THE COST OF CONFLICTING OBJECTIVES IN POLICY FORMULATION

This PDF is a selection from an out-of-print volume from the National Bureau

of Economic Research

Volume Title: Annals of Economic and Social Measurement, Volume 5, number 2

Volume Author/Editor: Sanford V. Berg, editor

Volume Publisher: NBER

Volume URL: http://www.nber.org/books/aesm76-2

Publication Date: April 1976

Chapter Title: The Cost of Conflicting Objectives in Policy Formulation

Chapter Author: Robert S. Pindyck

Chapter URL: http://www.nber.org/chapters/c10444

Chapter pages in book: (p. 239 - 248)

Annals

of

Economic

and

Social

Measurement,

5/2,

1976.

THE

COST

OF

CONFLICTING

OBJECTIVES

IN

POLICY

FORMULATION*

BY

ROBERT

S.

PINDYCK

By

applying

Nash

solution

strategies

for

a

linear-quadratic

discrete-time

differential

game

to

a

macroeconometric

model,

stabilization

policies

can

be

determined

for

the

case

when

fiscal

and

monetary

control

are

exercised

by

independent

authorities

who

have

conflicting

objectives.

Here

we

use

the

Nash

algorithm

to

calculate

the

increased

cost

to

each

authority

resulting

from

a

conflicting

objective

of

the

uther

authority.

These

results

can

be

applied

to

the

analysis

of

recent

monetary

and

fiscal

policy

in

the

United

States.

1.

INTRODUCTION

One

of

the

limitations

of

recent

applications

of

optimal

control

theory

to

economic

stabilization

policy

[3,

4,

5,

7,

10,

11,

12,

13,

14]

has

been

a

failure

to

account

for

the

fact

that

macroeconomic

control

in

the

United

States

is

decen-

tralized.

In

particular,

monetary

and

fiscal

policy

are

exercised

by

separate

authorities

that

are

largely

independent

of

each

other,

and

that

may

have

conflicting

objectives.

This

separation

of

monetary

and

fiscal

control

may

consid-

erably

limit

the

ability

of

either

authority

to

stabilize

the

economy,

particularly

when

the

conflict

over

objectives

is

at

all

significant.

Because

monetary

policy

operates

with

long

lags

and

fiscal

policy

with

short

lags,

the

proper

time-phasing

of

the

two

can

be

critical.

Thus

monetary

and

fiscal

policies

designed

with

different

objectives

in

mind

may

result

in

economic

performance

that

is

far

from

either

objective.

In

a

[15]

this

author

studied

the

problem

of

decentralized

policy

making

with

conflicting

objectives

by

calculating

open-loop

and

closed-

loop

Nash

strategies

for

a

linear-quadratic

discrete-time

differential

game,

and

applying

the

strategies

to

a

small

macroeconomic

model.

The

results

seemed

to

indicate

that

conflict

situations

could

indeed

result

in

a

deterioration

of

economic

performance,

particularly

in

the

short

term.

Of

course

Nash

strategies

are

based

on

a

restricted

set

of

assumptions

about

the

nature

of

the

conflict

and

the

characteristics

of

the

decision

making

processes,

and

alternative

assumptions

(e.g.

Stackleberg

strategies

or

more

complicated

strategies)

could

yield

different

results

about

the

effects

of

conflicting

objectives.

The

use

of

Nash

strategies,

however,

at

least

provides

a

first

approach

to

the

problem,

and

has

an

advantage

of

computa-

tional

tractability.

In

this

paper

we

review

the

approach

and

results

described

in

[15].

In

addition,

we

use

the

Nash

algorithm

and

the

small

econometric

model

to

calculate

the

increased

cost

to

each

authority

resulting

from

a

conflicting

objective

on

the

part

of

the

other

authority.

This

allows

us

first

to

quantify

the

“sub-optimality”

*Presented

at

the

Fourth

Annual

NBER

Conference

on

Control

Theory

and

Economics,

Cambridge,

Massachusetts,

May

21-23,

1975.

