) 41 9q
BANK ECONOMIC REVIEW
Determinants of Consumption and Savings
Behavior in Developing Countries
Lakshmi K Raut and Arvind Virmani
The determinants of savings generally and the specific effects of government policies
on savings and consumption are pivotal forces in investment and economic growth
The Hall hypothesis states that consumption is a function of lifetime ("permanent")
income, rather than income in each period independently Changes in interest and tax
rates, money supply, or government expenditure will affect permanent income and
hence consumption and savings only if they are unexpected and thus not already
incorporated in the estimation of permanent income We are unable to reject the Hall
hypothesis in tests for developing countries when we allow for varying interest rates
We do find evidence of a negative effect of inflation on consumption, and a positive
relatzonship between the real znterest rate and consumption The evidence for the Hall
hypothesis also suggests that Ricardian equivalence may be valid-this is Barro's
hypothests that the effect on savings is the same whether government deficits are
financed through taxation or debt Our preliminary testing, however, does not support
Savings is the part of one's current income that is not spent on current con-
sumption, and it constitutes a large part of a nation's aggregate savings and
mvestment and thus is a major determinant of the growth of future income and
consumption Households balance the tradeoffs between current and future
consumption possibilintes when making their mdividual consumption decisions
Understanding the determinants of households' consumption behavior has been
central to macroeconomics The three main theoretical approaches to this issue
are Keynesian consumption theory, the life-cycle-permanent-income hypothesis
under rational expectations, and the theory of the infinitely lived agent or
altruistically linked consumers The theories differ in the extent to which they
explain the observed consumer behavior, and in their predictions regarding the
effects of government policies on individual savings behavior For instance,
increased taxes, higher nominal interest rates, or an increase in the money
Lakshmi Raut is an assistant professor of economics at the University of California, San Diego
Arvind Virmani is an advisor to the Planning Commission of the government of India Much of this
work was done while the authors were at the World Bank They gratefully acknowledge conversations
with Clive Granger, the comments of three anonymous referees, and the computational assistance of
1 1990 The International Bank for Reconstruction and Development / THE WORLD BANK
Public Disclosure Authorized
Public Disclosure Authorized
Public Disclosure Authorized
Public Disclosure Authorized
THE WORLD BANK ECONOM[C
REVIEW, VOL. 3, NO. 3
s4ply will always affect household consumption according to Keynesian the-
ory, but the other two approaches predict that these policies will have no effect
on individual consumption unless they come as a surprise. Similarly these
theories differ substantially regarding the effects on savings of the government
budget deficit and its financing.
Observations of consumption behavior from time-series data differ from
those of cross-sectional data (see Sargent 1979, chap. 12). What is observed is
that the average propensity to consume out of current income is higher than
the marginal propensity to consume in the cross-sectional data. But in time-
series data when the variables are averaged over ten years, these two propensi-
ties are equal. Friedman's (1957) celebrated permanent-income hypothesis as
well as the life-cycle hypotheses of Modigliani and Brumberg (1954) and Ando
and Modigliani (1963) were partly a response to this empirical puzzle. Hall
(1978) addressed this issue using the life-cycle-permanent-income hypothesis,
which assumes that capital markets are perfect, the interest rate is constant
over time, and consumers have rational expectations regarding the income-
generating process. Given this framework, he showed that consumption follows
a random walk-that is, it will have a time trend around which it will fluctuate.
This is known as the random-walk hypothesis for consumption, which can be
explained intuitively as follows. While a consumer's earnings fluctuate over his
lifetime, if capital markets are perfect and there is no uncertainty about the rate
of interest, then by borrowing and lending, a consumer will smooth out his
consumption stream evenly over his lifetime. Thus if his utility function satisfies
some general conditions, consumption in each period will be proportional to
life-cycle wealth or permanent income rather than to current income. Since
permanent income has greater persistence, that is, it follows a random walk,
so does the share of consumption in income.
