Testing Hall’s Permanent Income Hypothesis: a Case study of Pakistan
Khalid Khan
Lecturer
Department of Economics
Lasbela University of Agriculture, Water and Marine Sciences,
(LUAWMS), Uthal, Balochistan
Dr. Mohammad Nishat
Professor
Department of Finance and Economics,
Institute of Business Administration (IBA),
Karachi
Abstract
The objective of this study is to test the Hall’s permanent income hypothesis for Pakistan
using annual data from 1992 to 2009. The basic model of permanent income hypothesis
(PIH) shows the validity of absolute income hypothesis (AIH) in Pakistan while the
Campbell and Mankiw (1990) model finds that the proportion forward looking
individuals are 8% and the remaining consumes are backward looking. It’s due to this
that in Pakistan there is a larger fluctuation in per capita income and small opportunity
for consumption smoothing for individuals.
JEL:
KEYWORDS: Hall’s Permanent Income Hypothesis, Permanent Income Hypothesis,
Absolute Income Hypothesis, Per Capita Income, Consumption Smoothing.
1. Introduction
According to permanent income hypothesis (PIH) the consumption of individuals’
depends upon its permanent income rather than current income (absolute income). To test
the PIH Friedman (1947) postulated that individual’s can estimate his permanent income
on the basis of current income lags, thus Friedman introduce lags in consumption
function. Lucase (1976) postulate that the lags of current income cannot explain the
current consumption, in the response of this critique, Hall (1978) presented his theory of
Rational Expectation –Permanent Income Hypothesis (RE-PIH). He argued that current
consumption is adequate to estimate future consumption because any information which
affect future consumption is already include in current consumption, Hall further explain
that disposable income, both current and past have no affect on future consumption.
Therefore according to Hall consumption follow a random walk.
Flavine (1985), Hall and Miskin (1982), Hayashi (1982), Bernanke (1985), Campbell and
Mankiw (1990), Rao (2005), have test the Hall’s random walk hypothesis but their result
both do not support or partly support the RE-PIH.
In case of Pakistan only Khalid (1992) explicitly tested the Hall’s random walk
hypothesis and he concluded that Hall’s random walk hypothesis is not valid for Pakistan.
Khalid (1992) neither used Euler equation approach and nor he used the Campbell
Mankiw (1990) model which separate the proportion of forward looking consumers from
backward looking consumers.
In this study we used these both models Euler equation approach and Campbell
and Mankiw model to test the PIH for Pakistan. The rest of the paper organize as follow,
section two describe methodology and data section three present the empirical result and
section four offer conclusion and remarks.
2. Methodology and Data Description
2.1 Methodology
The pioneer of testing PIH under the rational expectation with Euler equation was
Hall (1978). According to PIH usually assumed that aggregate consumption function can
be representing the individual’s decision. So the typical individual’s maximizes:
T −t
MaxEt ∑ (1 + δ ) −i U (C t +i )
i =0
T −t
Subject to
∑ (1 + r )
i =0
−i
U ′ > 0, U ′′ < 0
(1)
(C t +i − YLt +i ) = Wt
Where
Ct = Private consumption at period t
E t = Expectations subject to information at period t
T = Life time of the individual
Wt = Wealth excluding human capital at period t
YLt = Disposable labor income at period t
δ = Rate of subjective time preference
r = Real rate of interest
If the typical consumer can easily borrow and lend at the real interest r, then for two
successive periods (t and t+1) the first order condition (Euler equation) can be obtained
from the maximization of above equation (1) as:
⎡1 + δ ⎤
(2)
E t U ′(C t +1 ) = ⎢
U ′(C t )
⎣1 + δ ⎥⎦
This equation says that marginal utility of today with constant multiple is the best
forecast of marginal utility of tomorrow.
If we assume that marginal utility is linear and r = δ , then we find that current
consumption is the best predictor in the next period consumption:
Et (C t +1 ) = C t
This is turn implies:
ΔC t = ε t
(3)
(4)
Where ε t , is a rational forecasting error and innovation in permanent income, Thus,
according to this arrangement of the permanent income hypothesis, the change in
consumption is unforecastable.
To test the Basic model PIH with the data, for this purpose the econometrics
model is as under:
ΔC t = α + βΔYt + ε t
(5)
Where ΔCt , is log difference of real consumption, ΔYt is log difference of current real
labor income, ε t is random error.
If β = 0 this shows the validity of PIH, otherwise it shows that current income can affect
current consumption of individuals in Pakistan.
In the above model we assume that all consumers are forward looking and
consume their permanent income, but in the real world it may not be possible. Therefore,
we also use the Campbell and Mankiw (1990) consumption model to find out the separate
proportion of forward looking and backward looking consumers, which follow the rule of
thumb and consume their current income.
2.1.1 Campbell and Mankiw (1990) Consumption Model
The Campbell and Mankiw model assume that the proportion of ( 1 − λ ) individuals are
forward looking and satisfy the PIH while the proportion of ( λ ) follow “rule of thumb”
and consume their current income. Furthermore the Campbell and Mankiw Consumption
model also allows some intertemporal substitution ( δ ) for the forward looking
consumers. Thus the Campbell Mankiw Consumption Model as:
ΔC t = α + λΔYt + (1 − λ )δ .rt + ε t
(6)
Where r is the real interest rate, ε t is the random term.