This

work

was

funded

by

the

National

Science

Foundation

under

Grant

No.

GS-41519.

The

author

acknowledges

the

helpful

comments

of

Y.

C.

Ho

and

two

anonymous

referees.

239

resulting

from

conflict,

and

second

to

better

determine

which,

if

any,

authority

(fiscal

or

monetary)

has

an

advantage—i.e.

is

better

able

to

reach

its

own

objectives.’

Finally,

we

evaluate

the

implications

of

these

results

for

mac-

roeconomic

policy.

2.

STABILIZATION

POLICIES

UNDER

DECENTRALIZED

CONTROL

Our

analysis

begins

with

the

assumption

that

each

authority

arrives

at

its

policy

using

the

same

econometric

model

(i.e.

each

has

the

same

view

of

the

way

the

world

works),

but

that

the

two

have

different

sets

of

objectives.

The

economet-

ric

model

is

linear,

so

that

we

can

represent

it

in

state

variable

form

as

(1)

X41

—

X,

=

Ax,

+

By

u;,

+

Bou2,

+

Cz,

with

initial

condition

x9

=

€.

Here

x,

is

a

vector

of

n

state

variables,

u,,

and

u2,

are

vectors

of

r;

and

r2

control

(policy)

variables

manipulated

by

the

fiscal

and

monetary

authorities

respectively,

and

z,

is

a

vector

of

s

uncontrollable

exogenous

variables

whose

future

values

are

known

or

can

be

predicted.

A,

B,,

B2,

and

C

are

nXn,nXr1,nXr2,

and

n

Xs

matrices

respectively.

Each

authority

chooses

an

optimal

trajectory

(a

“‘strategy”’)

for

its

own

set

of

control

variables

over

the

time

period

t=0,1,...,

N—1.

The

first

authority

chooses

its

strategy

{u;,}

to

minimize

its

cost

functional

N-1

(2)

Jy

=

1/2(xn

—

£1)’

Qi

(en

—

£1n)

+

1/2

y

{(x,—¥1,)'Qi(%,

—

£1.)

+

(uy,

—

Gy.)

Riy(ua,

—

Gy.)

+

(U2,

—

Ga,)'

Ri2(U2:

—

b2,)}

and

the

second

authority

chooses

its

strategy

{u2,}

to

minimize

its

cost

functional

N-1

(3)

Jn

=1/2(xn

—

£2n)'Q2(xn

—

£2)

+

1/2

y

{(x;

—

£2)’

Qo(x;

—

£24)

+(Uy,—

&,)'

Roi(ui,

—

Gy.)

+

(U2,

—

fi2,)’

Ro2(u2,

—

G,)}.

Here

£,,

and

£2,

represent

nominal

(desired)

values

for

the

state

variables

from

the

points

of

view

of

authorities

1

and

2

respectively,

and

similarly

@,,

and

2,

represent

nominal

values

of

the

control

variables

for

each

authority.

The

matrices

Q,

and

Q,

represent,

for

each

authority,

the

relative

weights

assigned

to

devia-

tions

from

the

nominal

paths

for

each

state

variable,

and

R,,

and

R,

designate

the

relative

weights

that

each

authority

assigns

to

deviations

from

the

nominal

path

for

its

own

control

variables.

R,2

and

R2,;

designate

the

relative

weights

that

each

authority

assigns

to

deviations

from

the

nominal

path

for

the

other

author-

ity’s

control

variables;

thus

these

matrices

indicate

how

important

it

is

for

each

authority

that

the

other

authority

stay

close

to

its

policy

variable

targets.”

If

R12

is

‘In

[15]

it

was

found

that

relative

advantage

depended

considerably

on

the

particular

objectives

over

which

the

conflict

arises.

Here

we

will

consider

only

the

objectives

of

reducing

the

unemployment

rate

and

reducing

the

rate

of

inflation.

