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This PDF is a selection from an out-of-print volume from the NationalBureau of Economic Research

Volume Title: A Rational Expectations Approach to Macroeconomics:Testing Policy Ineffectiveness and Efficient-Markets Models

Volume Author/Editor: Frederic S. Mishkin

Volume Publisher: University of Chicago Press

Volume ISBN: 0-226-53186-4

Volume URL: http://www.nber.org/books/mish83-1

Publication Date: 1983

Chapter Title: Does Anticipated Aggregate Demand Policy Matter?

Chapter Author: Frederic S. Mishkin

Chapter URL: http://www.nber.org/chapters/c10248

Chapter pages in book: (p. 110 - 155)

6 Does Anticipated AggregateDemand Policy Matter?

6.1 Introduction

Recent theorizing has focused on business cycle models that incorporate features of the natural rate model of Friedman (1968) and Phelps(1967) with the assumption that expectations are rational in the sense ofMuth (1961). An important neutrality result from this research (Lucas1973; Sargent and Wallace 1975) is that anticipated changes in aggregatedemand policy will have been taken into account already in the behaviorof economic agents and will evoke no further output or employmentresponse. Therefore, deterministic, feedback policy rules \\'ill have noeffect on output fluctuations in the economy. This policy ineffectivenessproposition of what Modigliani (1977) has dubbed the Macro RationalExpectations (MRE) hypothesis runs counter to much previous macroeconomic theorizing (and to views prevailing in policymaking circles).This proposition is of such importance that it demands a wide range ofempirical research for verification or refutation.

This chapter applies the econometric methodology developed in Chapter 2 to the important question whether anticipated aggregate demandpolicy matters to the business cycle. It begins with a brief review of themethodology in Section 6.2, then follows with the empirical results inSection 6.3, and ends with a section of concluding remarks.

6.2 A Review of the Methodology

The tests here are based on the MRE model of the form

(1)

110

111 Does Anticipated Aggregate Demand Policy Matter?

where

Yt == unemployment or real output at time t,Yt == natural level of unemployment or real output at time t,

X t == aggregate demand policy variable, such as money growth, inflation, or nominal GNP growth,

X~ == anticipated X conditional on information at time t - 1,~i == coefficients,Et == error term.

A forecasting equation that can be used to generate these anticipationsof X t is

(2)

where

Zt - 1 == a vector of variables used to forecast X t available at time t - 1,"I == a vector of coefficients,

U t == an error term which is assumed to be uncorrelated with anyinformation available at t-1 (which includes Zt-i or Ut-i forall i ~ 1, and hence U t is serially uncorrelated).

A rational forecast for X t then involves sirnply taking expectations ofequation (2) conditional on information available at t - 1:

(3)

Substituting into equation (1), we have

(4)

The MRE hypothesis embodies two sets of constraints. The neutralityproposition implies that deviations of output and unemployment fromtheir natural levels are not correlated with the anticipated movements inaggregate demand policy. That is, 8i == 0 for all i in

(5)N N

Yt== Y;+ L ~i(Xt-i- X~-i)'+ L 8iX~-i+ Et ·i=O i=O

Rationality of expectations implies that (5) can be rewritten as

(6)

where "I == "1*.The joint nonlinear estimation procedure outlined in Chapter 2 is used

here to estimate both the constrained (2) and (4) system and the unconstrained (2) and (6) system where "I == "1* is not imposed. It corrects forserial correlation with a fourth-order autoregressive (AR) specificationfor the Et error term, and this is successful in reducing the residuals to

(7)

112 Empirical Studies

white noise. l The conventional identifying assumption found in previousresearch on this topic is made that the output or unemployment equationis a true reduced form. The joint MRE hypothesis of rationality andneutrality is then tested with a likelihood ratio statistic constructed from acomparison of the two estimated systems. It is distributed asymptoticallyas X2(q) under the null hypothesis where q is the number of constraints.

If the joint hypothesis of rationality and neutrality is rejected, we canobtain information on how much the rationality versus the neutralityconstraints contributes to this rejection. The neutrality constraints aretested under the maintained hypothesis of rational expectations by constructing a likelihood ratio statistic as above where the constrained systemis (2) and (4), and the unconstrained system is (2) and (6) subject tothe rationality constraints, "I == "1*. A separate test for the rationalityconstraints proceeds similarly: the constrained system is (2) and (6)imposing "I == "1*, and the unconstrained system is (2) and (6) where "I ==

"1* is not imposed.In the results to follow, rejections of the MRE hypothesis occur when

the number of lags (N) in the unemployment or output equation is large.However, although many degrees of freedom are used up in these estimations, there is no allowance for the loss of degrees of freedom in thelikelihood ratio statistics. The danger thus arises that spurious rejectionsof the null hypothesis may occur because the small sample distributions ofthe test statistics differ substantially from the asymptotic distributions.

The nature of the problem here becomes more obvious if we look at thefollowing analogous example. In an OLS regression, a test of restrictionscan be carried out with a finite sample test, the F, or with an asymptotictest, the likelihood ratio. Asymptotically, the test statistics have the samedistribution, but misleading inference with the likelihood ratio statisticscan easily result in small samples. The F statistic is calculated as

F(q,df) = [(SSR~;:"SRU)~]

while the likelihood ratio statistic is

(8) n [log (SSRc/SSRU)] ,

1. In the output and unemployment equations estimates here, the Durbin-Watsonstatistics range from 1.82 to 2.26, and none indicates the presence of first-order serialcorrelation. Furthermore, the Ljung and Box (1978) adjusted Q statistics for the first twelveautocorrelations of the residuals cannot reject the null hypothesis that these autocorrelations are zero. The Q(12) statistics range from 5.84 to 15.0 for all the models except those inAppendix 6.1, while the critical Q(12) at 5 percent is 15.5. For the models in Appendix 6.1,the Q(12) statistics range from 8.26 to 15.90, while the critical Q(12) at 5 percent is 18.2.


where

df = the degrees of freedom of the unconstrained model,n = the number of observations,q = the number of constraints.

For over 100 degrees of freedom qF(q,df) is nearly distributed as X2(q),and for small percentage differences, (SSRC

- SSRU)/SSRU is approximately equal to log (SSRCISSRU). Inference \\rith the Fstatistic in the caseof over 100 degrees of freedom involves approximately the comparison ofdf[log(SSRCISSRU

)] with the X2(q) distribution. Inference with the likelihood ratio statistic on the other hand involves the comparison ofn[log(SSRCISSRU)] with the X2(q) distribution. Even in the case where dfis large, if nldf is substantially greater than one, the likelihood ratiostatistic will reject the null hypothesis far morf~ often than will the F. In thecase of the freely estimated unemployment or output model in Appendix6.3 and N = 20, the degrees of freedom of the unconstrained model forthe joint or rationality tests is 111, while the number of observations is184. The nidi of 1.7 in this case demonstrates that there is a potentiallyserious small sample bias in the likelihood ratio test when this manydegrees of freedom are used up.

To make certain that rejections are valid, the output and unemployment models are estimated both with and without the smoothness restriction that the anticipated and unanticipated money growth coefficients (&iand ~i) lie along a fourth-order polynomial "vith an endpoint constraint.This particular polynomial distributed lag (PDL) specification waschosen because it is rarely rejected by the data and it has the advantage ofusing up few degrees of freedom. 2

The anticipated aggregate demand X variable is constructed so that itwill be serially uncorrelated, so that a smoothness restriction is notrequired to make coefficients on unanticipated aggregate demand intelligible. However, anticipated aggregate de:mand variables are highly

2. The PDL constraints are not rejected in models where money growth or inflation arethe aggregate demand X variable. E.g., in model 2.1, X2(4) = 3.34, while the critical valueat 5 percent is 9.49; in model 4.1, X2(17) = 12.94, while the critical value at 5 percent is27.59; and in model A9.1, X2(14) = 20.54, while the critical value at 5 percent is 23.7. ThePDL constraints receive somewhat less support in the models using nominal GNP as the Xvariable. They are not rejected for the A5.1 output model at the 5 percent level, but arenearly so: X2(17) = 26.95, while the critical X2(17) at 5 percent is 27.6. However, they arerejected at the 1 percent level in the unemployment model: X2(17) = 34.91, while the criticalX2(17) at 1 percent is 33.4. I experimented with an eighth-order PDL to see if this would fitthe data substantially better, but it did not. Although this rejection of the PDL constraints isbothersome, the fact that the unrestricted models in Appendix 6.3 yield results so similar tothose in tables 6.A.5 and 6.A.6 indicates that, imposing or not imposing, the PDL constraints yields the same conclusions.


serially correlated, and the use of PDLs has the advantage of providingmore intelligible and more easily interpretable estimates of the anticipated aggregate demand coefficients, 8i . The main results reported inthis chapter thus are based on a PDL restriction. Comparing the mainresults with those in Appendix 6.3 obtained without a PDL restrictiondemonstrates that estimating with or without the restriction yields similar~ coefficients and similar statistical inference on the validity of the MREhypothesis. Therefore, we can be confident that any rejections of theMRE hypothesis are not due to small sample bias.

The specifications of the forecasting equations needed to estimate theMRE model are derived with the multivariate Granger (1969) procedureoutlined in Chapter 2. The policy variable, Xt, is regressed on its own fourlagged values (to insure white noise residuals) as well as on four laggedvalues of the following set of macrovariables: the quarterly M1 and M2growth rate, the inflation rate, nominal GNP growth, the unemploymentrate, the Treasury Bill rate, the growth rate of real government expenditure, the high employment surplus, the growth rate of the federal debt,and the balance of payments on current account. The four lagged valuesof each variable are retained in the equation only if they are jointlysignificant at the 5 percent level. This results in a specification of themoney growth forecasting equation, for example, which is quite differentfrom that used by Barro (1977, 1978) and Barro and Rush (1980): inaddition to past money growth, past Treasury Bill rates and high employment budget surpluses appear as explanatory variables. Weintraub(1980) also finds significant explanatory power of short-term interestrates in the money growth equation, and the magnitude of his coefficientsis similar to that found here. The specifications for the forecasting equations can be found in Appendix 6.4 as well as the Fstatistics for significantexplanatory power of the four lagged values of each variable in thesespecifications. 3

Earlier research on the MRE hypothesis (e.g., Barro 1977, 1978, 1979;Barro and Rush 1980; Grossman 1979; Leiderman 1980) uses a fairlyshort lag length-two years or less-on the anticipated and unanticipatedX variables. This chapter looks at longer lag lengths for two reasons.Experimenting with plausible, less restrictive models that have longer laglengths is appropriate for analyzing the robustness of results because thisstrategy has the disadvantage only of a potential decrease in the power of

3. Chow (1960) tests that split the sample into equal halves indicate that both the moneygrowth and nominal GNP growth equations have the desirable property that the stability ofthe coefficients cannot be rejected. However, stability of the coefficients is rejected for theinflation equation. For the M1 growth equation, F(13,66) = 1.37, while the critical Fat 5percent is 1.88; for the nominal GNP equation, F(9,74) = .60, while the critical F at 5percent is 2.0; and for the inflation equation, F(13,55) = 3.40, while the critical F at 5percent is 1.9.


tests, but not of incorrect test statistics. In addition, estimates in thischapter and in Gordon (1979) find that unanticipated and anticipatedaggregate demand variables lagged as far back as twenty quarters aresignificantly correlated with output and unemployment.

6.3 The Empirical Results

The tests of the MRE hypothesis in the text use seasonally adjusted,postwar quarterly data over the 1954-1976 period. The sample starts with1954-the earliest possible starting date if models with long lags are to beestimated. 4 An advantage of excluding the e~arly postwar years from thesample is that the potential change in policy regime occurring with theFed-Treasury Accord in 1951 is avoided. In pursuit of information onrobustness, both output and unemployment models are estimated, withM1 growth, nominal GNP growth, and inflation as the aggregate demandvariable. The natural level of unemployment or output, Yr, is estimated asa time trend here, as in Barro (1978). A more complicated Barro (1977)specification has been avoided because, as Srnall (1979) and Barro (1979)indicate, its validity is doubtful.

6.3.1 The Data

The definitions and the sources of data used in this chapter are asfollows:

M1 G = average growth rate (quarterly rate) of M1, calculated as thechange in the log of quarterly M1, from the NBER databank.

M2G = average growth rate (quarterly rate) of M2, calculated as thechange in the log of quarterly M2, from the NBER databank.

RTB = average treasury bill rate at an annual rate (in fractions),from the MPS data bank.

'IT = inflation (quarterly rate), calculated as the changes in the logof the GNP deflator, from the 1v1PS data bank.

GNP = real GNP ($billions 1972), from~ the MPS data bank.UN = average quarterly unemployment rate, from the MPS data

bank.NGNP = growth rate (quarterly) of nominal GNP, calculated as the

change in the log of nominal GNP, from the MPS data bank.

The other variables used in the search procedure for the forecastingequations were obtained from the NBER data bank.

4. Quarterly data on such variables as SURP do not become available until 1947. Withtwenty lags on anticipated or unanticipated Xt, the additional four lags in the forecastingequation and another four lags due to the fourth-order A.R correction, the first twenty-eightobservations are used up. This leaves us with a 1954: 1 start date.


6.3.2 Results with Money Growth as theAggregate Demand Variable

The text will focus its attention on results obtained when money growthis the aggregate demand variable in the MRE model. However, resultswith inflation and nominal GNP growth as the aggregate demand variableare presented in Appendix 6.2 and they are consistent with the moneygrowth results. The money growth results deserve more attention for tworeasons. Research with money growth as the aggregate demand variable(e.g., Barro 1977, 1978, 1979; Barro and Rush 1980; Leiderman 1980;Germany and Srivastava 1979; Small 1979) is more common in theliterature and produces results most favorable to the MRE hypothesis.The methodology employed in this research has been criticized, however,and another look at the question of whether anticipated monetary policymatters to the business cycle is called for. Furthermore, the identifyingassumption used to estimate the MRE model, that it is a true reducedform, is on firmer ground when money growth is the aggregate demandvariable. Although the exogeneity of money growth in output or unemployment equations is still controversial, economists are more willing toaccept the exogeneity of money growth than the exogeneity of nominalGNP growth or inflation.

