of housing in the main cities of importance in Canada. This set of data gives
information on the average price of all types of dwellings, as well as the average price
per type of dwelling, namely single-family dwellings, townhouses and condos. We
used monthly data from January 2005 to August 2018 for the cities of Vancouver,
Toronto and Montreal. Figure 3.1 presents the evolution of the composite price
index between 2005 and 2018 for all of Canada, as well as for the cities of Vancouver,
Toronto and Montreal. We see that the cities of Vancouver and Toronto are the ones
that have had the most important growth, with an average annual growth of 6% and
6.8%, respectively, while the city of Montreal has had an average annual growth of
3.7%. The cities of Vancouver and Toronto also have higher variability than the city
of Montreal.
81
Figure 3.1: MLS Home Price Index for the cities of Vancouver, Toronto and
Montreal, from 2005 to 2018
Tu & Zhou (2015) studied the volatility of house prices in major Canadian cities.
They applied an adjusted Dickey-Fuller test and a Phillips-Perron test and rejected
the null hypothesis of the presence of a unit root for these cities. In addition, they
found that an AR(1) is a good representation of the stochastic process of these cities.
Therefore, we estimated parameters of the house price dynamic using a simple an
AR(1) with a deterministic trend:
log(H
h,p,m
) = δ
h,p
m +
h,p,m
(3.6)
h,p,m
= ρ
h,p
h,p,m−1
+ η
h,p,m
, (3.7)
where H
h,p,m
is the average house price of type h, in the city p in the month m, δ
h,p
is the deterministic trend and η
h,p,m
is an error term normally distributed with an
average of zero and a variance of σ
2
h,p
. The table 3.1 presents estimates per type of
dwelling for the cities of Vancouver, Toronto and Montreal. In each specification, the
82
coefficient of the deterministic trend and the auto-correlation coefficient are signific-
ant at a level of 1%. These estimates were used to calibrate the risk of downward
variation of house prices in the provinces of Quebec (Montreal), Ontario (Toronto)
and British Columbia (Vancouver).
Table 3.1: House price dynamic
δ
h,p
ρ
h,p
σ
2
h,p
prov type
Vancouver SFD 0.006*** 0.964*** 0.023
Townhouse 0.004*** 0.988*** 0.018
Condo 0.004*** 0.993*** 0.018
Toronto SFD 0.006*** 0.949*** 0.022
Townhouse 0.006*** 0.956*** 0.021
Condo 0.005*** 0.966*** 0.020
Montreal SFD 0.003*** 0.965*** 0.011
Townhouse 0.004*** 0.912*** 0.016
Condo 0.003*** 0.968*** 0.011
Note: This table reports estimated parameters of the house price dynamics by city
and type of dwelling. SFD refers to a single-family dwelling. δ
h,p
is the monthly
deterministic trend, ρ
h
p
is the AR(1) coefficient and σ
2
h,p
is the variance for a dwelling
of type h and in city p. * p < 0.1, ** p < 0.05, *** p < 0.01.
3.3 Canadian Home Income Plan
Canadians have access to reverse mortgage products through the Canadian Home
Income Plan (CHIP) offered by HomeEquity Bank. They are the only ones to offer
reverse mortgages in Canada. This program was first offered in the Vancouver area
83
in 1986, and then in Ontario and Alberta starting in 2001. In the following years,
the program was gradually offered across the country.
In order to be eligible to the program, the borrower must be a Canadian citizen and
at least 55 years old. In addition, they must be the owner of their own residence, and
it must be their primary residence. The initial advance must be at least $25,000.
The program allows the borrower to remain the owner of the residence, as long
as certain conditions are met. These conditions are that the residence must be
maintained in good condition, the property taxes must continue to be paid, a home
insurance must be had and there must be no delay of payment on the property in
the case of those who have another mortgage attached to the residence.
The CHIP program also gives a NNEG, which means that it guarantees that the
amount to be repaid will never exceed the fair market value of the property at the
time of sale. Once a loan-to-value has been granted, the homeowner has several
options to choose from in order to receive the funds. They can receive 100% of the
funds allowed in one lump sum. They can also initially receive a fraction of the funds
granted, in the form of an initial lump sum of $25,000, with subsequent advances.
In our case, we based our analysis on the option of receiving 100% of the funds in
one lump sum.
There are some fees charged to the borrower. First, CHIP charges a closing and ad-
ministrative fee of $1,495, which includes security lookup, title insurance and mort-
gage registration. Added to this are fees ranging from $175 to $400 for an assessment
of the property. Finally, it charges a fee between $300 and $500 for independent legal
advice.
84
In 2017, the CHIP program allowed people to borrow between 10% and 55% of the
estimated equity of the residence. The loan-to-value depends on the borrower’s age,
sex and marital status. It also depends on the type of residence and its geographical
location. Table 3.2 provides an example of a loan-to-value for a single-family dwelling
that can be borrowed by a single woman between 55 and 75 years old, in the cities
of Montreal, Toronto and Vancouver, in 2017. All these reverse mortgages are lent
at an interest rate of 5.59%.
Table 3.2: Maximum loan-to-value
Montreal Toronto Vancouver
Age
55 0.260 0.253 0.245
65 0.354 0.364 0.347
75 0.420 0.434 0.413
Note: This table presents the maximum loan-to-value ratios of the home equity that
can be borrowed by a single woman living in a single-family dwelling. These results
are divided by age and city. Source: HomeEquity Bank, 2017.
In order to reduce the losses related to the NNEG, the loan-to-value is lower for
younger borrowers. It is also lower for women, since they have a higher life expect-
ancy than men. When compared with single individuals, couples can borrow at a
lower loan-to-value since the joint probability of survival is taken into consideration.
Finally, according to the type of dwelling and its location, a higher loan-to-value
will be loaned to those for which a higher price growth and a lower volatility are
expected.
85
3.3.1 Actuarially Fair Mortgage Insurance Premium in Canada
We used the pricing framework to calculate actuarially fair mortgage insurance premi-
ums based on the loan-to-values offered by the CHIP program. We first calibrated
the interest rate of a home equity line of credit r
LC
at 4%, which is the average rate
that was offered on the Canadian market in 2017
4
. Next, we calibrated the condi-
tional probabilities of dying and surviving using the prospective life tables produced
by Statistics Canada (Bohnert & Statistics Canada, 2015). These life tables are di-
vided by cohort, gender and province. We finally calibrated the loan-to-values using
the maximum loan-to-values offered by CHIP as reported in the Table 3.2.
Using our pricing framework, we calculated the actuarially fair mortgage insurance
premium for women living in a single-family dwelling, 55, 65, and 75 years old, in the
cities of Montreal, Toronto and Vancouver. In each case, we ran 100 simulations and
took the average actuarially fair mortgage insurance premium. Table 3.3 reports the
actuarially fair interest rate, r
LC
+ π
fair
, by age and province. These results suggest
that actuarially fair premiums are between 0% and 0.03%. These actuarially fair
premiums are very low when compared to the 1.59% premium charged by CHIP
5
.
We repeated this exercise for men, couples and other types of dwelling, and results
were very similar
6
.
4
https://www.ratehub.ca
5
The interest rate for the CHIP program in 2017 was 5.59%. We then calculated the CHIP
premium as the CHIP interest rate minus the average interest for a home equity line of credit of
4%.
6
These results can be provided on request.
86
Table 3.3: Actuarially fair rates
Montreal Toronto Vancouver
Age
55 0.0401 0.04 0.0401
65 0.0401 0.04 0.0402
75 0.0400 0.04 0.0403
Note: These rates correspond to a home equity line of credit rate (r
LC
) of 4%, plus
an actuarially fair premium (π
fair
), for women owners of a single-family dwelling.
These results are divided by age and city.
To analyze which factors could justify a mortgage insurance premium as large as
the one charged by CHIP, Figure 3.2 presents different static comparatives to see
how actuarially fair mortgage insurance premiums and the probability of loss for the
loaner are affected by different parameters. We show results for the case of a 65-
year-old woman, owner of a single-family dwelling in Montreal. The three graphs on
the left present the actuarially fair mortgage insurance premium as a function of the
house price growth, the relative standard deviation of the house price uncertainty,
and the loan-to-value ratio, respectively. The three graphs on the right present the
probability of loss, defined as P r(NNEG > 0), as a function of the same parameters.
In each case, the dotted line represents the premium charged by CHIP (1.59%) and
the dashed line represents the actual value of these parameters.
Figure (a) shows how the actuarially fair premium decreases as a function of the
house price growth. All other things being equal, the premium charged by CHIP
corresponds to a fair premium in an environment of negative house price growth. As
shown in Figure (b), CHIP is exposed to the probability of a loss below 5% with
87
the actual house price growth, while a negative house price growth scenario would
expose CHIP to the probability of a loss of more than 50% and could justify such a
high premium.
Figure (c) shows how the actuarially fair mortgage insurance premium increases as
a function of the relative standard deviation of house price uncertainty in Montreal.
All other things being equal, the premium charged by CHIP corresponds to the
situation where the standard deviation is 8 times higher than the actual one. As
shown in Figure (d), CHIP is exposed to the probability of a loss of less than 5%,
while an 8 times higher standard deviation corresponds to the probability of a loss
of approximately 40%.
Figure (e) shows how the actuarially fair mortgage insurance premium increase as a
function of loan-to-value ratio. All other things being equal, the premium charged by
CHIP corresponds to a situation where the loan-to-value ratio corresponds to 90% of
the equity of the home, while the effective loan-to-value for a 65-year-old woman in
Montreal is 35.4%. As presented by Figure (f), CHIP is exposed to the probability
of a loss of less than 5%. On the other hand, the probability of a loss increases to
more than 80% with a loan-to-value ratio of 90%
7
.
7
A probability of loss of 80% may seem high. However, it is important to note that the
probability of loss is not necessarily related to the size of the loss
88
Figure 3.2: Comparative statics
Actuarially fair premium
(a)
Probability of loss
(b)
(c) (d)
(e) (f)
Note: This figure presents different static comparatives to see how actuarially fair
premiums and the probability of loss for the loaner are affected by different paramet-
ers in the case of a female owner of a single-family dwelling, 65 years old and living in
Montreal. Figures (a) and (b) present actuarially fair premium and the probability
of loss as a function of the house price growth; Figures (c) and (d) present the actu-
arially fair premium and the probability of loss as a function of the relative standard
deviation of house price growth; and Figures (e) and (f) present the actuarially fair
premium and the probability of loss as a function the loan-to-value corresponding to
the loan.
89
The actual maximum loan-to-value ratio offered by CHIP ensures that they take no
risk related to the no-negative equity guarantee (NNEG), making it a missing feature
in the Canadian reverse mortgage market. In this context, it is hard to differentiate a
reverse mortgage from a home equity line of credit. The price difference between these
two products may be hard to justify to buyers, which could explain why the market
is currently so small. Finally, it is important to note that our pricing framework
does not take into account the possibility of terminating the contract before death.
However, a pricing framework allowing the termination of the contract before death
would have brought a downward pressure on the actuarially fair premium, making
the premium charged by CHIP even more difficult to justify. Moreover, our pricing
framework does not take into consideration the possibility of moral hazard, where
homeowners who contract a reverse mortgage could stop maintaining their residences,
with the consequence of decreasing their values. However, one of the conditions
attached to reverse mortgage contracts offered by the CHIP program is that the
residence must be maintained in good condition. Hence, this condition prevents
potential losses related to the moral hazard and justify the fact that moral hazard
is not taken into consideration in the pricing framework. Finally, even if it had no
effect on house prices, the 2008 crisis may have considerably changed expectations
about events that could possibly have a negative impact on house prices, due to the
American experience. Household debt relative to household income has increased
significantly since 2008 in Canada, much like it had in the United States before the
crisis. However, Figure (e) shows that we would need very high uncertainty relative
to what we estimated to justify such a high premium.
90
3.4 Survey
Since 2016, the Retirement and Savings Institute at HEC Montréal regularly con-
ducts web surveys on different topics related to retirement preparation. In fall 2016,
they first conducted a survey to examine the cause of the low market penetration of
long-term care insurance in Canada (Boyer et al., 2019). These surveys are conduc-
ted in partnership with AskingCanadians, an online survey company. By responding
to surveys, participants accumulate points that can be redeemed for products from
companies such as Hudson’s Bay, Aeroplan, Petro-Points and Via Preference. Based
on the same survey structure, we surveyed 3,000 Canadians in the summer of 2017.
Respondents were aged 55 to 75 and lived in the provinces of Quebec, Ontario or
British Columbia. In each province, 50% of respondents came from the census met-
ropolitan area (CMA), while the rest came from outside the CMA.
The questionnaire was presented in 5 parts relevant to the study of the demand for
reverse mortgages. First, we asked general questions in order to have information on
the socio-economic, demographic and health characteristics of respondents. There
was also a section on preferences, risk perception and expectations for the future.
Another section measured respondents’ level of financial literacy and knowledge of
probabilities. A fourth section focused on respondents’ general knowledge about
reverse mortgages. Finally, the last section ran a stated-choice experiment, where
respondents were offered different reverse-mortgage products and had to evaluate
them by giving their probability of buying each of these financial products within
the next year. A copy of the questionnaire can be found in Appendix C.2.
In order to represent the distribution of the population characteristics of these three
provinces, we created a weighting based on the weighting of the Canadian Community
91
Health Survey (CCHS) for the year 2010. The weight cells are divided by age group
(5-year), gender, province and education (3 levels).
Of the 3,000 Canadians surveyed, 2,399 reported owning a home. As many of them
still held mortgages on their homes, 2,306 of them reported having a home equity of
over $25,000. 2,163 of them were single or had a spouse aged 55 or older, making
them eligible for the CHIP program. Finally, 2,140 respondents did not have any
missing information. A description of those eligible respondents is reported in Table
3.4.
Canadians corresponding to our weighted sample are 63 years old on average, and
half of them are male. Around 20% of them are from British Columbia, 30% from
Quebec and 50% from Ontario. 75.5% of them are married or in a common-law
relationship, and 76.5% reported having at least one living child. Most of them
have at least a college education. 66% of them consider themselves retired. On
average, their annual income is around $89,000 and they have average total savings
of $266,000
8
. In both cases, the median values are below the mean values. The
average current market value of their home is $570,000 and an average of 11.1% of
the current market value is still owed on their mortgages. As a result, the median
equity value of their residence is around $520,000. 80.3% of households are house
rich and cash poor, which means that the equity of their house is worth more than
their accumulated non-housing wealth. Finally, 56.1% of them have an employer
pension plan.
Respondents were questioned on their bequest motive, their level of attachment to
8
To prevent the effect of outliers, we imposed a maximum annual income of $500,000 and
maximum total savings of $5,000,000
92
their house and their expectations about the care and financial support they will
receive from their family in the future. They were also asked a sequence of four
multiple-choice questions to assess their level of financial literacy
9
. 17.8% of them
agreed with the fact that parents should set aside money to leave their children as
inheritance, even if it means somewhat sacrificing their own comfort in retirement.
On average, they evaluate at 44.7% the probability that their family would take
up the responsibility of taking care of them if they had important ADL limitations
and at 45.2% the probability that their family would take care of them financially
if needed. They also evaluate on average at 43.9% their probability of staying in
their current home until death, and 44% agreed with the statement that a house is
an asset that should only be sold in case of financial hardship. Finally, 50.1% of
respondents answered all four questions evaluating their financial literacy correctly.
9
The following questions were asked:
• Suppose you have $100 in a savings account, the interest rate is 2% per year and you never
withdraw money. After 5 years, how much will you have in this account in total?
• True or False? You should invest most of your money in a single stock that you select rather
than in lots of stocks or in mutual funds.
• Imagine leaving $1,000in a savings account that pays 1% interest and has no charges. Imagine
that inflation is running at 2%. Do you think that if you withdraw the money in a year’s time
you will be able to buy more than, exactly the same as, or less than today with the money in
this account?
