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ECONOMIC REVIEW
FEDERAL RESERVE BANK
of CLEVELAND
QUARTER IV
Economic Review
Federal Reserve Bank
of Cleveland
Quarter IV 1985
Stochastic Interest Rates
in the Aggregate Life-Cycle/
Permanent Income Cum Rational
Expectations Model .................................. 2
Recent tests of the life cycle/permanent income
cum rational expectations model have assumed
either that real interest rates are constant, or
that consumers know the future path of real
rates. This article estimates a life cycle cum
rational expectations model that allows for sto
chastic real interest rates. The results show
that the model is strongly rejected using postWorld War II U.S. data.
New Classical and
New Keynesian Models
of Business Cycles..................................
20
Both Keynesian and Classical economists have
developed new models of the business cycle dur
ing the 1970s and 1980s. Both have striven to
establish firm microfoundations for their the
ory of fluctuations, so that events may be un
derstood in terms of the basic economic en
vironment and the actions of individual agents.
In this article, economic analyst Eric Kades pre
sents bare-boned models of both schools, at
tempting to lucidly illustrate sources of busi
ness cycles. Simulations show that both models
can mimic observed time series convincingly.
Theoretical strengths and weaknesses are dis
cussed, followed by a cursory examination of
empirical evidence for and against each model.
Economic Review is published quarterly by the
Research Department of the Federal Reserve Bank
of Cleveland, P.O. Box 6387, Cleveland, OH 44101.
Telephone: 216/579-2000.
Editor: William G. Murmann. Assistant editor:
Meredith Holmes. Design: Jamie Feldman.
Typesetting: Liz Hanna.
Opinions stated in Economic Review are those of the
authors and not necessarily those of the Federal
Reserve Bank of Cleveland or of the Board of Gover
nors of the Federal Reserve System.
Material may be reprinted provided that the source
is credited. Please send copies of reprinted materials
to the editor.
K.J. Kowalewski is
an economist at the
Federal Reserve
Bank o f Cleveland.
The author would
like to thank James
Hoehn, Eric Kades,
and Alan Stock
man, who provided
useful comments on
an earlier draft.
1. See Tobin (1980)
and Tobin and
Buiter (1980) fo r
good discussions o f
these points.
Stochastic Interest
Rates in the Aggregate
Life - Cycle / Permanent
Income Cum Rational
Expectations Model
by Kim J. Kowalewski
There has been renewed interest in consump
tion behavior in the past 10 years. The origin
of this interest is not so much due to deteri
oration in the ability of economists to predict
future output and prices, although that is
clearly important.
The main impetus is the challenge of the
“ New Classical” school. Barro (1974) argued
that rational private agents do not view bondfinanced increases in government spending or
decreases in taxes as increases in wealth, be
cause they know that the new bonds must be
retired by additional future taxes. Rational
private agents therefore will increase current
saving to pay for these future taxes, no mat
ter how far into the future they come due.
This additional saving is exactly enough to
purchase all of the new debt; interest rates
and aggregate wealth remain unchanged. This
implies that bond-financed increases in
government spending have a multiplier value
of 1 , and that bond-financed tax cuts have a
zero multiplier.
Money-financed increases in government
spending also have a zero multiplier, because
rational private agents view the faster growth
in money as leading to a higher inflation rate
in the future. This higher inflation is another
“ tax” that private agents will save for. That
is, money-financed tax cuts have no effect on
real variables, because one tax is just sub
stituted for another.
These “ New Classical” results are a direct
challenge to the Keynesian and Monetarist
schools, which assign higher values to these
multipliers (at least in the short run), because
the effects of fiscal policy actions are distin
guished by how they are financed.1
Barro’s result depends, among other things,
on the assumption that private agents have
the opportunity to offset these government
actions. This, in turn, assumes that capital
markets are perfect—that there are no trans
actions or other costs that drive a wedge
between borrowing and lending interest rates,
and that there are no informational asymme
tries that are controlled with down payments,
2. Muellbauer
(1983) and Wickens
and Molana (1984)
reject the model
using U.K. con
sumption and in
come data.
security interests, rationing the quantity of
credit, and other non-price loan provisions.
Thus, with perfect capital markets, the length
of a consumer’s spending horizon (that is, the
time span over which a permanent increase in
life-cycle wealth/permanent income is con
sumed) is as long as his remaining lifetime. It
may be longer if, as Barro assumes, a consum
er’s utility function includes the utility of his
direct descendants. A consumer can borrow
any amount up to the current value of his net
nonhuman wealth, plus the present value of
all his expected future after-tax labor income,
all discounted at the common rate of interest.
An increase in life-cycle wealth/permanent
income will be consumed over the remainder
of the horizon, making the amount consumed
in the short run very small.
If capital markets are imperfect, however,
then the length of a consumer’s planning hori
zon may be shortened. A consumer may not
be able to borrow against all of his life-cycle
wealth (or permanent income), or may do so
only at a penalty rate of interest. Increases in
life-cycle wealth/permanent income will be
consumed over this shorter horizon, enlarging
the (short-run) impact of bond-financed tax
cuts or spending increases. Clearly, shorter
horizons make it possible for stabilization pol
icies to affect real variables, at least in the
short run.
Thus, the recent interest in consumption be
havior centers on learning the length of con
sumer spending horizons. The approach taken
by most recent studies is to test some variant
of the life-cycle/permanent income cum ration
al expectations (RE-LC/PI) model assuming
perfect capital markets. Rejection of the RELC/PI model, incorporating perfect capital
markets, is taken to mean that horizon
lengths may not be long enough to diminish
the power of stabilization policies.
Hall (1978), Flavin (1981,1985), Hayashi
(1982), Muellbauer (1983), Wickens and Mol
ana (1984), Bernanke (1982), Mankiw (1983),
DeLong and Summers (1984), Boskin and Kot-
likoff (1984), Kotlikoff and Pakes (1984), and
Mankiw, Rotemberg, and Summers (1985) test
the RE-LC/PI model with aggregate time ser
ies data, while Hall and Mishkin (1982), Ber
nanke (1984), and Hayashi (1985) use crosssection or panel data on individual
households.
Of the studies employing micro-data, only
Bernanke (1984) can reject the model. Of the
studies that employ aggregate time series
data, Hall (1978), Hayashi (1982), Mankiw
(1983), Bernanke (1984), and Delong and Sum
mers (1984) cannot reject the model during
the post-World War II period. Kotlikoff and
Pakes (1984) can reject the model, but con
clude that the differences from the model are
not large enough to matter in practice.2
These studies are not the first to be con
cerned with the length of consumer spending
horizons. For example, Tobin (1951) argued
that capital market imperfections may have
accounted for the different savings behaviors
of black and white Americans in the late
1940s. Houthakker (1958), in his review of
Friedman’s (1957) permanent income hypoth
esis, argued that the exclusion of capital mar
ket imperfections was the main defect of
Friedman’s work. Friedman (1963) argued
that consumer horizon lengths were about
three years.
Before rational expectations came into
vogue, there were numerous tests of the life
cycle and permanent income models, begin
ning with Modigliani and Brumberg (1954)
and Friedman (1957). The debate about the ef
ficacy of the 1968 temporary tax increase fo
cused on the length of consumer spending hor
izons see, for example, Okun (1971) and
Blinder (1981). There has been considerable
theoretical work done on the impact of capital
market imperfections (see, for example, Tobin
and Dolde [1971], Dolde [1973], Pissarides
[1978], Heller and Starr [1979], Foley and Hellwig [1975], and Watkins [1975,1977]).
What is new about these recent studies is
their assumption of rational expectations. Un
fortunately, richness of detail seems to have
been sacrified for this assumption. For exam-
pie, none of the recent models that are esti
mated with U.S. aggregate time series data
allows for uncertain real interest rates. All of
the models, except Bernanke (1982) and Mankiw (1983) assume that the real interest rate
is constant. Bernanke (1982) and Mankiw
(1983) allow real interest rates to vary, but as
sume that consumers know all future real
interest rates.
It is rather curious that stochastic real inter
est rates have been ignored, because the real
interest rate is a key variable in the life
cycle/permanent income model (and in many
New Classical models). The interest rate mea
sures the exchange rate between consuming
today and saving today to consume more to
morrow. The life-cycle/permanent income
model determines the utility-maximizing al
location of life-cycle wealth (permanent in
come) across time by balancing the marginal
rate of transforming consumption today into
consumption tomorrow (the interest rate)
with the marginal rate of substitution (the dis
counted marginal utility from consuming to
morrow relative to that from consuming to
day). Changes in interest rates, expected or
unexpected, should lead to a reallocation of
consumption spending across time. Thus, an
allowance for stochastic real interest rates
should provide a more powerful test of the
RE-LC/PI model and indirectly of the (maxi
mum) length of the representative consumer’s
spending horizon.
In this article, we estimate a RE-LC/PI mod
el that allows for uncertain future interest
rates. The model is developed by Muellbauer
(1983), which he estimated with United King
dom (U.K.) data. To put Muellbauer’s model
into perspective, the Hall and Flavin (1981)
models are also discussed and estimated. Up
dating the Hall and Flavin results with the
1980s data also may reveal any structural
instabilities and shifts in the distribution of
horizon lengths across consumers, which is a
possibility ignored by all of the recent RELC/PI tests. Section II reviews the RE-LC/PI
models, section III briefly outlines the pro
cedures followed in estimating the three mod
els and explains the results, and the third sec
tion concludes our study.
I. The Life-Cycle/Permanent
Income Model With Rational
Expectations
Tests of the RE-LC/PI model begin with Hall
(1978). The consumer is assumed to maximize
the expected present discounted value of
current and future utility. Income is
exogenous and is known in the current period,
but unknown thereafter; the consumer’s
choice variable is the level of consumption
each period. The horizon begins with the
current period and ends at the (known) last
period of the consumer’s lifetime. There are
no bequests and no capital market
imperfections. Expectations are rational—
functions of all information available in the
current period. Real interest rates and rates of
time preference are assumed to be constant.
The model is:
T- t
(1)
m a x B .S t a 'W C w ) ]
C
t
i=o
subject to
Tt
X
1=0
T- t
( R - C „ i) - X
i—
0
(R'yiti) - A „
where
1 , plus the pure rate of
time preference, assumed constant,
R is the inverse of 1 plus the real, after-tax
rate of interest r, also assumed constant,
(8 > R ) ,
C is real life cycle consumption (not NIPA
personal consumption expenditures),
y is real labor income,
A is current real nonhuman wealth,
£/(•) is the instantaneous utility function, and
E t is the expectations operator, conditioned
on the information available at time t
(variables dated M and earlier).
8 is the inverse of
The first order conditions for this problem
are:
(2a)
(2b)
E tU ' ( C t+i) = ( R/ 8 ) E tU ' ( C t+il),
for i = 1 to T - 1;
in particular, for i - 1
E tU ' ( C t+i) = (R/ 8 ) U ' ( C ,).
There are two things to note about (2b).
First, C , can be thought of as a sufficient sta
tistic for C t+x, that is, no variable except Ct
helps predict future marginal utility of con
sumption U' ( C, +1). Second, with the assump
tion of rational expectations, marginal utility
follows the regression relation:
(3)
U ' ( C t+l) = y U ' ( C t) + e,+1.
The term e t+x represents the impact on
marginal utility of all new information that
becomes available in period t + 1 about the
consumer’s lifetime well-being. Under rational
expectations, E te t+i = 0 and e +i is orthogonal
to U'(C t). Moreover, e should be white noise,
that is, unpredictable using variables in the
information set.
If the utility function is quadratic or “ the
change in marginal utility from one period to
the next is small, both because the interest
rate is close to the rate of time preference and
because the stochastic change is small.” (See
Hall [1978, p. 975].) Then equation (3)
becomes:
(4)
C,=
7 Cm
+ e t.
That is, life-cycle consumption follows an
AR (1) process—no other variables dated M or
earlier affect Ct. If y = 1, then consumption
follows a random walk. It is important to
notice that (4) is not a structural model of life
cycle consumption behavior. Because it is only
the first-order condition for utility maximiza
tion, it is only an implication of the life-cycle
model under rational expectations. Indeed, it
is only a necessary condition for this RE-LC
model to be true.
Hall also shows that lifetime resources
evolve as a random walk with trend. First,
nonhuman wealth follows the relation:
(5)
A , = R \A M + y m
-
C M).
Second, human wealth, H ,, is the sum of
current labor income and the expected present
discount value of future labor income:
(6)
%
( R ‘E , y i . , ) ,
1=0
where
E , y t = y ,,
from which it follows that:
(7a)
H, = R l( H t.\ - _yM) + jut,
where m, represents the present value of the
changes in expectations of future income that
occur between period M and t:
Tt
(7b)
= £ [ * ' ( £ , JV, i=0
Again, under rational expectations, E t ln t
- 0, and n t should be white noise. Under cer
tainty equivalence, 8 , = a tn t, where a , is an
annuity factor modified to take account of the
fact that the consumer plans to make con
sumption grow at a proportional rate y over
his remaining lifetime. Then the equation for
total wealth is:
(8)
Al +tf,= fl-1(l-at.1)(AM +ffM) +M/.
Flavin (1981) estimates a different version
of the permanent income model using the in
sight from (7) to eliminate the unobserved H
She starts by defining current consumption
as the sum of permanent and transitory con
sumption. By equating permanent consump
tion with permanent income (jyf), she has:
(9)
C , = y f + e2t, where e 2/ is transitory
consumption.