Table 6.1 summarizes the major findings by presenting the likelihoodratio tests of the MRE hypothesis with M1 growth as the aggregatedemand variable. It tells the following story: When the lag length onunanticipated and anticipated money growth is only seven, the lag lengthused by Barro and Rush (1980), the likelihood ratio tests are not unfavorable to the MRE hypothesis. The joint hypothesis of neutrality andrationality is not rejected at the 5 percent level in either the output orunemployment models, 2.1 and 2.2. Separate tests of the rationality andthe neutrality hypotheses reject only in one case-neutrality in the employment model 2.2-and even here the rejection is barely at the 5percent level. However, when the lag length is allowed to be longer-upto twenty lags in the other models of the table-strong rejections of theMRE hypothesis occur. The output model displays especially strongrejections of the joint hypothesis-the probability of finding that value ofthe likelihood ratio statistic or higher under the null hypothesis is as lowas 1 in 10,000. Here, both sets of constraints contribute to this rejection,with the neutrality and rationality hypothesis rejected at the 1 percentlevel. The long lag, unemployment models are also unfavorable to thejoint MRE hypothesis, with the rejection at the 1 percent level. However, here the neutrality constraints are rejected far more strongly thanthe rationality constraints.

Excluding relevant variables from a model results in incorrect teststatistics, and including irrelevant variables will at worst only reduce thepower of tests and make rejections even more telling. The table 6.1

Tab

le6.

1L

ikel

ihoo

dR

atio

Tes

tsof

the

MR

EH

ypot

hesi

sw

ithM

lG

row

thas

the

Agg

rega

teD

eman

dV

aria

ble

Mod

el:

2.1

2.2

4.1

4.2

Dep

ende

ntV

aria

ble:

Lo

g(G

NP

t)U

Nt

log

(GN

Pt

)U

Nt

Des

crip

tion

:7

Lag

so

fM

IGt

-M

IG:

7L

ags

ofM

IGt

-M

IG:

20la

gsof

MIG

t-

MIG

:20

lags

of

MIG

t-

MIG

:

Join

thy

poth

esis

:L

ikel

ihoo

dra

tio

stat

isti

cX2

(15)

=22

.69

X2(1

5)=

22.8

0X2

(15)

=43

.83*

*X2

(15)

=31

.54

**M

argi

nal

sign

ific

ance

leve

l.0

909

.088

5.0

001

.007

4N

eutr

alit

y:L

ikel

ihoo

dra

tio

stat

isti

cX2

(4)

=3.

36X2

(4)

=9.

67*

X2(4

)=

15.4

5**

X2(4

)=

12.0

8*M

argi

nal

sign

ific

ance

leve

l.4

993

.046

4.0

039

.016

8R

atio

nali

ty:

Lik

elih

ood

rati

ost

atis

tic

X2(1

1)=

19.4

4X2

(11)

=13

.31

x2(1

1)=

29.1

7**

X2(1

1)=

19.8

9*M

argi

nal

sign

ific

ance

leve

l.0

536

.273

5.0

021

.046

9

Not

e:M

argi

nal

sign

ific

ance

leve

l=

the

prob

abil

ity

of

gett

ing

that

valu

eo

fth

eli

keli

hood

rati

ost

atis

tic

or

high

erun

der

the

null

hypo

thes

is.

*Sig

nifi

cant

atth

e5

perc

ent

leve

l.**

Sign

ific

ant

atth

e1

perc

ent

leve

l.


results therefore raise questions about previous empirical evidence fromshorter lag models that supports the MRE hypothesis, neutrality inparticular. Indeed, it appears that the shorter lag models are morefavorable to the MRE hypothesis only because misspecification yieldsincorrect test statistics.

A look at the estimates of unemployment and output equations fromthese models leads to a deeper understanding of the test results. Table 6.2contains the output, and unemployment equations with short lags, jointlyestimated from the (2) and (4) system which impose the cross-equationrationality constraints. The resulting 'Y estimates for the models of table6.2 and the following tables are in Appendix 6.4.

The table 6.2 models fit the data well, and the unanticipated moneygrowth variables have significant explanatory power: many of their coefficients' asymptotic t statistics are greater than four in absolute value. Thetest results in table 1 become clearer when we study the estimated outputand unemployment equations where current and lagged anticipatedmoney growth are added as explanatory variables. The table 6.3 resultsillustrate why the neutrality proposition is not rejected for the outputequation. The coefficients on anticipated money growth have no obviouspattern, are never significantly different from zero, and, in seven out ofeight cases, are smaller in absolute value than their asymptotic standarderrors. However, in the unemployment equation some coefficients onanticipated money growth are significantly different from zero at the 5percent level, and this is enough to reject neutrality. Here, the last twolag coefficients on anticipated money growth are the most significant,with asymptotic t statistics exceeding 2.5. This creates the suspicion thateven longer lag lengths for unanticipated and anticipated money growthmay lead to strong rejections of the MRE hypothesis.

Table 6.4 contains estimates of the output and unemployment equations in which longer lags (twenty) of unanticipated money growth areused as explanatory variables. Tables 6.5 and 6.6 demonstrate why strongrejections of the MRE hypothesis now occur. Many of the coefficients onanticipated money growth are now significantly different from zero at the1 percent level, with some asymptotic t statistics even exceeding four inabsolute value. Of course these coefficients may be statistically significantand still unimportant from an economic viewpoint; but this is clearly notthe case. The unanticipated coefficients not only tend to be greater inabsolute value than their unanticipated counterparts, but generally theyhave higher asymptotic t statistics as well. In fact, only one out oftwenty-one r3 coefficients is statistically significant, as opposed to nearlyhalf of the B coefficients. Contrary to what is implied by the MREhypothesis, anticipated monetary policy does not appear to be less important than unanticipated monetary policy. In fact, the opposite seems to bethe case.

Tab

le6.

2N

onli

near

Est

imat

eso

fO

utp

ut

and

Une

mpl

oym

ent

Equ

atio

nsE

xpla

nato

ryV

aria

bles

:U

nant

icip

ated

Mon

eyG

row

th,

Sev

enL

ags

(PD

L)

7

Yt=

C+

TT

IME

+I

f3i(

M1G

t-i

-M1G~-J

+P

1Et-

l+

P2E t

-2+

P3E t

-3+

P4E t

-4+

TIt

i=O

Mod

el:

Dep

end

ent

Var

iabl

e:2.

110

g(G

NP

t)

2.2

UN

t

C=

6.17

8(.0

47)*

*

~o

=.7

15(.

230)

**~l

=1.

617(

.340

)**

f32=

2.19

6(.4

14)*

*f33

=2.

412(

.467

)**

~4

=2.

273(

.485

)**

f3s

=1.

835(

.449

)**

~6

=1.

262(

.371

)**

f37=

.524

(.25

5)*

P1

=1.

109(

.117

)**

P2=

-.3

45(.

172)

*

T=

.008

(.00

05)

P3=

.162

(.16

9)P4

=.0

02(.

115)

C=

3.55

(1.5

4)*

~o

=-

20.0

1(8.

69)*

*f31

=-4

3.21

(15.

38)*

*f32

=-7

0.0

4(1

7.9

4)*

*f33

=-

87.8

0(19

.63)

**f34

=-

89.5

8(20

.20)

**f3

s=

-74.

20(1

8.30

)**

f36=

-46

.27(

14.2

3)**

f37=

-16

.16

(9.

04)

PI=

1.46

4(.1

12)*

*P2

=-

.763

(.20

1)**

T=

.024

(.01

8)

P1=

.077

(.20

2)P4

=.1

44(.

115)

R2

=.9

988

SE

=.0

0851

D-W

=2.

02R

2=

.950

7S

E=

.304

9D

-W=

2.18

Not

e:E

stim

ated

from

the

(2)

and

(4)

syst

em,

impo

sing

the

cros

s-eq

uati

onco

nstr

aint

sth

at'Y

iseq

ual

in(2

)an

d(4

).T

he

f3iar

eco

nstr

aine

dto

lie

alon

ga

four

th-o

rder

poly

nom

ialw

ith

the

endp

oint

cons

trai

ned.

Asy

mpt

otic

stan

dard

erro

rsar

ein

pare

nthe

ses.

SE

=st

anda

rder

ror

of

the

equa

tion

(th

eun

bias

edes

tim

ate)

=th

esq

uare

root

of

the

sum

of

squa

red

resi

dual

s(S

SR

)di

vide

dby

~th

ede

gree

so

ffre

edom

,e.

g.,

iteq

uals

V2(

SS

R)1

161

inta

bles

6.2

and

6.4;

TIM

E=

tim

etr

end

=29

in19

54:1

...

120

in19

76:4

;M

IG-

M1G

e=

unan

tici

pate

dM

lgr

owth

;10g

(GN

Pt)

=lo

go

frea

lGN

P;

UN

t=

aver

age

quar

terl

yun

empl

oym

ent

rate

.

*Sig

nifi

cant

atth

e5

perc

ent

leve

l.

**S

igni

fica

ntat

the

1pe

rcen

tle

vel.

Tab

le6.

3N

onli

near

Est

imat

esof

Out

put

and

Une

mpl

oym

ent

Equ

atio

nsE

xpla

nato

ryV

aria

bles

:U

nant

icip

ated

and

Ant

icip

ated

Mon

eyG

row

th,

Seve

nL

ags

(PD

L)

77

Yt=

C+

,.T

IME

+I

f3i(

M1G

t-i-

M1G~-i)

+I

8iM1G~-i

+P

IEt-

l+

P2

Et-

2+

P3

Et-

3+

P4

Et-

4+

l1t

i=O

i=O

Mod

el:

Dep

end

ent

Var

iabl

e:3.

110

g(G

NP

t)

3.2

UN

t

c=

6.19

4(.0

60)*

*

f30=

.660

(.2

43)*

*f31

=1.

263(

.599

)*f32

=2.

191(

.814

)**

f33=

2.95

3(.9

93)*

*f34

=3.

240(

1.09

7)**

f35=

2.93

2(1.

046)

**f36

=2.

092(

.841

)*f37

=.9

67(

.533

)

PI

=1.

121(

.119

)**

P2

=-

.350

(.17

6)*

,.=

.008

(.00

08)

8 0=

.402

(.56

4)8 1

=-

.211

(.66

9)8 2

=-

.568

(.75

3)8 3

=-

.621

(.77

6)8 4

=-

.397

(.72

0)8 5

=-

.002

(.60

6)8 6

=.3

82(.

542)

8 7=

.495

(.48

3)

P3

=.0

75(.

193)

P4

=.0

91(.

128)

c=

3.00

(1.7

4)

f30=

-14

.90

(8.

70)

f31=

25.1

6(19

.53)

f32=

-61

.33(

24.9

0)*

f33=

-96

.52(

30.3

4)**

f34=

-11

3.5

9(3

4.0

7)*

*f35

=-1

05

.18

(32

.60

)**

f36=

-73

.70

(25

.42

)**

f37=

-31

.33(

14.5

1)*

PI

=1.

450(

.111

)**

P2

=-

.740

(.19

9)**

,.=

.04(

.025

)

8 0=

-10

.82

(15

.43

)8 1

=6.

32(1

9.82

)8 2

=12

.72(

23.4

3)8 3

=-7

.47

(25

.55

)8 4

=-7

.12

(24

.10

)8 5

=-

25.5

2(19

.10)

8 6=

-38

.98(

15.2

0)*

8 7=

-35

.54(

13.3

3)**

P3

=-

.031

(.20

5)P

4=

-.2

50(.

120)

R2

=.9

989

SE

=.0

0845

D-W

=2.

01R

2=

.954

3S

E=

.297

0D

-W=

2.20

Not

e:E

stim

ated

from

the

(2)

and

(6)

syst

em,

impo

sing

~=

~*.

Th

ef3i

and

8 iar

eco

nstr

aine

dto

lie

alon

ga

fou

rth

-ord

erpo

lyno

mia

lw

ith

the

endp

oint

cons

trai

ned.

*Sig

nifi

cant

atth

e5

perc

ent

leve

l.

**S

igni

fica

ntat

the

1pe

rcen

tle

vel.

Tab

le6.

4N

onli

near

Est

imat

esof

Out

put

and

Une

mpl

oym

ent

Equ

atio

nsE

xpla

nato

ryV

aria

bles

:U

nant

icip

ated

Mon

eyG

row

th,

Tw

enty

Lag

s(P

DL

)zo

Yt=

C+

7T

IME

+I

~i(M1Gt-i

-M1G~_i)

+P

IEt-

l+

PZE

t-2

+P

3Et-

3+

P4E

t-4

+'ll

ti=

O

Mod

el:

Dep

ende

ntV

aria

ble:

4.1

10g(

GN

Pt)

4.2

UN

t

c=

6.18

1(.0

53)*

*

~o

=.7

51(.

230)

**~1

=1.

578(

.328

)**

~z

=2.

060(

.440

)**

~3

=2.

266(

.519

)**

~4

=2.

255(

.573

)**

~s

=2.

086(

.612

)**

~6

=1.

806(

.645

)**

~7

=1.

459(

.674

)*(38

=1.

084(

.697

)~9

=.7

12(.

713)

J310

=.3

70(.

716)

PI

=1.

140(

.117

)**

P2=

-.3

33(.

174)

7=

.008

(.00

05)

~1l

=.0

76(.

682)

f312

=-

.154

(.68

2)J31

3=-

.313

(.64

5)~14

=-

.398

(.59

9)f3I

S=

-.4

14(.

549)

~16

=-

.370

(.49

8)f3

17=

-.2

81(.

447)

(318

=-

.169

(.38

7)~19

=-

.061

(.30

7)f3

20=

.008

(.18

5)

P3

=.1

30(.

171

)P

4=

-.0

11(.