• Suppose the chances of someone aged 50 living to age 85 are 60%. What do you think the
chances are that this same person will live to age 60?
93
Table 3.4: Sample Description
mean SD min max
Age 63.388 5.305 55.000 75.000
Men 0.488 0.500 0.000 1.000
Ontario 0.502 0.500 0.000 1.000
British Columbia 0.193 0.395 0.000 1.000
Quebec 0.305 0.460 0.000 1.000
Married 0.755 0.430 0.000 1.000
Has kids 0.765 0.424 0.000 1.000
Less than high school 0.180 0.384 0.000 1.000
High school 0.384 0.486 0.000 1.000
College 0.436 0.496 0.000 1.000
Retired 0.663 0.473 0.000 1.000
Total income ($1,000) 88.544 66.092 0.001 500.000
Total non-housing saving ($1,000) 265.681 424.297 0.000 5000.000
Home value 570.049 468.803 25.322 3000.000
Mortgage (% of the home value) 0.111 0.190 0.000 0.926
Equity ($1,000) 519.638 456.115 25.322 3000.000
House rich & cash poor 0.803 0.398 0.000 1.000
Employer pension plan 0.561 0.496 0.000 1.000
Bequest motive 0.178 0.383 0.000 1.000
Probability of family support if ADL 0.447 0.342 0.000 1.000
Probability of family support if financial need 0.452 0.368 0.000 1.000
Probability of staying home until death 0.439 0.337 0.000 0.990
House must be sold only if financial hardship 0.580 0.494 0.000 1.000
Financial literacy (4 correct answers) 0.501 0.500 0.000 1.000
Note: This table presents descriptive statistics on the Canadian population corres-
ponding to our sample. “House rich cash poor” refers to a dummy variable equal to
one if the equity of the house is superior to the total non-housing savings. Statistics
weighted according to 2010 Canadian Community Health Survey (CCHS).
3.4.1 Survival Rates
We used three sources in order to identify the probability of mortality q
a,a+t
and
survival s
a,a+t
of respondents:
94
1. Prospective survival rates from Statistics Canada,
2. Objective survival rates using microsimuation,
3. Subjective survival rates.
Prospective Life Tables
We first use the prospective life tables produced by Statistics Canada (Bohnert &
Statistics Canada, 2015). These prospective survival rates are divided by cohort,
gender and province. For each respondent, we then attached a specific life table
based on their specific characteristics. Let x
i
be a vector with the information on
the cohort, the gender and the province of individual i. Based on the prospective
life tables, we define q
LT
a,a+t
(x
i
) and s
LT
a,a+t
(x
i
) as individual i’s probability of dying or
surviving between the ages of a and a + t.
Objective Life Tables
To compute our objective life tables, we used COMPAS, a microsimulation model
that projects objective mortality rates specific to each respondent, based on their
characteristics (Boisclair et al., 2016). To make these projections, the model takes
into account the individual’s current age, gender, education level, and their self-
reported diagnosis of health conditions (heart disease, diabetes, cancer, lung disease
and hypertension)
10
. Let x
i
be a vector with the information on individual i’s current
age, gender, education, and the self-reported diagnosis of health conditions. Based on
the individual specific objective life table from the microsimulation model, we define
10
Statistics on the respondents health conditions are available upon request.
95
q
O
a,a+t
(x
i
) and s
O
a,a+t
(x
i
) as individual i’s objective probability of dying or surviving
between the ages of a and a + t.
Subjective Life Tables
To compute subjective life tables, we followed the approach used by Salm (2010b).
Let the subjective mortality hazard of respondent i at age a be given by:
λ
S
a
(x
i
) = ψ
i
λ
O
a
(x
i
), (3.8)
where λ
O
a
(x
i
) is the individual’s objective mortality hazard based on microsimulation.
In continuous time, let the subjective probability of surviving from age a to age 85
be given by:
s
S
a,85
(x
i
) = exp
−ψ
i
Z
85
a
λ
O
s
(x
i
)
, (3.9)
while the objective probability of surviving based on microsimulation for the same
ages is:
s
O
a,85
(x
i
) = exp
−
Z
85
a
λ
O
s
(x
i
)ds
. (3.10)
Let Λ
O
a,85
(x
i
) =
R
85
a
λ
O
s
(x
i
)ds. Then,
96
log(s
O
a,85
(x
i
)) = −Λ
O
a,85
(x
i
) (3.11)
and
log(s
S
a,85
(x
i
)) = −ψ
i
Λ
O
a,85
(x
i
) (3.12)
Dividing equation (3.12) by equation (3.11), we have:
ψ
i
=
log(s
S
a,85
(x
i
))
log(s
O
a,85
(x
i
))
. (3.13)
In the survey, each respondent was asked to give his subjective probability of surviv-
ing until the age of 85, s
S
a,85
(x
i
). We used this information to identify ψ
i
. To avoid
indeterminate values, we set s
S
a,85
(x
i
) = 0.01 as a minimum and s
S
a,85
(x
i
) = 0.99 as a
maximum. Based on the objective life table of individual i, it is then possible to use
ψ
i
and construct their subjective life table. Let x
i
be the same vector of information
used to compute the objective life table of individual i. We then define q
S
a,a+t
(x
i
)
and s
S
a,a+t
(x
i
) as individual i’s subjective probability of dying or surviving between
the ages of a and a + t.
Table 3.5 presents the average expected remaining years of life using the objective,
prospective and subjective life table. On average, the expected number of remaining
97
years of life is 22.4 years using the prospective life tables from Statistics Canada,
20.8 years using the objective life tables from microsimulations and 27 years using
the subjective life tables. It means that the respondents of our sample have a lower
survival rate than the average population with the same characteristics (cohort, age,
gender and province). On the other hand, respondents overestimate their probab-
ility of surviving. Finally, the use of subjective life tables instead of the other life
tables should contribute to increasing the mortgage insurance premium to cover the
additional survival risk.
Table 3.5: Expected remaining years of life
Objective Prospective Subjective
mean 20.82 22.4 27.03
SD 5.57 5.12 10.22
Note: This table presents the average expected remaining years of life using the
objective, prospective and subjective life tables. Statistics weighted according to the
2010 Canadian Community Health Survey (CCHS).
3.4.2 Experiment
For each of the respondents in our sample, we proposed 5 different scenarios. These
scenarios were distinguished from each other by different interest rates offered and a
different loan-to-value that can be borrowed. Here is the introductory text presented
to the respondents
11
:
11
A French version was presented to the respondents who chose to answer the questionnaire
in French.
98
We will refer to a reverse mortgage as a financial product that lets
you turn part of your current home equity into cash. Unlike many
mortgage-based financial products, you’re not obligated to make any
payments until you move, you sell your home, or you die. Import-
antly, you have the certainty that once your residence will be sold, the
amount required to repay the loan will not exceed the selling price of
the residence.When we use the expression “current home equity”, we
are referring to the current market value of your primary residence
after subtracting outstanding mortgage balances. For the rest of this
section, try to have your current home equity in mind. We are going
to show you some simple reverse mortgage products and ask you to
rate them. Each reverse mortgage has three attributes:
1. The percentage of your current home equity that you can borrow.
The amount borrowed must be a minimum of $25,000.
2. A fixed annual interest rate on the balance of the loan, generating
interests that you do not need to pay before you move, sell or
die.
3. A fixed fee of $2,245 that you only have to pay once. The money
you obtain from the reverse mortgage will be used to pay this fee.
We then presented the scenarios the following ways:
1. You can borrow a minimum of $25,000 and up to β% of your
current home equity.
2. You will be charged a fixed annual interest rate of r% on the
balance of the loan for as long as you hold the loan.
Reminder: You’re not obligated to make any payments until you
move, you sell your home, or you die; and you have the certainty
that once your residence will be sold, the amount required to
repay the loan will not exceed the selling price of the residence.
3. There is a fixed fee of $2,245 that you only have to pay once.
The money you obtain from the reverse mortgage will be used to
pay this fee.
99
For each individual i and scenario n, we exogenously propose an interest rate,
r
experiment
i,n
, which can take the values:
r
experiment
i,n
= [3.8%, 4.1%, 4.4%, 4.7%, 5%, 5.3%, 5.59%, 6%, 6.5%, 7%],
each with probability 1/10. Therefore, we randomized the rates around the interest
rate of 5.59% proposed by CHIP for a 5-year term at the moment when the survey
was conducted.
For each individual i and scenario n, a loan-to-value is proposed in term of percent-
ages of equity, β
i,n
, that can be borrowed. We denote the maximum loan-to-value
that can be borrowed by the individual i from CHIP as β
CHIP
i
. We have informa-
tion on the CHIP’s average maximum loan-to-value, by 5-year age group
12
, gender,
marital status (single or couple), and residence location (inside or outside the metro-
politan area)
13
. These values come from the CHIP calculator that can be found on
their website
14
and are presented at the end of Appendix C.2. To randomize the loan-
to-value around β
CHIP
i
, we exogenously created a percentage change in loan-to-value
by drawing a value, τ
i,n
, that can take the values:
τ
i,n
= [0.5, 0.75, 1, 1.25, 1.5], each with probability of 1/5.
12
For couples, we used the average age of the couple,
age
R
+age
S
2
, where age
R
is the age of
the respondent and age
S
is the age of the spouse as reported in the survey. We rounded the result
to the nearest integer and set the age as 79 when
age
R
+age
S
2
> 79.
13
To identify the residence location, we asked respondents to give us the first three characters
of their postal code. This information allowed us to identify the respondents who were or were not
part of the central city of the metropolis of their respective province.
14
https://www.chipadvisor.ca/calculator/
100
The loan-to-value proposed in the scenario n of the respondent i will therefore be
β
i,n
= τ
i,n
β
CHIP
i
.
With the objective of measuring the concern that some elements of the contract
could not be respected, we randomized the presence of the following sentence with a
probability of 0.5:
Suppose you have the certainty that you will never be put under pres-
sure to sell your residence and that the contract terms will be respec-
ted.
Finally, after presenting a scenario, we asked the respondent to evaluate the prob-
ability, from 0% to 100%, that they would buy this reverse mortgage if a trusted
financial institution offered it within the next year.
3.4.3 Relative Fairness
As we have seen above, it is not possible to compare different reverse mortgage
contracts simply by comparing their interest rates. Actually, the actuarially fair
mortgage insurance premiums will vary according to several factors, such as the re-
spondent’s age, sex, place of residence, type of home and the loan-to-value ratio of
the equity of the house that is lent. In order to create a measurement that allows
the comparison of the contracts offered with each other, we created an indicator
that we called the relative fairness. To do so, we first computed the actuarially fair
mortgage insurance premiums, π
i,n
, for each individual i ∈ {1, ..., N} and scenario
n ∈ {1, ..., 5}. For each scenario, we ran 100 simulations and calculated the average
actuarially fair mortgage insurance premium, π
i,n
. Then, we defined the relative fair-
101
ness, RF
i,n
, as a measurement of the actuarially fair interest rate, r
LC
+ π
i,n
, relative
to the rate proposed to the respondents, r
experiment
i,n
in their respective scenarios:
RF
i,n
=
r
LC
+ π
i,n
r
experiment
i,n
. (3.14)
A higher value of RF signifies a more advantageous reverse mortgage contract for
the consumer. Table 3.6 presents statistics on the relative fairness of the rates
proposed to the respondents in the experiment using the objective, prospective and
subjective life tables. On average, the relative fairness of the reverse mortgage
contract proposed was around 0.8. Also, these statistics did not differ between types
of life table.
Table 3.6: Relative Fairness
Objective Prospective Subjective
mean 0.7974 0.7978 0.7984
SD 0.1510 0.1513 0.1516
Note: This table presents the relative fairness of the reverse mortgage contract pro-
posed to the respondents during the experiment. The relative fairness is defined as
r
LC
+π
i,n
r
experiment
i,n
where r
LC
is the interest rate of a home equity line of credit, π
i,n
is the
actuarially fair mortgage insurance premium for the reverse mortgage contract, and
r
experiment
i,n
is the interest rate proposed to respondent i and scenario n during the
experiment. Statistics weighted according to the 2010 Canadian Community Health
Survey (CCHS).
102
3.5 Analysis
3.5.1 Knowledge and Intention of Buying
Respondents were asked a sequence of questions with the objective of measuring
their level of knowledge of reverse mortgages. Statistics on the answers are repor-
ted in Table 3.7. Without naming the financial product, we first presented a sen-
tence containing the definition of a reverse mortgage to the respondents
15
. Then,
respondents were asked if they had ever heard of this financial product. 77.3% of
eligible Canadian homeowners claimed to have heard of that kind financial product.
Fewer homeowners from Quebec answered having heard this definition, a difference
of nearly 20 percentage points with the two other provinces. Then, we asked those
who claimed to have heard of this financial product if they could name it. 59.5% of
these homeowners claimed to be able to name the product in question. Once again,
there was a noticeable difference between provinces. Fewer homeowners from Quebec
who had heard of this financial product claimed to be able to name it, a difference
of 15 percentage points with the two other provinces. Finally, those who claimed to
be able to name the product were asked to identify it from a list of financial product
names. 96.8% of them answered correctly. Once again, fewer homeowners from Que-
bec answered this question correctly. Overall, 44.52% of all homeowners had heard
of the existence and correctly identified the reverse mortgage as the name of that
financial product. Moreover, the level of knowledge was twice as important among
homeowners in Ontario and British Columbia than it was in homeowners in Quebec.
15
The definition was presented as follows: "Imagine a financial product that lets you turn
part of your current home equity into cash. You’re not obligated to make any payments until you
move, you sell your home, or you die. You have the certainty that once your residence is sold, the
required amount to repay the loan will not exceed the selling price of the residence."
103
One plausible explanation for this phenomenon is that the CHIP program has been
offered longer in Ontario and British Columbia than in the province of Quebec. Al-
though the level of knowledge is higher in Ontario and British Columbia, the level
of awareness of the very existence of this financial product remains very low among
eligible respondents. Hence, the simple fact that more than half of Canadians eligible
for a reverse mortgage do not have a basic knowledge of the existence of this product
could be the major factor that explains why this market is so small in Canada.
104
Table 3.7: Knowledge of reverse mortgages
Canada B.C. Ont. Que.
1: Ever heard of the existence of this fin product:
based on definition of reverse mortgages (N=2,163)
No 22.7% 15.3% 17.1% 36.5%
Yes 77.3% 84.7% 82.9% 63.5%
2: Can you name the financial product: based on
definition of reverse mortgages (if heard) (N=1,717)
No 40.5% 35.2% 36.5% 53.3%
Yes 59.5% 64.8% 63.5% 46.7%
3: Name that financial product: based on definition
of reverse mortgages (if can name) (N=1,067
Annuity 0.4% 0.1% 0.0% 1.7%
Reverse mortgage 96.8% 96.6% 98.9% 90.9%
Life insurance 0.1% 0.0% 0.0% 0.3%
Line of credit 1.2% 2.9% 0.4% 1.7%
None of the above 1.6% 0.4% 0.7% 5.4%
Correctly answered all three questions (N=2,163)
No 55.48% 46.94% 47.87% 73.09%
Yes 44.52% 53.06% 52.13% 26.91%
Note: Statistics weighted according to the 2010 Canadian Community Health Survey
(CCHS)
Another factor that should influence taking a reverse mortgage is the subjective
expectation of house price growth. Indeed, a part of the NNEG is an insurance
covering the risk of downward variation in house prices. For a given interest rate
and loan-to-value, it is therefore more advantageous for someone who anticipates a
drop in the price of their house to get a reverse mortgage. Each homeowner in the
survey was asked to categorize their expectation of their house’s price growth over
105
the next five years among the following answer choices: more than 20%, between 5%
and 20%, between -5% and 5%, between -20% and -5% and less than -20%. Table 3.8
reports the distribution of subjective expectation of house price growth over the next
5 years by province. Homeowners from the province of British Columbia are those
who expected a higher growth rate, with almost 80% of them expecting a growth
higher than 5%. Homeowners from Ontario and Quebec followed, with 75% and 66%
of them expecting a growth higher than 5%, respectively.
