Structural change in the import demand function for Pakistan.
Shabbir, Tayyeb ; Mahmood, Riaz
I. INTRODUCTION
The question of structural stability of the Aggregate Import Demand
Function (IDF) has important implications for modelling, forecasting as
well as policy-making related to the trade sector, in general and
imports in particular. A structural change, in quantitative terms, may
be reflected as a change in one or more parameters of the import demand
function. Analysing the possibilities, timing and the nature of such a
change is important since it affects the estimates of the relevant
elasticities.
In the case of Pakistan, the issue of the possible structural
change in the IDF has not been studied much in spite of its importance.
The two notable exceptions are Sarmad (1989) and Naqvi and Khan (1989).
In Sarmad (1989) while the main purpose was to choose between the
linear and log-linear functional forms for the IDF there is incidental
treatment of structural change when he specifies a dummy to account for
the dislocation of economic activity caused by the separation of East
Pakistan in 1971. Thus he implicitly hypothesizes that structural change
occurred only in term of the intercept. (1) However, he also reports
that there may have been a structural shift in 1982-83 in the import
demand for manufacturing.
Again, Naqvi and Khan (1989) report a significant 1971-72 dummy
coefficient in case of imports of manufactured goods and significant
1972-73 dummy for imports of services adjusted for interest payment on
foreign debt.
In fact, the relative paucity of the studies on the structural
change in the IDF for Pakistan is surprising given a general awareness
that in the early 1970s, Pakistan experienced significant political
upheavals including the breakup of the country in December 1971. (2)
The purpose of this paper is to determine the exact year of
structural change in Pakistan's aggregate import demand function
for the time period 1959-60 to 1987-88.
The rest of this paper is organized as follows. Section II
describes the methodology while Section III describes the data used.
Section IV discusses the empirical results. Finally, Section V presents
the conclusions of this paper.
II. METHODOLOGY
We combine a priori information and the methodology of
"Switching Regression" (SR) in order to determine the exact
year of structural change in Pakistan's aggregate import demand
function for the time period 1959-60 to 1987-88. (3)
The SR methodology is based on the pioneering work of Quandt (1958)
and its updated version in Goldfeld and Quandt (1973). Let the term
'regime' refer to a change in the parameters of the model
corresponding to the different mutually exclusive subsets of the total
sample. Then, the general approach of the SR methodology is based on the
assumption that there is a known (finite, in fact, small) number of
different regimes but the switching points are not known a priori. Such
points are determined by using a maximum likelihood procedure. In fact,
the essential features of the SR methodology can be described as
follows.
Let [Y.sub.1] = Natural logarithm (Ln) of Total Imports in year t ;
and [X.sub.T] = a k x l vacto r of independent variables such as Ln GNP which determine imports in year t. Suppose we have n sample observations
t = 1, .... n.
We hypothesize that the parameters of the aggregate import demand
function for Pakistan obey two separate regimes as defined below:
Regime 1: [Y.sub.t] = [[alpha].sub.1] + [[beta].sub.1] [x.sub.t] +
[U.sub.1t] holds for t [less than or equal to] [t.sup.*]
Regime 2: [Y.sub.t] = [[alpha].sub.2] + [[beta].sub.2] [x.sub.t] +
[U.sub.2t] holds for t > [t.sup.*]
Where [t.sup.*] is unknown. Assuming the error terms to be
independently and normally distributed with zero means and variances
[[sigma].sup.2.sub.1] and [[sigma].sup.2.sub.2], the log likelihood is
given by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
Where, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are the
maximum likelihood (ML) estimates of [[alpha].sub.i] [[beta].sub.i] and
[[sigma].sup.2.sub.i] respectively.
In fact, the above log likelihood function simplifies to the
following expression:
ln L = n / 2 ln 2 [PI] n / 2 - [t.sup.*] / 2 ln [[??].sup.2.sub.i]
- n - [t.sup.*] / 2 ln [[??].sup.2.sub.2] ... ... ... (2)
Then, in principle, an estimate of the switch point, [t.sup.*]
could be made by evaluating Equation (2) for all possible values of K
[less than or equal to] [t.sup.*] [less than or equal to] n - k and
choosing the one that maximizes the (logarithm of the) likelihood
function.
However, we decide to a priori restrict the search for the switch
point to a three-year period only i.e., 1970-71--1972-73 since it is
often posited that the Pakistan economy is most likely to have
experienced a structural change in the aftermath of the events in the
early 1970s. (4) Thus, essentially our approach is to maintain that
while a range for a probable structural change is known on a priori
grounds, the exact point of such a change within that range in unknown
and must be determined on the basis of the formal tests. Such an
approach is sort of a compromise between the Bayesian approach with its
emphasis on integrating a priori information into the analysis and that
of the classical inference theory based primarily on 'pure'
statistical test results.