The Hall hypothesis is not merely of technical interest but has several impli-
cations for forecasting and policy analysis. First, if the hypothesis is correct,
the forecast of future consumption is an extrapolation of the historical trend,
and there is no point in forecasting future income and using that to predict
future consumption. Second, government policy will affect consumption and
hence savings only through its effects on permanent income. A change in a
public policy regarding tax rates, interest rates, the money supply, or govern-
ment expenditures will have no effect on the estimation or perception of per-
manent income by a consumer if it was predictable in the past. A change in
government policy will have an effect on consumption only if it comes as a
surprise. Most estimates of the effects of government policy for developing
countries are based on estimations of Keynesian consumption functions. An
exception to this is a recent paper by Giovannini (1985), which compares
estimates of the interest elasticity of savings using traditional Keynesian and the
new approach. However, Giovannini did not carry out any formal testing of
the life-cycle-permanent-income hypothesis under rational expectations. The
main aim of our article is to test the Hall hypothesis for developing countries.
Raut and Virmani 381
The Hall hypothesis has implications for government policy that may support
those derived from the Ricardian equivalence hypothesis. The Ricardian equiv-
alence hypothesis, as derived in Barro (1974), states that the effect on national
savings is the same whether a government deficit is financed by current taxes
or borrowing from future. When the deficit is financed by government sale of
bonds, this creates current government dissavings and imposes a tax liability
on future generations. Barro shows that if it is assumed that individuals are
altruistic toward their children, the current generation will have adjusted its
bequests (private savings) to completely offset the increased tax liabilities of
future generations caused by the increased government debt (public dissavings).
Thus aggregate savings will be the same if instead the deficit is financed by
imposing taxes on the current generation. In this case individuals will offset the
increased public saving by lowering their savings as smaller bequests will be
required to guarantee a given stream of consumption for future generations.
This is similar to the results which would be expected under the Hall hypothesis
if an individual was infinitely lived and based consumption and savings deci-
sions on permanent income.
We derive the random walk of consumption from the life-cycle-permanent-
income hypothesis assuming rational expectations and a fixed interest rate, and
we report our empirical results on two excess sensitivity tests of the random-
walk hypothesis for developing countries. We then allow interest rates and
labor income in our model to vary and derive the random walk of consumption
with a time-varying drift. Then we extend the excess sensitivity tests to examine
the empirical validity of the Hall hypothesis. In conclusion, we summarize
some of the economic significance of our empirical findings and suggest what
I. THE RANDOM-WALK HYPOTHESIS: CONSTANT INTEREST RATES
Hall (1978) assumed that consumers have rational expectations about the
income generating process, and he combined Friedman's (1957) permanent-
income hypothesis with Modigliani and Brumberg's (1954) life-cycle hypothe-
sis. On this basis, he derived the random walk for consumption as follows:
assume that a representative consumer receives a stochastic stream of labor
income, W, + r, with r = 1, 2, ..
, T - t, where T is life expectancy. Let A,
be his nonhuman stock of wealth and Q, be the information set at the beginning
of period t which contains, among other things, his observed labor income and
chosen consumption stream up to period t. Assume that the interest rate is
constant over time and capital markets are perfect. This will mean that the
consumers can borrow and lend freely at the given interest rate, so that they
are not credit-constrained to finance their consumption. Income is the only
source of uncertainty.
The consumer's problem is to make a future consumption plan contingent
THE WORLD BANK ECONOMIC REVIEW, VOL. 3, NO. 3
upon information that will be available in each future period in such a way
that he maximizes utility as a function of his discounted lifetime stream of
(1) Max U = E(( 1 + 6) ru(C,+T))
subject to the limits of his income stream, stock of assets, and the interest rate:
S (1 + r)1(Ct±r W- T) -
where Et(x) denotes the conditional expectation of x given information, f2,, r is
the fixed interest rate, a > 0 is the rate of subjective time preference, and u(.)
is a differentiable strictly concave function. The first-order necessary condition
or what is also known as the Euler equation for this problem is
pu' (C,) = E[u' (C,+,)],
in period t. This equation states that the marginal utility of consumption
follows a random walk with a drift, where the drift, p, is determined by the
relative size of the rate of time preference and the interest rate.