Table 3.8: Subjective expectation of house price growth over the next 5 years
more than 20% 5 to 20% -5 to 5% -5 to -20% less than -20%
British Columbia 0.190 0.603 0.163 0.035 0.009
Ontario 0.165 0.583 0.217 0.020 0.014
Quebec 0.061 0.598 0.322 0.006 0.013
Note: This table presents the distribution of subjective expectation of house price
growth over the next 5 years by province. Statistics weighted according to the 2010
Canadian Community Health Survey (CCHS).
Table 3.9 shows the average stated probability of buying a reverse mortgage reported
in the experiment, by province and category of expectation of house price growth.
Respondents from British Columbia did not seem to base their probability of buying
a reverse mortgage on their expectation of house price growth. On the other hand,
the respondents from Quebec and Ontario who expected a higher price growth were
also those with a higher stated probability of buying a reverse mortgage. The average
stated probability of buying gradually decreased with a lower expectation of house
price growth rate. While we should expect that those who expected a lower house
price growth should also be the ones most interested in buying reverse mortgages,
it is the opposite that we observed. This is another clue that Canadians do not
106
fully understand how to take advantage of the NNEG. Misunderstanding can make
it difficult to differentiate a reverse mortgage from a home equity line of credit, and
thus make it hard to justify the payment of a mortgage insurance premium. As a
result, this may be a factor explaining the low average probabilities observed across
all subgroups.
Table 3.9: Probability of buying a reverse mortgage within the next year
more than 20% 5 to 20% -5 to 5% -5 to -20% less than -20%
British Columbia 0.059 0.052 0.050 0.064 0.000
Ontario 0.107 0.067 0.038 0.032 0.000
Quebec 0.188 0.052 0.070 0.031 0.052
Note: This table presents the average probability of buying a reverse mortgage within
the next year by province and category of subjective expectation on the house price
growth over the next 5 years. Statistics weighted according to the 2010 Canadian
Community Health Survey (CCHS)
3.5.2 Empirical Strategy
This section explains the empirical strategy used to estimate the demand elasticity
and to identify the factors determining the demand for reverse mortgages in Canada.
Since some respondents reported a probability of buying equal to zero, it was not
possible to directly compute the reverse mortgage demand elasticity utilizing the
log of the probability of buying as a dependent variable. Instead, we estimated the
elasticity in two steps. First, we ran OLS regressions
16
:
16
We did the same exercise using tobit estimation, where the lower bound was 0 and the
upper bound was 100. The results were very similar to the results from OLS estimations.
107
S
i,n
= αlog(RF
i,n
) + βX
i
+ ν
i,n
, (3.15)
where S
i,n
is the stated probability of buying a reverse mortgage reported by re-
spondent i for scenario n, log(RF
i,n
) is the log of the relative fairness of the reverse
mortgage offered, X
i
is a vector of control variables and µ is an error term assumed
to be normally distributed. X
i
groups all the variables presented in Table 3.4. It
includes demographic variables: the respondent’s age, gender, province, level of edu-
cation, marital status, if the respondent has children or not and retirement status.
It also includes variables on the household’s financial situation: the logarithm of the
house value, the logarithm of annual income, the logarithm of savings, the logarithm
of the mortgage (in terms of percentage of the house value), and a dummy variable
indicating if the respondent has an employer pension plan. It also controls for the
respondent’s financial literacy using a dummy variable equal to one if the respondent
answered all the questions assessing the familiarity with financial concepts correctly.
Another dummy variable equal to one was added if the respondent answered all the
questions on the knowledge of reverse mortgage presented in the table 3.7 correctly.
It includes a dummy variable indicating the presence of the sentence on the certainty
that the respondent will never be put under pressure to sell the residence. To control
for the bequest motive, it includes a dummy variable indicating if the respondent
agreed with the statement that parents should set aside money for their children’s
inheritance, even if it means somewhat sacrificing their own comfort in retirement.
We controlled for the expected financial and care support from the family using the
subjective probability that the family would take care of them financially if needed,
108
and the subjective probability that the family would take up the responsibility of
caring for them if they had important ADL limitations. We controlled for the level
of attachment to the house using the probability of staying in the current home until
they die, and use a dummy variable equal to one if they agreed with the statement
that a house is an asset that should only be sold in case of financial hardship. Finally,
we controlled for the subjective expected house price growth using a dummy variable
equal to one if the respondent expected a growth of more than 5%.
Hence, the coefficient of the log of the relative fairness can be interpreted by equation
(3.16):
ˆα =
∂S
∂log(RF )
= ∂S
RF
∂RF
. (3.16)
To calculate the elasticity at the mean, we divided ˆα by the average stated probability
of buying (6,36%):
buy
RM
=
∂S
¯
S
RF
∂RF
. (3.17)
First, we did this sequence of computations using the total sample. We then repeated
this exercise using different subsamples. We estimated the elasticity for a sample
composed of respondents who have a basic overall knowledge of reverse mortgages
and for a sample composed of those who don’t. We also computed elasticity by
province, gender and ten-year age group. In each case, a specification was made
109
using objective, prospective and subjective life tables.
3.5.3 Results
Table 3.10 reports OLS coefficients for the total sample. Table 3.11 reports demand
elasticities for the total sample and other subsamples. The relative fairness used
in the column (1) was computed using the objective life tables, while the relative
fairness of the column (2) and (3) were computed using prospective life tables from
Statistics-Canada and subjective life tables, respectively.
First of all, there was not much difference between the estimations based on object-
ive, prospective or subjective life tables, meaning that the nature of the life table
does not determine the stated demand. Therefore, the following discussion will focus
on the first column. An increase of one percent of the relative fairness significantly
increased the probability of contracting a reverse mortgage by 5.21 percentage points.
It represents a demand elasticity of 0.819, with a standard deviation of 0.139. As
a result, the demand for reverse mortgages in Canada is a little inelastic, but not
significantly so. The stated demand for reverse mortgages was significantly larger
for men (2.5 percentage points), and lower for retirees (1.9 percentage points). It
was also significantly higher for those who still had a traditional mortgage to pay.
An explanation could be that respondents who still have mortgages feel less intimid-
ated by mortgage contracts. Another possible explanation is that they are the ones
who have more financial needs. Those who have more savings were less interested
in reverse mortgages. The bequest motive was a significant factor determining the
demand for reverse mortgages. The stated demand for reverse mortgages was sig-
nificantly higher for those who agreed with the statement that parents should set
110
aside money for their children’s inheritance (1.7 percentage points). This result goes
in the opposite direction to the one estimated by Nakajuma & Telyukova (2017).
A scenario that could explain this result could be that respondents plan to leave a
bequest coming from their nonhousing wealth. Considering that a house is an asset
that should only be sold in case of financial hardship was positively and significantly
correlated with the stated demand (1.38 percentage points). This result seems to
show that reverse mortgages are a solution to those whose attachment to their home
prevents them from touching its equity by selling it. Indeed, one can consider that
a person experiencing a strong sense of attachment to their house will sell it only as
a last resort. Having the opportunity of touching some of the equity of your home,
while having the guarantee of being able to stay as long as you want, solves this
problem. Finally, a higher expectation of house price growth is significantly increas-
ing the stated demand (1.36 percentage points). This result support the view that
Canadians probably do not fully understand how to take advantage of the NNEG.
111
Table 3.10: Results
Objective Prospective Subjective
log(Relative fairness) 0.0521*** 0.0531*** 0.0527***
(0.009) (0.009) (0.009)
Age -0.00124 -0.00124 -0.00124
(0.001) (0.001) (0.001)
Men 0.0252*** 0.0252*** 0.0252***
(0.006) (0.006) (0.006)
Ontario 0.00238 0.00238 0.00243
(0.008) (0.008) (0.008)
British Columbia -0.0015 -0.00156 -0.00165
(0.009) (0.009) (0.009)
High school -0.00983 -0.00979 -0.00985
(0.025) (0.025) (0.025)
University -0.00947 -0.00939 -0.00948
(0.025) (0.025) (0.025)
Married -0.01246 -0.01244 -0.01224
(0.008) (0.008) (0.008)
Has kids -0.00287 -0.00287 -0.00288
(0.007) (0.007) (0.007)
Retired -0.0185** -0.0185** -0.0185**
(0.008) (0.008) (0.008)
log(House value) -0.00352 -0.00351 -0.00351
(0.005) (0.005) (0.005)
log(Income) -0.00066 -0.00065 -0.00067
(0.002) (0.002) (0.002)
log(Saving) -0.00124 -0.00124 -0.00124
(0.001) (0.001) (0.001)
log(Mortgage) 0.1006*** 0.1006*** 0.1005***
(0.025) (0.025) (0.025)
House Rich & cash poor 0.01175 0.01175 0.01175
(0.008) (0.008) (0.008)
Pension 0.00178 0.00179 0.00179
(0.006) (0.006) (0.006)
Financial literacy -0.00805 -0.00803 -0.00803
(0.007) (0.007) (0.007)
No pressure 0.00209 0.00207 0.00208
(0.006) (0.006) (0.006)
Bequest motive 0.0172* 0.0172* 0.0173*
(0.009) (0.009) (0.009)
Reverse mortgage knowledge 0.00235 0.00234 0.00234
(0.006) (0.006) (0.006)
Family support if ADL 0.00531 0.00528 0.00529
(0.011) (0.011) (0.011)
Family support if financial need 0.00939 0.00939 0.00941
(0.011) (0.011) (0.011)
Probability of staying home until death 0.00421 0.00419 0.00416
(0.009) (0.009) (0.009)
Sell only if financial hardship 0.0138** 0.0138** 0.0138**
(0.006) (0.006) (0.006)
Expected growth of more than 5% 0.0136** 0.0136** 0.0136**
(0.006) (0.006) (0.006)
Constant 0.1908** 0.1909** 0.1908**
(0.077) (0.077) (0.077)
N 10700 10700 10700
R2 0.0406 0.0408 0.0407
Column (1) presents OLS coefficients where the relative fairness has been computed
using the objective life tables from microsimulations. Column (2) presents OLS
coefficients where the relative fairness has been computed using the prospective life
tables from Statistics Canada. Column (3) presents OLS coefficients where the relat-
ive fairness has been computed using the subjective life tables. Standard deviations
are corrected for clustering at individual level. Standard errors in parentheses. *
p < 0.1, ** p < 0.05, *** p < 0.01.
112
Table 3.11 shows the elasticity of the total sample and of all the subsamples. In
each case, we test for the null hypothesis that the elasticity is equal to one. The
OLS coefficients of each subsample are reported in Tables C.1, C.2 and C.3 in Ap-
pendix C.1. Once again, there was not much difference between elasticity computed
using objective, prospective and subjective life tables. We first compared the sample
of those who had heard of and could identify the name reverse mortgage among
other products with those who couldn’t. Those with a better knowledge of reverse
mortgages had an elastic demand (1.184), while those with a worse knowledge had
a significantly inelastic demand (0.527). Therefore, the level of basic knowledge
about reverse mortgages seems to be a key determinant of demand elasticity. We
then compared elasticity between provinces. Respondents from British Columbia
had an elastic demand (1.333) while those from Ontario had an inelastic demand
(0.863). Respondents from Quebec had a significantly inelastic demand (0.35). The
more plausible explanation for this result is related to the level of knowledge since re-
spondents from Quebec are also those with the lower knowledge of reverse mortgages.
Among the three provinces, the province of Quebec is the one for which the reverse
mortgage offer was implemented the latest. It is therefore likely that the use of such
services is not part of the culture of that province. When we compare the elasticity
between genders, we see that men had an inelastic demand (0.725) while women had
a demand elasticity close to the unitary elasticity (1.017). Finally, respondents aged
between 55 and 64 had a demand elasticity close to the unitary elasticity (0.987),
while those aged between 65 and 75 had an inelastic demand (0.661).
113
Table 3.11: Elasticity
Objective Prospective Subjective
Total sample 0.8193 0.8336 0.8283
(0.139) (0.14) (0.141)
N=10,700 N=10,700 N=10,700
Know 1.1838 1.2149 1.2222
(0.216) (0.218) (0.221)
N=5,145 N=5,145 N=5,145
Don’t know 0.5265*** 0.5261*** 0.5069***
(0.181) (0.181) (0.18)
N=5,555 N=5,555 N=5,555
British Columbia 1.333 1.3765 1.3585
(0.282) (0.284) (0.286)
N=3,690 N=3,690 N=3,690
Ontario 0.8625 0.8624 0.8643
(0.224) (0.224) (0.224)
N=3,565 N=3,565 N=3,565
Quebec 0.3496*** 0.3504*** 0.3473***
(0.238) (0.238) (0.237)
N=3,445 N=3,445 N=3,445
Men 0.7253 0.7382 0.7433
(0.178) (0.177) (0.178)
N=5,295 N=5,295 N=5,295
Women 1.0168 1.0307 1
(0.215) (0.219) (0.22)
N=5,405 N=5,405 N=5,405
Age 55-64 0.9865 1.0009 0.9864
(0.19) (0.192) (0.192)
N = 5,475 N = 5,475 N = 5,475
Age 65-75 0.6608 0.6725 0.6812
(0.21) (0.209) (0.212)
N = 5,225 N = 5,225 N = 5,225
Note: Column (1) presents OLS coefficients where the relative fairness has been
computed using the objective life tables from microsimulations. Column (2) presents
OLS coefficients where the relative fairness has been computed using the prospective
life tables from Statistics Canada. Column (3) presents OLS coefficients where the
relative fairness has been computed using the subjective life tables. Estimates are
corrected for clustering at individual level. Control variables are the same as those
reported in Table 3.10. Know refers to a sample grouping respondents who had heard
of and could identify the name “reverse mortgage” among other products, while Don’t
know refers to a sample grouping those who couldn’t. Standard errors in parentheses.
We tested for the null hypothesis that the elasticity is equal to one. * p < 0.1, **
p < 0.05, *** p < 0.01.
114
3.6 Conclusion
The no-negative equity guarantee (NNEG) is the main feature that differentiates
reverse mortgages from a home equity line of credit. By offering a NNEG, the reverse
mortgage lender exposes himself to the risk that the amount of debt will exceed the
resale value of the home. This risk comes from the longevity risk of the borrower,
as well as the risk of downward variation in house prices. For a given loan-to-value
ratio of the house that is lent, the lender charges a mortgage insurance premium to
cover the losses related to the NNEG.
In this chapter, we used a pricing model to calculate actuarially fair mortgage insur-
ance premiums that should be charged to cover the losses related to the NNEG in
Canada. Given the size of the loans that are granted in the Canadian market, we
found that actuarially fair premiums are approximately zero. This result implies that
the lenders do not take any risks by offering a NNEG, making it a missing feature
in the Canadian market. It could explain the low demand for reverse mortgages in
Canada, since it is difficult for a buyer to differentiate a reverse mortgage from a
home equity line of credit and to justify a higher interest rate.
We then assessed the level of knowledge Canadians have about reverse mortgages and
conducted a stated-choice experiment where respondents were asked to rate various
reverse mortgage products. Our analysis shows that a majority of Canadians do
not even have basic knowledge about this financial product. We found that reverse
mortgages could be a solution for those whose attachment to their home prevents
them from accessing its equity by selling it. However, Canadians do not seem to
be able to distinguish in which situations it is advantageous to obtain a reverse
mortgage. Indeed, the stated demand was positively correlated with the subjective
115
expectation of house price growth. Finally, we found that the demand elasticity of
the entire Canadian market was inelastic. However, the demand elasticity of those
who had a basic knowledge of reverse mortgages was elastic, while the demand for
those who did not know the product at all was significantly inelastic. As a result, a
combination of price adjustment and reverse mortgage education could be a good way
to expand the size of the Canadian market and could represent a win-win solution
for both lenders and borrowers.