A

non-zero

element

in

one

of

these

matrices

might

indicate,

for

example,

that

the

monetary

authority

considers

it

somewhat

important

that

the

fiscal

authority

keep

government

spending

close

to

the

target

path

for

government

spending

specified

by

the

fiscal

authority.

240

large

(relative

to

Q,

and

R;,)

then

authority

1

will

design

its

strategy

so

as

to

force

authority

2

to

keep

its

policy

variables

close

to

their

nominal

paths.*

The

deterministic discrete-time

differential

game

described

above

can

be

“played”

in

two

alternative

ways:

(a)

Each

authority

designs

its

optimal

policy

(based

on

its

own

objectives)

at

the

beginning

of

the

planning

period,

and

then

sticks

to

that

policy

throughout

the

entire

planning

period.

This

is

called

an

open-loop

strategy.

In

effect,

the

optimal

controls

uj,

and

u3,

depend,

at

any

time

t¢,

on

the

initial

condition

Xp.

(b)

Each

authority

designs

a

control

rule

at

the

beginning

of

the

planning

period,

and

then

uses

that

control

rule,

together

with

observations

of

the

state

of

the

economy,

to

continuously

revise

his

policy.

‘This

is

called

a

closed-loop

strategy.

In

this

case

the

optimal

controls

uf,

and

u3,

depend

on

the

current

state

x,.

The

closed-loop

strategy

should

not

be

confused

with

the

notion

of

closed-

loop

optimal

control

in

the

centralized

case.

Our

planning

problem

is

determinis-

tic,

so

that

closed-loop

behavior

implies

adaptation

not

to

the

impact

of

random

shocks,

but

rather

to

the

evolving

strategy

of

the

other

authority.

A

closed-loop

strategy

for

a

particular

problem

may

differ

considerably

from

an

open-loop

strategy,

since

it

is

arrived

at

under

a

very

different

set

of

assuraptions.

Note

also

that

the

matrices

R,2

and

R>,;

are

relevant

only

to

closed-loop

strategies

Non-zero

values

for

these

matrices

imply

that

one

authority

will

try

to

influence

the

policy

of

the

second.

In

the

open-loop

mode

the

two

authorities

cannot

influence

each

other’s

policies,

and

R,2

and

R2,

do

not

appear

in

the

open-loop

solutions.

3.

NASH

SOLUTION

STRATEGIES

Nash

solutions

to

this

differential

game

are

defined

as

the

trajectories

(u*,

ux)

that

satisfy

the

conditions:

(4)

J,(ut,

ut)

=

Jy(uy,

ud)

and

(5)

J(uF,

u3)=<J,(ut,

U2)

for

all

possible

u,

and

u2.

Nash

solution

algorithms

for

both

the

open-loop

and

closed-loop

cases

have

been

derived,

and

are

described

in

detail

elsewhere

[15].

It

is

important

to

point

out

that

Nash

solutions

need

not

be

unique.

Friedman

[6]

“proved”

the

uniqueness

of

Nash

solutions

for

deterministic

two-person

decision

problems

with

linear

state

dynamics

and

quadratic

cost

criteria,

but

in

so

doing

he

ignored

the

fact

that

alternative

assumptions

can

be

made

regarding

memory

restrictions

on

the

controls.

As

Basar

[1]

recently

demonstrated,

these

alternative

assumptions

can

result

in

different

Nash

equilibrium

solutions.

For

Some

restrictions

must

be

placed

on

the

matrices

Q,, Q2,

R;,,

and

R22.

We

assume

that

Q,

and

Q,

are

positive

semi-definite,

and

that

R,,

and

R>,

are

positive

definite.

We

put

no

restrictions

on

Rj»

and

R>,;.

For

most

economic

problems

all

of

these

matrices

will

be

diagonal,

although

it

is

not

essential

that

this

be

the

case.