From equation 2, it follows that
(1 + 6)/(1 + r) and u' (C,) is the marginal utility of consumption
u' (C,+l) = pu' (C/) +
where the expected value of the error term, E,(¢,+,) = 0. For empirical pur-
poses, we assume a constant elasticity utility function:
u(c) = (cl" - 1)/(1 -
a), a > 0.
Then equation 2 becomes:
u' (C,+1) =t+l,
Where E,(t,+1) = 1
Multiplying by p and taking logs, we get
= Inp + Inn,
so that the change in consumption is determined by the elasticity of utility with
respect to consumption, and by the rates of interest and time preference.
Because this equation is based on the constant elasticity utility function,
u'(C) = C-,
it can be written as: ln C,,, -
Since the term (1/a Inn,) does not have expectation zero, it could not be
In C, = 1/a[-lnp
Raut and Virmani
treated as an error term in the regression. The above could be rewritten,
In Ct+, -In Ct = a + u,A,
where a = -1 /a[Et In 7t+I + In 0] and
Ut+ 1 =
-1 / o[ln ,+,± + E, In
Note that E,ut+, = 0.
Thus log consumption follows a random walk with a drift parameter a deter-
mined by a and p.
An interpretation of equations 3 and 4 can be given as follows: to predict
Ct+ 1in period t given the consumer's information f2t, that is, given Ct, C, 1,
W,, Wt-, . . ., what is important is only C,-no other information is
relevant. In other words, u' (C,) alone is sufficient to predict u' (C,,,). To test
this we nest the random-walk hypothesis in the following alternative model,
which includes current income as a regressor:
In Ct+1-In C, = a + 13 In C, + 02Y, + ,t+
According to the random-walk hypothesis, 02
Another way to view equations 3 or 4 is to treat them as surprise consump-
tion functions. All the information regarding last period's perception about
permanent income is captured in Ct. Then the error terms, At+, in equation 3
or u,+ 1in 4, represent any new information that has arisen at the beginning of
period t + 1 regarding permanent income. This surprise consumption function
interpretation provides an alternative test for the random-walk hypothesis as
follows. We assume that income is generated as a function of the prior period's
income plus an error term, that is, as a first-order autoregressive process.'
Yt+1= Yo + y1Ye + e,t+
Assume that individuals have rational expectations about their future income
stream, that is, they know the true income-generating process and use it to
predict future income, which in turn is used to predict permanent income.
Denote by P(y,,+) the predicted y,+ and the residual y,t,[R(y,,,)] in the above
regression. In our empirical analysis we estimate this equation for each country
separately to get estimates of P(y,+1) and R(y,+,). According to the life-cycle-
permanent-income theory, a consumer's actual consumption in period t + 1 is
= 0; this is the null hypothesis
1. A general income-generating process could be incorporated easily. Blinder and Deaton (1985) use
a vector autoregressive prediction formula with both lagged exogenous and endogenous variables; and
Pagan (1984) discusses the econometric issues involved when the regressors are generated this way.