APPENDIX A
INCOME VOLATILITY, HEALTH AND WELL-BEING
A.1 Health Variables
1. Mental health: “In the last month, how often (‘never,’ ‘rarely,’ ‘sometimes,’
‘most of the time,’ or ‘all the time’) did you feel. . . ”":
(a) tired out for no good reason?
(b) nervous?
(c) so nervous that nothing could calm down?
(d) desperate?
(e) restless or be unable to stand still?
(f) so restless that could not stand still?
(g) sad/depressed?
(h) so depressed that nothing could cheer up?
(i) everything was an effort?
(j) good for nothing?
117
2. Life satisfaction: “What feelings do you currently have about your life in gen-
eral: very unsatisfied (0) [. . . ] very satisfied (10)?”
3. Self-assessed health: “Would you say your health in general is . . . : excellent,
very good, good, fair or poor?”;
A.2 Information Window on Income
Note: A respondent who is 75 years old in 2012 was 45 years old in 1982 and 55
years old in 1992. Thus, we end up with 11 observations on their annual income .
118
Figure A.1: Information Window on Income
Year
2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991 1990 1989 1988 1987 1986 1985 1984 1983 1982
50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20
51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21
52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22
53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23
54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24
55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25
56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26
57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27
58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28
59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29
60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30
Age 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31
62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32
63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33
64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34
65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35
66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36
67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37
68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38
69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39
70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40
71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41
72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42
73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43
74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44
75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45
APPENDIX B
CONSUMPTION AND HEALTH IN OLD AGE
120
Table B.1: Spending category and variable names across waves
Category Variable CAMS03 CAMS05-17
Refrigerator B2 B2
Durable Washer/Dryer B3 B3
(do not include Diswasher B4 B4
auto purchases) Television B5 B5
Computer B6 B6
Housing
Mortgage B13 B18
Home/Rent Ins B7 B7
Property Tax B8 B8
Rent B14 B19
Home Repair Supplies B24 B13
Home Repair Services B25 B14
Transportation
Auto Insurance B9 B9
Gasoline B38 B39
Vehicle Services B10 B10
Car Payments B19 B24
Utilities
Electricity B15 B20
Water B16 B21
Heat B17 B22
Phone/Cable/Internet B18 B23
Donations
Contributions B34 B16
Gifts B35 B17
Food
Food/Drink Grocery B36 B37
Dining out B37 B38
Leisure
Vacations B12 B12
Tickets B31 B34
Hobbies B33 B36
Sports Equipment B32 B35
Household Supplies & Services
Housekeeping Supplies B20 B25
Yard Supplies B22 B27
Housekeeping Services B21 B26
Gardening/Yard Services B23 B28
Clothing Clothing B26 B29
Health
Health Insurance B11 B11
Drugs B28 B31
Health Services B29 B32
Medical Supplies B30 B33
Personal Care B27 B30
Note: We created spending categories based on CAMS variables. A total nondur-
able spending was also created. This variable includes the sum of all the variables
excluding the durable spending categories. We dropped the 2001 wave because of
differences in spending categories.
APPENDIX C
122
REVERSE MORTGAGE
C.1 Regression Tables
Table C.1: Results using objective life tables
Know Don’t know B.C. Ont. Que. Men Women Age 55-64 Age 65-75
log(Relative fairness) 0.0724*** 0.0345*** 0.0697*** 0.0566*** 0.02338 0.0577*** 0.0493*** 0.0652*** 0.0396***
(0.013) (0.012) (0.015) (0.015) (0.016) (0.014) (0.01) (0.013) (0.013)
Age -0.00076 -0.0017* -0.00104 -0.0029*** -0.00033 -0.0018* -0.00088
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
Men 0.0294*** 0.0245*** 0.01578 0.0307*** 0.0328*** 0.0261*** 0.027***
(0.009) (0.009) (0.01) (0.011) (0.011) (0.009) (0.008)
Ontario 0.01343 -0.00456 -0.00235 0.00809 0.00907 -0.00415
(0.013) (0.01) (0.012) (0.01) (0.011) (0.012)
British Columbia 0.00731 -0.00662 -0.0118 0.00916 -0.00129 -0.00346
(0.013) (0.012) (0.013) (0.01) (0.013) (0.012)
High school -0.00955 -0.00967 0.00214 0.02825 -0.06423 -0.02817 0.00247 0.0434** -0.04529
(0.042) (0.029) (0.027) (0.025) (0.058) (0.04) (0.019) (0.02) (0.036)
University -0.00632 -0.0107 0.01167 0.01391 -0.06267 -0.02822 0.00347 0.036* -0.03809
(0.043) (0.029) (0.027) (0.024) (0.058) (0.04) (0.018) (0.019) (0.036)
Married -0.01728 -0.00829 -0.00983 -0.02066 -0.00477 -0.02035 -0.00866 -0.00226 -0.0237**
(0.012) (0.01) (0.013) (0.013) (0.014) (0.013) (0.009) (0.011) (0.01)
Has kids -0.00337 -0.00448 0.00406 -0.01402 -0.00171 0.00942 -0.00939 -0.0092 0.00026
(0.01) (0.01) (0.012) (0.014) (0.012) (0.011) (0.01) (0.01) (0.01)
Retired -0.028** -0.01124 -0.01857 -0.01289 -0.0255* -0.00773 -0.0241** -0.0183** -0.02055
(0.012) (0.011) (0.015) (0.013) (0.015) (0.013) (0.01) (0.009) (0.014)
log(House value) -0.00067 -0.0033 -0.00578 0.01213 -0.0191** 0.00075 -0.00429 -0.00227 -0.00388
(0.008) (0.006) (0.008) (0.01) (0.009) (0.008) (0.007) (0.007) (0.007)
log(Income) -0.00741 0.00275 -0.00402 -0.0033 0.007 -0.00449 0.00246 -0.00122 0.00056
(0.005) (0.003) (0.004) (0.004) (0.005) (0.004) (0.003) (0.005) (0.003)
log(Saving) -0.00188 -0.00053 -0.004** -0.00068 0.00154 -0.00301 0.00037 -0.00071 -0.00226
(0.002) (0.001) (0.002) (0.002) (0.002) (0.002) (0.001) (0.001) (0.002)
log(Mortgage) 0.0886*** 0.1169*** 0.0934** 0.132*** 0.1049** 0.04476 0.1565*** 0.1469*** 0.0227
(0.034) (0.036) (0.044) (0.046) (0.041) (0.031) (0.037) (0.034) (0.034)
House rich & cash poor 0.00822 0.01554 -0.00287 0.01303 0.02336 0.00853 0.01083 0.01426 0.0101
(0.011) (0.011) (0.014) (0.014) (0.015) (0.011) (0.011) (0.012) (0.01)
Pension 0.0019 0.00273 0.00596 0.00873 -0.00996 0.00065 0.00309 0.00257 7e-05
(0.009) (0.009) (0.011) (0.011) (0.013) (0.01) (0.008) (0.01) (0.008)
Financial literacy -0.01108 -0.0063 0.00192 -0.00523 -0.0217** -0.00803 -0.00735 -0.00643 -0.00963
(0.01) (0.009) (0.011) (0.012) (0.011) (0.011) (0.009) (0.009) (0.009)
No pressure -0.00454 0.00614 0.00702 -0.00788 0.00979 -0.00845 0.01119 -0.00546 0.01051
(0.008) (0.008) (0.01) (0.01) (0.011) (0.009) (0.007) (0.009) (0.008)
Bequest motive 0.02227 0.0137 0.0332** 0.01559 0.00377 0.028** 0.00195 0.0293** 0.00811
(0.014) (0.012) (0.016) (0.013) (0.017) (0.013) (0.011) (0.013) (0.012)
Knowledge 0.005 0.01302 -0.01118 0.00688 -0.00059 -0.00034 0.00506
(0.01) (0.011) (0.012) (0.009) (0.009) (0.009) (0.009)
Family support if ADL 0.02173 -0.01128 0.0172 0.0341* -0.0284 0.01302 0.00273 0.0318** -0.01486
(0.014) (0.018) (0.016) (0.018) (0.023) (0.015) (0.017) (0.015) (0.016)
Family support if financial need 0.00014 0.0196 -0.01329 -0.01207 0.0538** 0.01872 -0.00243 -0.01127 0.02296
(0.012) (0.019) (0.015) (0.016) (0.023) (0.015) (0.016) (0.014) (0.015)
Probability of staying home until death -0.00494 0.01119 0.00498 -0.00447 0.0084 0.00162 0.006 -0.00545 0.01402
(0.015) (0.012) (0.014) (0.018) (0.016) (0.014) (0.013) (0.013) (0.013)
Sell only if financial hardship 0.0031 0.0239*** 0.00608 0.0174* 0.0187* 0.018** 0.01308 0.01338 0.0133*
(0.008) (0.008) (0.009) (0.01) (0.01) (0.009) (0.008) (0.009) (0.008)
Expected growth of more than 5% 0.0286*** 0.00103 0.0204** 0.0259** -0.00523 0.0346*** -0.00233 0.01157 0.0175**
(0.009) (0.009) (0.009) (0.011) (0.012) (0.01) (0.008) (0.01) (0.008)
Constant 0.2141* 0.15846 0.2599** 0.07727 0.266* 0.2586** 0.12466 0.04913 0.14354
(0.122) (0.1) (0.117) (0.152) (0.139) (0.124) (0.091) (0.098) (0.092)
N 5145 5555 3690 3565 3445 5295 5405 5475 5225
R2 0.0544 0.0411 0.0587 0.0633 0.0536 0.0426 0.0541 0.0543 0.037
Note: Control variables are the same as those reported in Table 3.10. Know refers to
a sample grouping respondents who had heard of and could identify the name “reverse
mortgage” among other products, while Don’t know refers to a sample grouping those
who couldn’t. Estimates were corrected for clustering at individual level. Standard
errors in parentheses. * p < 0.1, ** p < 0.05, *** p < 0.01.
123
Table C.2: Results using prospective life tables
Know Don’t know B.C. Ont. Que. Men Women Age 55-64 Age 65-75
log(Relative fairness) 0.0743*** 0.0345*** 0.072*** 0.0566*** 0.02345 0.0587*** 0.05*** 0.0662*** 0.0403***
(0.013) (0.012) (0.015) (0.015) (0.016) (0.014) (0.011) (0.013) (0.013)
Age -0.00077 -0.0017* -0.00105 -0.0029*** -0.00033 -0.0018* -0.00088
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
Men 0.0294*** 0.0245*** 0.01571 0.0307*** 0.0328*** 0.0261*** 0.027***
(0.009) (0.009) (0.01) (0.011) (0.011) (0.009) (0.008)
Ontario 0.01344 -0.00456 -0.00235 0.0081 0.00906 -0.00416
(0.013) (0.01) (0.012) (0.01) (0.011) (0.012)
British Columbia 0.0072 -0.00664 -0.01189 0.00913 -0.00132 -0.00354
(0.013) (0.012) (0.013) (0.01) (0.013) (0.012)
High school -0.00945 -0.00965 0.00239 0.02824 -0.06422 -0.02816 0.00259 0.0433** -0.04521
(0.042) (0.029) (0.027) (0.025) (0.058) (0.04) (0.019) (0.02) (0.036)
University -0.00615 -0.01065 0.01206 0.0139 -0.06265 -0.02818 0.00365 0.036* -0.03797
(0.043) (0.029) (0.027) (0.024) (0.058) (0.04) (0.018) (0.019) (0.036)
Married -0.01722 -0.00829 -0.00969 -0.02066 -0.00478 -0.02026 -0.00868 -0.00231 -0.0237**
(0.012) (0.01) (0.013) (0.013) (0.014) (0.013) (0.009) (0.011) (0.01)
Has kids -0.00334 -0.00449 0.00408 -0.01402 -0.00171 0.00944 -0.00941 -0.0092 0.00028
(0.01) (0.01) (0.012) (0.014) (0.012) (0.011) (0.01) (0.01) (0.01)
Retired -0.0279** -0.01123 -0.01853 -0.01289 -0.0255* -0.00773 -0.0241** -0.0182** -0.02052
(0.012) (0.011) (0.015) (0.013) (0.015) (0.013) (0.01) (0.009) (0.014)
log(House value) -0.00064 -0.00329 -0.00573 0.01212 -0.0191** 0.00078 -0.0043 -0.00224 -0.00388
(0.008) (0.006) (0.008) (0.01) (0.009) (0.008) (0.007) (0.007) (0.007)
log(Income) -0.00739 0.00276 -0.00398 -0.00329 0.007 -0.00449 0.00248 -0.00121 0.00057
(0.005) (0.003) (0.004) (0.004) (0.005) (0.004) (0.003) (0.005) (0.003)
log(Saving) -0.00188 -0.00053 -0.004** -0.00068 0.00154 -0.00301 0.00037 -0.00071 -0.00225
(0.002) (0.001) (0.002) (0.002) (0.002) (0.002) (0.001) (0.001) (0.002)
log(Mortgage) 0.0884*** 0.117*** 0.0933** 0.132*** 0.1049** 0.04474 0.1565*** 0.1469*** 0.02272
(0.034) (0.036) (0.044) (0.046) (0.041) (0.031) (0.037) (0.034) (0.034)
House rich & cash poor 0.00821 0.01554 -0.00287 0.01303 0.02336 0.00853 0.01083 0.01424 0.01011
(0.011) (0.011) (0.014) (0.014) (0.015) (0.011) (0.011) (0.012) (0.01)
Pension 0.0019 0.00274 0.00602 0.00873 -0.00996 0.00065 0.0031 0.00259 7e-05
(0.009) (0.009) (0.011) (0.011) (0.013) (0.01) (0.008) (0.01) (0.008)
Financial literacy -0.01108 -0.00627 0.00199 -0.00523 -0.0217** -0.00804 -0.00731 -0.00639 -0.00962
(0.01) (0.009) (0.011) (0.012) (0.011) (0.011) (0.009) (0.009) (0.009)
No pressure -0.0046 0.00614 0.00692 -0.00789 0.00979 -0.00848 0.01117 -0.00548 0.01048
(0.008) (0.008) (0.01) (0.01) (0.011) (0.009) (0.007) (0.009) (0.008)
Bequest motive 0.02224 0.0137 0.0332** 0.01558 0.00376 0.028** 0.00195 0.0293** 0.00811
(0.014) (0.012) (0.016) (0.013) (0.017) (0.013) (0.011) (0.013) (0.012)
Knowledge 0.00497 0.01302 -0.01118 0.00686 -0.0006 -0.00038 0.00508
(0.01) (0.011) (0.012) (0.009) (0.009) (0.009) (0.009)
Family support if ADL 0.02167 -0.01128 0.01711 0.0341* -0.02839 0.01299 0.0027 0.0318** -0.01489
(0.014) (0.018) (0.016) (0.018) (0.023) (0.015) (0.017) (0.015) (0.016)
Family support if financial need 0.00015 0.0196 -0.01329 -0.01208 0.0538** 0.0187 -0.00241 -0.01125 0.02296
(0.012) (0.019) (0.015) (0.016) (0.023) (0.015) (0.016) (0.014) (0.015)
Probability of staying home until death -0.00499 0.01119 0.0049 -0.00447 0.0084 0.00161 0.00599 -0.00546 0.01401
(0.015) (0.012) (0.014) (0.018) (0.016) (0.014) (0.013) (0.013) (0.013)
Sell only if financial hardship 0.00313 0.0239*** 0.00618 0.0174* 0.0187* 0.018** 0.01313 0.01342 0.0133*
(0.008) (0.008) (0.009) (0.01) (0.01) (0.009) (0.008) (0.009) (0.008)
Expected growth of more than 5% 0.0285*** 0.00102 0.0203** 0.0259** -0.00523 0.0346*** -0.00233 0.01156 0.0175**
(0.009) (0.009) (0.009) (0.011) (0.012) (0.01) (0.008) (0.01) (0.008)
Constant 0.2141* 0.15836 0.2592** 0.0773 0.266* 0.2586** 0.12481 0.04898 0.14344
(0.122) (0.1) (0.117) (0.152) (0.139) (0.124) (0.091) (0.098) (0.092)
N 5145 5555 3690 3565 3445 5295 5405 5475 5225
R2 0.0548 0.0411 0.0593 0.0633 0.0536 0.0428 0.0542 0.0545 0.0371
Note: Control variables are the same as those reported in Table 3.10. Know refers to
a sample grouping respondents who had heard of and could identify the name “reverse
mortgage” among other products, while Don’t know refers to a sample grouping those
who couldn’t. Estimates were corrected for clustering at individual level. Standard
errors in parentheses. * p < 0.1, ** p < 0.05, *** p < 0.01.