116)

C=

3.94

(1.8

5)*

~o

=-

25.3

0(7.

94)*

*~1

=-

53.6

4(12

.97)

**J3

2=

-69.

55(1

7.46

)**

~3

=-7

5.53

(20.

28)*

*f34

=-7

3.85

(21.

92)*

*f3

s=

-66

.55(

22.9

7)**

~6

=-

55.4

7(23

.83)

*(3

7=

-42

.23(

24.6

9)~8

=-2

8.21

(25.

51)

~9

=-1

4.56

(26.

15)

(310

=-

2.23

(26.

45)

PI=

1.46

0(.1

13)*

*P2

=-

.720

(.20

2)**

7=

.019

(.21

)

J311

=8.

07(2

6.27

)f31

Z=

15.8

3(25

.57)

f313

=20

.79(

24.3

9)f3

14=

22.8

8(22

.85)

f31S

=22

.30(

21.1

1)J3

16=

19.4

2(19

.29)

~17

=14

.87(

17.3

8)f31

8=

9.48

(15.

12)

~lQ

=4.

31(1

2.00

)f3z

o=

.65(

7.27

)

P3=

.063

(.20

4)P

4=

.124

(.13

3)

RZ

=.9

987

SE

=.0

0872

D-W

=2.

00R

2=

.949

3S

E=

.308

9D

-W=

2.13

Not

e:E

stim

ated

from

the

(2)

and

(4)

syst

em,

impo

sing

the

cros

s-eq

uati

onco

nstr

aint

sth

at'Y

iseq

ual

in(2

)an

d(4

).T

he

J3iar

eco

nstr

aine

dto

lie

alon

ga

four

th-o

rder

poly

nom

ial

wit

hth

een

dpoi

ntco

nstr

aine

d.*S

igni

fica

ntat

the

5pe

rcen

tle

vel.

**Si

gnif

ican

tat

the

1pe

rcen

tle

vel.

Tab

le6.

5N

onli

near

Est

imat

esof

Out

put

Equ

atio

nE

xpla

nato

ryV

aria

bles

:U

nant

icip

ated

and

Ant

icip

ated

Mon

eyG

row

th,

Tw

enty

Lag

s(P

DL

)2

02

0

Lo

g(G

NP

t)=

c+

,.TIM

E+

2f3

i(M1G

t-i-

M1G~-i)

+2

oiM1G~-i+

PI

Et-l+

P2

Et-

2+

P3

Et-

3+

P4

Et-

4+

TIt

i=O

i=O

Mod

el:

Dep

ende

ntV

aria

ble:

130=

.645

(.23

7)**

131=

.402

(.40

5)132

=.3

05(.

570)

133

=.3

16(.

666)

134=

.400

(.71

3)13

5=

.525

(.73

6)f36

=.6

66(.

756)

137

=.8

00(.

780)

138

=.9

09(.

811)

139=

.980

(.84

0)13

10=

1.00

4(.8

61)

5.1

10g(

GN

Pt)

c=

6.21

2(.0

32)*

*

1311

=.9

78(.

865)

1312=

.899

(.84

9)13

13=

.773

(.81

3)f31

4=

.608

(.76

1)131

5=.4

17(.

700)

1316=

.217

(.63

0)131

7=.0

30(.

561)

1318

=-

.117

(.48

3)131

9=-

.196

(.38

2)13

20=

-.1

70

(.2

32

)

PI=

1.05

1(.1

15)*

*P2

=-

.238

(.17

1)

,.=

.007

(.00

06)

00=

1.29

3(.3

65)*

*01

=1.

733(

.388

)**

02=

1.94

4(.4

29)*

*03

=1.

972(

.446

)**

04=

1.85

8(.4

40)*

*05

=1.

639(

.419

)**

06=

1.35

1(.3

93)*

*07

=1.

023(

.370

)**

08=

.682

(.35

4)09

=.3

49(.

345)

010

=.0

44(.

339)

P3=

.081

(.16

9)P4

=-.

106

(.11

1)

011

=-

.219

(.33

3)01

2=

-.4

29(.

326)

013

=-

.578

(.32

2)8 1

4=

-.6

64(.

322)

*01

5=

-.6

86(.

329)

*01

6=

-.6

49(.

338)

017

=-

.561

(.34

2)8 1

8=

-.4

35(.

328)

019

=-

.285

(.27

8)02

0=

-.1

33(.

176)

R2

=.9

989

SE

=.0

0838

D-W

=2.

16

Not

e:E

stim

ated

from

the

(2)

and

(6)

syst

em,

impo

sing

"(=

"(*.

The

J3ian

d8 i

are

cons

trai

ned

tolie

alon

ga

four

th-o

rder

poly

nom

ial

wit

hth

een

dpoi

ntco

nstr

aine

d.*S

igni

fica

ntat

the

5pe

rcen

tle

vel.

**Si

gnif

ican

tat

the

1pe

rcen

tle

vel.

Tab

le6.

6N

onlin

ear

Est

imat

eso

fU

nem

ploy

men

tE

quat

ion

Exp

lana

tory

Var

iabl

es:

Una

ntic

ipat

edan

dA

ntic

ipat

edM

oney

Gro

wth

,T

wen

tyL

ags

(PD

L):

20

20

UN

t=C

+1"

TIM

E+

I~i(M1Gt-i

-M1G~_i)

+I

8iM1G~-i+

PIEt-

l+

P2Et-

2+

P3Et-

3+

P4Et-

4+

11t

i=O

i=O

Mod

el:

Dep

ende

ntV

aria

ble:

~O

=-1

8.3

8(

8.36

)*~1

=-

25.4

1(14

.34)

~2

=-

28.0

9(19

.95)

~3

=-

27.3

0(23

.51)

~4

=-

28.8

5(25

.74)

~5

=-

18.5

0(27

.40)

~6

=-1

1.8

9(2

8.9

8)

~7

=-

4.65

(30.

62)

138=

2.71

(32.

71)

~9

=9.

73(3

3.36

)f31

0=

16.0

2(33

.93)

6.1

UN

t

C=

3.28

(1.7

9)

f311

=21

.29(

33.6

9)~12

=25

.28(

32.5

5)f3

13=

27.8

3(30

.59)

~14

=28

.84(

27.9

8)f3

15=

28.3

0(25

.00)

~16

=26

.24(

21.9

6)~17

=22

.79(

19.0

5)~18

=18

.14(

16.1

8)13

19=

12.5

6(12

.76)

~20

=6.

37(

7.78

)

P1=

1.44

2(.

112)

**P2

=-

.690

(.19

9)**

1"=

.067

(.03

1)*

8 0=

-17

.09

(12

.27

)8 1

=-3

8.80

(12.

87)*

*8 2

=-5

2.16

(14.

38)*

*8 3

=-5

8.66

(15.

37)*

*8 4

=-

59.6

7(15

.70)

**8 5

=-

56.4

3(15

.56)

**8 6

=-5

0.10

(15.

18)*

*8 7

=-

41.6

9(14

.69)

**8 8

=-3

2.1

0(1

4.1

7)*

8 9=

-22

.13(

13.6

1)8

10=

-12

.44

(12

.96

)

P3=

-.0

08(.

202)

P4=

.171

(.11

3)

8 11

=-

3.59

(12.

22)

8 12

=3.

98(1

1.47

)8 1

3=

9.95

(10.

84)

8 14

=14

.11(

10.5

2)8 1

5=

16.3

9(10

.58)

816

=16

.80(

10.9

1)8 1

7=

15.4

8(11

.13)

8 18

=12

.71(

10.7

5)8 1

9=

8.86

(9.

19)

8 20

=4.

42(

5.82

)

Not

e:S

eeta

ble

6.5.

*Sig

nifi

cant

atth

e5

perc

ent

leve

l.**

Sign

ific

ant

atth

e1

perc

ent

leve

l.

R2

=.9

539

SE

=.2

983

D-W

=2.

26


Interpreting the 8 coefficients of anticipated money growth poses somedifficulties. One natural tendency is to make inferences about long-runneutrality by testing whether the sum of the 8 coefficients differs fromzero. The following implicit question is being asked: What will be theoutput or unemployment response to a permanent increase of 1 percentin the expected rate of money growth? Lucas (1976), Sargent (1971,1977), and Mishkin (1979) show that this question cannot be answeredwith reduced-form models, of which the MRE model is one example. Theparameters of the MRE model are not invariant to changes in the timeseries process of money growth and thus cannot yield reliable inferencesabout what will happen when the time-series process of money growthdiffers from that in the sample period. As the money growth equations inthe appendices in this and in Chapter 5 indicate, the time-series process ofmoney growth is stationary and is quite different from a random walk.Yet a permanent increase in expected money growth is consistent onlywith a random walk time-series process. Trying to use the estimatedMRE model here to make inferences about the response to a permanentincrease in expected money growth is thus inappropriate.

Furthermore, most structural macroeconometric models in use do notdistinguish between anticipated and unanticipated monetary policy andare incapable of interpreting the lag patterns of the 8' s versus the J3's intables 6.5 and 6.6. It is not obvious what form these lag patterns shouldtake in a model where expectations are rational, yet anticipated monetarypolicy matters. Econometric models of this type are only now beingdeveloped-Taylor (1979), for example-but to my knowledge simulation results displaying the reduced-form ~ and 8 coefficients are not yetavailable.

Output and unemployment models were also estimated using M2growth rather than Ml growth as the policy variable. Here the Granger(1969) criterion generates a specification of the M2 equation that includesonly past M2 growth and Treasury Bill rates as explanatory variables. Theresults are not reported here in the interests of brevity, but they indicatethat using M1 rather than M2 in the estimated models does not change theconclusions. 5 However, using unanticipated M2 growth rather than M1growth does lead to some deterioration in the fit of the equations as wellas lower asymptotic t statistics.

It does not seem to matter, either, whether seasonally adjusted orseasonally unadjusted data are used in the empirical work here. Season-

5. E.g., the freely estimated A14.1 M2 model does not lead to rejection of the jointhypothesis. The likelihood statistic is X2(15) = 18.1 with a marginal significance level of .26.However, the M2 results for the longer lag models explored in this chapter are just asnegative to the MRE hypothesis. E.g., the freely estimated A15.1 model with M2 data leadsto a likelihood ratio statistic for the joint hypothesis of X2(28) = 58.90 with a marginalsignificance level of .0006.


ally unadjusted M1 data in output and unenlployment models give resultsnot appreciably different from seasonally adjusted data. 6 The empiricalwork in Chapters 4 and 5 that use models resembling the one here alsofind results not appreciably affected by the choice of seasonally adjustedover unadjusted data.

The money growth results here are much less favorable to the MREhypothesis than previous work. Which of the several differences in theanalysis here from that of earlier work might explain the less favorableresults? As pointed out in Chapter 2, the joint nonlinear estimationprocedure used here is even more favorable to the null hypothesis thanthe two-step procedure used in previous work, so this procedure cannotbe the cause of the rejections. Polynomial distributed lags have been usedin order to insure that rejections of the MRJE hypothesis are not spurious.They have made very little difference to the results and do not appear tobe a factor in the rejections.

The money growth specifications yielded by the procedure used here issubstantially different from specifications in previous studies. In contrastto those, neither real government expenditures nor unemployment areexplanatory variables in the money growth equation. Because so much ofthe debate on the MRE hypothesis has focused on the specification of themoney growth equation (see Barro 1977; Small 1979; Germany andSrivastava 1979; Blinder 1980; Weintraub 1980), we may wonder whetherthis different specification is central to the :findings. A comparison of thefindings here with those from the other study that analyzes postwarquarterly data, Barro and Rush (1980), should help answer this question.

The models of table 6.2 that have the same seven-quarter lag lengthused in Barro and Rush yield results very similar to theirs, even thoughthey use a different specification for the mloney growth equation. As inBarro and Rush, the models in this study fit the data well, the unanticipated money growth variables have significant explanatory power, andthe tests of the rationality and neutrality constraints are not unfavorableto the MRE hypothesis. Most striking is the similarity of the parameterestimates. Not only do the table 6.2 models display the same pattern ofserial correlation in the residuals as the Barro and Rush results, but thelag structure has the same humped pattern and peaks at identical lags.

6. Because a fourth-order autoregression is not sufficient to reduce the seasonallyunadjusted Ml growth to white noise, values of the unadjusted Ml growth for lags fivethrough eight replaced the SURP variables in the forecasting equation specification. Thecoefficients and asymptotic standard errors of the fret~ly estimated A14.1 model estimatedwith unadjusted data are close to those using the adjusted data. In this case the likelihoodratio statistic of the joint hypothesis is X2(19) = 29.75 with a marginal significance level of.0551. The unadjusted results for the long lag A15.l model are unfavorable to the MREhypothesis. So are the results using adjusted data: the likelihood ratio statistic for the jointhypothesis is X2(32) = 62.65 with a marginal significance level of .0010.


The close resemblance between the table 6.2 results and those of Barroand Rush is an important finding. Although misspecification of themoney growth forecasting equation would lead to an error-in-variablesbias in the coefficients of the unemployment or output equation, thepreceding chapter has argued and found evidence that the bias should notbe severe. The similarity of the results in table 6.2 to those of Barro andRush lends support to this view, and further support comes from thesimilarity of the M2 and M1 results where the specification of the moneygrowth forecasting equation also differs.

The similarity of the table 6.2 and Barro-Rush results certainly showsthat using a different sample period from Barro and Rush's is not whatcaused the MRE hypothesis to be rejected. By a process of elimination,we are left with the longer lag lengths as the key reason why this chaptercontains results so much more unfavorable to the MRE hypothesis.However, there are three other minor differences between the modelshere and those in Barro and Rush: (1) a fourth-order AR serial correlation correction rather than a second-order AR correction, (2) exclusionof government expenditure variables from the output and employmentequations, and (3) a different definition of the unemployment variable.Could these differences lead to the rejections found here? To ascertainthe effect of these differences, the long lag models were reestimated sothat the output and unemployment equations conformed to the Barroand Rush specification. The resulting models are found in Appendix 6.1.