THE WORLD BANK ECONOMIC REVIEW, VOL. 3, NO. 3
proportional to his perceived permanent income in period t + 1 given all the
new information available in period t + 1. Since consumers have rational
expectations about the income-generating process, the predicted part P(y,+,) of
y+, that was based on the previous period's information was already known to
the consumer in period t, and its effect on C,1 has been accounted for in the
term C,. The R(y,+±) part of Yt+, which is the news or surprise to the consumer
in period t + 1, is the only factor that will have an independent effect on C,
since this new information is used to reestimate permanent income. Under the
life-cycle-permanent-income hypothesis, assuming rational expectations and a
fixed interest rate, once again the null hypothesis (Ho: /2 = 0) could be nested
in the following alternative consumption function:
- In C, = a + 0, In C, + 02P(y,,,) + 03R(yt±,) + et+i
Data And Empirical Findings
Data availability in developing countries puts severe restrictions on the rigor
of the tests that can be carried out. Labor income data in most developing
countries are not available because the income of the self-employed cannot be
separated into its wage and capital components. Net national product data also
are seldom available, so private per capita income is constructed by subtracting
government taxes and nontax revenues from gross national product. The meas-
ure of consumption, Ct, is taken as per capita private expenditure (that is,
household plus corporate). Ideally, we would like to define C, as the flow of
per capita consumption, but many countries measure aggregate consumption
including expenditure on durables. This may bias the estimates somewhat (see
Leiderman and Razin 1988). Finally, variables are converted to U.S. dollars by
using official exchange rates, which biases results according to the extent of
overvaluation and purchasing power parity.
After discarding the countries having data for less than five continuous years
during the period 1970-82, we tested equations 5 and 7 for twenty-three
countries. Appendix A shows the time periods covered for each country in our
Table 1 reports the regression estimates of an excess sensitivity test of equa-
tions 5 and 7. If the life-cycle-permanent-income hypothesis under rational
expectations is true, then equation 4 should hold true, that is, In C,,, -
a + u,+1. Relatedly, in equations 5 and 7, when In C,+1- ln C is
regressed on ln C,, together with y, or P(y,+,), the regression should produce
no significant effect of current or predicted income. If, however, the effect of
these variables is found to be significant, then the change in (log) consumption
is excessively sensitive to current income, contradicting the theory. This is
known as the excess sensitivity test. Further discussion of the test and the
implications of cointegration theory for it are contained in appendix B.
Note that in equation S the coefficient of current income, y, and in equation
Raut and Virmani 385
Table 1. Determinants of Changes in Consumption with a Fixed Interest Rate
Current consumption, In C,
Current income, y,
Predicted income, P(y,,,)
Unexpected income, R(y,,,)
* = significant at the 5 percent level.
n.a. Not applicable.
Note: The dependent variable is changes in consumption, In C,+, - In C,. Figures in parentheses are
Source: Authors' calculations.
7 the coefficient of predicted income P(y,) are both significantly nonzero. Thus
both tests reject the random-walk hypothesis.
The significant relationship between current or predicted income and con-
sumption that we find in our tests could be due to several economic factors.
First, the assumption of fixed interest rates may not hold. The consumers will
have expectations about the interest rate based on current income, interest
rates, and inflation. If interest rate expectations are not instrumental in the
above regression models, the excess sensitivity is expected. In the next section
we will investigate the life-cycle-permanent-income hypothesis under rational
expectations when both interest rate and labor earnings are stochastic.
Next-period consumption may also be sensitive
predicted income if many consumers are liquidity-constrained,
being unable to borrow against future income when young. Capital markets
developing countries are imperfect (see Virmani
developing-country capital markets). There is also asymmetric
tween lenders and borrowers, and lenders
observable characteristics of the borrower
occasions based on the last two or three years' income) and the stock of physical
assets rather than predicted
lifetime income. A consumer
face tighter credit rationing if current
relative to the expected in the next period.
C, will reflect all the information about permanent
to have an independent negative effect on Ct,+. To test for the prevalence
we would need data on the aggregate
assets and unemployment rates which we do not have. The signs of the esti-
mates of y, and P(y,+1), however, are consistent
consumers are liquidity-constrained. A few empirical
that a large proportion of households
1985, and Hall and Mishkin
of the rational expectations
to changes in current
1986 for further discussion
such as recent income
base loan decisions
in period t also would
income and assets are low
Hence while current
y, is still expected
stock of physical
with the implications
studies on U.S. data show
also may be due to
THE WORLD BANK ECONOMIC
REV[EW, VOL. 3, NO. 3
problems of aggregation. The above derivation assumes a constant age struc-
ture over time and across countries. However, when the individual age-specific
consumption functions are aggregated over age groups, estimates of per capita
consumption will be affected by the dependency ratios. A more appropriate
test of the life-cycle hypothesis then should take into account such effects (see
Raut 1989 on this and the references cited therein).