124
Table C.3: Results using subjective life tables
Know Don’t know B.C. Ont. Que. Men Women Age 55-64 Age 65-75
log(Relative fairness) 0.0748*** 0.0332*** 0.0711*** 0.0567*** 0.02323 0.0591*** 0.0485*** 0.0652*** 0.0408***
(0.014) (0.012) (0.015) (0.015) (0.016) (0.014) (0.011) (0.013) (0.013)
Age -0.00077 -0.0017* -0.00104 -0.0029*** -0.00033 -0.0018* -0.00088
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
Men 0.0293*** 0.0245*** 0.01563 0.0307*** 0.0328*** 0.026*** 0.027***
(0.009) (0.009) (0.01) (0.011) (0.011) (0.009) (0.008)
Ontario 0.01347 -0.00451 -0.0023 0.00814 0.00916 -0.00414
(0.013) (0.01) (0.012) (0.01) (0.011) (0.012)
British Columbia 0.00698 -0.00663 -0.012 0.00907 -0.00132 -0.00368
(0.013) (0.012) (0.013) (0.01) (0.013) (0.012)
High school -0.00962 -0.00962 0.00201 0.02824 -0.06422 -0.02812 0.00244 0.0434** -0.04534
(0.042) (0.029) (0.027) (0.025) (0.058) (0.04) (0.019) (0.02) (0.036)
University -0.00645 -0.01063 0.01156 0.0139 -0.06264 -0.02821 0.0035 0.036* -0.03811
(0.043) (0.029) (0.027) (0.024) (0.058) (0.04) (0.018) (0.019) (0.036)
Married -0.01685 -0.0082 -0.00892 -0.02063 -0.00477 -0.01999 -0.00852 -0.00211 -0.0235**
(0.012) (0.01) (0.013) (0.013) (0.014) (0.013) (0.009) (0.011) (0.01)
Has kids -0.0034 -0.00448 0.00394 -0.014 -0.0017 0.00942 -0.00942 -0.00912 0.00021
(0.01) (0.01) (0.012) (0.014) (0.012) (0.011) (0.01) (0.01) (0.01)
Retired -0.0279** -0.01125 -0.01858 -0.01289 -0.0255* -0.00769 -0.0241** -0.0182** -0.02052
(0.012) (0.011) (0.015) (0.013) (0.015) (0.013) (0.01) (0.009) (0.014)
log(House value) -0.0006 -0.00331 -0.00571 0.01212 -0.0191** 0.00076 -0.00427 -0.00232 -0.00383
(0.008) (0.006) (0.008) (0.01) (0.009) (0.008) (0.007) (0.007) (0.007)
log(Income) -0.00739 0.00274 -0.00403 -0.0033 0.007 -0.00449 0.00244 -0.00123 0.00056
(0.005) (0.003) (0.004) (0.004) (0.005) (0.004) (0.003) (0.005) (0.003)
log(Saving) -0.00188 -0.00053 -0.004** -0.00068 0.00154 -0.003 0.00037 -0.00071 -0.00225
(0.002) (0.001) (0.002) (0.002) (0.002) (0.002) (0.001) (0.001) (0.002)
log(Mortgage) 0.0883*** 0.117*** 0.093** 0.1321*** 0.1049** 0.04475 0.1563*** 0.1467*** 0.02266
(0.034) (0.036) (0.044) (0.046) (0.041) (0.031) (0.037) (0.034) (0.034)
House rich & cash poor 0.0082 0.01555 -0.00291 0.01304 0.02337 0.00855 0.01083 0.01421 0.01013
(0.011) (0.011) (0.014) (0.014) (0.015) (0.011) (0.011) (0.012) (0.01)
Pension 0.00196 0.00274 0.00605 0.00874 -0.00996 0.00066 0.0031 0.00263 5e-05
(0.009) (0.009) (0.011) (0.011) (0.013) (0.01) (0.008) (0.01) (0.008)
Financial literacy -0.01102 -0.00628 0.00204 -0.00523 -0.0217** -0.00799 -0.00732 -0.00637 -0.00963
(0.01) (0.009) (0.011) (0.012) (0.011) (0.011) (0.009) (0.009) (0.009)
No pressure -0.00455 0.00614 0.00693 -0.00788 0.00979 -0.00844 0.01116 -0.00548 0.01049
(0.008) (0.008) (0.01) (0.01) (0.011) (0.009) (0.007) (0.009) (0.008)
Bequest motive 0.0222 0.01377 0.0333** 0.01558 0.00376 0.028** 0.00207 0.0294** 0.00813
(0.014) (0.012) (0.016) (0.013) (0.017) (0.013) (0.011) (0.013) (0.012)
Knowledge 0.00496 0.01301 -0.01118 0.00687 -0.00062 -0.00036 0.00507
(0.01) (0.011) (0.012) (0.009) (0.009) (0.009) (0.009)
Family support if ADL 0.02174 -0.01128 0.01713 0.0341* -0.02838 0.01304 0.00269 0.0319** -0.01496
(0.014) (0.018) (0.016) (0.018) (0.023) (0.015) (0.017) (0.015) (0.016)
Family support if financial need 0.00026 0.01958 -0.01326 -0.01206 0.0538** 0.01872 -0.00241 -0.01133 0.02304
(0.012) (0.019) (0.015) (0.016) (0.023) (0.015) (0.016) (0.014) (0.015)
Probability of staying home until death -0.00484 0.01111 0.00484 -0.00449 0.0084 0.00162 0.00592 -0.00546 0.01395
(0.015) (0.012) (0.014) (0.018) (0.016) (0.014) (0.013) (0.013) (0.013)
Sell only if financial hardship 0.00304 0.0239*** 0.00612 0.0174* 0.0187* 0.018** 0.01313 0.01337 0.0133*
(0.008) (0.008) (0.009) (0.01) (0.01) (0.009) (0.008) (0.009) (0.008)
Expected growth of more than 5% 0.0285*** 0.00098 0.0202** 0.0259** -0.00524 0.0346*** -0.00238 0.01151 0.0174**
(0.009) (0.009) (0.009) (0.011) (0.012) (0.01) (0.008) (0.01) (0.008)
Constant 0.2136* 0.1583 0.2593** 0.07735 0.2662* 0.2588** 0.12454 0.04974 0.14291
(0.122) (0.1) (0.116) (0.152) (0.139) (0.124) (0.091) (0.098) (0.092)
N 5145 5555 3690 3565 3445 5295 5405 5475 5225
R2 0.0549 0.0409 0.0591 0.0633 0.0536 0.0429 0.054 0.0543 0.0372
Note: Control variables are the same as those reported in Table 3.10. Know refers to
a sample grouping respondents who had heard of and could identify the name “reverse
mortgage” among other products, while Don’t know refers to a sample grouping those
who couldn’t. Estimates were corrected for clustering at individual level. Standard
errors in parentheses. * p < 0.1, ** p < 0.05, *** p < 0.01.
125
C.2 Survey
/ 24
1
INSTRUCTIONS INCLUDED WITH THIS ANONYMOUS QUESTIONNAIRE
FINANCIAL PRODUCTS FOR RETIREMENT
The following pages contain an anonymous questionnaire, which we invite you to complete. This questionnaire
was developed as part of a research project at HEC Montréal.
Since your first impressions best reflect your true opinions, we would ask that you please answer the questions
included in this questionnaire without any hesitation. We ask, however, that you take the time needed to
consider certain questions on knowledge, which might involve concepts with which you are less familiar. There is
no time limit for completing the questionnaire, although we have estimated that it should take approximately
15 minutes.
The information collected will be anonymous and will remain strictly confidential. It will be used solely for the
advancement of knowledge and the dissemination of the overall results in academic or professional forums.
The online data collection provider agrees to refrain from disclosing any personal information (or any other
information concerning participants in this study) to any other users or to any third party, unless the respondent
expressly agrees to such disclosure or unless such disclosure is required by law.
You are free to refuse to participate in this project and you may decide to stop answering the questions at any
time. By completing this questionnaire, you will be considered as having given your consent to participate in our
research project and to the potential use of data collected from this questionnaire in future research. Since the
questionnaire is anonymous, you will no longer be able to withdraw from the research project once you have
completed the questionnaire because it will be impossible to determine which of the answers are yours.
If you have any questions about this research, please contact the principal investigator, Pierre-Carl Michaud, at
the telephone number or email address indicated below.
HEC Montréal’s Research Ethics Board has determined that the data collection related to this study meets the
ethics standards for research involving humans. If you have any questions related to ethics, please contact the
REB secretariat at (514) 340-6051 or by email at [email protected].
Thank you for your valuable cooperation!
Pierre-Carl Michaud
Professor
Department of Applied Economics
HEC Montréal
514-340-6466
pierre-[email protected]
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2
Section 1: Background
A Are you…?
1.1. Male
1.2. Female
B How old are you?
2.1. Please Enter (terminate if not 55-75 INCLUSIVELY)
[PN: MUST ENTER THE 2 CHARACTERS]!
QC. Which province or territory do you live in?!
British Columbia 1.1.
Alberta [Screen!Out] 1.2.
Saskatchewan [Screen!Out] 1.3.
Manitoba [Screen!Out] 1.4.
Ontario 1.5.
Quebec 1.6.
New Brunswick [Screen!Out] 1.7.
Nova Scotia [Screen!Out] 1.8.
Prince Edward Island [Screen!Out] 1.9.
Newfoundland [Screen!Out] 1.10.
Northwest Territories [Screen!Out] 1.11.
Nunavut [Screen!Out] 1.12.
Yukon [Screen!Out]!1.13.
None of the above![Screen!Out]!1.14.
Q0 Can you please enter the first 3 characters of your postal code? Please type in below [PN: MUST
ENTER FIRST 3 CHARACTERS] *FSAs validated with FSA file
Q1 What is the highest degree, certificate or diploma you have obtained?
1 Less than high school diploma or its equivalent
2 High school diploma or a high school equivalency certificate
3 Trade certificate or diploma
4 College, CEGEP or other non-university certificate or diploma (other than trades certificates or
diplomas)
5 University certificate or diploma below the bachelor's level
6 Bachelor's degree (e.g. B.A., B.Sc., LL.B.)
7 University degree above the bachelor's level
Q2 What is your marital status?
1 married
2 living common-law
3 widowed
4 separated
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3
5 divorced
6 single, never married
IF Q2 ==1,2
Q2a How old is your partner (spouse)?
Numeric (>0)
END IF
Q3 Do you have children?
1 Yes
2 No
IF Q3==1 ask Q3b
IF Q3 = 2 skip to Q4
Q3b Have you experienced a loss of a child?
1 Yes
2 No
IF Q3b = 1 ask Q3a
IF Q3b = 2 ask Q3c
Q3a How many of your children are alive today?
Numeric (>=0)
Q3c How many children do you have?
Numeric (>=0)
END IF
Q4 For 2016, what is your best estimate of the total income received by all members of your
household, from all sources, before taxes and deductions?
Numeric (>0)
9999999 Don’t know or prefer not to say
IF Q4==9999999
Q4a Is it more than $60,000? 1 Yes 2 No 8888888 Refuse to answer 7777777 Don’t know
IF Q4a==1
Q4b Is it less than $120,000? 1 Yes 2 No 8888888 Refuse to answer 7777777 Don’t
know
IF Q4b == 1
Q4c Is it more than $90,000? 1 Yes 2 No 8888888 Refuse to answer 7777777
Don’t know
END IF
ELSE IF Q4a==2
Q4d Is it more than $30,000? 1 Yes 2 No 8888888 Refuse to answer 7777777 Don’t
know
END IF
END IF
Q5 Do you consider yourself retired?
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4
1 Yes
2 No
IF Q5==2
Q5a What is your best estimate of what total income received by all members of your
household will be once you are fully retired, as a fraction of your current income?
Numeric (0%-200%)
9999999 Don’t know
IF Q5a==9999999
Q5b Is it more than 50%? 1 Yes 2 No 8888888 Refuse to answer 7777777 Don’t know
IF Q5b==1
Q5c Is it less than 75%? 1 Yes 2 No 8888888 Refuse to answer 7777777 Don’t
know
IF Q5c == 1
Q5d Is it more than 62.5%? 1 Yes 2 No 8888888 Refuse to answer
7777777 Don’t know
ELSE IF Q5c == 2
Q5e Is it less than 87.5%? 1 Yes 2 No 8888888 Refuse to answer
7777777 Don’t know
END IF
ELSE IF Q5b==2
Q5f Is it more than 25%? 1 Yes 2 No 8888888 Refuse to answer 7777777 Don’t
know
IF Q5f == 1
Q5d Is it more than 37.5%? 1 Yes 2 No 8888888 Refuse to answer
7777777 Don’t know
ELSE IF Q5f == 2
Q5e Is it less than 12.5%? 1 Yes 2 No 8888888 Refuse to answer
7777777 Don’t know
END IF
END IF
END IF
END IF
Q6 Do you own your primary residence?
1 Yes
2 No
IF Q6==1
Q6a Which set of property type best fits your primary residence?
1 Single Family Dwelling / Detached Duplex, Triplex or Quadruplex / Link home / Semi-
Detached.
2 Townhouse, Rowhouse / Fiveplex and Sixplex / Attached Duplex, Triplex or Quadruplex /
Stratified SFD, Bare Land Strata / Semi-Detached Strata Condo / Modular Home
3 Condo-Townhouse / Mobile Home / Condo – Apartment Style
7777777 Don’t know
Q7 What is the current market value of your residence?
Numeric (>0)
9999999 Don’t know or prefer not to say
IF Q7==9999999
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5
Q7a Is it more than $300,000? 1 Yes 2 No 8888888 Refuse to answer 7777777 Don’t
know
IF Q7a==1
Q7b Is it less than $600,000? 1 Yes 2 No 8888888 Refuse to answer 7777777
Don’t know
IF Q7b == 1
Q7c Is it more than $450,000? 1 Yes 2 No 8888888 Refuse to answer
7777777 Don’t know
ELSE IF Q7b ==2
Q7d Is it less than $750,000? 1 Yes 2 No 8888888 Refuse to answer
7777777 Don’t know
IF Q7d == 2
Q7e Is it more than $900,000? 1 Yes 2 No 8888888 Refuse to
answer 7777777 Don’t know
END IF
END IF
ELSE IF Q7a==2
Q7f Is it more than $150,000? 1 Yes 2 No 8888888 Refuse to answer 7777777
Don’t know
END IF
END IF
Q8 What proportion of the current market value of your residence do you still owe on your
mortgage?
Numeric (0%-200%)
9999999 Don’t know or prefer not to say
IF Q8 == 9999999
Q8a Is it more than 50%? 1 Yes 2 No 8888888 Refuse to answer 7777777 Don’t
know
IF Q8a == 1
Q8b Is it less than 75 %? 1 Yes 2 No 8888888 Refuse to answer 7777777
Don’t know
IF Q8b == 1
Q8c Is it more than 62.5%? 1 Yes 2 No 8888888 Refuse to answer
7777777 Don’t know
ELSE IF Q8b == 2
Q8d Is it more than 87.5%? 1 Yes 2 No 8888888 Refuse to answer
7777777 Don’t know
END IF
END IF
ELSE IF Q8a == 2
Q8e Is it less than 25 % 1 Yes 2 No 8888888 Refuse to answer 7777777 Don’t
know
IF Q8e == 1
Q8f Is it more than 12.5%? 1 Yes 2 No 8888888 Refuse to answer 7777777
Don’t know
IF Q8f == 2
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6
Q8g Is it less than 5%? 1 Yes 2 No 8888888 Refuse to answer 7777777
Don’t know
END IF
ELSE IF Q8e == 2
Q8h Is it more than 37.5%? 1 Yes 2 No 8888888 Refuse to answer
7777777 Don’t know
END IF
END IF
END IF
END IF
Q9 We are interested in your pension plan and its nature, if you have one. Do you currently contribute
to, or receive benefits from (in the form of regular payments), an employer-provided pension plan?
