Robustness properties of a rule for monetary policy

Carnegie-Rochester Conference Series on Public Policy 29 ( 1988) 173-204 North- Holland

ESS PROPERT

R

and National Bureau of Economic Research

In a recent paper ( ccallum, 1987) I described, and began to explore the properties of, a specific rule for the conduct of monetary policy- This rule, which reflects ideas expressed in earlier writings by Allan (1984) and myself (1984), prescribes settings for the monetary base that are intended to keep nominal aggregate demand growing smoothly at a noninflationary rate.

The policy strategy represented by this rule is one

that is not open to objections frequently expressed by opponents of monetary rules, as it is fully operational and is designed to be insensitive to regulatory

changes

and

technological

innovations

in

the

payments

and

financial industries. The investigation begun in my previous paper is intended eventually to indicate whether above.

in fact the rule has the robustness properties claimed

In McCallum (1987) it was suggested that the rule would, if it had

been in effect, have kept nominal GNP for the United States close to a smooth target growth path over the period 1954-1985 despite the regulatory and financial turmoil that occurred during the latter part of thaL ;rpriod. But evidence for that suggestion was based upon one extremely simple model of nominal GNP determination and the associated set of implied random-shot estinates. To establish robustness -- which

is important since no SatiS-

factory structural model of the economy is in existence or on t MB it

ould also have perfor

needs to be determined Ghelher the rule

ell during 1954-85 actor

*The Henderson, pdrticipants

author

is

Finn

Mydland,

Robert

helpful

criticism.

for

0 167 - 2231/88/$3.50

indebted

ss

to

Cagan,

Phillip

Lucas,

@ 1988 Elsevier Sciewp

John

Robert

laylot=,

Publishers

and

B.V.

Flood, other

Benjamin

Carnegie

(North-Holland

Friedman,

Rochester

Dale

Confereme

expressing

different

views concerning

The

macroeconomic relationships.

purpose of the present paper is to provide evidence of precisely that type. To that end, the paper begins in Section II with a review of princiThen in Section III

ples and previous work.

evidence concerning the rule's

performance is reported for a variety of vector-autoregression (WAR) models -- VARs with different sets of included variables. In Section IV, attention is shifted to models that represent the profession's attempts to develop structural representations of the economy's workings. In particular, models are specified that represent three competing points of view regarding the the real business cycle view, the

nature of macroeconomic fluctuations: Lucas-Garro

monetary

misperceptions

view,

and

a

more

Keynesian

Estimates of

involving Phillips-type wage adjustments and markup pricing. such

models

are

reported

and

used

indicate, as with the VAR models, effective over

1954-85,

as

the

basis

for

view

simulations

that

hether the policy rule would have been

Section V contains results of three additional

investigations, ones designed to shed light on issues relating to (i) the Lucas critique, (ii) initiation of the rule under unfavorable conditions, and (iii) an alternative rule proposed by Meitzer (1984).

Conclusions are

briefly summarized in Section VI.

D PREVIOUSRESULTS Let

us

begin

the

discussion

with

a

brief

review

of

strategic

principles concerning the specification of a monetary policy rule.' most

fundamental

of

the

four

principles

stressed

in

involves the current state of macroeconomic knowledge.

McCallum

The

(1987)

In this regard the

crucial point is that neither theory nor evidence points convincingly

to

any one of the many competing models of the dynamic interaction between nominal and reaP variables.

1

It

wi 1 I

he

presumed

monetary

pol ir

: according

average)

than

bo7uld obtain

no

less

Prescott

that to

As is illustrated by several recent survey

there

some rule, with

no

need

to

namely,

is

that

it

“discretionary”

period-by-period

emplOyWnt (1977)

review tc.r.ls

the to

rationale

result

in

conducting

inflation

decision-making

OrO~JtpUt. This tendency was recognized in the analysis whose wopk ‘“3s usefully extended by &r-r0 and Cordon (1983).

174

for less

-of

and

Kydland

(On with and

2 articles,

the

macroeconomics

profession

has

not

produced

a

reliable

quantitiative (or even qualitative) model of Phillips-curve or aggregatesupply behavior.

In other words, there

predictions concerning the way nominal GNP

ill be

divided

in

is very

little basis

for

any

hich quarterly or annual changes

between

real output growth

and

in

inflation.

Consequently, a policy rule's design should not be predicated

upon any

particular model of that division.3 At

the

same time, however, theory and evidence

validity of

the natural

rate

hypothesis,

Le.,

both

to

the

point

to

the

absence

of

any

permanent tradeoff relating inflation (or money growth) and output levels or growth rates.4 Over long spans of time, in other words, output and employment levels will be essentially independent of the averdqe rate of growth of nominal variables.5 The

combination

of

ignorance

and

knowledge

expressed

in

the

t

preceding paragraphs leads rather naturally to the first ingredient of my proposed policy rule, which is a target path for nominal GNP6 that grows steadily at a prespecified rate that equals the economy's prevailing longterm average rate of real output growth. For the United States, upon which the present discussion will focus, the figure is about 3X per year.