As Barro and Rush found, the coefficient on their government expenditure variables do have the expected sign, indicating that a rise in government expenditure is associated with higher output and lower unemployment. Although the government expenditure variable does not exhibitsignificant additional explanatory power in the unemployment equation,it does so in the output equation. There the coefficient on the log ofgovernment expenditure is significantly different from zero at the 1percent level: it is over three times its standard error. However, it is notclear that actual government expenditure belongs in an output or unemployment equation consistent with the MRE hypothesis. Some distinction between anticipated and unanticipated seems called for in this case.An attempt was made to estimate models that make this distinction, butthe attempt was not very successful: the Granger criterion led to aspecification of the government expenditure forecasting equation wherethe identification condition discussed in Chapter 2 was not satisfied: thatis, no other variables besides past government expenditure were found tobe significant explanatory variables in this equation. This is the reasonwhy, despite its use by Barro and Rush, no form of government expenditure was included as an explanatory variable in the models of tables6.1-6.6.


The basic finding in Appendix 6.1 is that the three changes in specification suggested by Barro and Rush (1980) clo not appreciably affect theresults. The test statistics are quite close to those found for the models intables 6.1-6.6. The strong rejections of the MRE hypothesis hold up.Furthermore, contrary to the MRE hypothesis, anticipated monetarypolicy continues to be more important than unanticipated monetarypolicy in these results. As in tables 6.5 and 6.6, the coefficients onanticipated money growth are larger and more statistically significantthan those of unanticipated money growth.

6.4 Conclusions

This chapter asks the question, "Does Anticipated Aggregate DemandPolicy Matter?" The reported findings answer this question with a strong"yes": anticipated policy does seem to matter.

The most important results are those with money growth as the aggregate demand variable. These results strongly reject the neutrality proposition of the MRE hypothesis. Furthermore, contrary to the implications of the MRE hypothesis, unanticipated movements in monetarypolicy do not have a larger impact on output and unemployment thananticipated movements. The other proposition embodied in the MREhypothesis, that expectations are rational, fares better in the empiricaltests here. When the MRE component hypotheses of rationality andneutrality are tested jointly, strong rejections occur in both the outputand unemployment models. In one case, the probability of finding thesame or higher value of the likelihood ratio statistic under the nullhypothesis is only 1 in 10,000. The crucial factor in the unfavorablefindings on the MRE hypothesis appears to be the inclusion of long lags inthe output and unemployment equations. The results here thus givefurther impetus to theoretical research (see Blinder's 1980 discussion)that is currently exploring why long lags may exist in rational expectationsmodels of the business cycle.

Models with longer lags are less restrictive. The rejections in thesemodels are therefore very damaging to earlier evidence in support of theMRE hypothesis obtained from models with shorter lags. As discussed inChapter 2, the only cost to estimating the models with longer lags is apotential decrease in the power of the test statistics. Rejections in thiscase are thus even more telling. The failure to reject the MRE hypothesisin shorter lag models appears to be the result of an overly restrictivespecification that leads to inconsistent paranleter estimates and incorrecttest statistics.

There is one qualification of the results that warrants further discussion. The methodology used here follows previous research in this area


by using the identifying assumption that the output and unemploymentequations are true reduced forms. It is not clear whether, if this assumption proved invalid, it might lead to rejections of the MRE hypothesiseven if the hypothesis was true. The money growth results here are thenby no means a definitive rejection of this hypothesis. However, this workdoes cast doubt on the previous evidence, also of a reduced-form nature,marshaled to support the view that only unanticipated monetary policy isrelevant to the business cycle.

The above qualification is even more important for the results inAppendix 6.3 where the aggregate demand variables are nominal GNPgrowth or inflation, both of which are less likely to be exogenous. However, these results confirm the money growth results. Rejections ofneutrality are extremely strong. In one case, for example, the probabilityof finding that value of the likelihood ratio statistic under the null hypothesis of neutrality is only 1 in 200,000. The hypothesis of rational expectations fares much better in these tests. Although the rationalityhypothesis does not come out unscathed-there is one rejection at the 5percent level, but just barely-it is not rejected in any other tests in thisappendix at the 5 percent level. 7 This result might encourage those whoare willing to assume rationality of expectations in constructing theirmacro models, yet are unwilling to assert the short-run neutrality ofpolicy.

7. I do not cite the rationality test results in Appendix 6.3. In Chapter 2 I explain whythey may not be reliable because of small sample bias.

App

endi

x6.

1:O

utpu

tan

dU

nem

ploy

men

tM

odel

sw

ith

Bar

roan

dR

ush

Spec

ific

atio

n

Tab

le6.

A.l

Non

line

arE

stim

ates

ofO

utpu

tan

dU

nem

ploy

men

tE

quat

ions

Exp

lana

tory

Var

iabl

es:

Una

ntic

ipat

edM

oney

Gro

wth

,T

wen

tyL

ags

(PD

L)

and

Gov

ernm

ent

Exp

endi

ture

Var

iabl

eszo

Yt=

C+

TT

IME

+eG

t+I

~i(M

1Gt-

i-M1G~_i)

+P

IEt-

1+

pzE

t-Z+

Tit

i=

0

Mod

el:

Dep

ende

ntV

aria

ble:

A1.

1lo

g(G

NP

t)

A1.

2lo

g[U

Ntl(1

-U

Nt)

]

~zo

=.3

94(.

162)

*

C=

-2.

86(.

53)*

*T

=.0

06(.

004)

e=-4

.30

(2.4

6)

r30=

-4.

98(1

.58)

**r31

1=

-12.

67(6

.43)

*~l

=-

9.38

(2.8

2)**

~IZ

=-1

1.2

7(6

.26

)~z

=-1

2.65

(3.7

8)**

r313

=-9

.84

(5.9

3)

r33=

-14.

93(4

.34)

**r31

4=

-8.

43(5

.48)

~4

=-1

6.37

(4.6

9)**

~15

=-7

.06

(4.9

6)

~5

=-1

7.10

(4.9

7)**

~16

=-5

.76

(4.4

2)

~6

=-1

7.24

(5.2

7)**

r317

=-4

.51

(3.8

9)

r37=

-16.

90(5

.62)

**~18

=-

3.34

(3.3

4)(J

-_1~10('-::0"7\**

0-

'1'1

1f'

1t:

:If\

fJ8

-.L

v•.L

./\.

.J•./

I)

fJ1

9-

~.~~\~.U"1')

~9

=-1

5.20

(6.2

6)*

r3zo

=-1

.11

(1.6

0)

r310

=-1

4.00

(6.4

2)* PI

=1.

460(

.089

)**

pz=

-.6

28(.

087)

**

e=

.139

(.03

0)**

~ll

=.5

30(.

340)

~12

=.4

26(.

324)

~13

=.3

86(.

309)

~14

=.4

03(.

300)

~IS

=.4

64(.

297)

r316

=.5

46(.

303)

r317

=.6

19(.

307)

*~18

=.6

49(.

296)

*A

-,,

01

("'

''A\*

""1

')'-

..J/.J.\...

.J""TJ

C=

5.57

9(.1

40)*

*T

=.0

08(.

0003

)**

~o

=.7

36(.

218)

**~l

=1.

523(

.269

)**

~z

=1.

974(

.345

)**

~3

=2.

162(

.389

)**

r34=

2.15

2(.4

05)*

*r3s

=2.

004(

.403

)**

r36=

1.76

7(.3

92)*

*~7

=1.

485(

.381

)**

J38=

1.19

5(.3

71)*

*r39

=.9

26(.

363)

*~10

=.6

99(.

353)

*

PI=

.993

(.11

0)**

pz=

-.2

73(.

110)

*

RZ

=.9

989

SE

=.0

0808

D-W

=2.

02R

Z=

.951

2S

E=

.058

8D

-W=

2.14

Not

e:E

stim

ates

from

(2)

and

(4)

syst

em(w

here

[4]

incl

udes

the

eGtte

rm)

impo

sing

the

cros

s-eq

uati

onco

nstr

aint

sth

at~

iseq

uali

n(2

)an

d(4

).T

he~i

are

cons

trai

ned

tolie

alon

ga

four

th-o

rder

poly

nom

ial

wit

hth

een

dpoi

ntco

nstr

aine

d.G

t=lo

g(G

EX

Pt)

inA

Ll,

whe

reG

EX

Pti

sre

alfe

dera

lgo

vern

men

tex

pend

itur

efo

rqu

arte

rt,

and

Gt=

GE

XP

tlG

NP

tin

A1.

2.*S

igni

fica

ntat

the

5pe

rcen

tle

vel.

**Si

gnif

ican

tat

the

1pe

rcen

tle

vel.

Table 6.A.2 Likelihood Ratio Tests for the Models of Table 6.A.l

Model

Joint hypothesis:Likelihood ratio statisticMarginal significance level

Neutrality:Likelihood ratio statisticMarginal significance level

RationalityLikelihood ratio statisticMarginal significance level

*Significant at the 5 percent level.**Significant at the 1 percent level.

ALl

X2(15) = 43.02**.0002

X2( 4) = 13.13*

.0106

X2(11) = 30.45**.0013

A1.2

X2(15) = 31.26**.0081

X2(4) = 13.78**.0081

X2(11) = 18.80.0648

Tab

le6.

A.3

Non

line

arE

stim

ate

ofO

utpu

tE

quat

ion

Exp

lana

tory

Var

iabl

es:

Una

ntic

ipat

edan

dA

ntic

ipat

edM

oney

Gro

wth

,T

wen

tyL

ags

(PD

L),

and

Gov

ernm

ent

Exp

endi

ture

Var

iabl

e2

02

0

Log

(GN

Pt)

=C

+T

TIM

E+

eGt+

I~i

(M1

Gt~

i-

M1

qe_

J+

I8 i

M1

qe_

i+

PIE

t-l

+P

2Et-

2+

llti

=0

i=

0

Mod

el:

Dep

ende

ntV

aria

ble:

~o

=.5

66(.

225)

*~1

=.1

84(.

366)

~2

=-

.098

(.53

6)~3

=-

.300

(.66

0)~4

=-

.440

(.74

8)~5

=-

.535

(.81

3)~6

=-

.597

(.86

5)~7

=-

.638

(.90

8)~8

=-

.667

(.94

0)~9

=-

.692

(.95

9)~10

=-

.716

(.96

1)

C=

5.57

0(.1

84)*

*

~11

=-

.742

(.94

5)~12

=-.

771(

.909

)~13

=-

.799

(.85

4)~14

=-

.822

(.78

5)~15

=-

.834

(.70

6)~16

=-

.825

(.62

3)~17

=-.

785(

.538

)~I8

=-

.699

(.44

9)~19

=-

.552

(.34

4)~20

=-

.326

(.20

3)

A3.

1lo

g(G

NP

t)

T=

.007

(.00

06)*

*e=

.129

(.03

8)**

8 0=

1.32

1(.3

37)*

*8 1

=1.

690(

.337

)**

8 2=

1.88

1(.3

72)*

*8 3

=1.

926(

.402

)**

8 4=

1.85

6(.4

16)*

*8 5

=1.

701(

.418

)**

8 6=

1.48

5(.

411

)**

8 7=

1.23

2(.3

99)*

*8 8

=.9

61(.

384)

*8 9

=.6

91(.

364)

8 10

=.4

34(.

341)

PI

=.9

67(.

113)

**P

2=

-.1

64(.

109)

8 11

=.2

04(.

313)

812

=.0

10(.

282)

8 13

=-

.143

(.25

2)8 1

4=

-.2

50(.

226)

8 15

=-

.311

(.21

1)8 1

6=

-.3

28(.

207)

8 17

=-

.304

(.20

9)8

18

=-

.248

(.20

3)8

19=

-.1

70(.

177)

8 20

=-

.082

(.11

4)

R2

=.9

990

SE

=.0

0779

D-W

=2.

08

Not

e:E

stim

ated

from

the

(2)

and

(6)

syst

em(w

here

[6]

incl

udes

the

eGtte

rm),

impo

sing

-y=

-y*.

The

~i

and

8;ar

eco

nstr

aine

dto

lieal

ong

afo

urth

-ord

erpo

lyno

mia

lw

ith

the

endp

oint

cons

trai

ned.

Gt=

10g(

GE

XP

t),

whe

reG

EX

Pt=

real

fede

ral

gove

rnm

ent

expe

ndit

ure

for

qu

arte

rt.

*Sig

nifi

cant

atth

e5

perc

ent

leve

l.

**Si

gnif

ican

tat

the

1pe

rcen

tle

vel.

Tab

le6.

A.4

Non

line

arE

stim

ate

of

Une

mpl

oym

ent

Equ

atio

nE

xpla

nato

ryV

aria

bles

:U

nant

icip

ated

and

Ant

icip

ated

Mon

eyG

row

th,

Tw

enty

Lag

s(P

DL

),an

dG

over

nmen

tE

xpen

ditu

reV

aria

ble

20

20

Log[

UN

el(l

-U

NJ]

=c

+,.

TIM

E+

aGe

+I

J3;(M

IGe-

;-

MIG

re _;)

+I

8;M

IGre

_;+

PIE

e-l

+P

2Ee-2

+TI

c;

=0

;=

0

Mod

el:

Dep

ende

ntV

aria

ble:

~o

=-4

.32(

1.53

)**

~1

=-

5.71

(2.7

5)*

J32=

-6.

60(3

.79)

J33=

-7.0

5(4

.36

)J34

=-7

.16

(4.6

1)

~5

=-6

.99

(4.7

4)

~6

=-6

.59

(4.8

8)

~7

=-

6.04

(5.1

0)~8

=-

5.38

(5.3

7)~9

=-

4.66

(5.6

3)~1O

=-

3.92

(5.8

2)

A4.

1lo

g[U

NcI

(l-

UN

e)]

c=

-2.6

4(.