1 Yes
2 No
3 Don't Know
IF Q9==1
Q9a Do you agree with the following statement: “I have/expect to have sufficient pension
income”?
1 Completely disagree
2 Disagree
3 Somewhat disagree
4 Neither agree nor disagree
5 Somewhat agree
6 Agree
7 Completely agree
END IF
Q10 What is your best estimate of how much you have accumulated in Registered Retirement Savings
Plans (RRSPs), Tax-Free Savings Accounts (TFSAs) and other non-employer provided savings
accounts?
Numeric
9999999 Don’t know or prefer not to say
IF Q10==9999999
Q10a Is it more than $50,000? 1 Yes 2 No 8888888 Refuse to answer 7777777 Don’t know
IF Q10a==1
Q10b Is it less than $200,000? 1 Yes 2 No 8888888 Refuse to answer 7777777 Don’t
know
ELSE IF Q10a==2
Q10c Is it more than $10,000? 1 Yes 2 No 8888888 Refuse to answer 7777777 Don’t
know
END IF
END IF
Q11 Looking at the following list of health conditions, has a doctor ever said you suffered from:
[Check any of:]
1 Heart disease
2 Stroke
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7
3 Lung disease
4 Diabetes
5 Hypertension
6 Depression or other mental health problems
7 Cancer
8 None of the above
Q12 At the present time, do you smoke cigarettes daily, occasionally or not at all?
1 Daily
2 Occasionally
3 Not at all
IF Q12==1 GOTO Q13
ELSE IF Q12==2,3
Q12a Have you ever smoked cigarettes daily?
1 Yes
2 No
IF Q12a==1 GOTO Q13
ELSE IF Q12a==2
Q12b Have you smoked 100 cigarettes or more in your life?
1 Yes
2 No
IF Q12b==1 GOTO Q13
ELSE IF Q12b==2
Q12c Have you ever smoked a whole cigarette?
1 Yes
2 No
END IF
END IF
END IF
Section 2: Risk Perception
Q13 On a scale of 0 to 100, where 0 is absolutely no chance and 100 is absolutely certain, what do you
believe is the percent chance you will live to age 85 or more?
Numeric (0-100)
9999999 Don’t know
IF Q2==1,2 & Q2a < 85
Q13a On a scale of 0 to 100, where 0 is absolutely no chance and 100 is absolutely
certain, what do you believe is the percent chance your partner (spouse) will live to age
85 or more?
Numeric (0-100)
9999999 Don’t know
END IF
Q14 On a scale of 0 to 100, where 0 is absolutely no chance and 100 is absolutely certain, what do you
believe is the percent chance you will leave a bequest of more than $10,000?
Numeric (0-100)
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8
9999999 Don’t know
IF Q14 >0 & Q6 ==1
Q14a How likely is it that your primary residence will play a role in the bequest you plan to
leave?
1 Not likely at all
2 Not very likely
3 Somewhat likely
4 Very likely
5 Extremely likely
END IF
Q15 On a scale of 0 to 100, where 0 is absolutely no chance and 100 is absolutely certain, what do you
believe is the percent chance that your family would take up the responsibility of taking care of you if
you had important limitations in activities of daily living such as bathing, eating, cleaning?
Numeric (0-100)
9999999 Don’t know
Q16 On a scale of 0 to 100, where 0 is absolutely no chance and 100 is absolutely certain, what do you
believe is the percent chance that your family would take care of you financially if you needed
financial support?
Numeric (0-100)
9999999 Don’t know
IF Q6==1
Q17 Here are three possibilities concerning your future expected residence. On a scale of 0 to
100, where 0 is absolutely no chance and 100 is absolutely certain, what is the percent chance
that each of these possibilities comes true. Given that only one of these possibilities can occur,
the sum of the three probabilities must equal 100.
Q17a I’m going to stay in my current home until I die.
Numeric (0-100)
Q17b I will eventually move from my current home to live in another house or
apartment.
Numeric (0 to (100 – Answer Q17a))
Q17c I will eventually move from my current home to live in a long-term care home.
Numeric (0 to (100 – Answer Q17a – Answer Q17b))
[NOTE: SUM OF ANSWERS TO Q17a, Q17b AND Q17c MUST EQUAL 100.]
[NOTE: MAKE SURE THE QUESTION IS PROPERLY NUMBERED ON THE SCREEN.]
[NOTE: WOULD IT BE POSSIBLE TO INCLUDE A COUNTER TO LET THE RESPONDENT
KNOW HOW MANY % LEFT TO FILL IN?]
Q18 Over the next five years, do you think the value of your home will:
1 Increase a lot (greater than 20 %)
2 Increase moderately (between 5% and 20%)
3 remain rather stable (between +5% and -5%)
4 decrease moderately (between -5% and -20%)
/ 24
9
5 decrease a lot (less than -20%)
Q19 Do you agree with the following statement: “House prices can fluctuate a lot”?
1 Completely disagree
2 Disagree
3 Somewhat disagree
4 Neither agree nor disagree
5 Somewhat agree
6 Agree
7 Completely agree
END IF
Q20 Do you agree with the following statements? (Answers: 5 Strongly Agree; 4 Agree; 3 Disagree; 2
Strongly Disagree; 1 Don’t know)
Q20a It is the responsibility of the family, when feasible, to take care of elderly parents
Q20b Parents should set aside money to leave to their children or heirs once they die, even when it
means somewhat sacrificing their own comfort in retirement
Q20c Children should inherit their parents’ family home
Q20d A house is an asset that should only be sold in case of financial hardship
Q20e Being in debt is never a good thing
[NOTE: Make sure the question is properly numbered on the screen.]
[NOTE: Might the scale for each statement be inverted (i.e. “increasing” from left to right)? We leave
this with your expertise.]
Q21 Which of the following statements comes closest to describing the amount of financial risk that
you are willing to take when you save or make investments?
1 I am willing to take substantial financial risks expecting to earn substantial returns
2 I am willing to take above average financial risks expecting to earn above-average returns
3 I am willing to take average financial risks expecting to earn average returns
4 I am willing to take below average financial risks expecting to earn below-average returns
5 I am not willing to take any risk, knowing I will earn a small but certain return
Section 3: Literacy and Knowledge
Now we would like to ask some questions about your familiarity and comfort with financial concepts.
Please answer these questions the best you can.
Q22 Suppose you have $100 in a savings account, the interest rate is 2% per year and you never
withdraw money. After 5 years, how much will you have in this account in total?
1 More than $110
2 Exactly $110
3 Less than $110
4 Don’t know
Q23 True or false? You should invest most of your money in a single stock that you select rather than
in lots of stocks or in mutual funds.
1 True
2 False
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10
3 Don’t know
Q24 Imagine leaving $1,000 in a savings account that pays 1% interest and has no charges. Imagine
that inflation is running at 2%. Do you think that if you withdraw the money in a year's time you will
be able to buy more than, exactly the same as, or less than today with the money in this account?
1 More than today
2 Exactly the same as today
3 Less than today
4 Don't know
Q25 Suppose the chances of someone aged 50 living to age 85 are 60%. What do you think the chances
are that this same person will live to age 60?
1 Less than 60%
2 Greater than 60%
3 Don’t know
Section 4: Annuities
For the purposes of this section, when we use the term ‘annuity’, we are referring to a financial
product that guarantees you a regular payment every month or year until death (the “benefit”), in
exchange for an initial one-time payment (the “premium”).
Q26 This section is going to ask you questions about annuities. Which of the following best describes
your current knowledge about this type of product?
1 A lot
2 A little
3 None at all
Q27 Have you purchased an annuity in the private market, for which you are currently receiving or will
eventually receive benefits (please exclude all government provided annuities such as your provincial
pension plan, the Canada Pension Plan and Old Age Security)?
1 Yes, I have purchased an annuity
2 Yes, I have purchased more than one annuity
3 No
4 Don't know
IF Q27==4(Don’t know) GOTO Q28
ELSE IF Q27==3 (No)
Q27a Why haven’t you bought an annuity? Choose the main reason.
1 I never thought about buying one, and I have never been offered one (for instance by a
financial advisor).
2 I thought about buying one, but I have not (yet) made a decision.
3 I do not have sufficient savings to purchase one.
4 Such products do not offer good value for money.
5 Such products do not cover my needs.
6 I do not think I will need such a product.
7 I don’t know what an annuity is.
8 Other, open...
GOTO Q28
ELSE IF Q27==1,2 (Yes)
/ 24
11
Q27b How did you come to purchase the annuity? If you have purchased more than one
annuity, please think about the one you purchased most recently.
1 I was offered an annuity (by my financial advisor, pension plan representative, insurance
company, etc.)
2 I searched myself for an annuity
3 Other, open …
Q27c What was the premium of the annuity (what did you pay)? If you have purchased more
than one annuity, please indicate what you paid for the one you purchased most recently.
Numeric (>$0)
7777777 Don’t know
IF Q27c==7777777
Q27d Was it more than $250,000? 1 Yes 2 No 8888888 Refuse to answer 7777777
Don’t know
IF Q27d==1
Q27e Was it less than $1,000,000? 1 Yes 2 No 8888888 Refuse to answer
7777777 Don’t know
IF Q27e == 1
Q28f Was it more than $500,000? 1 Yes 2 No 8888888 Refuse to answer
7777777 Don’t know
END IF
ELSE IF Q27d ==2
Q27g Was it more than $150,000? 1 Yes 2 No 8888888 Refuse to answer
7777777 Don’t know
IF Q27g == 2
Q27h Was it less than $100,000? 1 Yes 2 No 8888888 Refuse to answer
7777777 Don’t know
IF Q27h==1
Q27i Was it more than $50,000? 1 Yes 2 No 8888888 Refuse to
answer 7777777 Don’t know
END IF
END IF
END IF
END IF
Q27j What is the benefit amount the annuity pays out (monthly)? If you have purchased more
than one annuity, please indicate the benefit paid by the one you purchased most recently.
Numeric (>$0)
7777777 Don’t know
IF Q27j==7777777
Q27k Is it more than $1,000? 1 Yes 2 No 8888888 Refuse to answer 7777777 Don’t
know
IF Q27k==1
Q27l Is it less than $4,000? 1 Yes 2 No 8888888 Refuse to answer 7777777
Don’t know
IF Q27l == 1
Q27m Is it more than $2,000? 1 Yes 2 No 8888888 Refuse to answer
7777777 Don’t know
END IF
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12
ELSE IF Q27k ==2
Q27n Is it more than $600? 1 Yes 2 No 8888888 Refuse to answer 7777777
Don’t know
IF Q27n == 2
Q27o Is it less than $400? 1 Yes 2 No 8888888 Refuse to answer
7777777 Don’t know
IF Q27o==1
Q27p Is it more than $200? 1 Yes 2 No 8888888 Refuse to answer
7777777 Don’t know
END IF
END IF
END IF
END IF
END IF
Q28 Do you have life insurance for which you currently pay a premium or that is fully paid and still in
force?
1 Yes
2 No
3 Don’t Know
IF Q28==1 (Yes)
Q28a What type of life insurance policy do you have?
1 Term life insurance
2 Whole life insurance or Universal life insurance
3 Don’t know
4 Other, open…
END IF
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13
Section 6: Preferences for Annuities [SCENARIOS]
We are going to show you some simple annuities and ask you to rate them. You can assume that the
institution offering the annuity will pay the monthly benefit no matter the circumstances. Once you pay
the premium, you receive monthly benefits and have nothing else to pay.
Each product has two attributes:
a) a premium you have to pay;
b) a monthly benefit starting at a given age and lasting until death.
The benefit is adjusted for inflation (indexed).
Q30-34
[SCENARIOS]
What are the chances, 0% meaning no chance and 100% meaning for sure, that you would purchase
this product if it were offered to you by [a trusted / an] insurance company within the next year?
Numeric (0-100)
*****
Randomize [a trusted / an] across individuals with probability 0.5, and keep constant for each
respondent for questions 30-34 (i.e., present all of Q30-34 either with [a trusted] or with [an] for a
given individual).
*****
Scenarios randomization scheme
Parameters:
Age_benefit = [(age+1), 75,85] with probability [2/5, 2/5, 1/5]
where (age+1)=the age of the respondent+1
Benefit = [200,600,1000] each with probability 1/3
Load = [0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0]
each with probability 1/16
For each combination of Age_benefit and Benefit we provide EPremium, which is the fair premium by
age and sex (3 x 3 = 9 data points; see table attached).
The premium for the contract is given by (please round to nearest $500):
prem = EPremium x Load
Randomize Age_benefit, Benefit and Load independently (3 x 3 x 16 possibilities) for 5 draws (i.e.,
each respondent is presented with 5 combinations of Age_benefit, Benefit, and “prem” according to the
above probabilities).
Present each draw following this example:
When you buy the annuity
Starting at age [Age_benefit]
/ 24
14
You pay $[prem]
You receive $[Benefit] per
month until death, indexed
annually for inflation
*****
/ 24
15
FAIR PREMIUMS (VALUES FOR "EPremium”)
For$Age_benefit=age+1$
$
$
$
$
$
$
$
$
$
$
Benefit$=$200$
$
$
Benefit$=$600$
$
$
Benefit$=$1000$
Age$
Male$
Female$
$
Age$
Male$
Female$
$
Age$
Male$
Female$
55-59$
$$$$$45,111.40$$
$$$$$49,890.91$$
$
55-59$
$$135,334.20$$
$$149,672.72$$
$
55-59$
$$225,557.00$$
$$249,454.53$$
60-64$
$$$$$38,942.44$$
$$$$$43,719.50$$
$
60-64$
$$116,827.32$$
$$131,158.51$$
$
60-64$
$$194,712.20$$
$$218,597.52$$
65-69$
$$$$$32,755.36$$
$$$$$37,352.10$$
$
65-69$
$$$$$98,266.07$$
$$112,056.30$$
$
65-69$
$$163,776.79$$
$$186,760.50$$
70-75$
$$$$$26,135.90$$
$$$$$30,292.54$$
$
70-75$
$$$$$78,407.71$$
$$$$$90,877.61$$
$
70-75$
$$130,679.51$$
$$151,462.69$$
$
$
$
$
$
$
$
$
$
$
$
For$Age_benefit=75$
$
$
$
$
$
$
$
$
$
$
Benefit$=$200$
$
$
Benefit$=$600$
$
$
Benefit$=$1000$
Age$
Male$
Female$
$
Age$
Male$
Female$
$
Age$
Male$
Female$
55-59$
$$$$$13,691.16$$
$$$$$17,442.92$$
$
55-59$
$$$$$41,073.47$$
$$$$$52,328.77$$
$
55-59$
$$$$$68,455.79$$
$$$$$87,214.61$$
60-64$
$$$$$15,677.30$$
$$$$$19,700.10$$
$
60-64$
$$$$$47,031.89$$
$$$$$59,100.30$$
$
60-64$
$$$$$78,386.48$$
$$$$$98,500.51$$
65-69$
$$$$$18,361.54$$
$$$$$22,559.95$$
$
65-69$
$$$$$55,084.62$$
$$$$$67,679.85$$
$
65-69$
$$$$$91,807.70$$
$$112,799.74$$
70-75$
$$$$$22,467.80$$
$$$$$26,560.34$$
$
70-75$
$$$$$67,403.40$$
$$$$$79,681.01$$
$
70-75$
$$112,339.00$$
$$132,801.69$$
$
$
$
$
$
$
$
$
$
$
$
For$Age_benefit=85$
$
$
$
$
$
$
$
$
$
$
Benefit$=$200$
$
$
Benefit$=$600$
$
$
Benefit$=$1000$
Age$
Male$
Female$
$
Age$
Male$
Female$
$
Age$
Male$
Female$
55-59$
$$$$$$$3,912.57$$
$$$$$$$5,959.01$$
$
55-59$
$$$$$11,737.70$$
$$$$$17,877.03$$
$
55-59$
$$$$$19,562.83$$
$$$$$29,795.06$$
60-64$
$$$$$$$4,480.15$$
$$$$$$$6,730.13$$
$
60-64$
$$$$$13,440.45$$
$$$$$20,190.39$$
$
60-64$
$$$$$22,400.75$$
$$$$$33,650.65$$
65-69$
$$$$$$$5,247.24$$
$$$$$$$7,707.14$$
$
65-69$
$$$$$15,741.71$$
$$$$$23,121.41$$
$
65-69$
$$$$$26,236.18$$
$$$$$38,535.69$$
70-75$
$$$$$$$6,535.00$$
$$$$$$$9,210.44$$
$
70-75$
$$$$$19,605.01$$
$$$$$27,631.32$$
$
70-75$
$$$$$32,675.02$$
$$$$$46,052.19$$
/ 24
16
IF Q6 == 1
Section 5: Financial product to extract the equity value of a primary residence
For the purposes of this section, when we use the expression “current home equity”, we are
referring to the current market value of your primary residence after subtracting outstanding
mortgage balances. This section is going to ask you questions about financial products on the
basis of your current home equity.