Since

that azgnitude will, according to the natural rate hypothesis, be virtually independent of vinetary policy over any extended period of (say) 20 years or more, keeping nominal GNP growth at the indicated 3% rate should yield approxirrrately zero inflation over such a period. Furthermore, there is some

2

These

include

3 his

feature

concerning

that

by Phillips

the

4The

present exists

(1957),

Dotsey

approach of

sets

it

monetary

a rich

literature

Bronfenbrenner

( 987),

and King

(1961),

apart

and McCallum

fron

much of It

policy

rules.

on that

subject

Fiscrlsr

the

previous

should

which

and Cooper

(1988).

be

includes

(1973),

ana 1ys

is

mentioned,

notable

Friedzqn

items (1975).

and many others.

hypothesis or

(1988),

properties

there

(1954)

(1981),

cons tant

of

stabilizing

nevertheless,

Tay or

Blanchard

does

not

of

past

independent

claim,

it

might

be

noted,

that

t-ate

,3turai

the

is

itself

conditions.

c

‘ik effects bel ieve than

inflation

to

be quite

by affecting 6

Some

i ncome, of

rl;.Sl if ier of

the

or

other final

present

‘Fesjeniiai cn

the

smal I, the

paper

alter

average

measure sales

-v iewe

ly9’ size

inserted the

output

level

of

is of

of

nominal

might that

allow

for

discrepancy

aggregate

activity

as a matter

175

of

possibility

--

actual such

(1935)

adliiinistrative

has

of

which

effects,

by changing between

as Go Ion

be ignored.

the

These

stock.

and employment the

be preferable, Iscue

to

capital

natural-rate

T&in

nominal

suggested. det3i

I that

analysts

values

and natural-rate ab

(1!%5i

most

GDP,

rather values. personal

The discussIon can

Initial\y

reason to believe that the prevention of fluctuations in nominal GNP growth would help to prevent swings in output away from its natural-rate path.7

In this case, steady growth of nominal GNP at 3% per year would help to reduce cyclical fluctuations in output as well as to prevent inflation. Our specification of a smooth, noninflationary target path for nominal GNP is of course related to policy proposals for "nominal GNP targeting" that have been put forth in recent years by Gordon Taylor

(1985), Tobin

(1985), Hall

(1983),

The present proposal

(1983), and others.

differs

significantly from these earlier suggestions, however, in its emphasis on an operational -mechanism for achieving the specified targets--i.e., keeping nominal GNP ciiose to the 3% target path.

for

Thus the present proposal

conforms to the third of the strategic principles referred to above, which is that a policy rule should specify settings of an instrument variable The

that the monetary authority can control directly and/or accurately. rationale for this principle is entirely straightforward:

to specify the

behavior of some magnitude

(such as PO1 or M2, for example) that controllable is to leave the rule seriously incomplete.8

is not

A fourth principle is that the rule should not 1d.y upon the absence of regulatory change and technical innovation in the payments and financial industries. turmoil

While these processes are perhaps unlikely to produce as much

in the

future

as

they

have

in the recent

past,'

it would

be

unreasonable and unnecessary to presume that they will not be present again to a significant extent, In light of the last two principles, it is rather natural to adopt as an operating instrument the monetary base, which is a variable that can be accurately

‘In the

particular,

1954-85

greater

8The

9

to

One

lead escape

on

a day-to-day basis 3y the central bank of any

quarterly

(seasonally

than

different

that

set

rates data

cf

real

for

thL

and nominal U.S.,

GNP are

the

hiahly

correlated.

In

correlation

is

contemporaneous

0.80.

use

of

Ml

type

of

strategy.

reason to

growth

adjusted)

for

inflation,

Lcr+nin

or

MZ 2s

this

conjecture

which

regulaf’ons.

an

raises lhis

“indicator”

is

that

nominal point

variable,

the

processes

i-terest has

been

among others.

176

rather

rates stressed

than

are and

in

a

part

thereby by

target,

Brunner

induct?

enhances

represents

b‘; the

and Meftzer

Y?: ;cieS +rbcentive (1983),

a

nation.lo l1

Thus in my 1984 paper it was suggested that a desirable rule

ould adjust the base growth rate each month or quarter, increasing the rate if nominal GNP is below its target path, and vice versa" (1984, p. 390). After

an unfrrtunate delay,

begun recently. eltzer

led

investigation of

that suggestion was

A brt of experimentation and some discussions with Allan a slightly modified version of the rule, 12 which was

to

proposed in concrete quantitative form in McCallum (1987). of the monetary base, xt'

of

bt = log

xt = target-path value

Then the proposed rule for quarterly base growth rates can be

as:

written

O-00739 - (1/16)[xt l-xt 17-bt l+bt_L7] + ~(x; I-~t ,),

=

abt

xt = log of nominal GNP, and

Let

(1)

with x non-neg.itive, In expression (1) the constant term 0.00739 is simply a 3% annual growth rate expressed in quarterly logarithmic units, whrle the second term subtracts from this the average growth rate of base velocity

‘°Controllabilit7 advocated the

Fed

banks’

can

figure

taken

the

base

“There to to

of

interest

not

rate

indicate

that

the

direction

extremely

unclear

specify

settings

12

The

alqebraical

experimentation form would ru;2

in be

interest

(1).

unsatisfactory

oroposed

by Meltzer

rate

suggestion a!

,

+

that

that It and

this

should that

(1984)

be the

and

are

rate, the

rule

than

form

more

noted

that

first

two

if

a

can

the

be

level

of

interest

increased

rate,

nominal

feasible objection

seems to be

below

(for

rates,

would

take

if

the

which

Consequently,

discussions.

as

principle

is

W’

reported interest

below)

in

An important

to

those

available

lar

it

it

is is

were

to

an aggr;Ldte.

i3

pap”r

with is

action

thus

be sini

below.

(1)

and

Then

keep

and

connection

to

that

outstanding

sheet.