47

)**

,.=

.011

(.00

4)**

~1l

=-

3.19

(5.8

7)~12

=-

2.51

(5.7

8)~13

=-1

.88

(5.5

4)

~14

=-1

.34

(5.1

7)

J315

=-

.89(

4.73

)~16

=-

.54(

4.26

)~17

=-

.29(

3.79

)~18

=-

.12(

3.27

)~19

=-

.03(

2.60

)~20

=.0

0(1.

58) P

I=

1.37

2(.0

94)*

*P

2=

-.5

26(.

090)

**

a=-

4.51

(2.4

9)

8 0=

-3.

34(2

.38)

8 1=

-8.

05(2

.63)

**8 2

=-1

0.95

(2.9

7)**

8 3=

-12.

34(3

.13)

**8 4

=-1

2.53

(3.1

2)**

8 5=

-11.

80(2

.99)

**8 6

=-1

0.37

(2.8

2)**

8 7=

-8.4

9(2

.66

)**

8 8=

-6.

35(2

.52)

*8 9

=-4

.12

(2.4

1)

8 10

=-1

.95

(2.3

1)

8 11

=.0

4(2.

21)

8 12

=1.

74(2

.13)

8 13

=3.

08(2

.10)

8 14

=4.

02(2

.16)

8 15

=4.

51(2

.30)

8 16

=4.

57(2

.47)

817

=4.

22(2

.58)

8 18

=3.

50(2

.52)

8 19

=2.

49(2

.17)

8 20

=1.

28(1

.37)

R2

=.9

572

SE

=.0

558

D-W

=2.

14

Not

e:E

stim

ated

from

the

(2)

and

(6)

syst

em(w

here

[6]

incl

udes

the

aGe

term

),im

posi

ng"I

="1

*.T

he

J3;an

d8;

are

cons

trai

ned

tolie

alon

ga

four

th-o

rder

poly

nom

ial

wit

hth

een

dpoi

ntco

nstr

aine

d.G

e=G

EX

Pel

GN

Po

whe

reG

EX

Pe

=re

alfe

dera

lgo

vern

men

tex

pend

itur

efo

rq

uar

ter

t.*S

igni

fica

ntat

the

5pe

rcen

tle

vel.

**S

igni

fica

ntat

the

1pe

rcen

tle

vel.


Appendix 6.2: Results with Nominal GNP Growth and Inflationas the Aggregate Demand Variable

Nominal GNP Growth as the Aggregate Demand Variable

The models here follow Gordon (1979) and Grossman (1979) in usingnominal GNP growth as the aggregate demand variable in the output andunemployment equations. We should be cautious in interpreting theresults because the assumptions that nominal GNP growth is exogenousand that the models are reduced forms are questionable. Nevertheless,these results will shed light on previous evidence on the MRE hypothesisusing nominal GNP growth as the X variable. Table 6.A.5 reports theoutput and unemployment equations that have been estimated from the(2) and (4) system, imposing the cross-equation constraints that the 'Yareequal in both equations. Twenty lagged quarters of unanticipated nominal GNP growth have been included in the models because coefficients onlags as far back as this are significantly different from zero at the 5 percentlevel-a result confirmed by Gordon (1979).8

The signs and shape of the A5.1 and A5.2 IIlodels are sensible, showingan increase in unanticipated nominal GNP growth usually associated withan increase in output or a decrease in unelIlployment. The fit of theseequations is good too-compare them, for example, with the results intable 6.2 and table 6.A.9-and several of the coefficients on unanticipated nominal GNP growth even exceed their asymptotic standard errorsby a factor of 10. The good fit is not surprising because we would expectnominal GNP fluctuations to track short-run movements accurately inreal GNP or unemployment if price level movements are smooth.

Despite these attractive results, table 6.A..6 indicates that the MREhypothesis is not supported. Both the unemployment and output modelslead to strong rejections of the joint hypothesis. Rejection in the outputmodel is at the .00001 level; in the unemploylnent model it is at the .0009leve1. 9 One reason for the stronger rejections here with nominal GNPgrowth as the aggregate demand variable may be that the higher correlation of this aggregate demand variable with output or unemploymentleads to tests with greater power. The most interesting aspect of theseresults is that the rationality constraints contribute very little to theserejections. In both models, the data do not reject the rationality ofexpectations. The culprit behind the rejections of the joint hypothesis is

8. See McCallum (1979b) for a critique of the Gordon (1979) study.9. As in the money growth results, the long lags for the unanticipated and anticipated

nominal GNP variables are critical to the negative findings on the MRE hypothesis. E.g., anoutput model with only seven lags of nominal GNP growth and the lag coefficients freelyestimated does not reject the joint hypothesis: X2(15) = 23.07 with a marginal significancelevel of .0827.

Tab

le6.

A.5

Non

line

arE

stim

ates

ofO

utpu

tan

dU

nem

ploy

men

tE

quat

ions

Exp

lana

tory

Var

iabl

es:

Una

ntic

ipat

edN

omin

alIn

com

eG

row

th,

Tw

enty

Lag

s,P

olyn

omia

lD

istr

ibut

edL

ags

20

Yt=

C+

Tti

me

+I

~lNGNPt-i

-NGNP~-i)

+P

IEt-

1+

P2

Et-

2+

P3

Et-

3+

P4

Et-

4+

TIt

i=O

Mod

el:

Dep

end

ent

Var

iabl

e:A

5.1

10g(

GN

Pt)

A5.

2U

Nt

C=

6.19

1(.0

43)*

*

~o

=.9

27(.

043)

**~I

=1.

134(

.106

)**

~2

=1.

246(

.171

)**

~3

=1.

281(

.220

)**

~4

=1.

253(

.256

)**

~5

=1.

178(

.280

)**

~6

=1.

067(

.296

)**

~7

=.9

33(.

305)

**~8

=.7

86(.

307)

*~9

=.6

36(.

304)

*~1O

=.4

88(.

294)

PI

=1.

285(

.110

)**

P2

=-

.073

(.17

9)

T=

.008

(.00

05)

~Il

=.3

51(.

279)

~12

=.2

29(.

258)

~13

=.1

26(.

233)

~14

=.0

44(.

203)

~15

=-

.016

(.17

2)~16

=-

.053

(.13

9)~17

=-

.069

(.10

7)~18

=-

.067

(.07

7)~19

=-

.051

(.05

2)~20

=-

.027

(.02

8)

P3

=-

.086

(.17

9)P

4=

-.1

65(.

110)

~O

~I ~2

~3 ~4 ~5 ~6 ~7 ~8 ~9 ~1O

=

C=

-138

.011

(184

0)

-25

.529

(2.

626)

**-5

3.5

59

(5.

102)

**-7

1.5

35

(7.

559)

**-

81.3

00(

9.40

9)**

-84

.534

(10.

785)

**

-82

.760

(11.

831)

-77.

342(

12.6

33)*

*-

69.4

86(1

3.22

5)**

-60

.237

(13.

595)

**-

50.4

83(1

3.71

5)**

-40

.952

(13.

549)

**

PI

=1.

227(

.112

)**

P2

=-

.300

(.17

8)

T=

.519

(3.4

08)

~1l

=-

32.2

13(1

3.07

7)*

~12

=-

24.6

76(1

2.29

7)*

~13

=-

18.5

93(1

1.23

6)~14

=-1

4.0

57

(9.

948)

~15

=-1

1.0

00

(8.

519)

~16

=-

9.19

9(7.

057)

~17

=-

8.26

8(5.

670)

~18

=-

7.66

4(4.

424)

~19

=-

6.68

5(3.

253)

*~20

=-

4.47

0(1.

911)

*

P3

=.0

58(.

179)

P4

=.0

12(.

115)

R2

=.9

998

SE

=.0

0350

D-W

=1.

89R

2=

.975

4S

E=

.212

67D

-W=

2.01

Not

e:E

stim

ated

from

the

(2)

and

(4)

syst

em,

impo

sing

the

cros

s-eq

uati

onco

nstr

aint

sth

at'Y

iseq

ual

in(2

)an

d(4

).T

he

~iar

eco

nstr

aine

dto

lie

alon

ga

four

th-o

rder

poly

nom

ial

wit

hth

een

dpoi

ntco

nstr

aine

d.

*Sig

nifi

cant

atth

e5

perc

ent

leve

l.

**S

igni

fica

ntat

the

1pe

rcen

tle

vel.


Table 6.A.6 Likelihood Ratio Tests for the Models of Table 6.A.5

Model

Model



Rationality:Likelihood ratio statisticMarginal significance level


A5.1

X2(11) = 43.19**1.01 x 10- 5

X2(4) = 30.22**4.41 x 10- 6

X2(7) = 12.86.0756

A5.2

X2(11) = 31.69**.0009

X2(4) = 19.90**.0005

X2(7) = 11.28.1269

the neutrality proposition. These neutrality rejections are exceedinglystrong: the probability of finding the same or higher value of the likelihood ratio statistic under the null hypothesis of neutrality is 1 in 2,000 forthe unemployment model and 1 in 200,000 for the output model! Clearly,in these models, anticipated nominal GNP growth does matter, andrejection of the neutrality constraints cannot be blamed on the failure ofthe maintained hypothesis of rationality. These results then lend somesupport to modeling strategies in which expectations are assumed to berational.

Tables 6.A.7 and 6.A.8 contain the results from the (2) and (6) systemwith rational expectations imposed. As we would expect from table6.A.6, many of the coefficients on anticipated nominal GNP growth aresignificantly different from zero at the 1 percent level, with some asymptotic t statistics even exceeding 7 in absolute value. The coefficients onanticipated nominal GNP growth are of a similar magnitude to thecoefficients on unanticipated nominal GNP growth. Contrary to what isimplied by the MRE hypothesis, anticipated aggregate demand policy asrepresented by nominal GNP growth is not obviously less important thanunanticipated aggregate demand policy.

Inflation as the Aggregate Demand Variable

The next set of results explores tl Lucas (1973) supply function whereinflation is the aggregate demand variable. We should be cautious ininterpreting these results, not only because the assumption that inflationis exogenous is tenuous, but also because the 'Y coefficients in the inflation-forecasting equation were not found to be stable. Table 6.A.9presents the output and unemployment equations estimated from theconstrained (2) and (4) system. The seventeen-quarter lag length on

Tab

le6.

A.7

Non

line

arE

stim

ates

ofO

utpu

tE

quat

ions

Exp

lana

tory

Var

iabl

es:

Una

ntic

ipat

edan

dA

ntic

ipat

edN

omin

alG

NP

Gro

wth

,T

wen

tyL

ags

(PD

L)

zozo

Log

(GN

Pt)

=C

+'T

TIM

E+

I~i(NGNPt-i

-NGNP~-i)

+I

8iNGNP~-i

+PI

E t-l+

pzE

t-z+

P3E t

-3+

P4E t

-4+

TIt

i=O

i=O

Mod

el:

Dep

ende

ntV

aria

ble:

A7.

1lo

g(G

NP

t)

~O

=.9

13(.

040)

**~1

=.8

15(.

058)

**~z

=.7

25(.

075)

**~3

=.6

40(.

090)

**~4

=.5

60(.

101)

**~5

=.4

86(.

110)

**~6

=.4

15(.

117)

**~7

=.3

49(.

123)

**~8

=.2

86(.

127)

*~9

=.2

27(.

130)

~10

=.1

72(.

130)

C=

6.12

7(.0

49)*

*

~11

=.1

21(.

128)

~12

=.0

75(.

124)

~13

=.0

34(.

117)

~14

=-

.002

(.10

9)~15

=-

.031

(.09

8)~16

=-

.052

(.08

7)~17

=-

.064

(.07

4)~18

=-

.067

(.06

1)~19

=-

.058

(.04

5)~zo

=-

.036

(.02

6)

PI=

1.20

7(.1

05)*

*pz

=.0

09(.

171)

'T=

.009

(.00

07)

8 0=

.744

(.09

8)**

8 1=

.745

(.10

4)**

8 z=

.688

(.12

6)**

8 3=

.588

(.15

0)**

8 4=

.460

(.17

3)**

8 5=

.315

(.19

5)8 6

=.1

63(.

215)

8 7=

.014

(.23

3)8 8

=-

.123

(.24

7)8 9

=-

.244

(.25

6)8 1

0=

-.3

42(.

266)

P3=

.030

(.17

0)P4

=-

.273

(.10

6)*

8 11

=-

.415

(.25

7)8 1

2=

-.4

60(.

248)

8 13

=-

.477

(.21

4)*

8 14

=-

.467

(.21

4)*

8 15

=-

.431

(.19

1)*

8 16

=-

.374

(.16

6)*

8 17

=-

.301

(.13

9)*

8 18

=-

.218

(.11

1)*

8 19

=-

.134

(.08

1)8 z

o=

-.0

58(.

046)

RZ

=.9

998

SE

=.0

0332

D-W

=1.

95

Not

e:E

stim

ates

from

the

(2)

and

(6)

syst

emim

posi

ng"I

="1

*.T

he

~ian

d8 i

are

cons

trai

ned

toli

eal

ong

afo

urth

-ord

erpo

lyno

mia

lw

ith

the

endp

oint

cons

trai

ned.

*Sig

nifi

cant

atth

e5

perc

ent

leve

l.**

Sig

nifi

cant

atth

e1

perc

ent

leve

l.

Tab

le6.

A.8

Non

line

arE

stim

ates

of

Une

mpl

oym

ent

Equ

atio

nE

xpla

nato

ryV

aria

bles

:U

nant

icip

ated

and

Nom

inal

GN

PG

row

th,

Tw

enty

Lag

s(P

DL

)2

02

0

UN

t=c

+T

TIM

E+

I~i(NGNPt-i-NGNP~-i)

+I

8iNGNP~-i+

PIEt-

l+

P2Et-

2+

P3Et-

3+

P4Et-

4+

'Ylt

i=O

i=O

Mod

el:

Dep

ende

ntV

aria

ble:

~O

=-2

3.90

(2.6

4)**

(31

=-3

5.22

(4.0

0)**

(32

=-4

1.42

(5.3

3)**

~3

=-4

3.60

(6.1

4)**

(34=

-42.