241

example,

the

open-loop

solution

assumes

that

the

controls

u;,

and

u2,

depend

only

on

the

initial

state

xo,

while

the

closed-loop

solution

typically

assumes

that

u;,

and

uz,

depend

only

on

the

current

state

x,

One

might

instead

assume

a

dependence

of

the

controls

on

last

period’s

state,

or

on

some

weighted

average

of

past

states.

These

assumptions

would

generally

yield

different

solutions,

so

that

there

might

not

be

a

single

Nash

equilibrium.*

In

applying

Nash

solution

strategies

to

the

problem

of

economic

stabilization

policy,

it

seems

most

reasonable

to

work

only

with

the

simple

open-loop

and

closed-loop

cases,

calculating

strategies

based

on

the

usual

linearity

and

(in

the

closed-loop

case)

“‘no

memory”

restrictions.

The

point

here

is

that

our

objective

is

neither

to

predict

nor

prescribe

monetary

and

fiscal

policies

for

two

conflicting

authorities;

rather

it

is

to

use

the

Nash

solution

concept

as

a

tool

to

analyze

the

characteristics

of

conflicting

policies

and

the

characteristics

and

degree

of

degra-

dation

in

economic

performance

that

results

from

conflict.

In

performing

this

exercise

we

must

keep

‘a

mind

that

we

are

considering

only

one

particular

set

of

Nash

solutions,

and

alternative

assumptions

could

yield

different

Nash

solutions—just

as

alternative

formulations

of

the

basic

conflict

model

could

yield

different

non-Nash

solutions

(see

[15]).

We

must

leave

to

future

research

the

problem

of

how

alternative

assumptions

effect

the

characteristics

of

the

solutions.

The

effect

of

a

conflict

situation

on

macroeconomic

performance

was

studied

by

applying

the

open-loop

and

closed-loop

Nash

algorithms

described

above

to

a

small

linear

econometric

model.”

Despite

the

size

and

simplicity

of

the

model,

the

results

do

illustrate

some

of

the

general

characteristics

of

decentralized

policies

and

some

of

the

general

implications

of

conflicting

objectives.

We

found,

for

example,

that

when

the

conflict

is

between

unemployment

and

inflation,

the

fiscal

objectives

will

be

more

nearly

met.

This

is

particularly

the

case

in

the

closed-loop

mode,

and

is

a

result

of

the

longer

lag

inherent

in

monetary

policy.

Certain

targets,

however,

can

be

reached

only

by

a

particular

authority;

rapid

increases

in

residential

investment,

for

example,

will

not

be

achieved

unless

it

is

an

Objective

shared

by

the

monetary

authority

or

is

indirectly

linked

to

some

other

monetary

objective.

In

addition,

the

results

indicated

that

the

“‘suboptimal-

ity”

resulting

from

a

conflict

situation

could

indeed

be

severe,

but

only

in

the

first

four

to

six

quarters

of

the

planning

period.

After

about

six

quarters

a

““comprom-

ise”’

behavior

begins

to

occur

where

neither

authority

is

as

close

to

its

targets

as

it

would

be

in

a

cooperative

situation,

but

there

are

no

wide

deviations

from

targets

as

a

result

of

time-phasing

problems

arising

from

the

conflict.

None

of

these

results

are

particularly

surprising

(which

reinforces

the

mean-

ingfulness

of

Nash

solution

strategies).

It

makes

intuitive

sense,

for

example,

that

“Assumptions

can

also

be

made

regarding

a

nonlinear

dependence

of

the

controls

on

current

and

past

states,

and

this

will

also

result

in

different

Nash

solutions.

For

a

discussion

of

this

problem,

see

Basar

[1].

*The

resuits

are

described

in

[15].

The

model

was

constructed

and

used

by

this

author

in

earlier

studies

of

optimal

stabilization

policies,

and

is

described

in

detail

in

[13].