Thus, permanent income is defined to be
the annuity value of the expected present dis
counted value of human and nonhuman
wealth ( A t+ H t), assuming the real, after-tax
rate of interest, r, is constant:
(10)
y pt = r ( A t + ^ [ R ,+1 E ty ,+I]).
i=0
3. This assumption
is not unreasonable,
given that her model
explains short-run
changes in con
sumption. However,
in her later paper,
Flavin (1985) uses
annual data where
it seems less likely
that changes in the
rate o f return to cap
ital dominate endog
enous changes in
wealth accumu
lation.
Flavin shows that E y f+1 = y fusing the
insight implicit in equation (7b). Substituting
(10) into (9) and using the nonhuman wealth
constraint:
(11)
A /+1 = R 1 A i + y t - C t.
Unlike equation (5), current period saving
does not earn interest in equation (11). Equa
tion (9) can be used to solve for C /+i in terms
of Ct:
00
(12) C , . r C , + r S [ r l( £ , . , - £ , ) j w .,)]
1=0
- R t 2t +
Flavin notes that because the coefficient of t 21
is not -1, C t will not evolve as a random walk
unless the transitory consumption term 621 is
zero for all t.
Equation (12) contains revisions in expecta
tions of future real labor income. Flavin notes
that “ [a]s an empirical matter however, unan
ticipated capital gains and losses on non
human wealth probably constitute a signifi
cant fraction of the revisions in permanent
income this model is trying to capture.” (See
Flavin [1981, p. 988].) She defines unantici
pated capital gains as the present value of the
revision in the expected earnings associated
with the current nonhuman wealth position.
By then assuming “ ... that changes in the rate
of return to capital... are quantitatively more
important than the endogenous changes (in
nonhuman wealth) in determining the timeseries properties of the observed path of non
labor income ...” , unanticipated capital gains
can be approximated as the present value of
the revision in expected future nonlabor in
come. (See Flavin [1981, p. 988].) This permits
her to use disposable personal income (YD) in
place of labor income (y) in equation (12).3
Flavin next derives an expression for the
revision in expectations of future YD by
assuming that YD follows an ARMA process.
She shows that the revision in the expectation
of YD,+S(s> 0) between periods t and M is the
product of the moving average error of YD in
period t (u, and the sth coefficient from the
corresponding moving average representation
for YD (Bs). Then the present discounted
value of the set of revisions is:
(13)
(£ [# * £ * ])« /.
Thus, she demonstrates that the revision in
income expectations is white noise.
The ARMA model for YD plus the equation
formed by substituting (13) into (12) is Flav
in’s permanent income consumption model.
Note that (13) still contains an unobserved var
iable u t. This term is included with the other
error terms in estimation, making her con
sumption equation very similar to Hall’s. The
difference is that Hall’s model can be viewed
as a reduced form of Flavin’s structural
model. Flavin argues that the error terms in
the two equations are correlated because her
model is incomplete. The income equation
error will contain additional terms because
the information set probably contains varia
bles other than past income. These omitted in
formation set variables will also appear in the
consumption equation error through (13),
thus producing the correlation between the
two equation errors. She dismisses this ap
parent specification bias by assuming that
these omitted information set variables are
serially uncorrelated and uncorrelated with
the lagged income terms.
Hayashi (1982) also uses equation (7) to elim
inate the unobserved H t. He starts with the
permanent income model in level form:
(14)
C t = a ( A , + H t) + e t,
where et is defined as “ transitory con
sumption” —a shock to preferences or meas
urement error in Ct and A t. He notes that a ,
the propensity to consume, is a function of the
expected real rates of return from nonhuman
wealth and the subjective rate of time prefer
ence: but, like Hall and Flavin, assumes that
these factors are constant over time and indi
viduals. Using (7a) with an “ overall” discount
rate 1 +d in place of R, Hayashi eliminates H ,
from (14):
(15)
C l= ( l + d ) C t.I + a [ A r ( l + d ) ( A tl
+ yt-\)] + v „
where vt = u t- (\ + d)u M + a yut. Like Flavin,
Hayashi also uses a two-equation model, com
posed of equation (15) and a stochastic version
of equation (5). He adds an error term to
Hall’s nonhuman wealth identity to capture
unanticipated movements in asset prices and
measurement errors in A t, A t.\,yM, and CM.
Note that Hayashi’s model uses labor in
come instead of YD and is slightly more gen
eral than either Hall’s or Flavin’s, because it
does not assume that 1 + d = R 1.
Hall, Flavin, and Hayashi test their models
by adding other variables to the right-hand
side of (4), the modified version of (12), and
(14). It is clear that by doing so they test the
joint hypothesis that both the life-cycle/
permanent income model and the rational ex
pectations assumption are correct. If they
were interested in testing only the assump
tion of rational expectations, conditional upon
the LC/PI model, for example, they would
have compared their models with suitable
transformations based on different hypoth
eses about expectations formation. If the joint
hypothesis is correct, then no other variable
in the information set except CM will help
forecast Ct. Although any set of variables
could be used to test these models, income is
an obvious choice, because a direct relation
ship between consumption and current income
in these models would be strong evidence
against the simple life-cycle/permanent in
come model assuming perfect capital markets
and against Barro’s neutrality hypothesis.
Recall that there is no direct structural
relationship between consumption and income
in these models. Current income may be cor
related with current consumption, but the
correlation arises only indirectly, because cur
rent income represents new information
about human wealth/permanent income.
Unlike Friedman (1957) and Modigliani and
Brumberg (1954), who allowed for the possi
bility that some unexpected changes in
income would not alter a consumer’s estimate
of his permanent income or life-cycle wealth,
all unexpected income changes in the Hall,
Flavin, and Hayashi models lead to revisions
in permanent income or life-cycle wealth and,
hence, consumption.
The models are estimated and tested with
post-World War II U.S. aggregate time series
data. Unfortunately, it is difficult to compare
their results because they use different data
and sample periods. This is partly due to the
lack of reliable data on life-cycle/permanent
consumption. Hall uses real, per capita PCEnondurables and services as the consumption
variable, ignoring the service flow from con
sumer durables because of the lack of reliable
data. Flavin uses only real per capita PCEnondurables as the consumption variable. She
notes that the consumption of durable services
should exhibit a lagged response to changes in
permanent income due to the transactions
costs of adjusting durable good stocks. The
same is true of housing services, which form a
large part of PCE-services. By using only
PCE-nondurables, she says that she gives the
benefit of the doubt to the random walk
hypothesis of one-quarter adjustment.
However, this point is probably irrelevant,
because Flavin detrends the consumption and
income data before estimation. The strong
trend in PCE-services most likely would be
eliminated with detrending, allow ing her to
use PCE-nondurables and services as the de
pendent variable. Indeed, as shown below,
Flavin’s model rejects the RE-LC/PI model,
using PCE-nondurables and services as the de
pendent variable. Hayashi uses real, per cap
ita annual data constructed by Christensen
and Jorgenson (1973 and updates) for the con
sumption variable and a modification of their
labor income variable for y. The consumption
data contain imputations for the service flow
of consumer durables. Flavin uses real per
capita YD for the income variable, and all
three use this variable (or its lagged value) for
testing their models.
Hall’s first test consists of adding three addi
tional lagged C terms to the right-hand side of
(4) and finds them to be statistically insignif
icant individually and taken together. He
finds the same result when one, four, and 12
lagged YD terms are added. In all cases, the
coefficient on C M is not significantly different
from 1, which leads Hall to conclude that
aggregate consumption is a random walk
process.
However, when Hall adds four lagged stock
price variables (Standard and Poor’s compre
hensive index of stock prices deflated by the
implicit deflator for PCE-nondurables and ser
vices and divided by population), he finds that
they are individually and collectively statisti
cally significant. Hall argues that this evi
dence does not contradict the joint hypothesis,
if it is assumed that “ some part of consump
tion takes time to adjust to a change in per
manent income. Then any variable that is cor
related with permanent income in period t -1
will help in predicting the change in con
sumption in period t, since part of that change
is the lagged response to the previous change
in permanent income.” (See Hall [1978, p.
985].) He also says that “ the discovery that
consumption moves in a way similar to stock
prices actually supports this modification of
the random walk hypothesis, since stock prices
are well known to obey a random walk them
selves.” (See Hall [1981, p. 973].) In all tests,
the Durbin-Watson statistic, which is biased
downwards in these models when the auto
correlation of the errors is positive, cannot
reject the hypothesis of no first-order auto
correlation. Hall thus concludes that the
model cannot be rejected.
This is a rather curious inference. Hall
finds a variable that contradicts the null
hypothesis, and he subjectively rationalizes it!
Moreover, it seems highly improbable that
two truly random walks will be strongly cor
related with each other. Since the two series
are correlated, does this mean that the two
series are not random walks, that they are
random walks around a common trend, that
there is a structural relationship between the
two series, that the correlation is simply spur
ious, or that they are an artifact of aggregate
time series data? Unfortunately, Hall does not
report any tests of these possibilities.
Flavin adds the current and first seven
lagged changes in real per capita YD to equa
tion ( 12) with A C;as the dependent variable.
By adding these eight terms, she obtains a
just-identified system. The reduced form of
her model thus becomes:
(12a) YD t = m + a i YD M + a 2 YD t.2 + •••
+ as YD ,-8+ 7711
A C /= H2 + /3o( U\ + ( a i- l ) YDt.i
+ (x2 YD +... + otsYD t.s)
+ fii AYD t i + ($2 A YD ,.2+ ...
+
AYD t 7+ r]2 U
where «2 / contains e 2 1 and (13). The (3’s are
“ measures of the ‘excess sensitivity’ of con
sumption to current income, that is, sensitiv
ity in excess of the response attributable to
the new information contained in current
income.” (See Flavin [1981, p. 990].) Thus, a
test of the joint statistical significance of the
(3’s is a test of the RE-PI model. Over the
1949:IIIQ to 1979:IQ sample, Flavin can reject
the model at a 0.5 percent significance level.
The coefficient /3o on the A YD t term allows
her to test for a direct effect of current income
on C, although her estimate of (3o is quite
large relative to those of the other A YD
terms, its /-statistic is only 1.3, suggesting
that the test “ falls short of providing conclu
sive evidence that the permanent incomerational expectations hypothesis fails in a
quantitatively significant way.” (See Flavin
[1981 p. 1002].)
Hayashi adds YD tto equation (14) and finds
its coefficient to be of the same order of mag
nitude as the estimate of the discount factor,
but statistically insignificant in his twoequation model. He also finds that the dis
count rate is statistically different from the
constant real rate of return, contrary to Hall’s
and Flavin’s assumptions. Although this is
4. It is not clear how
Bernanke lets the
real interest rate
vary over time.
evidence in favor of the permanent income
cum rational expectations hypothesis, Haya
shi argues that
the relevant measure of
consumption for the liquidity-constrained
households is personal consumption expendi
tures as defined in the National Income and
Product Accounts (NIPA), which excludes ser
vice flows from consumer durables and in
cludes expenditures on consumer durables.
The foregoing test of the permanent income
hypothesis seems to be in some sense unfair
to the alternative hypothesis of liquidity con
straints.” (See Hayashi [1978, p. 908].) When
he uses PCE as the dependent variable and
estimates only the consumption equation (be
cause the asset equation includes consumer
durables), he finds the coefficient on current
YD to be fairly large (0.892) with a /-statistic
of about 20. On the basis of this result, he is
persuaded to reject the permanent income
cum rational expectations model. Here again
is a rather curious inference. In effect, Haya
shi is saying that only PCE-durables pur
chases can be liquidity-constrained.
Other authors have tried to relax some of
the assumptions made by these writers. Ber
nanke (1982) and Mankiw (1983) focus on the
separability issue by adding consumer dura
bles to the life-cycle cum rational expectations
model. They argue, like Flavin, that lagged
stock adjustment and accelerator effects may
lead to an incorrect rejection of the model.
This is even true when durables are excluded
from the analysis, if nondurables and dura
bles are not separable in consumer utility
functions. Moreover, as Hayashi points out,
imperfections in capital markets are likely to
show up in the pattern of durables purchases.
Bernanke derives a two-equation system in
current period PCE-nondurables and services
and next period’s stock of consumer durables
as the solution to the utility maximization
problem. A quadratic utility function contain
ing quadratic costs of adjusting consumer dur
able stocks is used. Mankiw also obtains a
two-equation model, only based on the firstorder conditions for utility maximization.
Both show that consumption is not a random
walk. In Bernanke’s model, this is due to the
adjustment costs, which supports Hall’s asser
tion that adjustment costs can be consistent
with the life-cycle cum rational expectations
model. In Mankiw’s model, consumption is
not a random walk, because the real rate of
interest and the relative price of durables are
non-constant.
Both economists test their models with postWorld War II U.S. aggregate time series data.
Under the assumption of constant real inter
est rates, Bernanke finds that the response of
consumers to an income innovation is signifi
cantly greater than predicted by the theoreti
cal model and thus rejects the life-cycle cum
rational expectations model. He claims, but
unfortunately does not prove the evidence,
that a similar result obtains if the real inter
est rate is allowed to vary.
Mankiw adds disposable income growth terms
to both equations in his model and finds them
statistically insignificant. He thus finds no
evidence against the life-cycle cum rational
expectations model and argues that his model
“ ...is a useful framework for examining the
linkage between interest rates, prices, and
consumer demand.” (See Mankiw [1983, p.
23].) As in many past studies, he also finds
that consumer durables are quite sensitive to
the real rate of interest. Depending on the
parameter values chosen, the short-run elas
ticity of the stock of consumer durables with
respect to the real interest rate varies between
-1.7 and -4.3. Mankiw’s results also suggest
that the assumption of rational expectations
is unimportant because he obtains results
similar to those studies that do not assume
rational expectations.