THE HALL HYPOTHESIS WITH VARIABLE INTEREST RATES
In this section we relax the assumption that the interest rate is constant.
Instead, we assume that the real interest rate as well as labor earnings vary
stochastically. As in equation 1, the consumer faces the following intertemporal
utility maximization problem:
Max U = E, T
(1 + 6)-u(Ct+))
but he is now subject to:
r-OL(l + rJ) + (1 + r2) . . . (1 + r,)i A
in which the interest rate, r, may differ across periods, i. The first necessary
condition gives the Euler equation as
u'(C,) = Et Lu'
(CC )(1 + rt+lj
Et Lu (CtC,)
1 + r ]1
By adding and subtracting the expected value of the log of this equation, we
(11) E n [u'(C+) 1 + rt '
[U' (ct+ 1) 1 + r,+±
+ Et L '(C)
u' (Ct+,) 1 + rt+1
1+ ,3 - ln L u'(C) 1 + 6 jj
Assume that Cr, and 1 + r,± 1 have a jointly stationary bivariate normal
distribution. Assuming this and that the rate of time preference, 6, is fixed, the
middle term is a constant which we denote by (1 - a). Thus we can rewrite
the above equation as
(12) E, ln u' (C+,) - ln u' (C) = a- ln (1 + 6)- E ln (1 + r±+,)
Razt and Virmani 387
Assuming further that the utility function has constant elasticity, as in the
previous section, we get
C1= yo + y,E, In (1 + r1+1) + Et+
where y0= [In (1 + 5) - a]/r, y1 = -1/a,
information dated t or earlier, and E,(e,+,) = 0. This is the null hypothesis that
consumers behave according to the life-cycle-permanent-income hypothesis un-
der rational expectations. Once again, equation 13 can be interpreted as stating
that log consumption follows a random walk with a time-varying drift param-
eter, at = To + y1E,(1 + r,+,).
We define variables r r, and rnt as real and nominal interest rates, and infl, as
the inflation rate in period t. Assume that these factors are used by the con-
sumer to evaluate expected interest rates over time, Et In (1 + r1+1).
The null hypothesis, equation 13, can now be nested in the alternative
and E,+, is uncorrelated with all
(14) In (C,+,) - In C, = -y0+ 'yr,, + 73 In C + 74Y, + U,+ I
(15) In (C,+,) - In Ct = y + ylr
n, + y2inflt + y3 In C, + TY4Yt + U't+l
The error term ut+1equals E, plus the prediction errors of In (1 + r,+,) and is
uncorrelated with the regressors under the null hypothesis. Hall's life-cycle-
permanent-income hypothesis under rational expectations is equivalent to test-
ing Ho: -y4 = 0 against the general alternative hypothesis Hl: T4
the surprise consumption function under varying interest rates (the equivalent
of equation 7) we also replace y, in equations 14 and 15 by P(y,+±) and R(y,+,).
We thus test four specifications of the Hall hypothesis under varying interest
* 0. To test
Data and Empirical Results
We use the same variables and countries as in section II. The most widely
available interest rate variable was the central bank discount rate; this will be
our nominal interest rate, rnt. The real interest rate, r tr is constructed by
subtracting the consumer price index, our proxy for predicted inflation, from
Table 2 shows the regression estimates of equations 14 and 15, with the last
two columns including predicted and residual income. Our estimates of the
coefficients of both current and predicted future income are very low and
insignificantly different from zero. Thus the null hypothesis (Hall's life-cycle-
permanent-income hypothesis) could not be rejected for these countries. In
principle, inflation can affect not only the real interest rate, but also can have
a direct effect on consumption if consumers do not have rational expectations
(due to money illusion) or if money enters a consumer's utility function (see
Deaton 1977; Juster and Wachtel 1972a, 1972b; and von Furstenburg 1980).