The

model

contains

nine

behavioral

equations

that

explain

consumption,

nonresidential,

residential,

and

inventory

investment,

short

and

long-term

interest

rates,

the

price

level,

the

unemployment

rate,

and

the

money

wage

rate,

as

well

as

a

single

tax

relation

and

an

income

identity.

Fiscal

control

is

exercised

through

government

expenditures

(the

model

contains

a

surtax

as

a

second

fiscal

policy

variable,

but

this

is

fixed

at

zero

in

order

to

simplify

the

experiments),

and

monetary

control

through

the

money

supply.

242

over

time

a

conflict

in

objectives

would

be

“‘resolved”

by

implicit

compromise.

Macroeconomic

policy,

however,

is

often

designed

with

rather

short

time

horizons

in

mind,

and

objectives

may

change

from

year

to

year.

Thus

there

is

little

consolation

in

the

fact

that

economic

performance

suffers

the

most

from

conflict-

ing

objectives

only

in

the

first

year

or

so.

It

would

be

useful

to

measure

the

economic

“‘cost”’

of

conflicting

objectives;

if

that

“‘cost’’

is

high

it

might

suggest

the

desirability

of

institutional

changes

that

would

result

in

better

fiscal-monetary

coordination.

4.

THe

Costs

oF

CONFLICTING

OBJECTIVES

Fhe

costs

of

one

or

another

economic

“trajectory”

have

meaning

in

the

context

of

particular

objectives;

if

a

low

unemployment

rate

is

a

policy

objective,

then

a

cost

can

be

associated

with

a

high

unemployment

rate.

When

optimal

economic

policies

are

calculated

in

the

centralized

case,

costs

are

specified

through

a

scalar-valued

cost

functional,

and

the

policies

are

considered

optimal

in

that

the

cost

functional

is

minimized.

Presumably

the

cost

functional

reflects

the

overall

objectives

of

the

groups

or

individuals

who

determine

or

influence

economic

policy

(although

it

might

not

reflect

the

objectives

of

a

majority,

or

even

any

part,

of

the

population).

When

control

is

decentralized

and

objectives

differ

it

is

not

meaningful

to

associate

a

single

“cost”

with

a

particular

economic

trajectory.

In

the

context

of

our

analysis,

each

authority

will

associate

its

own

cost

with

any

economic

trajectory,

and

that

cost

is

specified

by

the

authority’s

own

cost

functional.

We

therefore

measure

the

costs

of

conflicting

objectives

for

each

authority,

and

see

how

those

costs

depend

on

the

policy

(i.e.

the

extent

of

conflict)

of

the

other

authority.

We

will

examine

a

single

example

of

conflict—the

fiscal

authority

wishes

only

to

reduce

the

rate

of

inflation

(so

that

Q,

has

a

weight

only

on

the

price

level),

while

the

monetary

authority

wishes

only

to

reduce

the

unemployment

rate

(so

that

Q,

has

a

weight

only

on

that

variable).

(The

costs

for

other

conflicts

are

likely

to

be

quite

different,

but

our

main

purpose

here

is

simply

to

illustrate

an

approach

to

the

problem.)

We

are

interested

in

how

the

cost

to

each

authority

increases

as

the

other

authority

has

increasing

flexibility

to

pursue

its

own

conflicting

objective.

We

therefore

evaluate

the

cost

functionals

J,

and

J,

as

follows.

First,

the

money

supply

is

tied

to

its

nominal

path

(by

attaching

a

large

weight

to

it

in

R22)

while

government

spending

is

allowed

to

move

with

relative

flexibility

(a

low

weight

is

attached

to

it

in

R;,).

Nash

solutions

are

determined

for

the

econometric

model,

and

J,

is

evaluated.

Next,

the

money

supply

is

allowed

to

move

somewhat

more

freely

by

reducing

its

weight

in

R22,

and

J,

is

again

evaluated.

This

is

repeated

several

times,

each

time

reducing

the

weight

of

the

money

supply

in

R22,

until

the

money

supply

is

given

as

much

flexibility

as

is

government

spending.