72(6

.51)

**~5

=-3

9.67

(6.5

8)**

~6

=-

35.2

1(6.

46)*

*(37

=-

30.0

1(6.

26)*

*~8

=-2

4.62

(6.0

4)**

(39=

-19.

50(5

.82)

**(3

10=

-15.

00(5

.61)

**

c=

-16

8.2

(24

20

)

~11

=-1

1.3

5(5

.38

)*~12=

-8.7

0(5

.14

)(3

13=

-7

.08(

4.88

)~14

=-

6.41

(4.6

4)(3

15=

-6.5

0(4

.41

)~16

=-7

.09

(4.2

0)

~17

=-7

.78

(3.9

5)*

(318

=-

8.06

(3.5

7)*

1319

=-7

.35

(2.9

2)*

(320

=-4

.93

(1.7

9)*

*

PI=

1.22

2(.1

12)*

*P2

=-

.324

(.18

0)

A8.

1U

Nt T

=.5

75(3

.85)

8 0=

-36

.46(

5.78

)**

8 1=

-40

.33(

5.36

)**

8 2=

-42.

27(5

.97)

**8 3

=-4

2.5

8(6

.71

)**

8 4=

-41

.55(

7.32

)**

8 5=

-39

.44

(7.8

0)*

*8 6

=-

36.5

1(8.

19)*

*8 7

=-

32.9

9(8.

50)*

*8 8

=-

29.0

7(R

.73)

**8 9

=-2

4.9

4(8

.86

)**

8 10

=-

20.7

8(8.

86)*

P3=

-.0

07(.

179)

P4=

.106

(.11

2)

8 11

=-

16.7

3(8.

73)

8 12

=-1

2.9

1(8

.47

)8 1

3=

-9.

44(8

.11)

8 14

=-

6.39

(7.6

9)8 1

5=

-3.8

4(7

.24

)8 1

6=

-1.8

2(6

.77

)8 1

7=

-.3

7(6.

24)

8 18

=.5

1(5.

50)

&1

9=

.84(

4.39

)8 2

0=

.65(

2.65

)

Not

e:S

eeta

ble

6.A

.7.

*Sig

nifi

cant

atth

e5

perc

ent

leve

l.

**S

igni

fica

ntat

the

1pe

rcen

tle

vel.

R2

=.9

766

SE

=.2

0999

D-W

=2.

06

Tab

le6.

A.9

Non

line

arE

stim

ates

ofO

utpu

tan

dU

nem

ploy

men

tE

quat

ions

Exp

lana

tory

Var

iabl

es:

Una

ntic

ipat

edIn

flat

ion,

Sev

ente

enL

ags,

Pol

ynom

ial

Dis

trib

uted

Lag

s17

Yt=

C+

TT

IME

+I

f3l7

Tt-

i-

7T~-

i)+

P1

Et-

1+

P2

Et-

2+

P3

Et-

3+

P4

Et-

4+

l1t

i=O

Mod

el:

Dep

ende

ntV

aria

ble:

A9.

1lo

g(G

NP

t)

A9.

2U

Nt

C=

6.15

9(.0

35)*

*

~o

=-

.523

(.32

2)~1

=-

.843

(.52

0)~2

=-

1.05

7(.6

67)

~3

=-1

.19

2(.

73

6)

~4

=-

1.27

0(.7

53)

~5

=-1

.30

9(.

74

6)

f36=

-1.3

24

(.7

33

)f37

=-1

.32

6(.

72

3)

~8

=-1

.32

2(.

71

5)

P1

=1.

320(

.112

)**

P2

=-

.419

(.18

6)*

T=

.009

(.00

04)

~9

=-1

.31

6(.

70

1)

~1O

=-1

.30

8(.

676)

~11

=-1

.295

(.63

6)*

~12

=-1

.22

0(.

583)

*~13

=-1

.221

(.52

4)*

~14

=-1

.135

(.46

4)*

~15

=-

.994

(.40

3)*

f316

=-

.775

(.32

6)*

~17

=-

.453

(.20

5)*

P3

=.0

21(.

185)

P4

=-

.044

(.11

2)

C=

4.17

6(1.

124)

**

f30=

2.50

9(10

.799

)f31

=2.

501(

19.8

58)

f32=

7.36

0(24

.992

)(3

3=

15.5

19(2

6.36

8)(3

4=

25.5

89(2

5.55

3)(35

=36

.349

(24.

121)

f36

=46

.755

(23.

308)

*(3

7=

55.9

34(2

3.60

3)*

(38

=63

.189

(24.

639)

*

P1=

1.60

1(.

112)

**P

2=

-.8

55(.

210)

**

T=

.016

(.01

3)

(39

=67

.993

(25.

671)

**f31

0=

69.9

93(2

6.06

8)**

~11

=69

.012

(25.

512)

**(3

12=

65.0

44(2

3.98

8)**

f313

=58

.255

(21.

715)

**

(314

=48

.987

(19.

013)

**(3

15=

37.7

53(1

6.07

6)*

(316

=25

.242

(12.

646)

*(3

17=

12.3

13(

7.79

6)

P3

=.0

55(.

208)

P4

=.0

56(.

106)

R2

=.9

986

SE=

.009

42D

-W=

2.02

R2

=.9

435

SE

=.3

2652

D-W

=2.

15

Not

e:S

eeta

ble

6.A

.5.

*Sig

nifi

cant

atth

e5

perc

ent

leve

l.**

Sig

nifi

cant

atth

e1

perc

ent

leve

l.


unanticipated inflation has been included in the models again becausecoefficients on lags as far back as this are significantly different from zeroat the 5 percent level.

The suprising result of table 6.A.9 is that the coefficients on unanticipated inflation are often significantly different from zero and yet theyhave the opposite sign to what we would expect from a Lucas supplyfunction. These results contradict Sargent's (1976a) finding of a negativecorrelation between unanticipated inflation and employment, but are inagreement with Fair (1979). Our results may contradict Sargent because1973-1975 data are included in the sample period. Sargent takes unanticipated inflation to be a response to aggregate demand shifts, possibly amore reasonable assumption for the sample period he used in estimation.However, it is plausible that the supply shock effect of a decreased supplyof food and energy-which would be linked to an unanticipated upwardmovement in the U. S. inflation rate coupled with an output decline-isdominating the aggregate demand effects on unanticipated inflation inthe data used here. Thus the estimated coefficients on unanticipatedinflation may not contradict the MRE hypothesis, but they certainly donot support it.

The likelihood ratio tests in table 6.A.IO indicate that the MREhypothesis is not supported for the models with inflation as the aggregatedemand variable. The joint hypothesis is rejected for both models at the 5percent significance level, with the neutrality hypothesis the major contributor to these rejections. The neutrality constraints are rejected at the.001 marginal significance level for the output model and .01 for theunemployment model. The rationality constraints again fare better withthe marginal significance levels equaling .51 for the output model and .04for the unemployment model. The evidence, as before, seems to be

Table 6.A.I0 Likelihood Ratio Tests for Models of Table 6.A.9

Model

A9.1 A9.2





X2(15) = 28.45*.0189

X2(4) = 18.52**.0010

X2(11) = 10.23.5098

X2(15) = 32.34**.0058

X2(4) = 13.20*.0104

X2(11) = 20.16*.0432


negative on the neutrality implications of the MRE hypothesis, but farless so on the rationality implication.

Tables 6.A.ll and 6.A.12 show that, contrary to the MRE hypothesis,the effects from unanticipated inflation are not stronger than from anticipated inflation. Not only are the coefficients on anticipated inflationsubstantially larger than the unanticipated coefficients, but their asymptotic t statistics are substantially larger as well. Overall, the Lucas supplymodel estimated here is not successful. Its coefficients have the "wrong"signs, it fits the data worse than a corresponding model with moneygrowth as the aggregate demand variable, and it strongly rejects neutrality, with anticipated inflation proving to be more significantly correlatedwith output and unemployment than unanticipated inflation.

Tab

le6

.A.l

lN

onli

near

Est

imat

esof

Out

put

Equ

atio

nE

xpla

nato

ryV

aria

bles

:U

nant

icip

ated

and

Ant

icip

ated

Infl

atio

n,S

even

teen

Lag

s(P

DL

)17

17

Log

(GN

Pt)

=C

+T

TIM

E+

I~i

(7Tt

-i-

7T~-

i)+

I8i

7T~-

i+PI

E.t-

1+

P2E.

t-2

+P3

E.t-

3+

P4E.

t-4

+TI

ti=

Oi=

O

Mod

el:

Dep

ende

ntV

aria

ble:

~O

=-

.082

(.31

1)f3I

=.0

32(.

466)

~2

=.1

92(.

624)

~3

=.3

58(.

730)

f34=

.498

(.80

0)~5

=.5

89(.

836)

~6

=.6

15(.

861)

~7

=.5

66(.

875)

~8

=.4

41(.

879)

r39=

-.2

46(.

869)

~1O

=-

.006

(.84

4)

A11

.110

g(G

NP

t)

C=

6.08

9(.0

68)*

*

~11

=-

.293

(.80

3)f31

2=

-.5

89(.

748)

~13

=-

.856

(.68

0)~14

=-1

.05

2(.

600)

f315

=-1

.12

6(.

50

7)*

~16

=-1

.02

1(.

38

9)*

*~17

=-

.669

(.22

8)**

PI=

1.09

2(.1

21)*

*P2

=-

.312

(.17

1)

T=

.011

(.00

1)

8 0=

.128

(.53

8)8 1

=-

.994

(.39

7)*

8 2=

-1.5

44

(.3

90

)**

8 3=

-1.6

82

(.3

91

)**

8 4=

-1.5

47

(.3

78

)**

8 5=

-1.2

58

(.3

69

)**

8 6=

-.9

12(.

373)

*8 7

=-

.588

(.38

6)8 8

=-

.342

(.39

3)8 9

=-

.211

(.38

4)8 1

0=

-.2

10(.

361)

P3=

.202

(.17

2)P4

=-

.067

(.11

9)

8 11

=-

.334

(.34

3)8 1

2=-

.559

(.35

4)8 1

3=

-.8

38(.

405)

*8 1

4=

-1.1

04

(.4

69

)*8 1

5=

-1.

272(

.508

)*8 1

6=

-1.2

33

(.4

75

)**

8 17

=-

.858

(.32

3)**

R2

=.9

988

SE

=.0

0855

D-W

=1.

99

Not

e:E

stim

ates

from

the

(2)

and

(6)

syst

emim

posi

ng~

=~.

*T

he

~1

and

8 iar

eco

nstr

aine

dto

lieal

ong

afo

urth

-ord

erpo

lyno

mia

lw

ith

the

endp

oint

cons

trai

ned.

*Sig

nifi

cant

atth

e5

perc

ent

leve

l.

**S

igni

fica

ntat

the

1pe

rcen

tle

vel.

Tab

le6.

A.1

2N

onli

near

Est

imat

esof

Une

mpl

oym

ent

Equ

atio

nE

xpla

nato

ryV

aria

bles

:U

nant

icip

ated

and

Ant

icip

ated

Infl

atio

n,S

even

teen

Lag

s(P

DL

)2

02

0

UN

t=C

+T

TIM

E+

IJ3

i('TT

t-i-

'TT~

-i)

+I

8i'TT~-i+

P1

Et-

1+

P2

Et-

2+

P3

Et-

3+

P4

Et-

4+

TIt

i=O

i=O

Mod

el:

Dep

ende

ntV

aria

ble:

130=

4.54

(10.

27)

J31=

12.6

5(18

.50)

~2

=13

.15(

25.0

1)J33

=8.

66(2

8.65

)J34

=1.

47(3

0.32

)135

=-

6.55

(30.

89)

J36=

-13.

86(3

1.00

)J37

=-1

9.32

(30.

96)

J38=

-22

.14(

30.8

3)139

=-

21.9

1(30

.47)

J310

=-1

8.61

(29.

73)

A12

.1U

Nt

C=

6.98

1(2.

687)

**

1311=

-12

.57(

28.5

3)13

12=

-4.

50(2

6.86

)131

3=4.

52(2

4.77

)13

14=

13.0

4(22

.27)

1315

=19

.23(

19.1

9)13

16=

20.8

9(15

.05)

1317

=15

.46(

9.04

)

PI=

1.41

0(.1

22)*

*P2

=-

.665

(.20

3)**

T=

-.0

68(.

045)

8 0=

-42

.90(

26.2

3)8 1

=11

.15(

16.7

2)8 2

=43

.03(

15.7

7)**

8 3=

58.1

4(15

.99)

**8 4

=61

.24(

15.2

8)*

*8 5

=56

.47(

14.3

4)**

8 6=

47.3

1(14

.04)

**

8 7=

36.6

2(14

.44)

*8 8

=26

.63(

14.8

9)8 9

=18

.92(

14.8

3)8 1

0=

14.4

4(14

.24)

P3=

.016

(.20

1)P4

=.1

61(.

115)

8 11

=13

.52(

13.8

3)8 1

2=

15.8

4(14

.71)

8 13

=20

.45(

17.1

9)8 1

4=

25.7

5(20

.23)

8 15

=29

.53(

22.0

5)8 1

6=

28.9

3(20

.73)

8 17

=20

.46(

14.1

5)

Not

e:S

eeta

ble

6.A

.l1

.*S

igni

fica

ntat

the

5pe

rcen

tle

vel.

**Si

gnif

ican

tat

the

1pe

rcen

tle

vel.

R2

=.9

530

SE

=.3

0255

D-W

=2.

10

App

endi

x6.

3:R

esul

tsN

otU

sing

Pol

ynom

inal

Dis

trib

uted

Lag

s

Tab

le6.