Table 2. Determinants of Changes in Consumption with Variable Interest Rates
Using inflation and
nominal interest rates with
Using real interest rates with
Current consumption, In Ct
Real interest rate, r,,
Nominal interest rate, rn,
Current income, y,
Predicted income, P(y,,1)
Unexpected income, R(y,,,)
* = significant at the 5 percent level.
n.a. Not applicable.
Note: The dependent variable is changes in consumption, In C,, - In C,. Figures in parentheses are t-statistics.
Source: Authors' calculations.
Raut and Virmani 389
An alternative explanation for the negative effect of inflation on consumption
is that higher inflation rates increase uncertainty about the real value of future
income and thus increase the precautionary demand for savings (see Leland
1968, Levhari and Srinivasan 1969). Another possible explanation is that since
in developing countries governments control the returns to most financial assets
(including money), higher inflation will mean a lower value of financial assets,
and hence consumers spend less and save more to restore the real value of their
The first two columns in table 2 show that the real interest rate has a
significantly positive effect on consumption. This should be contrasted with the
findings of Giovannini (1985), who found that the real interest rate has no
significant effect on consumption for most countries in his sample.
The sensitivity of consumption to interest rate expectations may also signify
that many consumers are liquidity-constrained (see Muellbauer 1983). How-
ever, one needs to model liquidity-constrained consumption behavior rigor-
ously and test it statistically using appropriate data on asset holdings and
unemployment rates. Household survey analysis will throw better light on the
III. RICARDIAN EQUIVALENCE
Failure to reject Hall's hypothesis under variable interest rates also suggests
the possibility of Ricardian equivalence. As Barro (1974) has shown, when
capital markets are perfect and consumers are interlinked by intergenerational
altruism, a representative consumer will take into account the welfare of all
future generations while making consumption decisions. Technically, in this
case the consumers could be treated as infinitely lived. The main difference
between the life-cycle and altruistically linked consumer approaches lies in the
planning horizon of each. Under certain general conditions, the altruistically
linked consumer's problem is as follows:
Max U= E,(E (1 + 6)-Tu(C+T))
cT- w t
+ r2) . .
(1 + rJ1
(1 + r)(
which will also yield the same Euler equation as the finite-horizon life-cycle
models that we have considered so far. The policy implication of this model of
consumer behavior is that private consumption decisions will not be responsive
to whether a rise in government expenditures in any period is financed by
increasing taxes or by issuing bonds (and thus borrowing against future gener-
ations by creating larger budget deficits). The hypothesis is true provided that
390 THE WORLD BANK ECONOMIC REVIEW, VOL. 3, NO. 3
the increment in the budget deficit does not exceed the present value of all
future tax liabilities that are required for debt servicing of the government's
borrowing. If the hypothesis is true, then government bonds would not be
perceived by households as net wealth (Barro 1974).
In preliminary testing, we estimated Keynesian type consumption functions
in which we included among the regressors current per capita real gross na-
tional product, per capita taxes, and the per capita budget deficit to see if
consumers perceive the budget deficit or government borrowing as net wealth
and hence increase their consumption (specification and results are available
from Raut upon written request). Our regression results show that the coeffi-
cient of the per capita budget deficit is significantly positive, and hence there is
evidence against the neutrality hypothesis. This test is very preliminary, and
more rigorous tests should be carried out along the lines of Blanchard (1985),
Evans (1988), and Leiderman and Razin (1988) with more appropriate data.