Fed can

would

to

long

is

a month.

some other

policy

1984

my

I-~t_l),

(1987).

in

the

controllable

by

who has

open-market

(e.g.1

analogous

(anafwous

rather

of

described

be enhanced

pre sumed

own balance

aggregate or

one

(19691,

rely own argument on currency

its

manner,

quantitative

would

in

A(x;

this

Regressions

GNP growth a simple

=

funds

that

on

periods that

Meltzer

a corrective

some reserve from

base.

form

an

Abt

is

the

usually

indicated

equation

rule

effect

what of

as

federal

for

qualitative ly

the

nominal of

variables

different

instrument than

in over

by

instrument.

frequently,

items

value,

path

of

an

more

are

operating

otner

as

even

which

desired

adoption

Use of

a very

complex

the

The

or

of

discussed

base

rule-prescribed

course,

base.

require

much more base)

of

the

daily, both

the

to

briefly

use

By continually close

are, the

would an

day.

was

that

Fed,

from

instruments.

use

but

the

differs

extremely

potential

base

observations

with

next

the

procedures

collect

deposits

day’s the

of

operating

s;mbols susceptible

Lindsey term-,

tn

in

might

,-luation

to dynamic

(1986) (1)

thd i

one as

conjectured

correspond

to

be

(1) ;-+taL;lity that the

expressed Brief

below. than the

1984

infldtioc-tdrget

the form

Finally, the third term adds a feedback

over the previous four years. l3

adjustment in response to departures of GNP from the target path. The value of

should be large enough to provide adequate responsiveness of base

x

growth to target misses but small enough to avoid dynamic instability of the type that can obtain when feedback responses are too strong. In my 1987 a

paper,

value

of

0.25

was

tentatively

suggested

as

an

appropriate

compromise. To determine whether equation (1) -- with

A set at 0.25 or some other

chosen value -- would perform well, one needs to experiment with a quantitative model, one

that

is subjected to random

shocks of the magnitude

experienced in actuality. The difficulty in this regard is, of course, that there is no agreement as to the appropriate model. expressed in ell

ith a

cCallum (1987), is that rule (1) with

But my conjecture,

A = 0.25 would perform

ide variety of quantitative models pertaining to developed

market economies. It is important to be clear, in this regard, about what IS

meant

here

by

the

term

"perform well."

In particular,

it must

be

emphasized that, according to the principles expressed above, the criterion should involve only the time path of nominal GNP.

Since we do not know how

changes in GNP will be divided between inflation and output growth, the rule's performance should not be evaluated on predictions in that regard.

the basis of any model's

conjecture, then, was that simulations with

rule (I) used in place of actual historical policy would, in a variety of models, result in nominal GNP paths that are smoother than those actually experienced and

also

nominal demand.

Confidence in the rule would be enhanced if this type of

et-e

noninflationary

in terms of the average growth of

obtained with models that are constructed along both Keynesian

and classical lines. The preliminary results reported in my previous paper were based on o

"model" that is simply an atheoretic regression relating

versions of a and ith

13 resulting enough

As

the from

to avoid

purpose

past

values of

seasonally

of

this

term

regulatory

and

dependence

on ryciical

itself.

adjusted

is

tc

technological

take

The

quarterly

-1vmjnt -_ sources,

conditions

178

of

first of these equations, United States

possible

the period of (which are reflected

changes

in

data

weloc i ty

for

growth

averaging should be in the third term).

long

1954.1-1985.4, is as follows:14

AXt

= 0.00740+ 0.262bxt 1 + 0.488dbt + e2t (.0020) (.079) (-120)

R2= 0.23

(2)

SE = 0.010

Here

denotes the estimated disturbance or shock realization for e2t quarter t. Using this equation and policy rule (13, simulated values for bt and

xt

were calculated for 128 periods beginning with initial conditions

pertaining to 1954.1 and with e2t values fed in each period as estinates of shocks that hit the economy during

1954-85.The result of this simulation

exercise (with a = 0.25) is shown in Figure path and LX the simulated values for

1, where TAR denotes the target

xt. Evidently, the rule induces xi. t.3

follow the target path rather closely, according to model (2). While plots such as Figure

1 are quite informative, they are much less

compact than some summary statistic reflecting the overage "closeness" of Xt to x;.

In what follows, consequently, the discussion will emphasize the

root-mean-square control error. This statistic, denoted RMSE, is the square root of the mean (over the 128 simulation periods) of (xt-xi)2. value for the path shown in Figure

The RMSE

1 is 0.0197, a value that is about 2.0%

in percentage terms. Beforz turning to analogous values based on other models, it will be useful to nut the 0.0197 RMSE value in perspective. One hay of doing that is to compare it with the RMSE va?ue actually experienced--i.e., the value obtained with actual historical &bt valzes for 1954-85 used instead of rule (I). For that case the RMSE Ils 0.771, over 30 times as large as with rule (1) and x = 0.25. Another relevant basis for comparison, since a large part of the foregoing actual value reflects inflation, is the extent nominal GNP variability about its (inflationary) trend path.

of

actual

Consequently,

relative to a fitted trend line has also been 15 is over Cour calculated. The resulting number, about 0.0854 (or 8.5%), the RMSE value for

xt

times as large as the value obtained with policy rule (I), suggesting that

’ 4Here, while

SE

and

denotes

Durbin-Watson becaur;c

“ln

of

II,

what

the

estimated

statistic. datd

the

follows, The

t ig!rres

standard figures

in

in parentheses

jevIti*ion (2)

differ

of

the

s!iqhtly

are

est imated

disturbance frm

those

revision.

McCallum

(1987)

the

figure

was Incorrectly

179

reported

as 0.0616.

standard

term in

and

errors,

DW is

McCallum

the

(1987)

I

2

A=

aI

180

0.25

the rule

ould

have provided

actually occurred, 16 The

smaller fl

ell as zero inflation.

second version of model

includes

Abt_l

Lions 7

rather than

in nominal

(2) considered previously

Abt

G

is one that

as an explanatory variable for

bxt. One

purpose of considering that variant is to eliminate thc2 possibility that estimated effects of monetary policy on nominal GNP are actually due co a reverse-causation response of

Ab, to Axt,

as suggested by King and Plosser

(1984) and other real-business-cycle theorists.