Real interest rates are not handled very sat
isfactorily by Mankiw .4Consumers are as
sumed not to know future income, but are
assumed to know future interest rates (and
the relative price of durables). Thus, interest
rates are allowed to vary over time in a very
uninteresting way. Muellbauer (1983) and
5. In general, when
real interest-rate ex
pectations are proba
bilistic the coeffi
cient on
i
depends on the joint
distribution o f ex
pected real incomes
and real interest
rates. In both cases,
the optimal forecast
o f current consump
tion requires more
information than
provided by C t.\.
Wickens and Molana (1984) allow for random
and unknown future real interest rates.
Wickens and Molana show that when the in
terest rate in the life-cycle cum rational expec
tations model is random, the first order con
dition for utility maximization becomes:
(16)
E t.xU'{ C t+Il) =
8 E t l [ a / R t+i)U'(Ct+l)]
( i > 0).
This expression is obtained by substituting C,
out of the utility function with the period-toperiod budget constraint ( 11 ) and maximizing
the present discounted value of expected
future utility with respect to A t. Expectations
are formed with the information set available
at the end of period M , which includes varia
bles dated M and earlier. With the necessary
assumptions, (16) can be written as:
(17)
E t.xCt+j = E t.\y t+i ( E t.iCt+i-i),
(i > 0 ).
where 2 is a function of the interest rate and
the rate of time preference. Thus, as in Hall’s
equation (2a), the coefficient on the lagged con
sumption term varies with the real interest
rate.5With the appropriate assumptions,
Muellbauer obtains an expression in poten
tially observable variables:
(18)
A l n C t - no + fis^Mr/.i
+
<5 1 ( 7 1 /
+
8 2 0 2 1
+
e f+ I t
where o 1 and 02 are the innovations in period
t real disposable income and the real interest
rate based on information available at the end
of period M, which includes variables dated t1 and earlier. The Wickens and Molana model
differs only slightly from this, using r t+x in
stead of r t_h because of a minor difference in
the dating of the interest rate in the cash flow
constraint. Both papers use post-World War II
U.K. aggregate time series data.
Also note that apart from the logarithms
and the dating difference on r, Flavin’s model
is nested in (18). However, Muellbauer and
Wickens and Molana estimate their models dif
ferently than Flavin, because the variables
they use to test their consumption equations
are all lagged at least one period. Recall that
the Flavin model is simultaneous, because she
uses A Y D , as one of her test variables. When
deriving the reduced form of her two-equation
system, the equation for YD is used to substi
tute out the current YD term in A YD t. The
revision to permanent income due to new in
formation provided by current YD (13) cannot
be identified and thus is thrown into the error
term. Because Muellbauer and Wickens and
Molana only use lagged variables to test their
models, the income and interest-rate innova
tions remain identified by the income and
interest-rate equations. Thus, unlike Flavin,
they can estimate the coefficients on the
innovation terms.
Ignoring the interest-rate terms in Muellbauer’s and Wickens and Molana’s model, it is
not clear that their test is more powerful than
Flavin’s. The presence of AYDtin the con
sumption equation gives Flavin a direct test of
the impact of current income on current con
sumption. If the RE-LC/PI model is rejected,
there is some knowledge about what the cor
rect alternative may be, or at least in what
direction the search for the correct alternative
might go, but she cannot test for the impact of
the income innovation, an important variable
of the null hypothesis. By not adding any cur
rent income terms, Muellbauer and Wickens
and Molana cannot test for a direct effect of
current income on current consumption, but
they do have a direct test of the impact of
innovations in income.
The estimation procedure used by Muell
bauer and Wickens and Molana requires two
steps. The first step estimates with ordinary
least squares (OLS) the simple reduced forms
for disposable income and the real interest
rate to generate the income and interest-rate
innovations and expected values. Muellbauer’s In YD equation uses the first two lags of
InYD and lnCt xas the information set. For
his real interest-rate equation, Muellbauer
argues that apart from seasonal factors, the
U.K. real interest rate varies randomly about
6. It was decided not
to update Hayashi’s
model, because it is
not so easily com
pared with the Hall
and Flavin models.
The Wickens and
Molana model was
not updated either,
because it is similar
to Muellbauer’s,
apart from some ad
ditional terms that
complicate the esti
mation procedure.
a constant from the 1950s until the pound ster
ling began to float in 1972:IIQ; it follows a
random walk thereafter. Wickens and Molana
say that a broader information set than one
that includes only lagged values of income
and real interest rates, should be used with
their more general model. They use the first
four lags of InYD, InC, r, InA, the latter being
the log of real consumer liquid assets, as the
information set for both real disposable
income and the real interest rate.
The second step uses the residuals for the
innovation terms and fitted values for the
expected value terms in OLS regressions of
the consumption equations. Both papers find
that their models appear to fit the U.K. data
very well. Wickens and Molana do not test the
joint life-cycle rational expectations hypothe
sis; Muellbauer does by adding the informa
tion set variables to the right-hand side of (18)
and tests for their joint statistical signifi
cance. He finds the additional lagged terms to
be significantly different from zero. He con
cludes that allowing for stochastic interest
rates does not seem to be a major cause for
the failure of the simple Hall model to explain
U.K. consumption found earlier by Daly and
Hadjimatheou (1981).
II. Updates of the Aggregate
Life Cycle Cum Rational
Expectations Model
We update the estimates, test the Hall (1978)
and Flavin (1981) models, and present esti
mates of the Muellbauer model using postWorld War II U.S. aggregate time series data.6
Updating the Hall and Flavin models serves
at least four purposes. First, the updates help
put the results from Muellbauer’s model in
perspective. The importance of allowing for
stochastic interest rates is immediately clear.
Second, by estimating the models through
1984, we can estimate their stability. Third, it
is interesting to know how the 1980s data fit
these models. Real output and prices varied
over wide latitudes during the 1980s and,
hence, offer macroeconometricians a rich set
of high-influence data, which may help them
estimate coefficients more precisely. It is
likely that the 1980s data provide even
stronger evidence against the RE-LC/PI model
than found by Flavin.
Finally, the different models are estimated
with different information sets (reduced
forms) and different sample periods. It is
reasonable to wonder if either the content of
the information set or the estimation period
has a large influence on the estimates. Our
interest in these models does not lie solely in
determining whether the RE-LC/PI model is
accepted or rejected, although that is a very
important consideration. If these models are
to be useful for policymaking and forecasting,
however, they should be robust to different
assumptions about the underlying structure
used to derive the reduced forms.
The Hall and Flavin models are updated
with their original samples, specifications,
and estimation techniques. To make the three
models comparable, we had to make at least
four decisions. The first concerns the specifi
cation of the dependent and independent vari
ables. Hall uses per capita PCE-nondurables
and services, Flavin uses the change in per
capita PCE-nondurables, and Muellbauer uses
the change in the logarithm of per capita
(U.K.) PCE-nondurables and services. The con
sumption definition used in these tests is per
capita PCE-nondurables and services. Although
Flavin’s reasons for ignoring PCE-services
may be valid, most of these problems should
be eliminated once the data are detrended.
The change in the logarithm of consumption
and the logarithm of income are used here to
facilitate comparison with the Muellbauer spec
ification. This logarithmic specification
should also minimize heteroskedasticity prob
lems. The income definition is real disposable
income per capita. The log real per capita in
come and consumption data are detrended by
their average growth trends over the 1947:IQ
to 1984:IVQ period. When the same dependent
7. See Kowalewski
(1985) fo r more
detail on this point.
variable is used, Flavin’s consumption equa
tion is, for all practical purposes, the same as
Muellbauer’s with constant interest rates.
The second decision involves seasonal
adjustment of the data. Muellbauer uses
seasonally unadjusted data, while Hall and
Flavin use seasonally adjusted data. We used
seasonally adjusted data to maintain compar
ability with other U.S. consumption results.
A third choice concerns estimation tech
niques. Hall uses OLS, Flavin uses maximumlikelihood to estimate her consumption equa
tion jointly with her income forecasting
equation, and Muellbauer uses a two-step
OLS procedure. The original estimation tech
niques used by Hall and Flavin are used to up
date their models with the most recent data.
Maximum-likelihood is used to estimate Muell
bauer’s model, because the computer-generat
ed coefficient standard errors produced by the
two-step method are incorrect.7
A fourth choice is that of the definition of
the real interest rate. Instead of using an ex
post real interest rate, Muellbauer uses some
thing like an ex ante rate—a nominal interest
rate minus an expected inflation rate. He com
putes this real rate by subtracting from the
nominal rate a fitted value from an inflation
equation. This choice of real rate is rather
odd, for it means that instead of using an
expected real interest rate as his theory
requires, he is using an expected expected real
interest rate in his consumption equation. It
also means that he is using a three-step esti
mation process, with the estimation of the in
flation equation as the first step. Moreover,
the inflation equation uses an information set
different from that used for the income and
interest-rate equations. A logical extension
and correction of his model would be to spec
ify separate forecasting equations for the
nominal rate and the inflation rate, to use the
same information set for all of the equations,
and to use the fitted values and residuals
from both equations to compute the expected
real rate and its innovation. An equivalent
strategy employed here is to use an ex post
rate, as Wickens and Molana do. This re
quires only one forecasting equation. The ex
post real three-month U.S. Treasury bill rate,
(nominal rate, minus current-quarter com
pounded annual actual growth rate in the
PCE-nondurables and services deflator) is
used as the real interest rate in the estima
tions of Muellbauer’s model shown below.
Because there is no reason to think that U.S.
real interest rates have behaved as random
walks during the post-World War II period,
the real interest-rate equation for Muell
bauer’s model will have information set vari
ables as regressors, and these will be the same
as those used for the income equation—the
first two lags of income, the first two lags of
the real interest rate, and the first lag of con
sumption. This is a simple extension of Muell
bauer’s original information set, which con
sisted of the first two lags of income and the
first lag of consumption.
The estimation results are shown in tables 1
to 5. The data used for the computations con
tain revisions through the second revised esti
mates for 1984:IVQ dated March 31, 1985. The
models in tables 1 to 3 were estimated over
their original samples and over 1949:IIIQ to
1984:IVQ. For the re-estimates of Hall’s mod
el, the data were not detrended. For the reestimates of Flavin’s model, the consumption
and income data were detrended using their
average growth rates over the 1947:IQ to
1979:IQ period. When the two models are up
dated with the data through 1984:IVQ, the
consumption and income data are detrended us
ing their average growth rates over the
1947:IQ to 1984:IVQ period, and a dummy vari
able is added to control for the credit controls
of 1980:IIQ. Detrending biases the test in favor
of the random walk hypothesis, because it re
moves the main source of correlation from
these variables. Detrending may also remove
structural correlation between C and YD,
again favoring the random walk hypothesis. It
unfortunately leaves the trend unexplained.
The dummy variable is part of the maintained
8. Serially corre
lated errors may not
signal a breakdown
o f the model, if as
Hall argues when ra
tionalizing the sta
tistically significant
stock price index
terms, consumers
take more than one
quarter to assimilate
new information
and act upon a
changed expectation
o f life-cycle wealth.
hypothesis and is not included among the varia
bles included in the test of the RE-LC/PI model.
The first table contains OLS estimates of
Hall’s model. The first equation shows the reestimates of Hall’s model with only one lagged
income term. The coefficients, though differ
ent from Hall’s published numbers, yield the
same apparent inference: the RE-LC/PI model
cannot be rejected. The next equation shows
the original Hall model updated through
1984:IVQ. Note that the addition of the 1980s
data did not change the conclusion of the hy
pothesis test—the coefficient on lagged per
sonal income is small, has the wrong sign,
and is statistically insignificant. However, the
Durbin h-statistic rejects the hypothesis of
positive serially uncorrelated errors at better
than a 5 percent significance level using a
one-tailed test. Because the theory predicts
that the error should be white noise, the addi
tion of the 1980s data may be signaling a
breakdown of the model.8
The third equation contains the change in
the detrended log of per capita PCE-nondura
bles and services as the dependent variable
and the detrended logarithm of real per capita
disposable personal income as the income var
iable. The estimation period is 1948:IQ to
1977:IQ. Neither coefficient is large, the
/-statistics are very low, and the adjusted R 2
is negative. The results change very little
when the estimation period is extended through
1984:IVQ; all of the explanatory power of the
right-hand side variables comes from the
Table 1 Hall Estimates
C/ = ao +
Cm + ot2 Yt.\ +
0:3 DUM802
#1
+ et
#2
#3
#4
Chg in detrended
log of
Chg in detrended
log of
c
NDS/POP
NDS/POP
NDS/POP
NDS/POP
Y
Y D 72/P O P
Y D 72/P O P
Detrended log
of YD72/POP
Detrended log
of YD72/POP
4 8:1 Q -7 7 :IQ
4 8 :1 Q -8 4 :4 Q
4 8 :1 Q -7 7 :1 Q
4 9 :3 Q -8 4 :4 Q
-0.0376
(-2.2620)
-0.0059
(-0.5835)
0.0007
(1.1492)
0.0005
(0.8562)
1.0811
(24.8721)
1.0081
(31.3779)
-0.0480
(-1.6283)
-0.0008
(-0.0341)
-0.0063
(-0.4627)
-0.0060
(-0.4902)
-0.0068
-0.0131
(-2.3346)
0.0263
Sample
ao
<X2
C*3
-0.0441
(3.0626)
R2
0.9989
0.9994
Durbin h
1.358
1.7327
SER
0.0136
0.0290
Variables:
NDS = PCE-nondurables plus services, 1972 dollars.