A.1

3L

ikel

ihoo

dR

atio

Tes

tso

fth

eM

RE

Hyp

othe

sis

wit

hM

IG

row

thas

the

Agg

rega

teD

eman

dV

aria

ble

Mod

el

A14

.1A

14.2

A15

.1A

15.2

Join

thy

poth

esis

:L

ikel

ihoo

dra

tio

stat

isti

cX

2(1

9)=

22.3

7X

2(1

9)=

31.5

5*X

2(3

2)=

66.9

0**

X2(3

2)=

54.0

6**

Mar

gina

lsi

gnif

ican

cele

vel

.266

2.0

351

.000

3.0

087

Neu

tral

ity:

Lik

elih

ood

rati

ost

atis

tic

X2(8

)=

9.53

X2(8

)=

11.9

7X

2(2

1)=

45.2

2**

X2(2

1)=

36.4

7M

argi

nal

sign

ific

ance

leve

l.2

996

.152

4.0

016

.083

00

".;

"..

..."1

;.,,

.J.,

aU

Vllalll.J

'

Lik

elih

ood

rati

ost

atis

tic

X2(1

1)=

12.3

4X

2(1

1)=

20.1

4*

X2(1

1)=

27.1

0**

X2(1

1)=

27.0

1**

Mar

gina

lsi

gnif

ican

cele

vel

.338

6.0

435

.004

4.0

046

Not

e:T

heta

bles

here

corr

espo

ndto

prev

ious

tabl

esas

follo

ws:

6.A

.13

to6.

1,6.

A.1

4to

6.2,

6.A

.15

to6.

4,6.

A.1

6to

6.A

.5,

6.A

.17

to6.

A.6

,6.

A.1

8to

6.A

.9,

6.A

.19

to6.

A.1

0.

Tab

le6.

A.1

4N

onli

near

Est

imat

esof

Out

put

and

Une

mpl

oym

ent

Equ

atio

nsE

xpla

nato

ryV

aria

bles

:U

nant

icip

ated

Mon

eyG

row

th,

Seve

nL

ags,

Fre

ely

Est

imat

ed7

Yt=

C+

TT

IME

+I

~i(M1Gt-i

-M1G~_;)

+P

IEt-

1+

P2

Et-

2+

P3

Et-

3+

P4

Et-

4+

'Ylt

i=O

Mod

el:

Dep

ende

ntV

aria

ble:

A14

.1lo

g(G

NP

t)

A14

.2U

Nt

C=

6.17

5(.0

46)*

*

~o

=.7

43(.

247)

**~I

=1.

616(

.375

)**

~2

=2.

065(

.444

)**

~3

=2.

450(

.484

)**

~4

=2.

244(

.501

)**

~5

=1.

812(

.484

)**

~6

=.9

96(.

421)

*~7

=.5

09(.

269)

PI

=1.

138(

.119

)**

P2

=-

.379

(.17

7)*

T=

.008

(.00

05)

P3

=.1

95(.

177)

P4

=-

.027

(.11

9)

C=

3.56

3(1.

590)

*

~o

=-1

8.7

3(

9.03

)*~I

=-4

0.73

(16.

05)*

~2

=-

69.0

1(19

.33)

**~3

=-

86.4

1(20

.40)

**~4

=-

92.7

9(20

.85)

**~5

=-7

2.45

(20.

32)*

*~6

=-

42.2

6(16

.53)

*~7

=-1

5.1

4(

9.26

)

PI

=1.

474(

.114

)P

2=

-.

777(

.206

)

T=

.024

(.01

8)

P3

=.0

72(.

208)

P4

=.1

56(.

118)

R2

=.9

989

SE

=.0

085

D-W

=1.

97R

2=

.951

4S

E=

.306

2D

-W=

2.05

Not

e:E

stim

ated

from

the

(2)

and

(4)

syst

em,

impo

sing

the

cros

s-eq

uati

onco

nstr

aint

sth

at~

iseq

uali

n(2

)an

d(4

).N

ote

that

the

~iar

ees

tim

ated

wit

hout

cons

trai

nts.

*Sig

nifi

cant

atth

e5

perc

ent

leve

l.**

Sig

nifi

cant

atth

e1

perc

ent

leve

l.

Tab

le6.

A.1

5N

onli

near

Est

imat

eso

fO

utp

ut

and

Une

mpl

oym

ent

Gro

wth

Exp

lana

tory

Var

iabl

es:

Una

ntic

ipat

edM

oney

Gro

wth

,T

wen

tyL

ags,

Fre

ely

Est

imat

ed2

0

Yt=

C+

TT

IME

+l

~i(M1Gt-i-M1G~-i)

+P

IEt-l

+P2Et~2

+P3Et~3

+P

4Et-

4+

TIt

i=O

Mod

el:

Dep

end

ent

Var

iabl

e:A

15.1

log

(GN

Pt)

A15

.2U

Nt

C=

6.19

5(.0

48)*

*

~o

=.8

50(.

275)

**~1

=1.

784(

.430

)**

~2

=2.

320(

.523

)**

~3

=2.

935(

.614

)**

~4

=2.

989(

.722

)**

~5

=2.

605(

.796

)**

~6

=1.

637(

.822

)*~7

=1.

103(

.802

)~8

=.6

77(.

764)

P9=

.496

(.71

9)~1O

=.1

66(.

675)

PI

=1.

098(

.127

)**

P2

=-

.338

(.18

4)

T=

.008

(.00

05)

~11

=.2

00(.

640)

~12

=.4

82(.

620)

~13

=.6

25(.

616)

~14

=.6

24(.

631)

~15

=.7

51(.

640)

~16

=.8

89(.

616)

~17

=.8

82(.

574)

~18

=.5

12(.

534)

~19

=.3

00(.

444)

P2

0=

.099

(.27

7)

P3

=.1

84(.

184)

P4

=-

.042

(.12

9)

C=

3.37

5(2.

064)

~o

=-1

1.7

3(

9.92

)~1

=-

21.6

1(18

.24)

~2

=-

52.8

1(22

.04)

*~3

=-8

3.72

(23.

14)*

*~4

=-1

03.1

8(25

.16)

**~5

=-9

1.00

(27.

33)*

*~6

=-7

2.77

(28.

43)*

~7

=-

50.0

6(28

.90)

~8

=-

25.4

7(29

.57)

P9=

-5.

44(2

9.28

)~1O

=3.

16(2

4.15

)

PI

=1.

463(

.117

)**

P2

=-

.708

(.21

2)**

T=

.026

(.02

3)

~11

=6.

66(2

7.18

)~12

=10

.64(

26.6

3)~I3

=10

.52(

26.2

0)~14

=4.

85(2

5.94

)~15

=6.

02(2

5.22

)~I6

=1.

33(2

4.09

)~

17

=-

14.1

3(2

2.76

)~18

=-

24.5

6(21

.36)

~19

=-1

7.2

2(1

7.0

7)

P2

0=

-2.

57(

9.49

)

P3

=-

.070

(.21

7)P

4=

.249

(.12

6)*

R2

=.9

989

SE

=.0

086

D-W

=1.

97R

2=

.956

4S

E=

.302

7D

-W=

2.09

Not

e:S

eeta

ble

6.A

.14.

*Sig

nifi

cant

atth

e5

perc

ent

leve

l.

**S

igni

fica

ntat

the

1pe

rcen

tle

vel.

Tab

le6.

A.1

6N

onli

near

Est

imat

esof

Out

put

and

Une

mpl

oym

ent

Equ

atio

nsE

xpla

nato

ryV

aria

bles

:U

nant

icip

ated

Nom

inal

GN

PG

row

th,

Tw

enty

Lag

s,F

reel

yE

stim

ated

20~

=C

+T

TIM

E+

~J3

i(N

GN

Pt-

i-NGN~-i)

+P

1Et-

1+

P2

Et-2

+P

3Et-

3+

P4

Et-

4+

TIt

i=O

Mod

el:

Dep

ende

ntV

aria

ble:

A16

.1lo

g(G

NP

t)

A16

.2U

Nt

C=

6.17

6(.0

34)*

*

130=

.893

(.04

5)**

131=

1.14

2(.1

25)*

*132

=1.

060(

.191

)**

133=

.971

(.23

4)**

134=

.704

(.26

7)**

135=

.448

(.28

3)136

=.2

6O(.

282)

J37=

.157

(.27

5)138

=.0

43(.

262)

J39=

.014

(.25

2)J31

0=.0

02(.

245)

PI=

1.41

0(.1

19)*

*P2

=-

.150

(.20

3)

T=

.008

(.00

04)

1311=

-.0

35(.

237)

1312=

-.0

28(.

225)

1313

=-

.OO

l(.2

10)

1314

=-

.026

(.19

1)13

15=

-.0

94(.

168)

1316

=-

.101

(.14

4)131

7=-

.034

(.11

8)J3

18=

-.0

71(.

090)

1319

=-

.074

(.06

7)13

20=

-.0

15(.

039)

P3

=-

.191

(.20

4)P

4=

-.1

10(.

123)

C=

-20

8.83

1(35

01.0

0)

130=

-24

.549

(2.

614)

**131

=-

52.0

80(

5.05

8)**

132=

-63

.001

(7.

881)

**133

=-

66.1

26(1

0.21

5)**

134=

-59.

198(

11.9

31)*

*J35

=-

48.0

80(1

2.76

3)*

*136

=-4

3.59

7(12

.635

)**

137=

-39

.639

(11.

906)

**138

=-

31.9

64(1

0.62

4)**

139=

-26

.995

(9.

2(0)

**131

0=-

21.8

45(

8.31

3)**

PI=

1.35

7(.1

19)*

*P2

=-

.404

(.19

7)*

T=

.682

(5.8

28)

1311=

-15

.36

7(

7.71

3)*

1312

=-1

2.4

27

(7.

046)

1313=

-14

.26

3(

6.82

1)*

J314

=-1

4.3

19

(6.

523)

1315

=-1

2.3

99

(6.

009)

*J3

16=

-7.

101(

5.55

5)13

17=

-10

.16

6(

4.97

5)*

1318

=-

9.79

1(4.

262)

*13

19=

-7.

402(

3.64

7)*

1320

=-

5.61

0(2.

216)

*

P3

=.0

55(.

194)

P4

=-

.010

(.11

8)

R2

=.9

998

SE

=.0

0340

D-W

=1.

82

Not

e:S

eeta

ble

6.A

.14.

*Sig

nifi

cant

atth

e5

perc

ent

leve

l.**

Sign

ific

ant

atth

e1

perc

ent

leve

l.

R2

=.9

816

SE

=.1

9424

D-W

=1.

94

Table 6.A.17 Likelihood Ratio Tests for Models of Table 6.A.16

Model

A16.1 A16.2





X2(28) = 57.89**.0008

X2(21) = 56.11 **4.86 x 10-- 5

X2(7) = 1.85.9674

X2(28) = 71.21 **1.25 X 10- 5

X2(21) = 64.04**3.07 x 10- 6

X2(7) = 4.20.7561

Tab

le6.

A.1

8N

onli

near

Est

imat

esof

Out

put

and

Une

mpl

oym

ent

Equ

atio

nsE

xpla

nato

ryV

aria

bles

:U

nant

icip

ated

Infl

atio

n,S

even

teen

Lag

s,F

reel

yE

stim

ated

17

Yt=

C+

TT

IME

+I

f3i(

7T

t-i

-7T

~-i)

+P

IEt-l

+P

2Et-

2+

P3

Et-

3+

P4

Et-

4+

1")t

i=O

Mod

el:

Dep

ende

ntV

aria

ble:

A18

.1lo

g(G

NP

t)

A18

.2U

Nt

C=

6.15

5(.0

40)*

*

130=

-.6

34(.

344)

f31=

-1.0

67(.

565)

f32=

-1.0

12(.

695)

f33=

-.7

78(.

759)

134=

-1.

434(

.815

)135

=-

2.02

1(.8

70)*

f36=

-1.8

28(.

904)

*137

=-1

.173

(.93

6)f38

=-1

.608

(.93

9)

PI=

1.37

0(.1

17)*

*P2

=-

.440

(.19

8)*

T=

.009

(.00

05)

139=

-1.4

00(.

921)

1310=

-1.1

31

(.85

5)131

1=-

1.03

4(.7

45)

1312=

-1.3

76

(.66

0)*

1313=

-1.2

55

(.57

4)*

1314=

-.7

58(.

511)

1315=

-1.

147(

.466

)*131

6=-1

.400

(.38

8)**

1317=

-.8

52(.

242)

**

P3=

-.0

385(

.198

)P4

=.0

01(.

121)

C=

4.14

3(1.

207)

**

130=

4.39

9(12

.251

)f31

=12

.877

(22.

979)

132=

11.1

92(3

1.35

0)133

=11

.586

(35.

338)

134=

10.5

21(3

5.99

7)~5

=31

.214

(35.

693)

(36

=43

.389

(35.

602)

(37

=55

.321

(36.

368)

f38=

-67

.247

(36.

701)

PI=

1.65

0(.1

17)*

*P2

=-

.891

(.22

8)**

T=

.017

(.01

4)

139=

79.0

22(3

6.79

8)*

1310=

76.1

55(3

7.13

9)*

1311

=70

.156

(37.

001)

1312=

73.6

34(3

7.47

2)*

1313=

60.7

02(3

7.02

7)131

4=43

.523

(33.

948)

f315

=25

.826

(28.

163)

1316=

25.1

87(1

9.34

4)f31

7=

10.2

84(9

.580

)

P3=

.028

(.22

9)P4

=.0

86(.

114)

R2

=.9

989

SE

=.0

0876

D-W

=1.

95R

2=

.949

3S

E=

.323

33D

-W=

2.05

Not

e:Se

eta

ble

6.A

.14.

*Sig

nifi

cant

atth

e5

perc

ent

leve

l.**

Sign

ific

ant

atth

e1

perc

ent

leve

l.

Table 6.A.19 Likelihood Ratio Tests for Models of Table 6.A.18

Model

A18.1 A18.2




*Significant at the 5 percent level.