The estimates

with

this

change are as follows:

= 0.0078 + 0.198 dxt 1 + 0.549 Abt 1 + e3t (.0019) (.083) (.125) -

Ax

t

R2 = 0.248

SE = 0.0099

(3)

D

Clearly, the estimated coefficient values are almost the same as in (2), but the additional lag between target departures leads to

a

slight deterioration

simulation usin

and corrective

in performance:

(3) and rule (1) is 0.0212.

the RMSE

effects

value for a

That deterioration

is not

readily visible in the plot for this case,,which is therefore not included. It r's clear that these preliminary results are open to two major types of criticism, namely, that the "models" used to depict GNP determination are too

simple and

that they are unlikely

to

be policy

invariant.

To

respond to those potential criticisms is the main purpose of the present paper.

To that end, we now turn to experiments analogous to those just

described

but

conducted with

a

variety

of multivariable

models

of

the

economy utilized in place of regression equation (2) or its variant (3).

“Finn

Kydland

when measured fil+er

or

is only

depend

in

fiuctuations. theories, 17

0.028.

part

But the

The

pointed to

d ciigner-CrW-der

RMSE value wi I I

has

relative

the

.

In

values

are

not

most wroth

polynocirial

in

An analyst’s his

mean

judgment

inflation

described

fluctuations

of

of

provided

the

time.

type

Relative

choice

reported

entailed

cases

that path

figures

variability

simulated

quarter

on

out

a smoothed

copzerning

rate below,

to

the

indicate

(1)

is not

with the

rule mean

reportrng.

181

GrdP are

in

of

time, of

!.ivaI

whatever

much smaller

l-todrick-Prescott

measures

merits that,

norninal by the

a cklbic

among alternative

below

by rule

actual

for actual

the

variability

theories

one’s

(1980)

example,

of

judgment

CyCl ical concerning

large. (1) inflation

and

X rate

=

0.25 is

is

3nTy

SO c!OSe

t0

3.05% ZerO

Per that

e begin our robustness investigation with a number of vector autoregression

(VAR)

models.

AS

SUC!T

make

~~tiels

no

pretense

of

being

structural, there is no good reason to believe that their parameters would be

the

same

under

starting point,

alternative

policy

for

nevertheless,

regimes.

consideration

They of

provjde

a

useful

issues such

as

the

effect of including or excluding certain variables. And in practice it may be that parameter responses to regime chirnges are not large.'* Accordingly, exercises analogous to those described above for models

In each case

(2) an:: (3) have been conducted with a variety of VAR systems.

tk

1954.1 - 1985.4

procedure was to estimate parameters and residuals over

fw a VAR system that irzludes hbt as one of

Then a 128.

Jriables.

.

period simulation was conducted, based on initial conditions pertainir;g to

1954.1,

ith estimated

explaining Abt,

shocks fed

equations

except

the one

values of the latter being generated by pol?~y rule

rather than the VAR equation. used in (l),

in for all

Four values of the feedback para,leter A

(1) were

ith each VAR specification, to obtain evidence concerning the

desirability of x values larger or smaller than the 0.25 figure mentioned alJove. In most of the systems nominal GNP was not itselt included as one of the variables, but logarithms of real GNP and the GNP price deflator were. Consequently, simulated values of xt could easily be obtained and compared with the xt target path.

Results of these comparisons are summarized by Such statis!--&

means of the RSME statistic, as discussed in Section II. are reported for seven VAR systems in Table

Ai+

The

SmalleSt

and

A+

1.

VAR system considered includes the three variables Abt,

where pt and yt denote logs of the GNP deflator and real GNP, Four lagged values were

included for each variable?

The

SE values for this system are reported in the first row of Table 1. There ill be seen that the

SE with x = 0.25 is 0.0217, almost the same as

reported in Section II for regression model (3) -- a model

‘$hat is stu;

of

Taylor

in

of

“The

principle

a! .crnative

(l~d4)

change

; s implicitly

position

correct

has

Octcbner

but -onetary

examined

taken

unimportant policies the

for

all

has

parameter

1979 and found

same i ~j true

by many economists, quantitatively.

of

significant

the

been

stability but

VAR systems

182

who argue That

explicitly of modest

suggested

a

VAR model adjustments.

discussed

in

that

VAR models

thib

the can

by across

section.

Lucas be

used

Litterman the

Fed’s

critique for

the

(!982). pal icy

Table I ation Results with VAR E Values for 1954.1 - 1 --

Value of x in Policy Rule (1)-

Variables in VAR System

0.0 --

01 L

0.25

0.5

1.

Wt,tpt,Abt

.0414

.0257

-0217

.0244

2.

Ayt'Apt,Rt,Abt

.0479

.0216

.0220

.1656

3.

AytJq+Rg,Agt,Abt

4.

(a)

AC& gehaeratedby VAR

.0477

.0216

.0225

JO70

(b)

Actual Agt values

.0465

.0216

.0226

.1217

(c)

Actual Agt-Ayt

.0466

-0215

-0226

.0364

L?YtJPt,Rt,Ast,Abt

.0404

.a0253

-0265

1.2407

course, a two-variable VAR with only one lagged value. The other entries in

row 1 pertain to the alternative values of x that were considered:

0.19and

0.5.

0.0,

From the RMSE figures reported, it appears that ?. = 0.25 is

superior in this particular system.

The differtnces are not great uit31

respect to x = 0.1 and A = 0.5, RMSE values close i;o0.025 being obtak& in each of these cases. Performance in the absence of feedback (A -:0.0) is significantly worse, however. The second VAR model adds the 99-&y to the variables of the previous

Treasury bill

system.

rate, denoted

ith this change

Rt,

the results

become noticeably different, as can be seen from TnbTe 1 and also Figure 2, which presents simulatio:, plots for all four values of the smaliest RF%E results from A = 0.1, 0.1656 occurs when

x

x.

In particular, SE value of

and a very Kg

is set at the value 0.5.