YD72 = disposable personal income, 1972 dollars.
POP = non-institutionalized, civilian population.
ad j
a. Durbin-Watson statistic.
NOTE:
1. The variables in equations #3 and #4 are detrended over the 1947:IQ to 1984:IVQ period.
2. The /-statistics are shown below the coefficient estimates.
1.77528
0.0058
1.7460*
0.0056
9. Flavin (1981),
proves the equiva
lence o f these two
procedures in ap
pendix II.
dummy variable. Thus, Hall’s model can find
no evidence to reject the RE-LC/PI model.
The results for Flavin’s model (12a) are
shown in tables 2 and 3. Only the coefficients
of the A YD ( Ain YD) terms (the 0 coeffi
cients in equation ( 12a) are shown because
only they are relevant for the test of the RELC/PI model. Recall that these terms must be
jointly statistically different from zero in
order to reject the model. The first equation in
table 2 shows the re-estimates of her original
specification. Like the updates of Hall’s model,
these coefficients are not quantitatively the
same as the original estimates; qualitatively,
however, they are very similar. The coeffi
cient on A Y D t, fio, though fairly large, has a
very low /-statistic; of the 0’s, only 0i is sig
nificant at better than 5 percent using a one
tailed test. The likelihood ratio statistic (LRS)
tests the joint significance of the A YD terms.
Surprisingly, the RE-LC/PI model cannot be
rejected at the original significance level.
10. When the con
sumption and in
come variables are
detrended with their
average growth rates
between 1947: IQ
and 1984:IVQ, the
LRS fo r the joint
test o f the A In YD
terms becomes 13.5,
which implies the re
jection o f the null
hypothesis at about
a 10 percent signifi
cance level.
Table 2 Flavin Re-estimates
Var
#i
#2
0o
A YDt
0i
AYDt-i
@2
A YDt-2
03
A YDt-s
04
A YDt 4
05
A Y D t -5
06
A YDt- e
07
A YDt-i
0.3194
(1.1164)
0.0605
(1.8388)
0.0079
(0.2493)
-0.0662
(-1.2940)
0.0415
(0.8088)
-0.0081
(-0.1410)
0.0068
(0.2163)
0.0074
(0.2381)
0.2712
(1.4596)
0.0650
(2.3574)
-0.0099
(-0.3659)
-0.0535
(-1.4499)
0.0136
(0.3915)
-0.0082
(-0.1908)
0.0050
(0.1834)
0.0169
(0.6146)
0.0103
2.0101
0.0329
2.0008
11.754
0.0104
2.0521
0.0325
2.0009
17.148
4 9 :3 Q -7 9 :1 Q
4 9 :3 Q -8 4 :4 Q
Coef
C
C
Y
Y
SER
D -W
SER
D -W
LR Statistic
Sample
NOTE: Detrending occurs from 1947:1Q to 1979:1Q.
Flavin’s original likelihood ratio statistic,
which is asymptotically distributed as X 2( 8 ),
is 27.0, significant at better than 0.5 percent.
The LRS for the test of equation (1) is only
11.8, significant at slightly better than 25.0
percent. Identical test results are obtained by
estimating only the consumption-reduced-form
equation with OLS and by testing for the joint
significance of the lagged income terms.9
Apparently, the results are sensitive to revi
sions in the data and to the use of different
trend values for PCE-nondurables and Y D .10
Equation (2) in table 2 updates Flavin’s orig
inal model through 1984:IVQ. The 1947:IQ1979:IQ trend values are used to detrend the
post-1979:IQ data. Interestingly, the model
can now be rejected at better than a 5.0 per
cent significance level; the LRS is 17.2, while
the X 2 (8 ) cut-off value is 15.5 at 5.0 percent.
The coefficient 0 Ois now smaller, but its tstatistic is larger; the coefficient and tstatistic on A in Y D t l are also larger.
Moreover, the fit of the equation is improved
over the longer period; the standard errors of
the two equations are smaller in the longer
sample. Thus, as was expected, the 1980s
data appear to tighten up coefficient standard
errors and help reject the RE-LC/PI model.
Equations (3) and (4) in table 3 use the
change in the logarithm of per capita real
PCE-nondurables and services as the depend
ent variable, and the log per capita consump
tion and income data are detrended over the
1947:IQ to 1984:IVQ period. They compare to
the Hall equations (3) and (4) in table 1. The
third equation shows the unconstrained results
over the 1949:IIIQ to 1979:IQ sample period.
Notice that they are qualitatively similar to
those of equation (1); 0 o is about 0.3 and is statis
tically insignificant; 0i is large and is statisti
cally significant. Testing the joint significance
of the A In YD terms yields a LRS of 27.1,
which is significant at better than 0.5 percent,
Flavin’s original significance level. Note that
this result is much stronger than Flavin’s
original result, because the consumption vari
able includes PCE-services, which Flavin
argued would bias the results against the RELC/PI model.
The fourth equation shows the estimation
results over the 1949:IIIQ to 1984:IVQ sample.
Qualitatively, these results are similar to
those of equation (3). The LRS of the test of
the lagged A In YD terms is now 29.4, greater
than the LRS over the 1949:IIIQ to 1979:IQ
sample; the standard errors of the equation al
so are smaller in the longer sample. Again, it
appears that the 1980s data provide additional
stronger evidence against the RE-LC/PI model.
Tables 4 and 5 contain the estimates of
Muellbauer’s models. Only the coefficients on
the information set, innovation, and expected
interest-rate terms are shown. The dependent
variable is the change in the logarithm of real
per capita PCE-nondurables and services;
detrending of the log real per capita consump-
Table 3 Flavin Estimates Using Logs
Coef
Var
#3
#4
0o
&YDt
0i
AYDn
02
A YD t 2
03
A YD 13
04
A YD a
05
A Y D tz
06
A Y D t6
07
AYDt-i
0.2794
(0.8282)
0.1208
(2.9091)
0.0709
(1.7267)
-0.0977
(-1.7462)
0.0577
(0.6548)
-0.1296
(-2.7135)
0.0444
(1.1380)
0.0162
(0.4045)
0.2652
(0.9903)
0.1280
(3.3398)
0.0597
(1.6026)
-0.0762
(-1.5329)
0.0457
(0.6887)
-0.1095
(-2.5909)
0.0459
( 1.2202 )
0.0423
(1.1439)
0.0051
1.8636
0.0050
1.9003
0.0098
C SER
C D -W
Y SER
Y D -W
LR Statistic
Sample
0.0102
1.9942
27.068
4 9 :3 Q -7 9 :1 Q
2.0022
29.360
4 9 :3 Q -8 4 :4 Q
NOTE: Detrending occurs over the 1947:1Q-1984:4Q.
tion and income data occurs over the 1947:IQ
to 1984:IVQ period. Table 4 shows the esti
mates of equation (18) without the interestrate terms ii Mr Mand o 2/. The coefficient 61
on the income innovation should be positive,
because positive innovations in current
income should lead to upward revisions in
life-cycle wealth/permanent income and,
hence, in consumption. The first equation
shows the results using the 1949:IIIQ to
1979:IQ sample. This equation compares to
Flavin’s equation (3) in table 3. The coefficient
is 61 positive and statistically significant.
Surprisingly, the RE-LC/PI model cannot be
rejected by this form of Muellbauer’s model,
even though Flavin’s model could. The LRS is
only 3.8, significant at slightly less than 30
percent. Again, the results appear to be sensi
tive to the specification of the test.
The second equation in table 4 updates
Muellbauer’s model without the interest-rate
terms over the 1949:IIIQ to 1984:IVQ sample.
As was true of Flavin’s model, Muellbauer’s
model without the interest-rate terms fits bet
ter with the 1980s data. Moreover, the LRS is
now 14.2, significant at better than 1 percent.
Again, the 1980s data lead to a convincing re
jection of the RE-LC/PI model. Note that the
coefficients on the information set variables
are the same order both of magnitude and sta
tistical significance in equations ( 1 ) and (2);
the difference is that the model fits better
with the 1980s data.
Table 5 contains the estimates of Muellbau
er’s model including the interest-rate terms.
Recall from equation (18) that S3, the coeffi
cient on the expected interest-rate term, is a
positive function of the ratio of one, plus the
interest rate, to one, plus the rate of time
preference; hence, it should be positive. Pre
sumably, the coefficient <52 on the interest-rate
innovation is negative, since a higher-thanexpected interest rate should cause consum-
ers to save more in the current period. Equa
tion (3) shows the results over the 1949:IIIQ to
1979:IQ sample. The two interest-rate coeffi-
Table 4 Muellbauer Estimates Without
the Interest Rate
Coef
Var
<51
YRESID
Pi
InYDt-x
P2
lnY D t -2
p3
lnCt-\
C SER
Y SER
LR Statistic
Sample
#1
#2
0.2185
(4.7533)
0.1207
(2.2775)
-0.1683
(-3.4897)
0.0418
(1.0391)
0.2191
(5.3016)
0.1557
(3.4233)
-0.1585
(-3.5539)
-0.0112
(-0.4075)
0.0053
0.0104
3.800
0.0050
0.0104
14.200
4 9 :3 Q -7 9 :1 Q
4 9 :3 Q -8 4 :4 Q
NOTE: YRESID is the current income innovation term.
Table 5 Muellbauer Estimates with
the Real Interest Rate
Var
#3
#4
61
YRESID
0.2318
(5.2208)
82
RRESID
(0.2042)
0.0042
(1.8764)
0.0871
(1.6383)
-0.0000
(-0.0005)
0.0006
(2.2494)
-0.0024
(-2.1887)
0.2431
(5.8538)
-0.0001
(-0.3660)
0.0026
(2.1257)
0.1433
(2.9831)
-0.0419
(-0.6306)
0.0003
(1.0161)
-0.0017
(-2.6248)
-0.0738
(-1.0183)
-0.1109
(-1.7685)
0.0049
0.0050
0.0108
Coef
S3
E rt_i
Pi
InYD t_i
P2
InYD ,_2
P3
rm
Pi
r t-2
Ps
InC ;_i
C SER
Y SER
r SER
LR Statistic
Sample
0.0001
0.0111
1.9737
27.800
4 9 :3 Q -7 9 :1 Q
2.0102
26.200
4 9 :3 Q -8 4 :4 Q
NOTE: YRESID and RRESID are the current income and interestrate innovations. Ert.\ is the expectation of last period’s real interest
rate based on information available last period.
cients appear to be small in magnitude, but
this is simply a scaling difference because,
interest rates are measured in percentage
points. The interest-rate innovation coeffi
cient <52 is statistically insignificant, while 63
is significant at slightly better than 10 per
cent. The LRS for the test of the RE-LC/PI
model is 27.8, which is asymptotically distrib
uted as X 2(5), and is significant at better than
1 percent. Compared with equation (1) in table
4, the allowance for stochastic interest rates
now leads to the rejection of the RE-LC/PI
model. Again, the specification of the test has
an important effect on the results.
Equation (4) in table 5 shows the estimates
of Muellbauer’s model with the interest-rate
terms over the 1949:IIIQ to 1984:IVQ period.
All of the coefficients are estimated more pre
cisely, but unlike the previous results, the
equation fits the longer period less well. The
coefficients 8 2 and 8 3 now have the correct
signs and about the same statistical signifi
cance as the earlier estimates. The LRS sta
tistic for the test of the RE-LC/PI model is
26.2, rejecting the model at better than a 1
percent significance level, but it is a bit
smaller than the LRS from the shorter sample
period. Nevertheless, the results are qualita
tively the same for both estimation periods,
unlike the results of the Flavin tests.
The worse fit using the 1980s data occurs
because the interest-rate equation fits less
well in the longer period. This is not surpris
ing, given that interest rates behaved so dif
ferently in the 1980s than in the earlier
period.11 Does this mean that the test is
invalid because the equation generating the
interest-rate expectations is wrong? This does
not seem likely. Although the /-statistics on 8 2
and 8 3 do not provide support for the model,
the LRS of the joint significance of the two
interest-rate terms in equation (4) is 46.1.
Thus, the interest-rate terms are undoubtedly
important, even if they are poorly computed.
Moreover, it is not clear how quickly interest-
11. The standard
error o f the con
sumption equation
also increased, but
this is probably due
to the poorer fit o f
the interest-rate
equation through
the cross-equation
constraints.
rate forecasting models were adjusted in the
1980s. Given the lag in the learning process,
the number of quarters for which the interestrate equation may be wrong is probably small
er than 20. Even if the interest-rate equation
is wrong, it is not necessarily irrational.
Finally, the fit of the model did not worsen so
much that this is likely to be the sole reason
that the RE-LC/PI model is rejected.
III. What Has Been Learned?
The estimation results provide ample evi
dence to reject this form of the RE-LC/PI
model during the postwar period, especially
when the 1980s data are included. Even
though Hall’s specification cannot reject the
model, minor generalizations of Flavin and
Muellbauer can, and Muellbauer’s specifica
tion including uncertain interest rates can
reject the model with or without the 1980s
data. It would appear that an important
assumption for Barro’s neutrality hypothesis
does not hold.
Unfortunately, this rejection of the RELC/PI model does not offer an explicit alter
native as a replacement. As mentioned earlier,
these tests cannot distinguish the assumption
of rational expectations from that of the lifecycle/permanent income model. All that can
be inferred from these tests is that the joint
hypothesis can be rejected. Flavin (1985) at
tempts to determine whether the rejection of
the RE-LC/PI model is due to the assumption
of perfect capital markets or to that of the per
manent income model. She uses her original
model augmented with an equation for the
unemployment rate, which is a proxy for the
number of liquidity-constrained consumers.