Imagine a financial product that lets you turn part of your current home equity into cash.
You’re not obligated to make any payments until you move, you sell your home, or you
die. You have the certainty that once your residence will be sold, the required amount to
repay the loan will not exceed the selling price of the residence.
Q29 Have you ever heard of the existence of this type of financial product in Canada?
1 Yes
2 No
IF Q29 == 1
Q29a Can you name that product?
1 Yes
2 No
IF Q29a==1
[DROP-DOWN]
Q29b What is it called?
1 Annuity
2 Reverse mortgage
3 Life insurance
4 Line of credit
5 None of the above
END IF
END IF
/ 24
17
Section 7: Preferences for Reverse Mortgages [SCENARIOS]
We will refer to a reverse mortgage as a financial product that lets you turn part of your current
home equity into cash. Unlike many mortgage-based financial products, you’re not obligated to
make any payments until you move, you sell your home, or you die. Importantly, you have the
certainty that once your residence will be sold, the amount required to repay the loan will not
exceed the selling price of the residence.
When we use the expression “current home equity”, we are referring to the current market
value of your primary residence after subtracting outstanding mortgage balances. For the rest of
this section, try to have your current home equity in mind.
We are going to show you some simple reverse mortgage products and ask you to rate them.
Each reverse mortgage has three attributes:
a) The percentage of your current home equity that you can borrow. The amount borrowed
must be a minimum of $25,000.
b) A fixed annual interest rate on the balance of the loan, generating interests that you do not
need to pay before you move, sell or die.
c) A fixed fee of $2,245 that you only have to pay once. The money you obtain from the
reverse mortgage will be used to pay this fee.
[Suppose you have the certainty that you will never be put under pressure to sell your residence
and that the contract terms will be respected.]
*****
Randomize the presence of the sentence above for each respondent with probability 0.5 and
keep constant for questions 35-39.
*****
Q35-Q39
[SCENARIOS]
What are the chances, 0% meaning no chance and 100% for sure, that you would buy this
reverse mortgage if a trusted financial institution offered it to you within the next year?
Numeric (0-100)
IF Q35>0
Q35a In the event you purchased this reverse mortgage, considering you must borrow a
minimum of $25,000 and taking into account the maximum amount that can be
borrowed (« Reverse Mortgage » of your current home equity), what amount of money
do you think you would borrow?
Numeric (>=$25,000)
END IF
[NOTE: REPEAT THE ABOVE SUB-QUESTION AFTER EACH OF Q35 TO Q39, USING
THE EXACT SAME LOOP, WORDING AND CRITERIA]
END IF
Scenarios randomization scheme
/ 24
18
Parameters:
Interest_rates = [3.8%, 4.1%, 4.4%, 4.7%, 5%, 5.3%, 5.59%, 6%, 6.5%, 7%] each with probability 1/10
Load = [0.5, 0.75, 1, 1.25, 1.5] each with probability 1/5
With these products we provide Borrow (see tables attached), which is the proportion that can be
borrowed by city, marital status, age and sex.
The contract of the reverse mortgage is given by (please round to nearest percentage point):
Reverse Mortgage = Borrow x Load
Randomize both Interest_rates and Load independently (10 x 5 possibilities) for 5 draws (i.e., each
respondent is presented with 5 combinations of Interest_rates and “Reverse Mortgage” according to the
above probabilities).
Present each draw following this example:
You can borrow a minimum of $25,000 and up to [Reverse Mortgage] of your current home equity.
You will be charged a fixed annual interest rate of [Interest_rates] on the balance of the loan for as
long as you hold the loan.
Reminder: You’re not obligated to make any payments until you move, you sell your home, or you die;
and you have the certainty that once your residence will be sold, the amount required to repay the
loan will not exceed the selling price of the residence.
There is a fixed fee of $2,245 that you only have to pay once. The money you obtain from the reverse
mortgage will be used to pay this fee.
*****
/ 24
19
VALUES FOR “Borrow”
[FOR COUPLES, PLEASE USE THE AVERAGE AGE OF THE COUPLE :
!"# !!!!
!
, WHERE age IS
THE RESPONDENT’S AGE GATHERED FROM THE SAMPLING/TARGETING. PLEASE
ROUND THE RESULT TO THE NEAREST INTEGER AND SET THE AGE OF THE COUPLE AS
55 IF
!"# !!!!
!
< 55 AND AS 79 IF
!"# !!!!
!
> 79.]
!
If!Q0!begins!with!H1,!H2,!H3,!H4,!H5,!H8,!H9!&!Q2==1,2!!
(Island!o f!Montreal,!Couple)!
Age!
55-59!
60-64!
65-69!
70-74!
75-79!
IF!Q6a!== !1,!7777777!(Single!Family!Dw ellin g!/!D etac he d!
Duplex,!Triplex!or!Quadruplex!/!Link!Home!/!Semi-Detached)!
16.10%!
23.10%!
31.90%!
39.10%!
46.70%!
IF!Q6a!== !2 !(o w n h o u s e ,!R o w h o u s e !/!F iv e p lex !a n d !S ixp le x !/!
Attached!Duplex.!Triplex,!or!Quadruplex!/!Stratified!SFD,!Bare!
Land!Strata!/!Semi-Detached!Strata!Condo!/!Modular!Home)!!
15.30%!
21.90%!
30.30%!
37.10%!
44.50%!
IF!Q6a!== !3 !(C o n d o !- !Townhouse!/!Mobile!Home!/!Condo!–!
Townhouse)!
12.90%!
18.50%!
25.50%!
31.30%!
37.50%!
!
!
If!Q0!begin s !w it h !H1,!H2,!H3,!H4,!H5,!H8,!H9!&!Q2==3,4,5,6!and!sex!is!Male!!
(Island!o f!Montreal,!Single!Male)!
Age!
55-59!
60-64!
65-69!
70-74!
75-79!
IF!Q6a!== !1,!7777777!(Single!Family!Dw ellin g!/!D etac he d!
Duplex,!Triplex!or!Quadruplex!/!Link!Home!/!Semi-Detached)!
25.10%!
33.10%!
39.10%!
43.30%!
49.90%!
IF!Q6a!== !2 !(T o w n h o u s e ,!R o w h o u s e !/!F iv ep le x !a n d !Six p le x!/!
Attached!Duplex.!Triplex,!or!Quadruplex!/!Stratified!SFD,!Bare!
Land!Strata!/!Semi-Detached!Strata!Condo!/!Modular!Home)!!
23.90%!
31.50%!
37.30%!
41.10%!
47.30%!
IF!Q6a!== !3 !(C o n d o !- !Townhouse!/!Mobile!Home!/!Condo!–!
Townhouse)!
20.10%!
26.50%!
31.30%!
34.70%!
39.90%!
!
!
If!Q0!begin s !w it h !H1,!H2,!H3,!H4,!H5,!H8,!H9!&!Q2==3,4,5,6!&!sex!is!Female!!
(Island!o f!Montreal,!Single!Female)!
Age!
55-59!
60-64!
65-69!
70-74!
75-79!
IF!Q6a!== !1,!7777777!(Single!Family!Dw ellin g!/!D etac he d!
Duplex,!Triplex!or!Quadruplex!/!Link!Home!/!Semi-Detached)!
26.70%!
33.10%!
37.90%!
39.90%!
44.90%!
IF!Q6a!== !2 (T o w n h o u s e ,!R o w h o u s e !/!F iv ep le x !a n d !Six p le x!/ !
Attached!Duplex.!Triplex,!or!Quadruplex!/!Stratified!SFD,!Bare!
Land!Strata!/!Semi-Detached!Strata!Condo!/!Modular!Home)!!
25.50%!
31.50%!
36.10%!
37.90%!
42.70%!
IF!Q6a!== !3 !(C o n d o !- !Townhouse!/!Mobile!Home!/!Condo!–!
Townhouse)!
21.50%!
26.50%!
30.30%!
31.90%!
36.10%!
! !
/ 24
20
If!Q0!is!from !Quebec!and!DOES!NOT!begin!with!H1,!H2,!H3,!H4,!H5,!H8,!H9!&!Q2==1,2!!
(Rest!of!Quebec,!Couple)!
Age!
55-59!
60-64!
65-69!
70-74!
75-79!
IF!Q6a!== !1,!7777777!(Single!Family!Dw ellin g!/!D etac he d!
Duplex,!Triplex!or!Quadruplex!/!Link!Home!/!Semi-Detached)!
15.03%!
21.57%!
29.77%!
36.50%!
43.63%!
IF!Q6a!== !2 !(T o w n h o u s e ,!R o w h o u s e !/!F iv ep le x !a n d !Six p le x!/!
Attached!Duplex.!Triplex,!or!Quadruplex!/!Stratified!SFD,!Bare!
Land!Strata!/!Semi-Detached!Strata!Condo!/!Modular!Home)!!
14.30%!
20.50%!
28.30%!
34.70%!
41.50%!
IF!Q6a!== !3 !(C o n d o !- !Townhouse!/!Mobile!Home!/!Condo!–!
Townhouse)!
12.03%!
17.30%!
23.83%!
29.23%!
34.97%!
!
!
If!Q0!is!from !Qu e be c!and !DOES!NOT!begin!with!H1,!H2,!H3,!H4,!H5,!H8,!H9!&!Q2==3,4,5,6!&!sex!is!Male!!
(Rest!of!Quebec,!Single!Male)!
Age!
55-59!
60-64!
65-69!
70-74!
75-79!
IF!Q6a!== !1,!7777777!(Single!Family!Dw ellin g!/!D etac he d!
Duplex,!Triplex!or!Quadruplex!/!Link!Home!/!Semi-Detached)!
23.43%!
30.90%!
36.57%!
40.43%!
46.50%!
IF!Q6a!== !2 !(T o w n h o u s e ,!R o w h o u s e !/!F iv ep le x !a n d !Six p le x!/ !
Attached!Duplex.!Triplex,!or!Quadruplex!/!Stratified!SFD,!Bare!
Land!Strata!/!Semi-Detached!Strata!Condo!/!Modular!Home)!!
22.30%!
29.37%!
34.77%!
38.43%!
44.17%!
IF!Q6a!== !3 !(C o n d o !- !Townhouse!/!Mobile!Home!/!Condo!–!
Townhouse)!
18.77%!
24.70%!
29.30%!
32.37%!
37.23%!
!
!
If!Q0!is!from !Qu e be c!and !DOES!NOT!begin!with!H1,!H2,!H3,!H4,!H5,!H8,!H9!&!Q2==3,4,5,6!&!sex!is!Female!!
(Rest!of!Quebec,!Single!Female) !
Age!
55-59!
60-64!
65-69!
70-74!
75-79!
IF!Q6a!== !1,!7777777!(Single!Family!Dw ellin g!/!D etac he d!
Duplex,!Triplex!or!Quadruplex!/!Link!Home!/!Semi-Detached)!
24.97%!
30.90%!
35.43%!
37.23%!
41.97%!
IF!Q6a!== !2 !(T o w n h o u s e ,!R o w h o u s e !/!F iv ep le x!an d!Sixplex!/!
Attached!Duplex.!Triplex,!or!Quadruplex!/!Stratified!SFD,!Bare!
Land!Strata!/!Semi-Detached!Strata!Condo!/!Modular!Home)!!
23.77%!
29.37%!
33.70%!
35.43%!
39.90%!
IF!Q6a!== !3 !(C o n d o !- !Townhouse!/!Mobile!Home!/!Condo!–!
Townhouse)!
20.03%!
24.70%!
28.37%!
29.83%!
33.70%!
!
/ 24
21
If!Q0!begin s !w it h !M2,!M3,!M4G,!M4H,!M4J,!M4K,!M4M,!M4L,!M4M,!M4N,!M4P,!M4R,!M4S,!M4T,!M4V,!M4W,!M4X,!M4Y,!
M5,!M6,!M7A,!M9L,!M9M,!M9N!&!Q2==1,2!!
(City!of!Toronto,!Couple)!
Age!
55-59!
60-64!
65-69!
70-74!
75-79!
IF!Q6a!== !1,!7777777!(Single!Family!Dw ellin g!/!D etac he d!
Duplex,!Triplex!or!Quadruplex!/!Link!Home!/!Semi-Detached)!
14.50%!
21.10%!
29.70%!
36.90%!
44.50%!
IF!Q6a!== !2 !(T o w n h o u s e ,!R o w h o u s e !/!F iv ep le x !a n d !Six p le x!/ !
Attached!Duplex.!Triplex,!or!Quadruplex!/!Stratified!SFD,!Bare!
Land!Strata!/!Semi-Detached!Strata!Condo!/!Modular!Home!)!
13.70%!
20.10%!
28.30%!
35.10%!
42.30%!
IF!Q6a!== !3 !(C o n d o !- !Townhouse!/!Mobile!Home!/!Condo!–!
Townhouse)!
11.50%!
16.90%!
23.70%!
29.50%!
35.70%!
!
!
If!Q0!begin s !w it h !M2,!M3,!M4G,!M4H,!M4J,!M4K,!M4M,!M4L,!M4M,!M4N,!M4P,!M4R,!M4S,!M4T,!M4V,!M4W,!M4X,!M4Y,!
M5,!M6,!M7A,!M9L,!M9M,!M9N!&!Q2==3,4,5,6!&!sex!is!Male!!
(City!of!Toronto,!Single!Male)!
Age!
55-59!
60-64!
65-69!
70-74!
75-79!
IF!Q6a!== !1,!7777777!(Single!Family!Dw ellin g!/!D etac he d!
Duplex,!Triplex!or!Quadruplex!/!Link!Home!/!Semi-Detached)!
23.10%!
30.90%!
36.90%!
41.10%!
47.70%!
IF!Q6a!== !2 !(T o w n h o u s e ,!R o w h o u s e !/!F iv ep le x !a n d !Six p le x!/ !
Attached!Duplex.!Triplex,!or!Quadruplex!/!Stratified!SFD,!Bare!
Land!Strata!/!Semi-Detached!Strata!Condo!/!Modular!Home)!!
21.90%!
29.30%!
35.10%!
39.10%!
45.30%!
IF!Q6a!== !3 !(C o n d o !- !Townhouse!/!Mobile!Home!/!Condo!–!
Townhouse)!
18.50%!
24.70%!
29.50%!
32.90%!
38.10%!