:ke

reason

unsatisfactory performance in this 1 are encountered, as can be seen in parts (a) and (b), corresponding to

A =

aspects of positive feedback can be seen. 2(c) and from the

SE statistic, t

st as

183

0.0 and

A = kl,

t

for t

FIGURE2

(A)

A =

-.

LX

0.00

...*...

(8)

A =

184

0.1

7

I

6175 6I I 25

6I 5x

LX

7s0 ?825 7. a 6,45

. .. . . . .

Ml

consider a five-variable VAR system in which the additional

Next :‘:!

variable Bs Agt,

where gt denotes the Tog of real government purchases of

goods and se;-vices (at all levels of government).

In this case there are

various ways in which Agt can be trpaied, to reflect the notion of "other things equal," in the simulations that use policy rule (1) to generate Abt. Here three treaiments were considered

the first of which uses Agt values

generated by the Agt equation that was estimated as

the second treatment uses actual Agt values in the simulation,

By contrast, while

the

art of the VAR system.

third

uses

purchtisesto real GNP. slightly better

actual

values

for

the

ratio

of

real

government

With all three treatments, results with x = 0.1

than with

x = 0.25,

and results with

A = 0.5

are

are the

poorest by a considerable margin. The difference between these results and those

obtained

with

the

four-variable

VAR

is

negligible

for

the

intermediate x values of 0.1 and 0.25. The final VAR experiment involves a five-variable system in which an exchange-rate

measure

is

used

instead

of

government

purchases.

Since

figures on the trade-weighted value of the United States dollar (denoted St) are available only for periods beginning with 1967.1,

figures for 1954-

66 had to be constructed from series pertaining to jndividual currencies. The procedure adopted was to estimate

a least squares regression of St on

United States exchange rates relative to Canada (SE), the United Kingdom (StK),

the Netherlands (Sf), Italy (S:), and Belgium (SF).

For the sample

period 1967.1 - 1986,3 the estimated relation is

St = 14.00 Sk + 42 59 SF” + 18.70 StN + 0.00329 StI + 0.3930 5; + eqt

(4)

wit5 a~ R2 value of 0.9900. Formula (4) was then used to generate estimated values of St for 1953-66. Letting st = log St, the variable included in the VAR system is Ast. In both estimation and simulation steps, the actual ASt values are used for 1954.1 -

1971.3 and VAR-generated values for 1971.4 -

1985.4, the difference pertaining to periods of fixed and floating exchange rates. Results are reported in row 4 of Table 1. There it will be seen that the

SE values are

plosive oscillations

larger than with

the other systems, and highly ex-

are encountered with x = 0.5.

Effectiveness of the

policy rule is, nevertheless, entirely satisfactory with x equal to 0.1 or

0.25:

the

SE values are

ell below the 0.085 referb>nce

figure that per-

tains to actual variability (relative to trend) for the U.S. during 195485,

186

IV, RESULTS ITH CLASSICALA e now turn to models that are "structural" in the sense that they pertain to specific alternative theories concerning the nature of businesscycle fluctuations. These models are extremely small in scale and are not here rationalized by explicit maximizing represent

the

theoretical

principal

positions.

analysis, but are specified

characteristics

Three

of

important,

such positions

are

and

considered:

to

competing, the

real

business cycle position, the monetary misperceptions position, and one of a more Keynesian slant. AS suggested by the first principle set forth in Section II,

the main

difference among these theories concerns the aggregate-supply or Phillipscurve portion of the macroeconomic system, Consequently, the same specification is used in all three cases for the aggregate demand portion of the model --

i.e., for the relation describing

the quantity of output that

would be demanded at a given prfce level for consumption, investment, and government purposes together.

In order to keep the model small, a single

aggregate-demand relation is here used, instead of sectoral relations for consumption of

nondurables, consumption of services, investment in fixed

plant and equipment, investment in inventories, and so on.

The principal

determinants

are

of

demand quantities

in such

a

relationship

taken to be real money balances and government purchases.

typically

For our purposes

it is appropriate to utilize real quantities of the monetary base instead of the former variable, thereby implicitly incorporating into the specification banking sector relations reflecting the connection between the monetary base.

P and

The resulting relation is estimated in first-differ-

enced logarithmic form, with one lag of each variable included to reflect dynamics. Least squares estimates for the sample period 1954.1 - 1985.4 are as follows:

%Yt

= 0.0045 + 0.2591. ~y~_~ + 0.2795 (abt-apt) (.127) (.OOl) (.083)

+ 0.2731 (abt_l-apt_l) + 0.1476 agt - 0.1675 agt_l+ egt (.062) (.061) (.131)

Y2 \ =

0.276

SE = 0.00916

187

(5)

The point estimates

in (5) were

adopted for use in all simulations de-

scr%ed

in this section, with the residuals e5t being used as estimates of 20 shocks to aggregate demand. Next, consider

the

aggregate-supply

portion of

the three competing

theories. In the case of the RBC approach it is not necessary to estimate That convenient property stems from the

any relations in addition to (5).

exogeneity postulated by the RBC hypothesis of real variables with respect to nominal variables -- and therefore to monetary policy actions -- plus the assumption that any fiscal effects on output work through an inter21 Thus we take real output mediate impact on nominal aggregate demand. movements to be exogenous, which implies that the role of (5) is simply to determine

level. Since

the price

results

reported above

in lines

(3a),

(3b), and (3~) of Table 1 indicate that different treatments regarding Agt have

little

exogenous.

quantitative

importance,

we

In sum, the simulation exercise uses

Agt

values

to

be

(1) and (5) to generate

set at their actual historical

sequences for bt and pt with gt and yt values.

take

also

Values of xz are then calculated as xt=pt+yt and can be

compared

with target-path x1 values for the purpose of RMSE computations. The second of the three structural models is designed to represent the monetary misperceptions theory, developed by Lucas (1972) (1973).