**Significant at the 1 percent level.

X2(29) = 64.38* *.0002

X2(18) = 43.51 **.0007

X2(11) = 22.33*.0219

X2(29) = 57.03**.0014

X2(18) = 33.93*.0129

X2(11) = 32.01 *.0008

Appendix 6.4: Jointly Estimated Forecasting Equations

Table 6.A.20 Money Growth Equations Estimated Jointly with Outputand Unemployment Equations in Text

Model

2.1 2.2 3.1 3.2 4.1 4.2 5.1 6.1

Constant term .002 .003 .002 .002 .002 .002 .003 .003(.001) (.001) (.001) (.001) (.001) (.001) (.001) (.001)

M1Gt - 1 .768 .712 .770 .730 .740 .676 .672 .690(.110) (.111) (.113) ( .112) (.112) ( .112) ( .113) ( .112)

M1Gt - 2 -.018 -.052 -.006 .024 -.010 -.024 .039 .028(.143) (.142) (.147) ( .138) (.143) (.142) (.143) (.142)

M1G t - 3 - .116 -.058 - .073 - .032 -.092 -.042 - .012 -.004(.130) (.130) (.131) (.119) ( .130) (.129) (.129) (.132)

M1Gt - 4 - .161 - .133 - .149 - .116 - .055 -.065 -.016 -.026(.101) (.105) (.102) (.098) (.106) (.108) (.107) ( .115)

RTBt - 1 - .319 - .379 -.265 - .350 -.273 - .349 -.408 - .425(.089) (.092) (.088) (.093) (.093) (.094) (.099) (.101)

RTBt - 2 .628 .634 .558 .583 .560 .590 .541 .597(.161) ( .162) (.166) (.159) (.163) ( .160) (.163) ( .163)

RTBt - 3 -.237 - .258 -.237 -.219 - .188 - .188 -.210 - .205(.169) (.170) (.167) (.161) ( .171) (.169) (.170) (.171)

RTBt - 4 .002 .070 -.000 .031 -.057 -.030 .082 .036(.098) (.102) (.091) (.094) (.104) (.105) (.104) (.109)

SURPt - 1 -.140 - .143 - .152 - .156 - .156 - .165 - .197 - .176(.067) (.070) (.061) (.065) (.069) (.070) (.070) (.075)

SURPt - 2 .132 .099 .185 .153 .118 .093 .128 .072(.082) (.082) (.080) (.079) (.082) (.081) (.082) (.083)

SURPt - 3 .042 .047 -.006 .021 .048 .062 .018 .046(.086) (.086) (.085) (.083) (.086) (.085) (.086) (.087)

SURPt - 4 - .147 - .120 - .126 - .115 - .113 -.097 -.066 -.068(.069) (.071) (.067) (.066) (.069) (.070) (.070) (.075)

R2 .6290 .6369 .6284 .6469 .6322 .6475 .6548 .6584SE .00437 .00432 .00443 .00432 .00435 .00427 .00427 .00425D-W 1.95 1.92 1.97 1.99 1.94 1.90 2.02 2.03

Note: Forecasting equations were estimated with the output or unemployment equationimposing the cross-equation constraints that 'Y is equal in both equations. For purposes ofcomparison, OLS column shows the estimate of the unconstrained forecasting equation.Note that SE is the unbiased standard error and is calculated as described in the note to table6.2.

Model

ALI A1.2 A3.1 A4.1 A14.1 A14.2 A15.1 A15.2 OLS

.002 .002 .003 .003 .002 .003 .002 .002 .003(.001) (.001) (.001) (.001) (.001) (.001) (.001) (.601) (.001).741 .696 .699 .685 .755 .718 .810 .735 .673

(.111) (.111) (.114) (.110) (.111) (.113) (.118) (.119) (.113)-.060 -.034 .056 .006 -.002 -.045 .022 -.007 .047(.141) (.139) (.143) (.138) (.145) (.145) (.154) (.151) (.143)

- .095 -.005 .005 .017 - .131 - .078 - .108 -.091 - .035(.130) (.127) (.130) (.129) (.130) (.132) (.138) (.136) (.136)

- .150 -.053 .064 -.080 - .154 - .124 -.232 - .115 -.039(.105) (.106) (.107) (.112) (.102) (.107) (.110) (.113) (.118)

-.260 - .376 - .433 -.417 - .313 - .370 - .331 - .336 -.404(.092) (.092) (.100) (.099) (.091) (.093) (.092) (.094) (.103).574 .597 .533 .605 .613 .613 .657 .572 .592

(.162) (.157) (.165) (.159) (.162) (.164) (.163) (.163) (.164)-.216 -.236 -.206 -.220 -.229 - .231 - .247 - .165 - .190(.170) (.166) (.170) (.167) (.170) (.173) (.172) (.173) (.173)

-.024 .052 .087 .054 .003 .055 - .013 -.013 .009(.102) (.103) (.102) (.108) (.100) (.103) (.104) (.106) (.113)

- .147 -.134 -.190 - .168 - .157 - .152 - .164 - .137 -.206(.069) (.069) (.068) (.073) (.067) (.070) (.069) (.070) (.076)

.123 .099 .155 .075 .147 .108 .150 .009 .100(.082) (.080) (.082) (.081) (.080) (.082) (.085) (.083) (.084).054 .047 .019 .055 .042 .046 .064 .040 .039

(.087) (.084) (.086) (.085) (.085) (.082) (.090) (.088) (.088)- .137 - .105 -.013 - .095 - .149 - .119 - .175 - .101 - .078(.069) (.070) (.070) (.073) (.069) (.071) (.073) (.071) (.076)

.6231 .6504 .6397 .6568 .6306 -.6370 .6263 .6426 .6601

.00440 .00424 .00435 .00424 .00441 .00438 .00466 .00453 .004221.87 1.95 2.03 1.98 1.93 1.90 2.00 2.09 1.98

Tab

le6.

A.2

1N

omin

alG

NP

Gro

wth

For

ecas

ting

Equ

atio

ns,

Est

imat

edJo

intl

yw

ith

Out

put

and

Une

mpl

oym

ent

Equ

atio

nsin

Tex

t

Mod

el

A5.

1A

5.2

A7.

1A

8.1

A16

.1A

16.2

OL

S

Con

stan

tT

erm

.008

4**

.007

9**

.006

8**

.007

6**

.011

3**

.011

6**

.006

8**

(.00

22)

(.00

17)

(.00

24)

(.00

25)

(.00

25)

(.00

24)

(.00

25)

NG

NP

t-1

.313

9**

.443

7**

.148

1.2

645*

*.3

293*

*.3

000*

*.2

209*

(.09

52)

(.10

07)

(.09

56)

(.09

34)

(.11

12)

(.11

20)

(.10

47)

NG

NP

t-2

.058

7-.

00

62

-.1

712

-.1

470

-.1

141

-.1

390

-.1

368

(.04

85)

(.09

59)

(.09

43)

(.09

08)

(.11

04)

(.11

35)

(.10

86)

NG

NP

t-3

.064

3.1

448

-.0

13

1.1

082

.099

5.1

540

.040

7(.

0456

)(.

0894

)(.

0911

)(.

0902

)(.

1081

)(.

1112

)(.

1071

)N

GN

Pt-

4.0

177

-.0

90

0-

.105

4-

.225

6**

-.1

898*

*-

.206

1*

-.1

774

(.04

44)

(.07

52)

(.08

43)

(.08

64)

(.09

58)

(.09

93)

(.09

97)

M2

Gt-

1-

.004

0.2

049

.222

2.1

618

.083

3.1

891

.354

9(.

0808

)(.

1294

)(.

1667

)(.

1603

)(.

0790

)(.

1211

)(.

1898

)M

2G

t-2

-.0

05

1-

.301

5.0

074

.275

5.0

307

-.1

168

.008

5(.

1040

)(.

2196

)(.

2245

)(.

2115

)(.

1038

)(.

1886

)(.

2841

)M

2G

t-3

.214

1*

.402

4.5

786*

.187

7.1

828

.239

7.4

365

(.10

37)

(.22

10)

(.23

12)

(.20

92)

(.10

35)

(.18

74)

(.25

98)

M2

Gt-

4-

.133

2-

.247

4.0

180

-.0

12

0-.

06

31

-.0

77

8-.

07

99

(.08

95)

(.14

22)

(.18

06)

(.17

75)

(.08

85)

(.13

62)

(.21

03)

R2

.201

7.2

341

.345

3.3

552

.294

3.2

874

.371

2S

E.0

0994

.009

74.0

0912

.009

05.0

0987

.009

92.0

0880

D-W

1.86

2.14

1.93

2.22

2.10

2.04

2.11

Not

e:S

eeta

ble

6.A

.20.

*Sig

nifi

cant

atth

e5

perc

ent

leve

l.**

Sign

ific

ant

atth

e1

perc

ent

leve

l.

Tab

le6.

A.2

2In

flat

ion

For

ecas

ting

Equ

atio

ns,

Est

imat

edJo

intl

yw

ith

Out

put

and

Une

mpl

oym

ent

Equ

atio

ns

Mod

el--

A9.

1A

9.2

A1

t.1

A12

.1A

18.1

A18

.2O

LS

Con

stan

tT

erm

-.0

011

-.0

01

2-

.000

5-

.000

5-

.001

1-.

00

12

-.0

00

8(.

0010

)(.

0010

)(.

0011

)(.

0011

)(.

0011

)(.

0011

)(.

0011

)

'TT

t-l

.204

0*.2

405*

.240

8*.2

225*

*.2

126*

.234

3*.2

477*

(.10

30)

(.10

39)

(.09

53)

(.08

61)

(.10

28)

(.10

88)

(.10

54)

'TTt-

2.1

259

.131

4.1

491

.171

0.0

976

.158

0.1

598

(.10

53)

(.10

67)

(.09

93)

(.08

04)

(.10

56)

(.11

00)

(.10

87)

'TTt-

3.2

280*

.208

7*.2

249*

.219

6*.1

810

.227

1*

.274

4*(.

1048

)(.

1057

)(.

0999

)(.

0815

)(.

1034

)(.

1088

)(.

1089

)'TT

t-4

.088

8.0

240

.054

9.0

913

.154

1-.

00

19

.046

6(.

1003

)(.

1020

)(.

0953

)(.

0803

)(.

0957

)(.

1039

)(.

1036

)R

TB

t-1

.228

4**

.228

0**

.289

0**

.226

9**

.240

0**

.243

2**

.251

3**

(.08

02)

(.08

04)

(.07

47)

(.06

56)

(.07

01)

(.08

04)

(.08

16)

RT

Bt

-2

-.1

093

-.1

208

-.1

563

-.1

018

-.0

49

0-

.137

8-.

13

11

(.13

08)

(.13

23)

(.12

73)

(.09

87)

(.10

92)

(.13

03)

(.13

24)

RT

Bt-

3.1

819

.183

2.1

824

.184

9.0

250

.180

6.1

684

(.14

71)

(.14

88)

(.13

85)

(.11

54)

(.12

42)

(.14

64)

(.14

90)

Tab

le6.

A.2

2(c

onti

nued

)

Mod

el

A9.

1A

9.2

A11

.1A

12.1

A18

.1A

18.2

OL

S

RT

Bt

-4

-.2

40

8*

-.2

134*

-.2

366*

-.2

530*

*-

.154

9-

.210

7*-.

24

23

*

(.09

91)

(.09

91)

(.09

36)

(.08

45)

(.08

94)

(.09

96)

(.10

18)

M2

Gt

-1

.127

1.1

147

.088

9.0

238

.143

2.1

249

.123

4(.

0907

)(.

0915

)(.

0819

)(.

0734

)(.

0842

)(.

0906

)(.

0935

)

M2

Gt

-2

.008

3-

.004

2-.

02

38

.088

6-.

03

64

.005

2.0

051

(.11

88)

(.12

01)

(.11

04)

(.08

46)

(.10

73)

(.11

67)

(.11

04)

M2

Gt

-3

.209

3*.1

982

.208

2*.0

948

.202

9*.1

678

.187

4

(.10

67)

(.10

79)

(.10

25)

(.07

97)

(.09

84)

(.10

60)

(.10

90)

M2

Gt

-4

-.2

21

2*

*-

.196

4*-

.251

3**

-.1

464*

-.1

844*

-.1

845*

-.2

240*

*

(.08

45)

(.08

53)

(.07

78)

(.07

04)

(.07

93)

(.08

58)

(.08

68)

R2

.736

9.7

367

.735

9.7

306

.726

3.7

371

.741

1

SE

.003

47.0

0347

.003

52.0

0355

.003

70.0

0363

.003

47

D-W

1.92

1.99

2.01

1.92

1.65

1.70

1.74

Not

e:S

eeta

ble

6.A

.20.

*Sig

nifi

cant

atth

e5

perc

ent

leve

l.

**S

igni

fica

ntat

the

1pe

rcen

tle

vel.

Table 6.A.23 F Statistics for Significant Explanatory Power in ForecastingEquations of Four Lags of Each Variable

MIG Forecasting NGNP Forecasting 'IT ForecastingVariable Equation Equation Equation

NGNP 1.09 2.24 1.44'IT 1.69 .96 8.38**RTB 5.28** .11 5.01 **M2G 1.25 5.65** 3.04*MIG 15.80** .48 .60UN 1.66 1.62 .76RGNP .82 .94 1.44G .13 2.47 1.55BOP 1.28 .61 2.26GDEBT 1.52 .92 .61SURP 2.56* 1.66 1.35

Note: The F statistics test the null hypothesis that the coefficients on the four lagged valuesof each of these variables equals zero. The F statistics. are distributed asymptotically asF(4,x) where x runs from 75 to 83. The critical F at the 5 percent level is 2.5 and at the 1percent level is 3.6. NGNP = quarterly rate of growth of real GNP, 'IT = quarterly rate ofgrowth of the GNP deflator, RTB = average 90-day treasury bill rate, M2G = quarterlyrate of growth of average M2, MIG = quarterly rate of growth of average M1, UN =

average unemployment rate, RGNP = quarterly rate of growth of real GNP, G = quarterlyrate of growth of real federal government expenditure" BOP = average balance of payments on current account, GDEBT = quarterly rate of growth of government debt, SURP= high employment surplus.*Significant at the 5 percent level.**Significant at the 1 percent level.

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