However, there are many problems using such
a crude variable for such a complex hypoth
esis; her tests undoubtedly have little power.
Nor do these tests provide many clues about
the exact length of consumer spending hori
zons, or how the distribution of horizon
lengths changes as interest rates, the distri
bution of income, or the supply of consumer
credit changes.
That the distribution of consumer horizon
lengths may vary over time is suggested by
the increased significance of the likelihood
ratio tests when the 1980s data are included.
The early 1980s were apparently a time when
the distribution of horizons lengths was
skewed toward the shorter end, increasing the
correlation of aggregate consumption to cur
rent disposable income. Additional evidence
about changes in the distribution of consumer
spending horizons is provided by Kowalewski
(1982), who studies the time series behavior of
aggregate personal bankruptcy filings in the
United States. Personal bankruptcy filings are
countercyclical, increasing in recessions and
falling in recoveries. For a variety of reasons
discussed in the article, it is likely that just
before they file for bankruptcy, personal bank
rupts have about the shortest spending hori
zons of all consumers.
Thus, increases in the number of personal
bankruptcy filings might indicate a shift in
the distribution of consumer spending hori
zons towards shorter lengths. In a regression
explaining per capita personal bankruptcy fil
ings, transitory income had a much larger
impact than permanent income, suggesting
that liquidity is very important for these
financially distressed consumers. The compo
sition of consumer portfolios was also signifi
cantly related to the behavior of personal
bankruptcy filings. Unfortunately, this evi
dence is only about one tail of the distribution.
It is clear that much work remains to be done
before the time series behavior of aggregate
consumption is understood.
References
Barro, Robert. “ Are Government Bonds Net
Wealth?” Journal of Political Economy, vol.
82, no. 6 (November/December 1974), pp.
1,095-1,117.
Bernanke, Ben S. “ Permanent Income, Liquid
ity, and Expenditure on Automobiles: Evi
dence from Panel Data,” The Quarterly
Journal of Economics, August 1984, pp.
587-614.
______ “ Adjustment Costs, Durables, and
Aggregate Consumption,” NBER Working
Paper No. 1038, December 1982.
Blinder, Alan S. “ Temporary Income Taxes
and Consumer Spending,” Journal of Politi
cal Economy, vol. 89, no. 1 (February 1981),
pp. 26-53.
Boskin, Michael J., and Laurence J. Kotlikoff.
“ Public Debt and U.S. Saving: A New Test
of the Neutrality Hypothesis,” unpublished
manuscript, Carnegie-Rochester Confer
ence, November 1984.
Daly, Vince, and George Hadjimatheou. “ Sto
chastic Implications of the Life CyclePermanent Income Hypothesis: Evidence
for the U. K. Economy,” Journal of Political
Economy, vol. 89, no. 3 (1981), pp. 596-99.
Delong, Bradford J., and Lawrence H. Sum
mers. “ The Changing Cyclical Variability
of Economic Activity in the United States,”
NBER Working Paper No. 1450, September
1984.
Dolde, Walter. “ Capital Markets and the
Relevant Horizon for Consumption Plan
ning,” unpublished Ph.D. dissertation, Yale
University, 1973.
Flavin, Marjorie A. “ Excess Sensitivity of Con
sumption to Current Income: Liquidity
Constraints or Myopia?” The Canadian
Journal of Economics, vol. 18, no. 1 (Febru
ary 1985), pp. 117-36.
______ “ The Adjustment of Consumption to
Changing Expectations about Future
Income,” Journal of Political Economy, vol.
89, no. 5 (October 1981), pp. 974-1,009.
Foley, Duncan K., and Martin F. Hell wig.
“ Asset Management with Trading Uncer
tainty,” Review of Economic Studies, vol. 42,
no. 3 (July 1975), pp. 327-46.
Friedman, Milton. “ Windfalls, the ‘Horizon,’
and Related Concepts in Permanent-Income
Hypothesis,” in Carl F. Christ, et al., eds.,
Measurement in Economics. Stanford: Stan
ford University Press, 1963.
______ A Theory of the Consumption Func
tion. Princeton, NJ: Princeton University
Press, 1957. (National Bureau of Economic
Research General Series 63.)
Hall, Robert E., and Frederic S. Mishkin.
“ The Sensitivity of Consumption to Tran
sitory Income: Estimates from Panel Data
on Households,” Econometrica, vol. 50, no.
2 (March 1982), pp. 461-82.
______ “ Stochastic Implications of the Life
Cycle-Permanent Income Hypothesis: The
ory and Evidence,” Journal of Political
Economy, vol. 86, no. 6 (1978), pp. 971-87.
Hayashi, Fumio. “ The Effect of Liquidity Con
straints on Consumption: A Cross-sectional
Analysis,” The Quarterly Journal of Eco
nomics, vol. 100, issue 1 (February 1985),
pp. 183-206.
______ “ The Permanent Income Hypoth
esis: Estimation and Testing by Instrumen
tal Variables,” Journal of Political Economy,
vol. 90, no. 5 (October 1982), pp. 895-916.
Heller, Walter Perrin, and Ross M. Starr.
“ Capital Market Imperfection, the Con
sumption Function, and the Effectiveness
of Fiscal Policy,” The Quarterly Journal of
Economics, vol. 93, no. 3 (August 1979), pp.
455-63.
Houthakker, H.S. “ The Permanent Income
Hypothesis,” American Economic Review,
vol. 48 no. 3 (June 1958), pp. 396-404.
Kotlikoff, Laurence J., and Ariel Pakes. “ Look
ing for the News in the Noise—Additional
Stochastic Implications of Optimal Con
sumption Choice,” NBER Working Paper
No. 1492, November 1984.
Kowalewski, KJ. “ Stochastic Interest Rates
in the Aggregate Life-Cycle/Permanent
Income Cum Rational Expectations Model,”
Working Paper 8506, Federal Reserve Bank
of Cleveland, October 1985.
______ “ Personal Bankruptcy: Theory and
Evidence,” Economic Review, Federal
Reserve Bank of Cleveland, Summer 1982,
pp. 1-29.
Mankiw, N. Gregory, Julio J. Rotemberg, and
Lawrence H. Summers. “ Intertemporal
Substitution in Macroeconomics,” The
Quarterly Journal of Economics, vol. 100,
issue 1 (February 1985), pp. 225-51.
Mankiw, N. Gregory. “ Consumer Durables
and the Real Interest Rate,” NBER Work
ing Paper No. 1148, June 1983.
Mishkin, Frederic S. A Rational Expectations
Approach to Macroeconomics, Testing Policy
Ineffectiveness and Efficient-Markets Mod
els. NBER Monograph, Chicago: University
of Chicago Press, 1983.
Modigliani, Franco, and Richard Brumberg.
“ Utility Analysis and the Consumption
Function: An Interpretation of CrossSection Data,” in Kenneth K. Kurihara,
ed., Post-Keynesian Economics. New
Brunswick, NJ: Rutgers University Press,
1954.
Muellbauer, John. “ Surprises in the Con
sumption Function,” Supplement to The
Economic Journal, Conference Papers, 1983,
pp. 34-50.
Okun, Arthur M. “ The Personal Tax Sur
charge and Consumer Demand, 1968-70,”
Brookings Papers on Economic Activity, 1,
1971.
Pagan, Adrian. “ Econometric Issues in the
Analysis of Regressions with Generated
Regressors,” International Economic
Review, vol. 25, no. 1 (February 1984), pp.
221-47.
Pissarides, Christopher A. “ Liquidity Consid
erations in the Theory of Consumption,”
The Quarterly Journal of Economics, vol. 92,
no. 2 (May 1978), pp. 279-96.
Swamy, P.A.V.B., Roger K. Conway, and
Peter von zur Muehlen. “ The Foundations
of Econometrics: Are There Any?” Special
Studies Paper No. 182, Division of Research
and Statistics, Federal Reserve Board, Feb
ruary 1984.
Swamy, P.A.V.B., J.R. Barth, and P.A. Tins
ley. “ The Rational Expectations Approach
To Economic Modelling,” Journal of Eco
nomic Dynamics and Control, vol. 4, no. 2
(May 1982), pp. 125-47.
Tobin, James. “ Government Deficits and Cap
ital Accumulation,” in James Tobin, ed.,
Asset Accumulation and Economic Activity.
Chicago: The University of Chicago Press,
1980.
______ , and Willem Buiter. “ Fiscal and Mone
tary Policies, Capital Formation, and Eco
nomic Activity Vol. 11,” in George M. von
Furstenberg, ed., The Government and Cap
ital Formation. Cambridge, MA: Ballinger
Publishing Co., 1980.
______ , and Walter Dolde. “ Wealth, Liquidity,
and Consumption,” Consumer Spending
and Monetary Policy: The Linkages, Federal
Reserve Bank of Boston Monetary Confer
ence Series No. 5, June 1971, pp. 99-146.
Tobin, James. “ Relative Income, Absolute
Income, and Saving,” in Money, Trade, and
Economic Growth, Essays in Honor of John
Henry Williams. New York, NY: The Mac
millan Company, 1951.
Watkins, Thayer H. “ Borrowing-Lending
Interest Rate Differentials and the Time
Allocation of Consumption,” Southern Eco
nomic Journal, vol. 43, no. 3 (January 1977),
pp. 1,233-42.
______ “ The Time Allocation of Consumption
Under Debt Limitations,” Southern Econom
ic Journal, vol. 42, no. 1 (July 1975), pp.
61-8.
Wickens, M.R., and H. Molana. “ Stochastic
Life Cycle Theory with Varying Interest
Rates and Prices,” Supplement to The Eco
nomic Journal, Conference Papers, vol. 94,
1984, pp. 133-47.
Eric Kades is a
research analyst at
the Federal Reserve
Bank o f Cleveland.
1. See fo r example,
Lucas (1972),
(1979); Prescott and
Kydland (1980); or
Long and Plosser
(1983).
New Classical and
New Keynesian
Models of Business
Cycles
by Eric Kades
“Not the least misfortune in a
prominent falsehood is the fact that
tradition is apt to repeat it for truth. ”
H
osea
B
allou
The alleged demise of classical economics was
greatly exaggerated in the Keynesian era after
World War II. The supposed death blow was
the seeming inability of the purely competi
tive model to explain the vagaries of the busi
ness cycle. But in the last two decades, a
number of articles have demonstrated that
fluctuations with many of the central charac
teristics of observed business cycles can arise
in “ classical” market-clearing models.1
Market-clearing notions are among the strong
est in economics, and the New Classical ability
to explain business cycles has breathed new
life into the equilibrium approach and many
of its provocative conclusions. The existence
of business cycles is no longer a reason to ring
the death knell for classical models.
Keynesian models have never had trouble ex
plaining business cycles. Observed movements
of output and prices have shaped Keynesian
thinking first and foremost, and their models
have always admitted these facts. Perhaps
because of this preoccupation with empirical
regularities, general equilibrium microfounda
tions for Keynesian economics failed to arise
quickly. Much of the New Classical rebellion
against Keynesian orthodoxy in the late 1960s
and 1970s was understandably inspired by this
lack of a strong choice-theoretic basis for the
neoclassic synthesis (the IS-LM and Phillips
curve model). Economic theorists of all schools
have become less and less willing to accept
models not derived from explicit maximizing
behavior in a general equilibrium setting.
Such shortcomings led to premature eulo
gies for Keynesian theories; New Classical
economists found the inflation of the late
1960s and the stagflation of the 1970s evi
dence of the failure of Keynesian ideas and
policies. But the theoretical deficiencies have,
in large part, been remedied, and indeed, the
New Keynesian tradition employs more preci
sion and adherence to general equilibrium
rigor than the New Classical.2
Both New Keynesians and New Classical
theorists either implicitly or explicitly are
searching for the central cause or causes of
business fluctuations. Economists of both
2. For a New
Keynesian example,
see Benassy (1976);
Malinvaud (1977);
Bohm (1978); or
Grandmont (1982).
For a representative
New Classical exam
ple, compare exist
ence proofs in Dreze
(1975) or in van
den Heuvel with
Lucas (1979) or in
Long and Plosser
(1983). Although
the label “ New Key
nesian” is not uncontroversial, I feel
its use is warranted.
First, Keynes states
clearly in the Gen
eral Theory that his
model generalizes on
the classical perspec
tive. This is a cen
tral point o f this
paper, in reference
to present-day theor
ies. Second, market
failures are at the
root o f Keynes’s mod
el. New Keynesian
theory merely fo r
malizes insights due
in large part to the
General Theory. F i
nally, the modern
authors who devel
oped this approach
(Benassy, Younes,
Grandmont, and
Dreze) refer to their
models as “ Keyne
sian, ” “ neo-Key
nesian,, ’ ’ etc.
Thus the use o f
“ New Keynesian ” is
historically accurate.
schools agree that many factors are involved,
but find the rough equivalence of cycles (in co
variances; not in frequencies and amplitudes)
striking and believe the essence of the issue
can be illustrated in relatively simple models.
When examining Classical and Keynesian
models of the business cycle, one is weighing
the evidence and deciding which fundamental
insight best agrees with the data.
For Keynesians, the central cause of the bus
iness cycle has always been market failure.
The formal definition of market clearing equi
librium, that prices adjust to the attributes of
agents so that trades balance under desired be
havior, is employed by all theorists today.