As the

leading attempts to implement this approach empirically are those of Barro (1977) (1978), our formulation is based to a considerable extent on his. particular,

money-growth

surprises

-- measured

empirically

In

as residuals

from an equation designed to explain fluctuations in money growth rates -?re

taken

to be

**It

might

instrumental difficulty

endogenous

that

same

estimate squares

hand,

and

equation 21

of

tend

least

This

f?f3C proponenrs

is

the to

(5)

might

are

a relation true

for the

truly

therefore

In

this

least

so

(5)

is

are

estimated

disturbance

about

power

of

four policy

conservative, regard,

from the

to

times

rather

than

some

stems

from

no

forced with

to is

individual as

in

as

with

the

to

values much

of lagged

of

Ay,,

larger

parameters.

large

perspective

variables

turn

lagged

operatrons

discussion

base,

answer

variance

the

present

The

probably

is

one

attached

For

squares

bias.

There

errors is

iring

by

output.

in the monetary

simultaneity

estimated

standard

seems

preferable.

estimated

to

real

movements

exogenous,

on Abt-Apt stabil

of

instruments.

the the

coefficient

is

reduce

similar

instruments,

increase

estimates

probably (9)

as

why

that

that If

used

the

asked

surprise

appropriate

significance

Agt

would

be

finding

variables.

and

to use

estimator

in

accordingly point

naturally

variable

macroeconomic

Abt ,

important determinant

it is useful

pwgsses

the

an

in

(51,

Abt. of

the

paragraph

and The

a result

To use

the

issue

at

following

is relevant. is

a simplification, to technology

but shocks

one as the

that

seems just

source

188

of

Ificd

cyclical

in view

of

fluctuations.

the emphasis

given

by

instead of

the

1 money

stock considered by Barro.

For the first-step

regression used to represent the systematic component of base growth, the following autoregression was adopted:**

Abt = 0.0016 + 0.4679 Abt- 1 + 0.0426 Abt -2 -I0.3372 Ab (.OOl) (.082) (.093) (.083) t3

R2 =

0.651

SE

from

(6),

Residuals

n

0.00463

=

denoted

-+ Ab t

(6)

I= 2.07

ibt , were

then

employed

as

explanatory

variables in the "aggregate supply"'equation with estimates as follows:

= 0.0048 + 0.3028 ibt + 0.3776 ibt 1 + 0.3281 Ayt 1 + e7t (.OOl) (.193) (.191) (A83) -

AYt

R2

0.150

=

SE

=

0.00978

BW

=

2,lO

In the latter, it should be emphasized, standard errors associated with the coefficients attached to Abt technical reasons.

values are larger than in Barre's work for

Thus the yt variable appears in first-differenced form

and the specification includes Ayt_l as an explanatory variable, thereby tending These

to

attribute

surprises

considerable

less explanatory power

continue

to

influence of Abt

Since the policy rule

have

to the monetary

sizeable

coefficients,

surprises.

however,

so

a

irregularity on' output is implied by (7).

(1) is deterministic, there will of course be no The latter uses equations

surprises occurring in the simulation exercise.

(I), (B), and (7) to generate values for bt, pt, and yt -- which permit calculation

of xt magnitudes

for comparison with the target path as

in

other cases. Finally, we turn to our specification more representative of

In particular, this specification was designed to represent .-- in

views.

22

Some readers

implies

that

component

study

the

Ab, that

is

decompos i ton

however,

Sargent’s

will

there

Here,

simply

Keynesian

our

that

(!976) is

policy

the

--

the terms,

that

the

identification

objective

implications

assume

recognize an

for

“observational is our

residuals that

absence

problem

not

to

policy from

is,

additional

that

rule

if

are

we assume

the it

Rarro-type

were

stirpricer

that

invariant.

189

(6)

is

explanatory

with problem

equivalence”

argue

(6)

of

associated

the

discussed model

appropriate.

variables

surprise is Given

vs.

in

by Sargent

(1976).

appropriate, that

but

purpcje,

2nd

i n~ec_tin,atc the consequences.

the

version

of

(6)

systematic

an autoregression

to we

In for

simplified form -- the wage-price portion of the well-known MPS econometric In that model, nominal wage changes are dependent

(via an expec23 and a tational Phillips relation) on a measure of capacity utilization

model.

measure of expected inflation. Prices then adjust gradually toward values implied by the prevailing

level of wages and "'normal" labor productivity

growth. In our implementation, the first of these two relations is represented by the following equation estimated by least squares over 1954.P85.4: bwt=0.004a + 0.1838 (yt-y,) - 0.1327 (yt_I-&I) (.042) (.OOl) (.042) R2

=

0.545

SE

DW

'- 0.00479

=

+ 0.7594 APE + eat (-072)

(8)

x1.81

Were wt denotes the log of the nominal wage in manufacturing while yt-yt

is

the logarithmetic deviation of real GNP from a fitted trend, and the expetted inflation rate A$

is proxied

by actual inflation rates averaged

over the previous eight quarters. As the coefficient on A$

is signifi-

cantly less than 1.0, the specification does not possess the natural-rate property of

steady-state

independence between

inflation and yt-yt.

This

makes the model more "Keynesian," and perhaps more favorable to an XtiViSt strategy, than if the coefficient equalled unity. The

second

new

equation

in

this

model

is

the

MPS-style

price

adjustment equation. Our version was estimated in first differenced form -in principle obviating

the need for a trend term to reflect productivity

changes -- as follows: = 0.0003 + 0.4929 Awt + o.m8 A$ 1 + egt (.0007) (.064) (.063) -

Apt

R2 =

SE

0.692

=

0.003%

D

=

(9)

2.43

ith (8), a slight departure from steady-state neutrality is implied by

23Actually, model presented currently has

an

itself.

been

inverse

rneti_;a’e

A description in

McCallum

used provided

by

the

of

a

(1979). research

by Brayton

based

More staff

on

streamlined at

and Mauskopf

the

recently, the

unemployment

version Board

(1987).