!
!
If!Q0!begin s !w it h !M2,!M3,!M4G,!M4H,!M4J,!M4K,!M4M,!M4L,!M4M,!M4N,!M4P,!M4R,!M4S,!M4T,!M4V,!M4W,!M4X,!M4Y,!
M5,!M6,!M7A,!M9L,!M9M,!M9N!&!Q2==3,4,5,6!&!sex!is!Female!!
(City!of!Toronto,!Single!Female)!
Age!
55-59!
60-64!
65-69!
70-74!
75-79!
IF!Q6a!== !1,!7777777!(Single!Family!Dw ellin g!/!D etac he d!
Duplex,!Triplex!or!Quadruplex!/!Link!Home!/!Semi-Detached)!
24.70%!
30.90%!
35.70%!
37.70%!
42.70%!
IF!Q6a!== !2 !(T o w n h o u s e ,!R o w h o u s e !/!F iv ep le x !a n d !Six p le x!/ !
Attached!Duplex.!Triplex,!or!Quadruplex!/!Stratified!SFD,!Bare!
Land!Strata!/!Semi-Detached!Strata!Condo!/!Modular!)!
23.50%!
29.30%!
33.90%!
35.90%!
40.70%!
IF!Q6a!== !3 !(C o n d o !- !Townhouse!/!Mobile!Home!/!Condo!–!
Townhouse)!
19.70%!
24.70%!
28.50%!
30.10%!
34.30%!
! !
/ 24
22
If!Q0!is!from !On ta rio! an d!DOES!NOT!begin!with!M2,!M3,!M4G,!M4H,!M4J,!M4K,!M4M,!M4L,!M4M,!M4N,!M4P,!M4R,!M4S,!
M4T,!M4V,!M4W,!M4X,!M4Y,!M5,!M6,!M7A,!M9L,!M9M,!M9N!&!Q2==1,2!!
(Rest!of!Ontario,!Couple )!
Age!
55-59!
60-64!
65-69!
70-74!
75-79!
!!
!!
!!
!!
!!
!!
IF!Q6a!== !1,!7777777!(Single!Family!Dw ellin g!/!D etac he d!
Duplex,!Triplex!or!Quadruplex!/!Link!Home!/!Semi-Detached)!
15.03%!
21.77%!
30.43%!
37.63%!
45.23%!
IF!Q6a!== !2 !(T o w n h o u s e ,!R o w h o u s e !/!F iv ep le x !a n d !Six p le x!/ !
Attached!Duplex.!Triplex,!or!Quadruplex!/!Stratified!SFD,!Bare!
Land!Strata!/!Semi-Detached!Strata!Condo!/!Modular!Home)!!
14.23%!
20.70%!
28.97%!
35.77%!
43.03%!
IF!Q6a!== !3 !(C o n d o !- !Townhouse!/!Mobile!Home!/!Condo!–!
Townhouse)!
11.97%!
17.43%!
24.30%!
30.10%!
36.30%!
!
!
If!Q0!is!from !On ta rio! an d!DOES!NOT!begin!with!M2,!M3,!M4G,!M4H,!M4J,!M4K,!M4M,!M4L,!M4M,!M4N,!M4P,!M4R,!M4S,!
M4T,!M4V,!M4W,!M4X,!M4Y,!M5,!M6,!M7A,!M9L,!M9M,!M9N!&!Q2==3,4,5,6!&!sex!is!Male!!
(Rest!of!Ontario,!Single!Male)!
Age!
55-59!
60-64!
65-69!
70-74!
75-79!
!!
!!
!!
!!
!!
!!
IF!Q6a!==!1,!777 7 7 77!(Single!Fam ily!Dw ellin g!/!D etac he d!
Duplex,!Triplex!or!Quadruplex!/!Link!Home!/!Semi-Detached)!
23.77%!
31.63%!
37.63%!
41.83%!
48.43%!
IF!Q6a!== !2 !(T o w n h o u s e ,!R o w h o u s e !/!F iv ep le x !a n d !Six p le x!/ !
Attached!Duplex.!Triplex,!or!Quadruplex!/!Stratified!SFD,!Bare!
Land!Strata!/!Semi-Detached!Strata!Condo!/!Modular!Home)!!
22.57%!
30.03%!
35.83%!
39.77%!
45.97%!
IF!Q6a!== !3 !(C o n d o !- !Townhouse!/!Mobile!Home!/!Condo!–!
Townhouse)!
19.03%!
25.30%!
30.10%!
33.50%!
38.70%!
!
!
If!Q0!is!from !On ta rio! an d!DOES!NOT!begin!with!M2,!M3,!M4G,!M4H,!M4J,!M4K,!M4M,!M4L,!M4M,!M4N,!M4P,!M4R,!M4S,!
M4T,!M4V,!M4W,!M4X,!M4Y,!M5,!M6,!M7A,!M9L,!M9M,!M9N!&!Q2==3,4,5,6!&!sex!is!Female!!
(Rest!of!Ontario,!Single!Female)!
Age!
55-59!
60-64!
65-69!
70-74!
75-79!
!!
!!
!!
!!
!!
!!
IF!Q6a!==!1,!7777777!(Single!Family!Dwelling!/!Deta che d!
Duplex,!Triplex!or!Quadruplex!/!Link!Home!/!Semi-Detached)!
25.37%!
31.63%!
36.43%!
38.43%!
43.43%!
IF!Q6a!== !2 !(T o w n h o u s e ,!R o w h o u s e !/!F iv ep le x !a n d !Six p le x!/ !
Attached!Duplex.!Triplex,!or!Quadruplex!/!Stratified!SFD,!Bare!
Land!Strata!/!Semi-Detached!Strata!Condo!/!Modular!Home)!!
24.17%!
30.03%!
34.63%!
36.57%!
41.37%!
IF!Q6a!== !3 !(C o n d o !- !Townhouse!/!Mobile!Home!/!Condo!–!
Townhouse)!
20.30%!
25.30%!
29.10%!
30.70%!
34.90%!
! !
/ 24
23
If!Q0!begin s !w it h !V5K,!V5L,!V5M,!V5N,!V5P,!V5R,!V5S,!V5T,!V5V,!V5W,!V5Y,!V6A,!V6B,!V6C,!V6E,!V6G,!V6H,!V6J,!V6K,!V6L,!
V6M,!V6N,!V6P,!V6R,!V6S,!V6T,!V6Z,!V7G,!V7H,!V7J,!V7K,!V7L,!V7M,!V7N,!V7P,!V7R,!V7S,!V7T,!V7V,!V7W,!V7X,!V7T!&!
Q2==1,2!!
(City!of!Vancouver,!Couple)!
Age!
55-59!
60-64!
65-69!
70-74!
75-79!
IF!Q6a!== !1,!7777777!(Single!Family!Dw ellin g!/!D etac he d!
Duplex,!Triplex!or!Quadruplex!/!Link!Home!/!Semi-Detached)!
15.30%!
22.10%!
30.70%!
37.90%!
45.70%!
IF!Q6a!== !2 !(T o w n h o u s e ,!R o w h o u s e !/!F iv ep le x !a n d !Six p le x!/!
Attached!Duplex.!Triplex,!or!Quadruplex!/!Stratified!SFD,!Bare!
Land!Strata!/!Semi-Detached!Strata!Condo!/!Modular!Home)!!
14.50%!
21.10%!
29.30%!
36.10%!
43.30%!
IF!Q6a!== !3 !(C o n d o !- !Townhouse!/!Mobile!Home!/!Condo!–!
Townhouse)!
12.30%!
17.70%!
24.70%!
30.50%!
36.50%!
!
!
If!Q0!begin s !w it h !V5K,!V5L,!V5M,!V5N,!V5P,!V5R,!V5S,!V5T,!V5V,!V5W,!V5Y,!V6A,!V6B,!V6C,!V6E,!V6G,!V6H,!V6J,!V6K,!V6L,!
V6M,!V6N,!V6P,!V6R,!V6S,!V6T,!V6Z,!V7G,!V7H,!V7J,!V7K,!V7L,!V7M,!V7N,!V7P,!V7R,!V7S,!V7T,!V7V,!V7W,!V7X,!V7T!&!
Q2==3,4,5,6!&!sex!is!Male!!
(City!of!Vancouver,!Single!Male)!
Age!
55-59!
60-64!
65-69!
70-74!
75-79!
IF!Q6a!== !1,!7777777!(Single!Family!Dw ellin g!/!D etac he d!
Duplex,!Triplex!or!Quadruplex!/!Link!Home!/!Semi-Detached)!
24.10%!
31.90%!
38.10%!
42.30%!
48.70%!
IF!Q6a!== !2 !(T o w n h o u s e ,!R o w h o u s e !/!F iv ep le x !a n d !Six p le x!/ !
Attached!Duplex.!Triplex,!or!Quadruplex!/!Stratified!SFD,!Bare!
Land!Strata!/!Semi-Detached!Strata!Condo!/!Modular!Home)!!
22.90%!
30.30%!
36.10%!
40.10%!
46.30%!
IF!Q6a!== !3 !(C o n d o !- !Townhouse!/!Mobile!Home!/!Condo!–!
Townhouse)!
19.30%!
25.70%!
30.50%!
33.70%!
38.90%!
!
!
If!Q0!begin s !w it h !V5K,!V5L,!V5M,!V5N,!V5P,!V5R,!V5S,!V5T,!V5V,!V5W,!V5Y,!V6A,!V6B,!V6C,!V6E,!V6G,!V6H,!V6J,!V6K,!V6L,!
V6M,!V6N,!V6P,!V6R,!V6S,!V6T,!V6Z,!V7G,!V7H,!V7J,!V7K,!V7L,!V7M,!V7N,!V7P,!V7R,!V7S,!V7T,!V7V,!V7W,!V7X,!V7T!&!
Q2==3,4,5,6!&!sex!is!Female!
(City!of!Vancouver,!Single!Female)!
Age!
55-59!
60-64!
65-69!
70-74!
75-79!
IF!Q6a!== !1,!7777777!(Single!Family!Dw ellin g!/!D etac he d!
Duplex,!Triplex!or!Quadruplex!/!Link!Home!/!Semi-Detached)!
25.70%!
31.90%!
36.70%!
38.90%!
43.90%!
IF!Q6a!== !2 !(T o w n h o u s e ,!R o w h o u s e !/!F iv ep le x !a n d !Sixplex!/!
Attached!Duplex.!Triplex,!or!Quadruplex!/!Stratified!SFD,!Bare!
Land!Strata!/!Semi-Detached!Strata!Condo!/!Modular!Home)!!
24.50%!
30.30%!
34.90%!
36.90%!
41.70%!
IF!Q6a!== !3 !(C o n d o !- !Townhouse!/!Mobile!Home!/!Condo!–!
Townhouse)!
20.50%!
25.50%!
29.50%!
31.10%!
35.10%!
!
!
! !
/ 24
24
If!Q0!is!from !British!Columbia!and!DOES!NOT!begin!with!V5K,!V5L,!V5M,!V5N,!V5P,!V5R,!V5S,!V5T,!V5V,!V5W,!V5Y,!V6A,!
V6B,!V6C,!V6E,!V6G,!V6H,!V6J,!V6K,!V6L,!V6M,!V6N,!V6P,!V6R,!V6S,!V6T,!V6Z,!V7G,!V7H,!V7J,!V7K,!V7L,!V7M,!V7N,!V7P,!
V7R,!V7S,!V7T,!V7V,!V7W,!V7X,!V7T!&!Q2==1,2!!
(Rest!of!British!Columbia,!Couple)!
Age!
55-59!
60-64!
65-69!
70-74!
75-79!
IF!Q6a!== !1 ,!77 7 7 7 77 !(S in g le !Fa mily!Dwellin g !/!D e ta c h e d !
Duplex,!Triplex!or!Quadruplex!/!Link!Home!/!Semi-Detached)!
14.50%!
20.97%!
29.03%!
35.77%!
42.97%!
IF!Q6a!== !2 !(T o w n h o u s e ,!R o w h o u s e !/!F iv ep le x !a n d !Six p le x!/!
Attached!Duplex.!Triplex,!or!Quadruplex!/!Stratified!SFD,!Bare!
Land!Strata!/!Semi-Detached!Strata!Condo!/!Modular!Home)!!
13.77%!
19.97%!
27.70%!
34.03%!
40.83%!
IF!Q6a!== !3 !(C o n d o !- !Townhouse!/!Mobile!Home!/!Condo!–!
Townhouse)!
11.70%!
16.83%!
23.30%!
28.70%!
34.37%!
!
!
If!Q0!is!from !British!Columbia!and!DOES!NOT!begin!with!V5K,!V5L,!V5M,!V5N,!V5P,!V5R,!V5S,!V5T,!V5V,!V5W,!V5Y,!V6A,!
V6B,!V6C,!V6E,!V6G,!V6H,!V6J,!V6K,!V6L,!V6M,!V6N,!V6P,!V6R,!V6S,!V6T,!V6Z,!V7G,!V7H,!V7J,!V7K,!V7L,!V7M,!V7N,!V7P,!
V7R,!V7S,!V7T,!V7V,!V7W,!V7X,!V7T!&!Q2==3,4,5,6!&!sex!is!Male!!
(Rest!of!British!Columbia,!Single!Male)!
Age!
55-59!
60-64!
65-69!
70-74!
75-79!
IF!Q6a!== !1 ,!77 7 7 7 77 !(S in g le !Fa mily!Dwellin g !/!D e ta c h e d !
Duplex,!Triplex!or!Quadruplex!/!Link!Home!/!Semi-Detached)!
22.83%!
30.17%!
35.90%!
39.77%!
45.83%!
IF!Q6a!== !2 !(T o w n h o u s e ,!R o w h o u s e !/!F iv ep le x !a n d !Sixplex!/!
Attached!Duplex.!Triplex,!or!Quadruplex!/!Stratified!SFD,!Bare!
Land!Strata!/!Semi-Detached!Strata!Condo!/!Modular!Home)!!
21.70%!
28.70%!
34.03%!
37.77%!
43.50%!
IF!Q6a!== !3 !(C o n d o !- !Townhouse!/!Mobile!Home!/!Condo!–!
Townhouse)!
18.23%!
24.17%!
28.77%!
31.77%!
36.63%!
!
!
If!Q0!is!from !British!Columbia!and!DOES!NOT!begin!with!V5K,!V5L,!V5M,!V5N,!V5P,!V5R,!V5S,!V5T,!V5V,!V5W,!V5Y,!V6A,!
V6B,!V6C,!V6E,!V6G,!V6H,!V6J,!V6K,!V6L,!V6M,!V6N,!V6P,!V6R,!V6S,!V6T,!V6Z,!V7G,!V7H,!V7J,!V7K,!V7L,!V7M,!V7N,!V7P,!
V7R,!V7S,!V7T,!V7V,!V7W,!V7X,!V7T!&!Q2==3,4,5,6!&!sex!is!Female!!
(Rest!of!British!Columbia!Single!Female)!
Age!
55-59!
60-64!
65-69!
70-74!
75-79!
IF!Q6a!== !1 ,!77 7 7 7 77 !(S in g le !Fa mily!Dwellin g !/!D e ta c h e d !
Duplex,!Triplex!or!Quadruplex!/!Link!Home!/!Semi-Detached)!
24.37%!
30.17%!
34.70%!
36.63%!
41.30%!
IF!Q6a!== !2 !(T o w n h o u s e ,!R o w h o u s e !/!F iv ep le x!an d!Sixplex!/!
Attached!Duplex.!Triplex,!or!Quadruplex!/!Stratified!SFD,!Bare!
Land!Strata!/!Semi-Detached!Strata!Condo!/!Modular!Home)!!
23.10%!
28.70%!
32.97%!
34.77%!
39.30%!
IF!Q6a!== !3 !(C o n d o !- !Townhouse!/!Mobile!Home!/!Condo!–!
Townhouse)!
19.43%!
24.10%!
27.83%!
29.30%!
33.10%!
!
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