This rigorous definition of market clearing did
not arise until the 1950s (Debreu and Arrow
[1954]), and it was not for another decade that
Clower (1965) clarified the Keynesian idea of
market failure. This idea was then formalized
and rigorously established as valid in a gen
eral equilibrium framework (Benassy [1975]
and Dreze [1975]), by the New Keynesians in
the early 1970s. The basic notion of market
failure is that quantities adjust faster than
prices. Prices then do not clear markets, and
the entire market-clearing house of cards col
lapses. Such Keynesian models are compatible
with rational expectations and full informa
tion. And they do not rely on “ strange” utility
or production functions; indeed we will see
that, at present, disequilibrium models are
more robust than equilibrium models as to the
specification of these fundamentals.
One way to highlight the difference between
the Keynesian and Classical perspectives is to
describe their view of the existing market
mechanism. Keynesians view this market struc
ture as an endowment that, at least over
moderate horizons, agents must take as given,
much like their endowments of various goods,
such as labor, time, assets, etc. Conversely,
Classical theorists view the market structure
as much more fluid; any possibility for gains
from trade between agents (taking into consid
eration search and transactions costs) can and
will be exercised. This is reflected in a price
mechanism that works rapidly and effectively.
In Keynesian models, the imperfect market
structure causes business cycles. For Classi
cal theory, fluctuations must arise from
other sources.
The essence of New Classical business cycles
lies in agents’ intertemporal substitution of
consumption and labor in response to technol
ogy (supply) or other shocks. Agents desire to
smooth their consumption paths and, to achieve this end, substitute between present
and future consumption, present and future
leisure and, intratemporally, between labor
and leisure. Combined with very simple tech
nology shocks, such a model can mimic ob
served business cycles.
Both schools of thought, then, have con
structed models that “ explain” business cy
cles in that they reproduce the basic empirical
regularities of observed fluctuations. Trans
acted quantities of all goods exhibit high posi
tive correlation over time, and quantity move
ments tend to persist in the same direction for
many periods. Further, both generate pro-cycli
cal real wages. These are the most basic fea
tures of observed business cycles.
How are economists to choose which model
better explains economic fluctuations? Are the
two theories observationally equivalent so
that it is impossible to determine which truly
describes the real economy? This question is
important, since Keynesian models call for
activist policy to smooth business cycles,
while in Classical models these fluctuations
are desired paths for the economy.
We will demonstrate that the New Classical
(NC) model is a special case of the New Keyne
sian (NK) model. Thus, the NC model can be
distinguished by the restrictions it places on
the more general theory. In the decision-theo
retic foundations of statistical scientific in
quiry, we can state precisely that there will be
less risk in working with the NK model, since
it places less a priori restrictions on parame
ters. And although testing hypotheses on these
3. Lucas (1972,
1979) requires mon
etary policy mea
sures along with
asymmetric infor
mation to constantly
confound agents to
produce cycles.
Given the appear
ance o f business
cycles under an ex
tremely wide range
o f monetary policy
regimes, in all mod
ern economies, and
fo r hundreds o f
years, Lucas ’ model
cannot be considered
a general explana
tion offluctuations.
4. In a discrete time
model, prices are set
at intervals frequent
enough so that ex
cess demands do not
change within a
period.
highly abstract models is controversial (due to
lack of desired statistics, problems of aggrega
tion, and other problems with available data),
existing empirical evidence casts doubt on the
a priori restrictions of the NC model.
We illustrate these points by presenting sim
ple, but essentially complete, NC and NK mod
els of the economy and business cycles that il
lustrate the central forces behind fluctuations
in each. We then discuss theoretical and statis
tical arguments for and against each model.
The models examined are intentionally bare
boned; they assume perfect information, ration
al expectations, and model only labor and goods
markets. No assets exist; money is solely a unit
of account.
I. Equilibrium Model
We choose Long and Plosser’s (1983) equilib
rium model of business cycles for its simplic
ity; it captures the essence of the New Classi
cal explanation of economic fluctuations. Un
like earlier models, such as Lucas’, this formu
lation requires no monetary authority along
with asymmetric information to fool agents
and jolt the economy into fluctuations.3 For
Fig. 1 Equilibrium model
One-Period Solution
Leisure
0
Consumption
clarity, we assume perfect information and ra
tional expectations. Business cycles arise
from technology shocks and intertemporal
labor, leisure, and consumption substitutions
in response to these surprises.
In equilibrium models, the market works in
stantaneously at every date. Prices, although
theoretically exogenous to households and
firms, are actually precisely determined by
the attributes of these agents. Imagine a rep
resentative firm and household with very wellbehaved production and utility functions. For
this Robinson Crusoe and Friday economy, we
have equilibrium at the tangency of the indif
ference curves and production frontier in
leisure-commodity space. (See figure 1.)
The key point is the equating of prices and
marginal tradeoffs. Consumers equate the
wage with the marginal utility of leisure;
firms equalize wages and labor’s marginal
product. Although there are technical compli
cations in extending the equilibrium model to
a world with many periods, economically this
approach reduces to applying these marginal
equalities over time, while correcting for
interest rates and agents’ time preference.
These marginal conditions are equivalent to
the traditional notion of efficiency in econom
ics (Pareto optimality); full markets insure
that all gains from trade are achieved and
that exogenous (government) policy measures
cannot improve on this outcome.
Equilibrium prices at time t, then, are
determined precisely by the fundamental
nature of agents: endowments and utility (or
profit) functions. These basic parameters are
completely summarized by excess demand (Z).
Excess demands of the agents at time t (Z t)
must determine prices continuously for
market-clearing equilibrium to hold.4This
may seem obscure, but it is important in
understanding the nature of New Classical
price adjustments. The idea can be lucidly
illustrated by the basic functions involved.
5. In a representa
tive agent model,
with only one con
sumer, the interest
rate is determined
by his or her rate o f
time preference, i.e.
p = l/(l+r). This
would simplify the
equations in (5),
since 9 and (1+r)
would cancel out in
the denominators o f
(b) and (c). They
have been included
in (5) to explicitly
show the role o f r
and p in intertem
poral optimization.
The excess demands are constructed by the
hypothetical process of calculating excess
demands (i.e., quantity desired minus endow
ment level) at all possible price vectors. So we
have the function:
(1)
u (C „L ,\
where L, represents labor and C, consumption
in period t. Instead of a single-period maximi
zation problem, the consumer in this model
must solve the multi-period problem:
(4)
(5b)
(5c)
Wj_
du/dL,
P,
du/dCh
P,.i
(3(l + r,)P i
du/dC,+1
w ,+1
P (l+ r,)W ,
du/dCh
du/dL,+
du/dL,,
p*t = Z,(p*,).
Immediately we see that p* is defined by a
function of itself. To avoid any time paradox
in the determination of p* and the root of Z,
these quantities must be determined simul
taneously—instantaneous market clearing—
at every date.
Long and Plosser do not develop their price
dynamics in a full general equilibrium model;
they limit most of their study to a simple
example. We will carry the analysis of the
general case further, since it lucidly illus
trates some of the central issues in equilib
rium cycles.
Consumers have an unchanging utility
function:
(3)
(5a)
Z, = Z,(p).
This function is assumed to have a unique
root, p*, which gives an equilibrium. But this
equilibrium price vector p is determined by
the excess demands. That is:
(2)
in the budget set at any date, then there can
be no corner solution. In this case, the follow
ing first-order conditions must hold:
max
subject to labor constraints in each period. (3
is the discount factor of the representative
agent. Although solving this dynamic maxim
ization problem in general is not possible, if
the utility function is strictly concave and all
markets are perfect so that there are no kinks
where r is the interest rate, W is the nominal
wage, and P is the nominal price of the con
sumption good.5
These are the extensions of the marginal
conditions to a dynamic setting. Equation (a)
/w/ratemporally requires the real wage to
equal the marginal utility of leisure; (b)
equates trade-offs of consumption over suc
cessive periods via the rate of time preference
/3 times the price ratio across periods; and (c)
requires that the labor/leisure decisions equal
the interperiod wage ratio multiplied by the
time preference rate. Even though no assets
exist in the model, such intertemporal trades
are feasible because of the rich market struc
ture of the NC model. For example, there
exists a contingent futures market for the
consumption good in period t+s if a negative
technology shock occurs; contracts on this
market can be purchased with labor services
in any period between t and t+s. Of course,
the price on such a market varies over time
according to the tastes and technology of the
agents. The important point is that the mar
kets do exist, and so all trades are possible. It
is not yet clear that this model will produce
business cycles. Indeed, since the economy is
assumed to have a unique and stable equilib
rium, w*, the phase diagram (see figure 2) for
this model in the real wage w-W/P seems to
indicate that cycles will not occur:
As mentioned above, Long and Plosser do
not attempt to show that cycling occurs in the
unrestricted case. NC models have not, in gen
eral, been shown to produce cycles. To derive
concrete results, they specify a utility func
tion that embodies the intertemporal substitu
tions necessary for NC business cycles. Long
and Plosser continue their argument with
specific utility and production functions:
(6)
u(ChLt) = Q0lnL, + ^ Q ,ln C „
i =I
Yi> t+1 = ^ i> t+\L ?<n X ai, t
The standard logarithmic utility function
has elasticities ©i which are constrained to be
non-negative, ruling out inferior goods. Pre
Fig. 2 Phase Diagram for Equilibrium
Model
sumably, if a ©i is zero, the good has some use
in production. Otherwise, it is superfluous in
the economy, since Long and Plosser assume
free disposal. The Cobb-Douglas production
function is unusual only in the appearance of
Ai,£+i, the stochastic shock to the production
of good i in period t. The subscript t + 1 refers
to the date of completed production; that is,
when it is ready for consumption. X is the
vector of goods used as productive inputs.
Then, in each period, the consumer maxi
mizes expected utility according to:
(7)
E(U\S,) = E{ 2j8-'[e„l»A ,
+20,i«c„is,]},
where St = (F „ X ,,/+1). We require maximiza
tion under the expectations operator E, since
A is stochastic. A shock in the technology for
producing a good will obviously change pre
sent consumption. We expect co-movement of
most goods, since they are all normal—chang
es in income call for marginal increments or
decrements of each in the equilibrium con
sumption basket. Because leisure is also a
normal good, some of the gain or loss due to
the windfall will be taken in increased or
decreased work hours. Co-movement is the
first empirical regularity of the business cy
cle captured by the NC model.
Intuitively, persistence arises as consumers
spread unexpected income changes over time
as well as over all goods within a period. Sav
ings or dissavings due to windfall gains or
losses (from shocks) are used to increase or de
crease income in many future periods. So,
even without serially correlated shocks, we
will have persistence in fluctuations.
The utility function has been the source of
co-movement and persistence in quantity fluc
tuations discussed to this point. Production
technology is another source of these business
cycle characteristics. Since most goods are in
puts in the production of some other goods, a
technology windfall (disaster) not only in
creases (decreases) present and future con
sumption of that good, but also, since all goods
are superior, some of the windfall (disaster) is
used to produce more (less) of all other goods
requiring it as an input. Again, it is all part of
the smoothing over time, as well as among com
modities of any unexpected change in income.
This leads to cycles, even in response to serial
ly uncorrelated technology shocks.
The real wage can easily move pro-cyclically in this model. If tastes are fixed, then
any increase in output (which requires more
labor input) drives up the real wage required
to induce workers to provide necessary labor
services. As long as any decrease in labor’s
marginal product doesn’t dominate this effect,
the real wage will rise. Since increased output
is associated with a windfall of some good
that can serve as capital (increasing produc
tivity), a pro-cyclical real wage seems likely.
Although observed, it is beyond the scope of
simple non-monetary models like this to pro
duce co-movement among price for many or
all goods.
In an elaborate simulation for a six-sector
model of their economy (Long and Plosser
[1983], p. 65) observed the paths for sectoral
Fig. 3 Simulated Output of
Equilibrium Model
Logged Output
and aggregate output shown in figure 3.
Co-movement of different goods appears
clearly. The long swings in the time series in
dicates higher degrees of autocorrelation than
I, suggesting persistence.
Long and Plosser’s equilibrium model, then,
can generate three of the central aspects of ob
served business cycles: quantities in almost
all industries move roughly together, output
variations tend to persist for many periods,
and the real wage moves pro-cyclically. These
characteristics arise from intertemporal trade
offs to smooth consumption along with shocks
to the production function.
Long and Plosser emphasize that these are
not the only factors in the business cycle, but
claim their model is a “ useful benchmark” for
evaluating other models. We take this to mean
what we said at the outset: they are positing
the central driving force of business cycles.
They also point out that, in their model, busi
ness cycles are preferred paths; any policy at
tempting to smooth these fluctutations will be
at best Pareto-equivalent with the free market
outcome and may well be Pareto-dominated.
II. Disequilibrium Model
_ Manufacturing
-------- --Mining
. Services
_____ _Construction
Transportation/
trade
_____ Agriculture
Logged Output
SOURCE: Long and Plosser (1983, p. 65).
The only departure of disequilibrium models
from the purely competitive Arrow-Debreu
framework is the supposition that quantities
may adjust faster than prices. Taken to the
limit, this leads to fixprice models in each
period with quantity rationing to balance
trades. The market system that the economy
is endowed with may not permit the perfectly
fluid media for trade that exists in classical
models. Some mutually desirable trades may
simply not be possible under the constraint of
an imperfect market structure. Dreze and
Benassy (1975) laid the static foundations for
this model; dynamic extensions have been
numerous (see Bohm [1977] and Kades [1985]).