190

of

the

a

qualitative

of

Governors

rate

is

model’s

util

discussion of

the

ired

in

wage-price Federal

of

the MPS

sector the

Reserve

is

version System

the point estimates?

Thus this last model has quite different properties

from the RBC and monetary-misperception

representations.

Its simulations

use equations (l), (5), (8), and (9) to generate time paths for bt% yt, pt and wt, with xt and

RMSEvalues obtainable as in the other cases.

Before turning to the results of our simulation exercises, it will be useful

to

emphasize

the

relatively

innocuous

nature

of

econometric

weaknesses in the estimation of the three models. It is not crucial that least squares

estimates

of

(8) and

(9),

for

example,

are

subject

to

simultaneity bias or even that identification of (8) and (9) is dubious. The objective in estimating theFe models is not to build a case that any of the models is "true," but simply to 13htain numerical representations, which are consistent with United States data for 1954-85, of alternative theories of macroeconomic behavior. One could in principle simpiy assign conjectured parameter values so long as the shock estimates are based on those values. That parameter values are roughly consistent with the dirta, and that shock estimates are not too far from white noise, is guaranteed

by our approach.

Let us consider, then, results of the simulations using

(1)

with

tabulated,

each

of

these

three

structural

agciin for four values of x, in

models.

The

policy

rule

RMSEvalues

are

Table 2. It will readily be seen

that with each of these models the results are even more favorable to our

Table 2 Simulation Results with Structural Models RMSE Values for 1954.1 - 1985.4 Value of-

RBCModel Equation (5), actual yt Barro-Type Model Equations (5), (7) Phi 11 ips Curve Model Equations (5)‘) (8), (9)

24

imposition

a deterioration

of in

the

the

constraint

that

the

Policy Rule

0.00

0.10

0.25

O-50

.0281

.0200

AI160

-0132

.0238

-0194

A161

-0137

.0311

A236

,019l

Al74

coefficients

IIW statistic.

191

on Aw,

and Apt_,

sum to one

leads

to

policy rule than those obtained in Section III. in

each case the RMSE value declines

magnitude

policy

the

of

as

1 is increased9 to

response

feedback

Thus in contrast with

strengthened.

Also it bill be seen that i.e., as the errors

xt-x;

the VAR cases, no sign of

is

induced

dynamic instability is encountered for x values up to 0.5. There

are

two

features

of

these

models

that

responsible for these differences vis-a-vis the VAR

would

appear

to

systems. First,

smaller RMSE values reflect the possibility of better stabilization

be the

that

occurs when nominal GNP is dependent upon current-period values of bbt, as implied by equation (5).z5 Second, the danger of dynamic

instability

is

lessened both by this current-period response and also -- although this is not a logical necessity -- by the lower-order dynamics of the system that results from fewer lagged terms and shorter lags. Let us

conclude

this

section

by

exhibiting

plots

of

simulated

xt

values together with x; target paths for the Keynesian model (l), (5), (8), These plots, shown in Figure 3,

and (9) with A values of 0.0 and 0.25.

again illustrate the valun of the feedback term X(X:-~ -xt_l) in rule (1).

V, ADDITIONALRESULTS The results reported in Sections

III and IV indicate rather clearly

that performance of the policy rule (1)

has considerable robustness with

respect tc model specification, i.e., that its performance is good under a wide

variety of

specifications.

however, directly critique.

address

It does

not

the show,

That

issue

type

implied

:f demonstration

does

not,

by

the

Lucas

in other words,

reference that

to

performance

is not

seriously impaired for a given model specification by a significant change in parameter values. In

order

to

develop

a

bit

of

evidence

relating

to

this

last

possibility, one approach is to impose parameter changes on a given model and redo the simulation exercises values),

(while feeding

in the original

Results of an exercise of this type are reported in Table 3.

shock The

ith the simplified "model" reported in equation (3), for icients are as follows:

25

Also,

in

their

specific

models,

by equations

192

(7)

and

(8).

7

I

I

75

6I

LX

. . . . .. .

TMI

193

Table 3 Sensitivity Results -

-

Coefficient Valuesa --

Case Ib 2 3 4

J981,

-5489

.1981, .1981, .1981, .3981, .0981,

5 6

.0212 .0252

.34a9 .2489 -7489 .5489 .5489

.0291 .0202 .0274 .0193

-1 and abt_l, respectively

'Coefficients attached to bReference case

AXt

= 0.0078 + 0.1981 AXE 1 + 0.5489 Abt I + e3t.

(IO)

As described in Section II, the RMSE value for xt relative to XT is 0.0212 when

the value of

0.25

is used

for

the feedback

parameter

A, and the

equation (3) residuals are used as shock esr'imates in the simulation for bt and xt. The first variant on that simulation, reported as Case 2 in Table 3, repeats the simulation with everything unchanged except the coefficient in (lo),

attached to Abt_l

hich is reduced to 0.3489.

The resulting RMSE

value of 0.0252 is somewha

larger than in the reference Case 1, but not

enough to be disturbing. T

same can be said, moreover, for the four other

cases investigated -- in

1 of which

the RMSE

is less than 35% of

value pertaining to detrended actual experience (Le., Some analysts,

the

0.085).

Meltzer (1984) (1987) and Barro (1986), have

favored policy stra

her similar to the one here reco

designed to attempt to main

n a constant price level directly rather than

indirectly through

ationary

a

nonin

path 26 eltzer's preferred rule for Abt is as follows:

26 four.

Actual Here

ly,

Mel trer

we ignore

that

fecfxni~

, averaging

minor

terence

growth

over

for

the

194

the sake

previous of

clarity.

for

nominal

three

years,

GNP.