The

above

steps

are

repeated

for

the

monetary

authority,

i.e.

J>

is

evaluated,

first

with

government

spending

tied

to

its

nominal

path,

and

then

with

government

spend-

ing

allowed

to

move

more

and

more

freely.

The

Nash

strategies—and

resulting

economic

trajectories—are

calculated

over

a

time

horizon

of

twenty

quarters,

beginning

with

1957-I

and

ending

with

243

1962-I.

The

nominal

trajectories

{%,,}

and

{%2,}

are

taken

to

be

the

same

for

both

authorities,

so

that

differences

in

objectives

are

expressed

by

assigning

different

weights

in

Q;

and

Q,.

This

is

done

only

to

simplify

the

example;

it

is

reasonable

to

expect

different

authorities

to

have

different

nominal

trajectories.

In

particular,

the

price

level

is

assigned

a

weight

of

120

in

Q,,

and

the

unemployment

rate

is

assigned

a

weight

of

4

x

10’

in

Q,

(all

other

coefficients

in

Q,

and

Q,

are

zero).

These

weights

are

equivalent

in

terms

of

percentage

deviations

(squared)

from

mean

values.

For

the

nominal

trajectories

{i,,}

and

{#2,}

we

take

a

four

percent

annual

rate

of

growth

for

government

spending

(in

real

terms)

and

a

four

percent

rate

of

growth

in

the

money

supply.

The

matrices

R,2

and

R2,;

are

set

equal

to

zero.

All

of

the

solutions

are

calculated

under

open-loop

assumptions.

This

was

Gone

partly

to

minimize

computational

expense,

but

also

because

the

open-loop

assumption

is

most

basic,

and,

in

the

case

of

short-term

policy,

probably

the

most

realistic.

Overall

directions

in

monetary

policy,

and

certainly

fiscal

policy

are

not

usually

adjusted

from

quarter

to

quarter.°

The

results

are

summarized

in

Table

1.

Note

that

the

cost

to

the

fiscal

authority

of

monetary

“dissension”

is

quite

small;

J,

increases

by

only

about

4%

between

runs

Al

and A7.

The

cost

of

a

conflict

to

the

monetary

authority

can

be

much

higher

however;

J,

more

than

doubles

between

runs

B1

and

B7.

As

the

fiscal

authority

is

given

more

flexibility

it

reduces

government

spending

(Figure

1)

so

as

to

reduce

increases

in

the

price

level

(Figure

2).

The

monetary

authority

incurs

added

costs

as

it

attempts

to

compensate

by

increasing

the

money

supply

more

rapidly

(Figure

3)

and

as

the

unemployment

rate

becomes

higher

(Figure

4).

TABLE

1

Cost

INCREASES

FOR

FISCAL

AND

MONETARY

AUTHORITIES

Run

#

R,,(G)

R22(4M)

J

J,

Al

30

1.5x10*

1.000

A2

30

5000

1.001

A3

30

1500

1.004

A4

30

800

1.008

AS

30

400

1.017

A6

30

200

1.032

A7

30

150

1.041

Bi

1x

10°

150

1.000

B2

3x10

150

1.001

B3

3000

150

1.017

B4

800

150

1.066

BS

300

150

1.176

B6

80

150

1.636

B7

30

150

2.470

(Note:

The

numbers

for

J,

and

J,

have

been

normalized

as

the

ratio

to

their

values

in

runs

Ai

and

B1

respectively.

In

all

cases

Q,(P)

=

120

and

O,(UR)=4x

10’.)

*It

might

be

pointed

out

that

an

equilibrium

Nash

solution

in

the

class

of

open-loop

strategies

is

also

an

equilibrium

Nash

solution

in

the

class

of

closed-loop

strategies.

In

particular,

the

open-loop

strategy

is

that

closed-loop

strategy

with

the

particular

memory

restriction

that

the

controls

depend

only

on

the

initial

state

x9.