Here, we outline a simple version of a dynam
ic fixprice model (as outlined by Grandmont
[1982], this is called a temporary equilibrium
framework) and show how business cycles
arise in it.
In contrast to figure 1 above, a Robinson
Crusoe and Friday disequilibrium economy
can be illustrated, as in figure 4.
The price vector p 0is exogenous within each
period, so that the unique (under our same
assumptions of very well-behaved utility and
production functions) Pareto optimal Walra
sian price vector p outcome almost never
obtains. Under p 0, the consumer will wish to
trade to point and the producer to point £,
so it is not an equilibrium. Instead, we will
have a new type of equilibrium, a fixprice
equilibrium. We explicitly demonstrate this
new type of equilibrium below. In this out
come, in general, one or both agents fail to
obtain desired quantities at given prices and
so are rationed. Note that, if the exogenous
price vector is p, we have an equilibrium
model. Here we clearly see that in the static
world disequilibrium models are more general
than equilibrium models; they allow for both
Fig. 4
Basic Structure of Disequilibrium
equilibrium and rationing outcomes. NC
models maintain that agents will always be
able to find or create markets that will yield
market-clearing prices.
Since the marginal rates of substitution in
consumption and the marginal rates of trans
formation in production are not equated to
prices, this economy lacks the Pareto optimal
ity of the NC model. Within such a frame
work, it is likely that government policies
could improve the welfare of all agents.
We will more fully specify a dynamic dis
equilibrium model following Malinvaud
(1977) and Kades (1985a). Cycles occur in a
more general model here than with Long and
Plosser; there is no need to adopt specific util
ity and production functions.
We use L, C, P, W, and w, as in the equili
brium model. Consumers are described by a
utility function U that is constrained only to
be quasi-concave. Our representative consu
mer’s sole endowment consists of time that
may be “ spent” on either labor or leisure. A
simple concave stochastic production func
tion, F (L t) +£„ describes the activity of the
firm. Consumers maximize utility, and firms
maximize profits.
Instead of assuming that the very special
Walrasian price vector is found, the fixprice
approach imagines that the price vector is
truly parametric at a given trading date and
will be Walrasian only by accident. Between
dates, the price vector moves according to the
so-called law of supply and demand; excess
demand for a good in period t (and possibly in
previous periods) tends to pull prices up,
while excess supply causes prices to fall.
This does not restore the auctioneer and the
instantaneous achievement of the equili
brium price vector. It more modestly posits
that market forces work in the right direction
and possibly with lags. Thus, there are other
forces beyond current excess demands Z(p)
(and specifically, its root) that may enter into
the function determining prices.
It is already easy to illustrate that, dynam
ically, NC models are a special case of NK
models. The most general form of the price
equation is:
(8)
p, = i4(x),
where x is the vector of all conceivable state
variables in the world. The object of theory is
to pare down the size of the vector x as far as
Fig. 5 Firm’s Demand (Production
Function)
Fig. 6 Household’s Demand
(Consumption Expansion Line)
possible without ignoring anything of impor
tance. NC models reduce the dimension of x
to only contemporaneous excess demands Z t\
(9)
P '= f(Z ,).
They further require that f(0) obtain at every
date. NK models allow for a broader range of
variables to enter, such as lagged excess
demands or even lagged prices. Here are some
examples:
(10)
p t = g[\ Z t + (l-A )Z / J
p t = h [\ f(Z ) + (1 -\)p M]
Further, the Z t’s are allowed to take non-zero
values.
If the New Classical special case held in real
ity, proper econometric estimation of equation
(12) would find that k was statistically indis
tinguishable from 1. And only this singular
result could yield direct evidence that New
Keynesian theories were over-parametrized.
Returning to the outline of the model, there
is no reason to believe that Walrasian supplies
and demands will balance at an arbitrary price
vector in a disequilibrium world. More struc
ture must be imposed here to define demands
and to determine actual transactions. The
most basic requirement imposed in fixprice
models is voluntary trade: no agent is ever
forced to trade (supply or demand) more of a
good than he desires—what his preferences
dictate. Since markets do not clear and we
disallow forced transactions, agents will have
to be rationed in quantities at the given price
vector to balance trades. This model requires
a new definition of “ equilibrium.”
Fixprice equilibrium means the maximiza
tion of quantity-constrained utility and profit
functions with trades balancing. Disequilib
rium Benassy (1975) demands, which we will
refer to (following the ideas of Clower) as effec
tive demands, are derived from considering all
constraints except the constraint in the indi
vidual market where demand is being formed.
We denote them with a + superscript; they are
defined from the maximization problems:
(11)
Households:
L h+ = M AX u(L,C,w) subject to WL < pC
Ch+= M AX u(L, C,w) subject to WL < pC
Firms:
L,+ = M AX r(L, C, w) subject to C < F(L)
Cf+ = M AX r(L, C, w) subject to C < F(L),
where C and L are perceived constraints on
other markets, and r is the profits function.
Benassy showed that, when solved, these de
mands yield balanced trades while simultane
ously determining perceived constraints. The
perceived constraints are the minimum of the
effective demands when the system of simul
taneous demands is solved. Thus agents’ max
imizing decisions under these constraints bal
ance in the aggregate, yielding a fixprice equi
librium with rationing. The rationing mecha
nism is usually assumed to be stochastic.
Formally, however, this point needn’t be ad
dressed in representative agent models.
We develop some graphs to represent this
model. (See figures 5 and 6.) We will be using
graphs to show the behavior of the household
and firm in the trade space (L,C). The firm
simply obeys “ efficient production” in this
Fig. 7
Fixprice Static Equilibrium
model and always produces somewhere along
the production function C = F(L). However,
the firm will never produce beyond its Walra
sian point (Lf*, CJ*) under the given wage
and price (the exogenous parameter x) since,
beyond this point, the exogenous wage ex
ceeds labor’s marginal product. The shape
stems from our assumptions on the produc
tion function.
The household obeys “ efficient consump
tion” ; it consumes along a line going through
the origin (no work, no pay) whose slope is
dictated by the real wage rate.
The household will never work beyond its
notional quantities (L h*, Ch*) since, beyond
this point, the marginal utility of the good
falls below the marginal utility of leisure.
To determine the fixprice equilibrium, we
combine the two curves. (See figure 7.)
Beyond the possibility of a Walrasian equil
ibrium (WE) when notional points coincide,
there are two possible outcomes to this model.
If consumers are rationed in selling labor and
firms in selling the consumption good, then
we have general excess supply. This has been
labeled a Keynesian equilibrium (KE). If gen
eral excess demand prevails, we have an infla
tionary equilibrium (IE).
Thus, disequilibrium Benassy demands give
rise to a much broader range of market out
comes than Walrasian models, where Z t=0 in
all markets. Even at an arbitrary price vector,
Walras’ Law holds for New Classical de
mands: excess demand in one market is, by
definition of budget constraints, balanced by
excess supply in another market. General ex
cess supply or demand cannot arise even hypo
thetically in an equilibrium model. Clower
correctly stressed that the key to disequili
brium models must be to establish a rigorous
framework within which Walras’ Law did
not hold. This is one way to describe the main
accomplishment of New Keynesian theorists.
The dynamics of our disequilibrium model
are very simple, since there is only one state
variable, the real wage w. In the state space
R +, we have a unique value of w, w*, that
gives a Walrasian equilibrium. But the
movement of the real wage in KE and IE
regions (on either side of the Walrasian equil
ibrium) is, at first inspection, undetermined.
In the case of KE, labor is in excess supply in
terms of effective demands, so the nominal
wage should fall. But the commodity is also in
excess supply, and so its price also should
drop. Qualitatively, it seems difficult to
determine the direction of real wage move
ments. The same holds for IE, where we have
general excess (effective) demand.
Elsewhere (Kades 1985b), it has been shown
that it is likely that steady states exist in both
Fig. 8 Phase Diagram for
Disequilibrium Model
IE
KE
“Uw*
Fig. 9 Simulation of Disequilibrium
Model
Logged output
Time
the KE region and the IE region. How does
this occur? In Keynesian steady states, the
nominal price of both labor and the good fall
at the same rate in the price (vector-valued)
function. Then the real wage rate is unchang
ing, and since it is the only state variable in
this simple model, a steady state obtains. A
symmetric case explains a steady state in the
IE region.
Further, all Keynesian steady states of the
model are stable (Kades 1985b); in a one
dimensional model, this implies uniqueness.
Since lagged demands are generally included,
the WE will almost never be an equilibrium
(i.e., it is a measure zero event). Inflationary
steady states may be either stable or unstable.
Figure 8 presents a typical phase diagram for
this system.
This system can easily give rise to cycles in
the presence of exogenous shocks to the pro
duction function. The system can move
further and further into either the KE region
(a recession) or the IE region (boom). It can
move either towards a stable or away from an
unstable node until any type of shock moves
the system to the other side, changing the
cycle. The unstable IE effectively marks the
border between the two regimes. White noise
shocks can produce outcomes much like those
observed in real economies. Figure 9 shows a
simulation of this model similar to Long and
Plosser’s for aggregate output only. Further,
this model fully captures the observed co
movement of prices and quantities. By mak
ing C a vector, it is easy to show that different
quantities move together in the model.
So the fixprice/disequilibrium paradigm ex
plains the most fundamental aspects of ob
served business cycles, and does so without re
course to special utility and production func
tions. The only reason for such fluctuations
in the model is the general inability of the
market mechanism to always find the marketclearing price vector. This economy is en
dowed with a cumbersome market structure
that may or may not accurately reflect reality.
III.
The Evidence
It is difficult to directly test hypotheses on
whether or not all markets clear. But we can
heuristically and formally examine evidence
and arguments on a number of issues and
measure the degree to which equilibrium and
disequilibrium business cycle models agree
with observation and rigorous thought.
The Great Depression stands as perhaps
the most memorable single twentieth-century
cyclical swing. The ability of a business cycle
theory to plausibly explain this experience is
important in establishing its credibility.
Therefore, we first discuss the extent to
which both models can explain this event.
Pigou and other Classical theorists in the
1930s blamed the Great Depression on an ex
cessive reservation wage rate demanded by
laborers. Thus for them, recessions were
caused by a market imperfection in labor mar
kets. In a sense, this view stands closer to
disequilibrium paradigms, although the classi
cal notion of market failure differs substan
tially from the New Keynesian view discussed
above. For many early Keynesians, this was
also seen as the cause of the Great Depression;
they disagreed with Classical theorists only
on the effectiveness of expansionary policies.
Today’s New Classicals must argue that
recessions occur when low wages are ex
pected; workers then find leisure less costly in
terms of wages foregone and bide their time
until renumeration rates improve. But can the
Great Depression best be explained as a multi
year withdrawal from labor markets by most
Americans because they expected an eventual
wage rise? The other explanations that New
Classical theory can offer seem no more cred
ible. One is that the utility function of most
laborers called for a “ . . . spontaneous out
burst of demand for leisure . . . ” from 19291939. Another possibility is that a large nega
tive shock to production technology was
responsible, but then the problem becomes
specifying the source of this shock.
New Keynesian explanations of the Great
Depression are likewise unconvincing. Iron
ically, the most prominent possibility is due to
Milton Friedman, a theorist not usually asso
ciated with Keynesian ideas. Friedman and
Schwartz (1961) argued that a major cause of
the Great Depression was the decline in the
money supply from 1929-1933. In a slightly
modified version of our New Keynesian model
with money (Malinvaud 1977), it can be
shown that low money-growth rates (or a for
tiori money stock declines) are associated with
Keynesian recessionary outcomes. But farreaching questions have been raised about
this evidence (Temin 1975) and it is not clear
which way causation runs between money
and output. Further, as argued in footnote 3,
cycle theories based on monetary phenomenon
are less robust than real theories since cycles
have occurred under a wide range of mon
etary systems. Perhaps monetary factors con
tributed to the severity of the Great De
pression, but their role must be explicitly tied
into a general model of cycles to provide a
satisfactory story. Like New Classical theor
ies, New Keynesian explanations may point to
some particularly violent shock as the root
cause of the Great Depression, but then the
difficulty becomes uncovering and explaining
the shock. No convincing explanation has
been presented.
Although some economists find merit in
these heuristic arguments, they are based on
vague notions and “ stylized facts,” and lack
precision. In a formal econometric study, Man
kiw, Rotemberg, and Summers (1985) test the
first order conditions in equation (5) for a util
ity function more general than Long and Plosser’s. That is, they test the first-order condi
tions of consumers’ maximization in the NC
model. Although not sufficient, the first-order
conditions are still necessary for any interior
solution; if they are rejected, then the model
can be rejected. There are, of course, difficult
questions of aggregation in treating national
data as if it is created by a representative con
sumer. No consensus on a solution to this
issue exists, and this methodology is, at pre
sent, the de-facto standard for empirical work.
Mankiw, Rotemberg, and Summers find
that the data (NIPA) reject the hypotheses,
that these maximizations are carried out by
consumers. None of the three over-identifying
restrictions in equation (5) placed by equilib
rium models is supported by the data. Further,
the rejections occur for almost all permuta
tions of the specifications of the hypothesis
tests: separable or non-separable utility,
annual, or quarterly data. Indeed, many of the
restrictions actually force the shape of the
utility function to be convex, in which case a
maxima would occur at a corner and the Clas
sical tangency conditions illustrated in figure
1 could not hold. When the utility function is
concave, either leisure or “ consumption”
(NIPA) becomes an inferior good—which like
convexity casts serious doubt on the model.