Thus

rather

than

hbt= (l/16)

w

[ (yt_l-yt_17) - (xt_l-xt_17-bt_l+bt_17) 1.

Here the -00739 term in our rule is replaced by the average growth rate of real GNP over the previous sixteen quarters, while the third term in our rule is omitted.27

(feedback)

To consider the properties of rule (II),

one needs to select a criterion.

The one most directly suggested by this

approach is the RMSE of a simulated pt series relative to a constant price level.

aan unwilling to adopt such a criterion, however, because to do so

I

would require rejection of the first principle adopted above in Section II: that we do not possess an adequate model of the way in which nominal CNP changes are split, on a quarter-to-quarter basis, between real growth and inflation. An nominal

alternative GNP

predicted

as

by

possibility

the

the

criteria,

most

is to continue but

recent

with

four

future

years'

to use real

experience

RMSE GNP

growth

rather

constant value of 0.00739 (i.e.* 3% pe: Jear) used above. case one would continue to be

values

for

rates

than

the

But in such a

interested in noninflationary

nominal GNP

growth, so the target-path xt values should also be adjusted to conform to the altered real GNP predictions. Consequently,

the target path in this

case is as follows:

fe %t

=

* + Xt-1

(12)

ww(Yt_l-Yt_17)'

One might guess that results target for L

nominal GNP,

based on

would

be

rule

(ll),

with

little different

x;* used as the

from

those

obtained

previously with rule (1) -- with x - 0.0 -- and the target xt. To check that conjecture, results have been obtained using the simple two-variable model (3) with

As it happens, the FWE

x = 0.0.

value of 0.0458 obtained

with rule (11) agrees to the third nonzero digit with that for rule (I)! Simulation plots for these two cases are provided in Figure 4. Finally,

let

us

turn

emphasized by Gordon (1985).

27 results

The for

effect (1)

of with

omirting

the

to

"start-up"

considerations

of

the

type

These refer to the possible undesirability of

feedback

term

A = 0.0.

195

has

alredy

been

explored

by

means

of

the

FIGURE4

.

7

I

5

6

I

I

25

LX

....... NRA

Rule (l),

A

= 0.0

hen a rule such

adjusting nominal GNP growth toward a 3% rate too rapidly

as (1) is adopted at a time at which recent growth rates *have been much higher

(or,

in principle,

much

lower)

than

that

value.

Under

such

circumstances a reasonable way to begin might be to move gradually toward the 3% rate over a period of (say) three or four years.

To investigate the

workings of our rule with this sort of modification, consider an experiment in which the simulatien period begins with the quarter 1972.3 rather than 1954.1.28

Since recent growth rates for nominal GNP had been closer to 11%

than to 3X, a gradual-adjustment approach would then involve a target path that features nominal GNP growth rates such as the following:

Quarter

Quarter

AX”

.02494 .02377 .02260 -02143 .02026 .01909 .01792 .01675

AX*

.01558 -01441 .01324 .01207 .01090 .00973 -00856 .00739

9 10 11 12 13 :z 16

At the same time, it might be desirable to start with a constant term in the base-growth rule that was greater than 0.00739 and adjusted toward that value over (e.g.) sixteen quarters.

In the single experiment that has been

conducted, however, policy rule (1) was retained in its usual form. 29

The

results of that experiment, shown in Figure 5, are better than might be expected. 0.0297,

Indeed, the RMSE for the 1972.3-1985.4 simulation period is only

which

is

not

much

worse

than

for

the

entire

period

despite

inclusion of the 1981-82 episode, which contributes a large portion of the target misses in all cases.

28 was

One reason

a period 29

Effects

of

for

choosing

relatively of

the

altered

1954.1

little target

as the

inflation path

initial or

are

data

for

our

basic

simulations

is

that

unemployment. significant

197

for

base-growth

rates,

of

course.

it

FIGURE5

x = 0.25

'75 '76 '77 '78 '79 '8

'83 '$

Tt is clear that many

additional experiments could be conducted to

provioe additional infor ation concerning the apparent

(1)

for conducting monetary

models

policy, The

suita

ility of rule

use of more complex

is one obvious possibility; extension

of those

structural

IV to

in Section

incorporate exchange-rate effects and more detail in the determination of aggregate dcaand would be desirable. 30 ore experimentation with start-up reactions at varioub o&es is another possibility. 31 Enough different specifications and cases have been considered here, however, to suggest that a policy rule such as

(1) has considerable promise

as a device for obtaining improved macroeconomic performance. Specifically, our

simulation

results

indicate

rates specified by (1) would

that

adherence

to monetary

base-growth

yielded essentially zero inflation in the

hwe

United States over the period 1954-85, despite the financial and regulatory changes

of

that

period,

while

also

reducing

the

extent

of

cyclical

fluctuations in nominal -- and perhaps real -- GNP.

38

inclusion

variables

3’Several during

the

experienced probably

of

would

have

banking-sector

be another conference

1930s.

It

would

have

helped

linking

relationships

money

stock

and

monetary-base

possibility. participants seems called

considerably.

clear forth

raised that

a

massive I plan

to

the

issue

decline injections investigate

199

of i,I

how the nominal of

this

base

rule

would

GN? such money,

question

in

as s3

have

performed

that the

actual rule

a subsequent

ty

would study.

Barro, R-3. (1977)

Unanticipated

oney

Growth

States, American Economic (1978)

Unanticipated United States,

oneyp

and

Review,

Output,

Unemployment

in the

United

67: IOl-115.

and

the

Price

JournalofPoliticaT Economy,

Level

in

the

86: 549-580

Recent Developments in the Theory of Rules versus Discretion,

(1986)

EconomicJournal,

96, Supplement: 23-37.

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