2.2 Data description:
The study are based an annual data from 1992 to 2009. The data are taken from the
Internationals Financial Statistics (IFS) CD ROM. All the data series are represent in the
real term. The real consumption is used as a dependant variable. Real consumption is
computed by depleting nominal consumption with consumption deflator. GDP is used as
a proxy for labor income because GDP is highly correlated with labor income real value
is obtained by deflating with the consumption deflator. Long run interest rate is the yield
on the five year government bound while the short run interest rate is the rate of interest
on the state bank of Pakistan bills while The Consumer Price Index (CPI) is used as the
consumption deflator.
3. Empirical Results
The estimated result of the basic model of PIH and Campbell and Mankiw Model are
given in table 1 by using the three different econometrics methods i.e. ordinary least
square (OLS), instrument-variable (IV) approach and non-linear least squares (NLLS)
approach . The third, fourth and fifth row of table 1 offers the results of basic model of
PIH which show that there is strong and significant relationship between change in
consumption and changes in current income, consistent with AIH. Thus, it indicates that
the individuals’ consumption in Pakistan is strongly really on their current income rather
than his expected life time income. Therefore these results show the inconsistency of PIH
for Pakistan and show the strong validity of AIH.
The above estimation assumes that all individuals are forward looking but in real
world it may not be possible, therefore we use the Campbell and Mankiw Model. The
Campbell and Mankiw model which include both types of consumers forward looking
and backward looking, the best way to estimate the Campbell and Mankiw model is
instrument-variable (IV) approach is suggested by Campbell and Mankiw (1990)
because the error term “ ε t ” may be correlated with ΔYt due to this the OLS estimator
will becomes inconsistent. The empirical results of the Campbell and Mankiw model
supported the result of basic PIH model. Both OLS and IV regression shows the presence
of large number of forward looking individuals. The portion of forward looking
consumers is 6% and 8% of the total population shows by the OLS, IV and NLLS
regression respectively. Therefore both the Basic model of PIH and Campbell and
Mankiw model show the unreliability of PIH for Pakistan. The real interest rate appears
with a positive sign and very small value but it insignificant statistically in OLS, IV and
NLLS regression. Therefore in case of Pakistan current income plays a very vital role in
determination of individuals’ consumption. Thus consumption does not follow a random
walk in Pakistan.
4. Conclusion
This study tested the Hall’s permanent income hypothesis of Pakistan using the basic
model of PIH and Campbell and Mankiw (1989) consumption Model. The basic model
PIH shows that the consumer’s consumption in Pakistan depends upon their current
income rather than permanent income, its shows the validity of the AIH for Pakistan.
The same result is forwarded by the Campbell and Mankiw (1989) consumption model,
on the basis of Campbell and Mankiw model we found that the proportion of backward
looking consumers is much greater than the forward looking consumers, only 8% of
consumers consumption choices are based on permanent income and the remaining are
follow the rule of thumb.
The positive sing of the coefficient of interest rate implies that the positive income effect
is greater than negative substitution effect, due to this it may possible that with increase
of interest rate consumption of individual will rises in Pakistan. Furthermore due to the
positive interest rate effect it may be possible that Ricardian Equivalence Theorem (RET)
is not hold for Pakistan.
It is hoped this study results will encourage further work on micro data analysis of PIH
on the basis of different income groups of individuals, which will be very informative for
policy makers.
Table 1: Estimation of Basic Model of PIH and Campbell and Mankiw Model
Basic Model of PIH
Campbell and Mamkiw Model
1.OLS
Coefficient
T. Ratio
Prob:
2.IV
Coefficient
T. Ratio
Prob:
3.IV-NLLS
Coefficient
T. Ratio
Prob:
α
β
α
λ
(1 − λ )σ
σ
SE
0.0054
0.7168
0.7168
0.9604
9.6500
0.0000
-0.0138
-0.7630
0.4589
0.9447
9.526
0.0000
0.0017
1.1660
0.2642
0.0303
0.0230
-0.0172
-0.8876
0.0245
0.9680
9.5263
0.0000
0.0019
2.1350
0.0350
0.0583
0.0245
-0.0148
-0.4306
0.6778
0.9374
6.2221
0.0003
0.0017
0.7449
0.4776
0.0280
5. References
Khalid, A.M., (1994) “Empirical Test of the Rational Expectation and Permanent
Income Hypothesis Evidence from Pakistan”, The Pakistan Development Review 33,
1043- 1053
Bernanke, B. S., (1985) “Adjustment Costs, Durables Aggregate Consumption”,
Journal of Monitory Economics 15, 41-68
Campbell, J.Y. and Mankiw, N.G., (1990) “Permanent Income Current Income
and Consumption”, Journal of Business and Economic Statistic 8, 265-279
Flavin, M. A., (1981) “The Adjustment of Consumption Changing Expectations
about Future Income”, Journal of Political Economy 89, 974- 1009
Friedman, M., (1948) A Theory of Consumption Function, Princeton, NJ:
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Hall, R, E., (1978) “Stochastic Implications of the Life Cycle Permanent Income
Hypothesis: Theory and evidence”, Journal of Political Economy 86, 971-987
Hall and Fredric, S. M., (1982) “The Sensitivity of Consumption to Transitory
Income: Estimates from panel data on Households”, Econometrica 50, 461-481
Hayashi, F., (1982) “The Permanent Income Hypothesis: Estimation of Testing
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Lucase, R. E. J., (1976) “Econometric Policy Evaluation: Critique”, in Carnegie
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Rao, B.B., (2005) “Testing Hall’s Permanent Income Hypothesis for Developing
Country: The Case of Fiji”, Applied Economics Letters 12, 245-248
Rao, B.B., (2007) “Testing the Permanent Income Hypothesis in Developed
Countries a Comparison Between Fiji and Australia” School of Economics University of
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