Simultaneous estimation of all three restric
tions in (5) is similarly rejected and produces
either a convex utility function or inferiority
of either leisure or consumption.
This rejection can be interpreted in two
ways. Mankiw, Rotemberg, and Summers ar
gue that the data show that markets (both la
bor and capital) fail to clear. There is another
Fig. 10 Corner Solution for LiquidityConstrained Consumer
possibility: the structure of the utility func
tion may be such that intertemporal substitu
tion effects are very weak. In this case, a radi
cally different utility function must be speci
fied to dovetail with observation. At any rate,
either explanation leads us to question Long
and Plosser’s equilibrium paradigm of busi
ness cycles. It seems that either markets fail
to clear, or that substantial intertemporal elas
ticities of substitution do not exist; both inter
pretations of the evidence reject this NC ex
planation of business cycles.
The disequilibrium model cannot be reject
ed by any such hypotheses concerning the
structure of the utility function; it requires
only that the utility function be quasi-con
cave. Beyond this, the disequilibrium model is
robust to the form of the utility function.
Apart from rejecting the restricted form of
the utility function needed to generate equilib
rium business cycles, there is also strong eco
nomic evidence that key markets do not clear.
Specifically, we shall discuss evidence that
capital (lending) markets fail to clear.
Recall from the first-order conditions in the
equilibrium model (5) that the interest rate ap
pears in consumers’ decisions just as in any
other price. Equilibrium models require that
agents can buy or sell as much of a good as
they want at a uniform price, subject only to
their endowment constraint. This constraint
prevents any kinks from existing in the agents’
budget sets so that, with a concave utility
function, no corner solutions to maximization
problems exist.
Keynesians (Old and New) have long argued
that consumers, in reality, face liquidity con
straints: either they cannot borrow at all
against future income or they must pay an in
terest rate greater than the rate they receive
for lending funds (even accounting for risk
premia). Figure 10 shows that if agents lend
at one price, but borrow at another, they are
likely to solve maximization problems at cor
ners of their budget set. Here, the equality of
prices and intrapersonal utility trade-offs
breaks down, and the economy may no longer
be efficient.
6. It is interesting to
note that asset mar
kets are almost al
ways assumed to
more closely approx
imate the competi
tive ideal than other
markets. I f the data
show that these
markets fail to clear,
then it seems du
bious to assume that
labor and goods
markets clear.
Agents are endowed with e = (e 1 , e2) of a
good in periods one and two respectively. The
interest rate for borrowing in period one is r 1;
while the lending rate is less, r 2. With a con
cave utility map, it is then immediately
apparent that a corner solution can occur.
Strong evidence exists that such liquidity
constraints have been binding for significant
numbers of American consumers. Fumio Hay
ashi (1985), modifying an idea originally ap
pearing in Kowalewski and Smith (1979), uses
cross-sectional data and divides consumers in
to high-and low-savings groups. He assumes
that high-savings households are unlikely to
be liquidity-constrained, so they may be used
as a control group to be compared to other (po
tentially liquidity-constrained) households. By
estimating consumption behavior for each
group separately, and then by comparing the
two parameter sets, Hayashi finds a signifi
cant difference that can be explained by the
existence of liquidity constraints. Although
there are other explanations for the result,
they require the rejection of either the perma
nent income hypothesis or of market clearing.
Since both market clearing and the permanent
income hypothesis embody the New Classical
idea of the markets’ abilities to smooth con
sumption over time, this interpretation too,
casts doubt on the equilibrium business cycle
model. Flavin (1981) and Kowalewski (1985)
provide time series evidence that liquidity
constraints have persistently shaped agents’
budget sets in the postwar American economy.
On the other hand, the disequilibrium model
is robust to either interpretation of Hayashi’s
results. If liquidity constraints do exist, they
are an instance of the imperfect markets of
New Keynesian theory.6 If we view the results
as a rejection of all utility functions that give
rise to permanent-income consumption paths,
we already know that the NK model is not
subject to this criticism.
In discussing the compatibility of both mod
els with observed business cycles, we have
examined only three central patterns: the co
movement of different quantities, the persis
tence of trends, and the positive correlation
between quantities and the real wage. But
there are other empirical regularities in busi
ness cycles that both models should similarly
mimic if they are to be adequate representa
tions of the central force in business cycles.
Although they were raised by Arthur Okun
(1980) in objection to Lucas’s equilibrium mod
el (Lucas 1972), they also point to shortcom
ings in Long and Plosser’s model and in NC
models in general.
First, many secondary aspects of labor mar
kets (beyond pro-cyclical wages) are at odds
with the NC model. Productivity may or may
not be pro-cyclical in the NC model. It depends
on the size of the technology shocks and on
the intensity of the disutility of labor. But
observed productivity is strongly pro-cyclical.
In non-market clearing models, this pheno
menon is explained by implicit contract the
ory, where workers are insured against unem
ployment by their employers in return for a
lower wage. When demand slackens, there are
no layoffs; with the same amount of labor and
less production, productivity must decline. As
demand improves, the same work force is
called on to produce more; hence, productivity
increases. Implicit contract theory comprises
one market imperfection that could be the
fundamental source of fixed prices (wages) in
the short run. The market clears by a non
price mechanism. No institutional factor (that
is, exogenous parameter) explaining marketclearing could produce pro-cyclical productiv
ity in Long and Plosser’s model. Similarly,
quits induced by pro-cyclical factors, counter
cyclical layoffs (moreover, the existence of
layoffs, which involve rationing the sale of
labor), and wage increases in recessions seem
inexplicable in the present NC model.
Although Long and Plosser examine and dis
cuss only the consumer side of their model,
firms as well as the household may seek to
smooth over time their objective—profits. One
rationale for such behavior is that since house
holds own the firms, smoothing profits is
simply one part of smoothing income. This mo
tivation is superfluous in an NC model, since
in market-clearing models economic profits
have, by definition, a zero expected value in
each period (under the usual assumption of
constant returns to scale). However, we ob
serve very large pro-cyclical fluctuations in
profits. New Classical theorists must explain
Fig. 11 Continuous Market Clearing
with a Unique Stable Equilibria
Shock response
<C=)
Wf
-- u_-- u--- W2
W3
Wo = W0
c>
Shock
Fig. 12 Failure of Continuous Market
Clearing with Multiple Equilibria
c>
o
<=>
u
W i
UW2
o
* =
>
W
Move in
opposite
directions to
initial shock 1
parameter
correlation
why the value of entrepreneurial talent and
risking capital fluctuate so sharply with the
business cycle to lend credibility to their para
digm. Conversely, pro-cyclical profits exist
under implicit contracts in a New Keynesian
framework, since wage costs are constant
while productivity varies with business cy
cles. However, this criticism must be tem
pered by remembering the substantial contro
versies in defining and, moreover, in measur
ing economic profits.
Finally, Fisher (1984) has raised a methodo
logical objection to the equilibrium paradigm.
In response to any shock, these models re
quire that prices adjust so rapidly—almost in
stantly—that agents never face disequilib
rium prices. However, even in the world of
physics, adjustment to a new shock takes
time, and a mechanical system must move out
of one equilibrium before a new rest state is
attained. Even in the case of a unique equilib
rium, New Classical dynamic behavior vio
lates the usual properties of differential equa
tions in avoiding disequilibrium, but we can
imagine the shock (£t) and the real wage (wt)
move in tandem precisely to produce continu
ous market clearing. (See figure 11.) If NC
models contain a dynamic structure as
rich as the New Keynesian (to avoid the ne
cessity of specifying a restricted class of util
ity functions to produce cycles), then the hy
pothesis of continuous market clearing cannot
be maintained. (See figure 12.)
The system must move through the unsta
ble disequilibrium y and cannot give continu
ous market clearing. It is not clear why New
Classical theorists feel that economic adjust
ments can be approximated by instantaneous
movements from one equilibrium to another.
They must provide an explicit, testable mech
anism for this behavior before it can be used
convincingly. Disequilibrium dynamics call
for the economy to adjust along paths more in
line with established notions about change
over time.
IV. Conclusion
References
Arrow, Kenneth, and Gerard Debreu. “ Exist
Both equilibrium and disequilibrium theories
can construct model economies that mimic the
ence of Equilibrium for a Competitive Econ
basic behavior of real business cycles: strong
omy,” Econometrica, vol. 22, no. 3, (1954),
co-movement among quantities of different
pp. 265-90.
goods, persistence of quantity movements in
the same direction for many periods, and pro
Benassy, Jean-Pascal. “ The Disequilibrium
cyclical real wages. But existing NC models
Approach to Monopolistic Price Setting and
cannot explain other aspects of observed busi
General Monopolistic Equilibrium,” Review
ness cycles, such as pro-cyclical productivity
of Economic Studies, vol. 43, no. 1 (Febru
or other observed characteristics of the labor
ary 1976), pp. 69-81.
market. Further, evidence exists that capital
markets do not clear. Finally, the data reject
________ “ Neo-Keynesian Disequilibrium
the New Classical utility function exhibiting
Theory in a Monetary Economy,” Review of
strong intertemporal substitutions. Without
Economic Studies, vol. 42, no. 4, (October
such a utility function, the model has not been
1975), pp. 502-23.
shown to produce persistent output cycles.
The NK model is robust to most of these
Bohm, Volker. “ Disequilibrium Dynamics in a
criticisms. It requires no specific utility func
Simple Macroeconomic Model,” Journal of
tion to generate cycles, it fits the observed
Economic Theory, vol. 17, no. 2, (April
regularities of business cycles more fully, and
1978), pp. 179-99.
it employs a more general model of price move
ments over time. However, like the NC model,
Clower, Robert. “ The Keynesian Counterrevo
it provides no convincing explanation of the
lution: A Theoretical Appraisal,” in F.H.
Great Depression. Since equilibrium models:
Hahn and F.P.R. Brechling, eds., The The
(1) Comprise a subset of disequilibrium
ory of Interest Rates. London: Macmillan,
models;
1965.
(2) employ identifying restrictions that are
not empirically validated; and
Dreze, Jacques. “ Existence of an Exchange
(3) require nonstandard dynamical adjust
Equilibrium under Price Rigidities,” Inter
ments; it appears that, at present, despite this
national Economic Review, vol. 16, no. 2
shortcoming, New Keynesian theories provide
(June
1975), pp. 301-20.
a better paradigm of the business cycle.
Fisher, Franklin M. Disequilibrium Founda
tions of Equilibrium Theory, Econometric
Society Monograph in Pure Theory #6,
New York: Cambridge University Press,
1984.
Flavin, Marjorie. “ The Adjustment of Con
sumption to Changing Expectations about
Future Incomt," Journal of Political Econ
omy, vol. 89, no. 5 (October 1981), pp.
974-1009.
Friedman, Milton, and Anna Schwartz. A
Monetary History of the United States. Prin
ceton, NJ: Princeton University Press, 1963.
Long, John B., and Charles I. Plosser. “ Real
Business Cycles,” Journal of Political Econ
omy, vol. 91, no. 1 (1983), pp. 39-69.
Grandmont, Jean-Michel. “ Temporary Gen
eral Equilibrium Theory,” in Kenneth J.
Arrow and Michael D. Intriligator, eds.,
Handbook of Mathmatical Economics:
Volume II. Amsterdam: North-Holland Pub
lishing Company, 1982, pp. 879-922.
Lucas, Robert E., “ An Equilibrium Model of
the Business Cycle," Journal of Political
Economy, vol. 83, no. 6 (December 1975),
pp. 1,113-44.
Hayashi, Fumio. “ The Effect of Liquidity Con
straints on Consumption: A CrossSectional Analysis,” Quarterly Journal of
Economics, vol. 100, issue 1 (February
1985), pp. 183-206.
Kades, Eric. Dynamics of Fixprice Models,
Working Paper 8505, Federal Reserve Bank
of Cleveland, September, 1985a.
________ Fixprice Models for Dynamic Studies,
Working Paper 8504, Federal Reserve Bank
of Cleveland, August, 1985b.
Keynes, John Maynard. The General Theory of
Money, Interest, and Employment. London:
MacMillan, 1936.
Kowalewski, Kim. The Stochastic Interest
Rates in the Aggregate Life Cycle Permanent
Income Cum Rational Expectations Model,
Working Paper 8506, Federal Reserve Bank
of Cleveland, October 1985.
________ , and Gary Smith. “ The Spending
Behavior of Wealth- and Liquidity-Con
strained Consumers,” Cowles Foundation
Discussion Paper #56, New Haven: Yale
University, 1979.
________ “ Expectations and the Neutrality of
Money,” Journal of Economic Theory, vol. 4,
no. 2 (April 1972), pp. 103-124.
Malinvaud, Edmond. The Theory of Unem
ployment Reconsidered. Blackwell: Oxford
University Press, 1977.
Mankiw, N. Gregory, Julio Rotemberg, and
Lawrence H. Summers. “ Intertemporal
Substitution in Macroeconomics,” Quar
terly Journal of Economics, vol. 100, issue 1
(February 1985), pp. 225-51.
Okun, Arthur. “ Rational-Expectations-withMisperceptions as a Theory of the Business
Cycle,” Journal of Money, Credit, and Bank
ing, vol. 12, no. 4 (November 1980, Part 2),
pp. 817-25.
Prescott, Edward, and Finn Kydland. “ Time
to Build and Aggregate Fluctuations,” Econometrica, vol. 50, no. 6 (November 1982), pp.
1,345-70.
Temin, Peter. Did Monetary Forces Cause the
Great Depression? New York, NY: W.W.
Norton, 1976.
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