We have examined evidence on the determinants of consumption and savings
decisions and tested Hall's random-walk hypothesis of consumption on aggre-
gate data from twenty-three developing countries. The Hall hypothesis states
that individuals select a level of consumption in each period based on expected
lifetime income, rather than on current income. Since income in any term can
be seen to move stochastically while consumption is smoothed over time, the
ratio of consumption to current income will appear to vary randomly.
If we assume that interest rates are fixed, Hall's random-walk hypothesis
cannot be accepted in our tests. This rejection may be due to bias in aggregation
across age groups, liquidity constraints, or the stochastic nature of the interest
rate. Due to data limitations, we could not test the existence of liquidity
constraints or aggregation bias. We extended the analysis, however, to allow
for a stochastic interest rate and labor income in the life-cycle-permanent-
income framework, assuming rational expectations. This extension led to re-
sults consistent with the hypothesis that the path of consumption follows a
random walk with a time-varying drift. The tests do not reject this hypothesis.
We also find that while the real interest rate has a positive effect on consump-
tion, the nominal interest and inflation rates both have negative effects on
consumption; and the effect of inflation is significantly higher than the effect
of the nominal interest rate. Two plausible explanations for such an effect of
inflation are, first, that higher inflation can increase uncertainty regarding
future income, and thus increase the precautionary demand for savings; and,
second, that inflation has a negative effect on real financial wealth, requiring a
reduction in consumption to maintain the real stock of savings.
Since we cannot reject the life-cycle-permanent-income hypothesis under
rational expectations when the interest rate is assumed to be variable, this
suggests that the Ricardian equivalence hypothesis may be valid. We undertook
very preliminary testing of the hypothesis (limited by the availability of data)
Raut and Virmani 391
and found that the evidence did not support the hypothesis for developing
countries. However, careful testing of the Ricardian equivalence hypothesis
using more appropriate data would be useful, as would the explicit modeling
of liquidity-constrained consumption behavior.
APPENDIX A. COUNTRIES AND YEARS USED
Burundi (1973-81), Colombia (1973-81), Egypt (1975-82), Guatemala
(1973-81), India (1974-82), Indonesia (1973-82), Korea (1973-82), Malaysia
(1973-81), Mauritania (1975-79), Morocco (1973-82), Panama (1973-81),
Rwanda (1973-80), Singapore (1973-81), Sri Lanka (1973-82), Thailand
(1973-82), Togo (1977-82), Tunisia (1973-82), Turkey (1973-81), Venezuela
(1973-82), Zaire (1973-82).
APPENDIX B. IMPLICATIONS OF COINTEGRATION THEORY FOR THE ANALYSIS
Drawing upon the recent developments in cointegration theory, we can see
that there could be several econometric inconsistencies in estimating the null
specifications for equations 5 and 7. In this approach, stochastic process X, is
an I(1) process if X, - X,, is a stationary process. Two I(1) stochastic processes
Xt and Y, are cointegrated if there exists -y such that Z, = Y, + yX, is a
stationary process. U.S. time-series data on consumption and income reveal
that they are I(1) processes and are cointegrated. Since the left-hand sides of
equations 5 and 7 are I(0), and under the null specifications the right-hand side
has one I(1) regressor, in either specification, the coefficient of the 1(1) regressor
will be forced to zero (see Stock and Watson 1988 and Granger and Newbold
1974 for more on this issue). However, if the null hypothesis is to test both the
unit root for log consumption and no excess sensitivity to current or predicted
future income, then the regression specifications are consistent and the standard
statistical procedures are valid. This composite hypothesis is indeed the ran-
dom-walk hypothesis of consumption. The alternative specification is also con-
sistent, since C, and y, are cointegrated, so least squares estimates of the
coefficients of y, will be consistent although not efficient since we have not
subjected the estimates to the restriction on the parameters of C, and yt imposed
by their being cointegrated. All these facts are related to only long time-series
data. However, in our case we have short time series across many countries.
Since in the literature very little is known about these issues when one has
pooled time-series cross-sectional data, we have not pursued this line of econ-
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