Of

course

in

our

calculation

of

closed-loop

strategies

we

assume

the

memory

restriction

that

the

controls

depend

only

on

the

current

state

x,.

°

244

a

110

F

.

61,62

-

Nominal

100

+

B4

B6

OO

TLL

II

57

58

59

60

61

120

-

110

F-

100

F-

Figure

1

Government

spending

.

..

Runs

B1

to

B6

B1,

B2,

B3

B4

Nominal

LELE

TITEL

58

59

60

61

Figure

2

Price

level

245

0.06

0.05

0.04

0.03

0.02

Nominal

oe

eee

Li

TTT

Vivre

rieereee

TTTTITTITTITITIT

ITT

TT TT

58

59

60

61

Figure3

Quarterly

change

in

money

supply

[>

B6

BS

B4

B3

B1,

B2

Nominal

eS

ee

Rae

Ee

uo

~

58

59

60

61

Figure4

Unemployment

rate

246

The

difference

in

relative

costs

is

not

due

to

the

fact

that

for

the

particular

econometric

model

used

here

the

fiscal

multipliers

are

considerably

larger

than

the

monetary

multipliers;

this

was

already

accounted

for

in

setting

the

relative

weights

in

R,;,

and

R22.

The

major

reason

for

the

difference

is

the

longer

time

lag

inherent

in

monetary

policy.

Several

quarters

must

pass

before

changes

in

the

money

supply

have

any

effect

on

GNP

(and

the

unemployment

rate),

so

that

the

fiscal

authority

is

more

“cost-effective”

in

reaching

its

targets.

(The

difference

would

be

even

larger

if

the

solutions

were

computed

using

the

closed-loop

algorithm.)

One

should

not

conclude

from

these

results

that

monetary

policy

is

ineffec-

tive

and

that

there

is

no

cost

from

conflicting

objectives

as

long

as

you

hold

the

same

view

as

the

fiscal

authority.

To

begin

with,

a

conflict

can

involve

certain

target

variables

over

which

the

monetary

authority

has

greater

control

(e.g.

residential

investment),

and

in

this

case

the

fiscal

authority

will

incur

the

greatest

cost

from

the

conflict.

However,

even

when

the

conflict

is

focused

on

the

trade-off

between

inflation

and

unemployment,

as

it

was

here,

it

may

in

fact

result

in

high

costs

to

both

authorities.

The

reason

is

that

the

specification

of

our

experiments

has

in

a

way

stacked

the

deck

in

favor

of

the

fiscal

authority.

For

while

it

is

true

that

monetary

policy

operates

with

longer

lags

than

fiscal

policy,

it

is

also

the

case

that

fiscal

variables

(government

spending,

taxes)

cannot

be

manipulated

as

frequently

and

as

freely

as

monetary

variables.

The

limitation

on

the

ability

of

the

fiscal

authority

to

manipulate

its

policy

variables

would

probably

reduce

significantly

the

fiscal

“‘advantage”’

that

we

observe

in

Table

1.

It

would

be

interesting

to

repeat

the

analysis,

but

constraining

government

spending

so

that

it

can

change

in

value

only

once

per

year,

while

the

money

supply

is

allowed

to

change

more

frequently

(quarterly

or

monthly).

Unfortunately,

when

the

problem

is

framed

this

way,

a

solution

becomes

much

more

difficult

to

obtain.

I

expect,

however,

that

were

a

solution

to

be

obtained,

it

would

indicate

that

the

costs

of

conflicting

objectives

can

be

high

for

both

authorities.

Our

results

are

probably

too

preliminary

to

provide

specific

conclusions

about

the

effectiveness

of

recent

fiscal

and

monetary

policy.

The

fiscal-monetary

conflict

over

inflation

and

unemployment

during

1974

and

early

1975

is

a

good

example

(in

reverse)

of

the

hypothetical

conflict

that

we

created

as

an

example

for

this

paper.

During

these

recent

years,

however,

the

fiscal

authority

did

not

enjoy

the

advantage

that

our

results

would

have

indicated.

Better

insight

into

recent

fiscal-monetary

conflicts

might

be

obtained

if

the

approach

of

this

paper

were

extended

in

several

ways.

First,

as

suggested

above

it

is

necessary

to

account

for

the

relative

inflexibility

of

fiscal

policy.

Second,

the

analyses

should

include

the

changes

in

policy

objectives

that

occur

on

an

irregular

but

frequent

basis.

Finally,

large

and

more

realistic

econometric

models

should

be

used,

allowing

for

both

a

richer

description

of

economic

structure

and

the

inclusion

of

a

more

complete

set

of

policy

variables

and

parameters.

Massachusetts

Institute

of

Technology

247

REFERENCES

[1]

T.

Basar,

“A

Counter

Example

in

Linear

Quadratic

Games:

Existence

of

Non-linear

Nash

Solutions,”

Journal

of

Optimization

Theory

and

Applications,

Vol.

14,

No.

4,

1974.

[2]

C.

Y.

Chong,

“On

the

Decentralized

Control

of

Large-Scale

Systems,”

MIT

Electronic

Systems

Laboratory,

Technical

Report

ESL-R-503,

June,

1973.

[3]

G.

C.

Chow,

“How

Much

Could

be

Gained

by

Optimal

Stochastic

Control

Policies,”

Annals

of

Economic

and

Social

Measurement,

October,

1972.

[4]

J.

P.

Cooper

and

S.

Fischer,

“A

Method

for

Stochastic

Control

of

Non-Linear

Econometric

Models

and

an

Application,”

Econometrica,

January,

1975.

[5]

R.

C.

Fair,

“On

the

Solution

of

Optimal

Control

Problems

as

Maximization

Problems,”

Princeton

University

Econometric

Research

Memorandum,

No.

146,

February,

1973.

[6]

A

Friedman,

Differential

Games,

John

Wiley

and

Sons,

New

York,

1971.

[7]

B.

M.

Friedman,

Methods

in

Optimization

for

Economic

Stabilization

Policy,

North-Holland

Publishing

Company,

1975.

[8]

Y.

C.

Ho,

“Differential

Games,

Dynamic

Optimization

and

Generalized

Control

Theory,”

Journal

of

Optimization

Theory

and

Applications,

September,

1970.

[9]

Y.C.

Ho

and

K.

C.

Chu,

“Team

Decision

Theory

and

Information

Structures

in

Optimal

Control

Problems—Part

1,””

IEEE

Transactions

on

Automatic

Control,

February

,

1972.

[10]

R.

S.

Holbrook,

“A

Practical

Method

for

Controlling

a

Large

Non-Linear

Stochastic

System,”

unpublished

paper,

May,

1973.

[11]

D.

Kendrick

and

J.

Majors,

“Stochastic

Control

with

Uncertain

Macroeconomic

Parameters,”

unpublished

paper,

1973.

[12]

D. A.

Livesey,

“Optimizing

Short-Term

Economic

Policy,”

Economic

Journal,

September,

1971.

[13]

R.

S.

Pindyck,

Optimal

Planning

for

Economic

Stabilization,

North-Holland

Publishing

Com-

pany,

Amsterdam,

1973.

[14]

R.

S.

Pindyck,

“Optimal

Policies

for

Economic

Stabilization,’

Econometrica,

May,

1973.

[15]

R.

S.

Pindyck,

“Optimal

Stabilization

Policies

Under

Decentralized

Control

and

Conflicting

Objectives,”

MIT

Sloan

School

Working

Paper

No.

765-75,

January,

1975.

[16]

A.

W.

Starr

and

Y.

C.

Ho,

“Nonzero-Sum

Differential

Games,”

Journal

of

Optimization

Theory

and

Applications,

Vol.

3,

No.

3,

1969.

248