III. DATA DESCRIPTION
In this paper, we have used annual data for Pakistan for the period
1959-60 to 1987-88. The names of the relevant variables and their
definitions are being given below. Their respective source is noted in
the parenthesis while the Table 1 gives their means and standard
deviations for the different sub-periods.
IV. RESULTS
Tables 2 and 3 report the empirical results for this study. These
estimates are the Maximum Likelihood Estimates that take into account
first order autocorrelation of the error term. We may refer to them as
AR(1) ML and briefly discuss them below. (5)
First, in order to set the stage, we present AR(1) ML estimates of
the IDF that are based on the whole sample i.e., 1959-60--1987-88. It
can be seen that the coefficients of Ln GNP and of Ln P are of the
correct sign and are significant at the 95 percent level of
significance. With reference to Column (3), note that the output
elasticity (6) is 1.17 and the (relative) price elasticity is 0.69.
Again, while the dichotomous dummy variable S that accounts for the 1971
separation of East Pakistan is significant, the coefficient estimate of
Ln FR is not so (Column 4).
Let us now turn to Table 3 which gives results pertaining to the
main purpose of the paper i.e., an analysis of the timing of structural
change in the aggregate IDE Since the value of the Quandt's log
likelihood test statistic is the largest (7) when [t.sup.*] = 1971-72,
the relevant Regime 1 and Regime 2 for the import demand function
correspond to 1959-60-1971-72 and 1972-73-1987-88 respectively.
After having determined the timing of the structural change in the
IDF, the nature of this change was investigated. Was the change only in
the constant term (as results of Table 2 columns 2 through 4 would
indicate) or both slope and intercepts coefficients changed across
regimes? The Chow test rejected the null hypothesis of same
specification across Regime 1 and Regime 2 at the 1 percent level
([F.sub.calculated] = 7.44 > [F.sub.table] = 3.03). This implies that
there is more to the nature of the structural change between the above
regimes than can be captured by just introducing a dummy variable for
the suspected year of change. In fact, the null hypothesis of equality
of the respective elasticities of output and price across the regimes
was rejected at one percent level. (8)
In the light of the above result, an interesting aspect of the
problem of the structural change in the IDF would be to investigate the
economic reasons as to why these elasticities change across the two
regimes? In fact, this is one of the directions in which we plan to
extend this work in the future.
V. CONCLUSIONS.
The main conclusions of this study and their relevant policy
implications are being noted below:
(1) It is found that the Aggregate Import Demand Function (IDF) for
Pakistan experienced a structural break at the end of 1971-72. Thus, in
fact, the IDF obeys two distinct 'regimes': 'Regime
1' corresponds to 1959-60 to 1971-72 while 'Regime 2'
corresponds to 1972-73 to 1987-88.
(2) The nature of the above structural change cannot be captured
adequately by simply adding a dummy variable for the year 1971-72. In
fact, the Chow test rejects at the 1 percent level the null hypothesis
of similar structures across the regimes.
(3) It is found that both the output as well the price elasticities changed across the regimes. In fact, between Regime 1 and Regime 2, the
output elasticity increased by about 58 percent while the price
elasticity defined by nearly two-thirds.
Since imports related policy perscriptions take the output and
price elasticities as datum, the question of their stability or lack
thereof has very significant implications. The above findings regarding
the timing and the nature of structural break in the Aggregate Import
Demand Function may thus serve a very useful purpose in terms of
policy-making. These results also have important implications in terms
of modelling and forecasting of the trade sector in general, and of
imports in particular.
Comments on "Structural Change in the Import Demand Function
for Pakistan"
The paper by Tayyeb and Riaz explores the timing and nature of a
once for all shift in the aggregate import demand function for Pakistan.
The paper is well targeted and precise. The results confirm that the
import demand function shifted in the year 1972-73 in such a way that
imports became more sensitive (elastic) to GNP and less sensitive to the
relative price of imports. Thus, while after 1971-72 increase in income
has been a source of fast growth in imports in Pakistan, the increase in
the relative price of imports has not been a forceful disincentive for
imports. This finding is an indication towards the nature of change in
the tastes and technology for importables in Pakistan and the authors
can explore its implications for the import policy of Pakistan.
The possible causes for the shift in the structure of the import
demand function include changes in commodity/geographic composition of
imports and various forms of import restrictions. The authors may also
like to relate such factors with their finding in the discussion.
On the technical side of the paper I have two comments to make.
First, the authors estimate three parameters for each of the two
sub-samples and one parameter as the 'optimal' switching
point, [t.sup.*]. Since [t.sup.*] is determined endogenously, it can be
treated as a parameter along with the other six parameters and the
degrees of freedom can be defined for the two equations combined.
Second, I have some reservations on the use of a unique event dummy
(taking a non-zero value for one sample point and zero for the rest). It
has been established that use of a unique event dummy in a regression
equation is equivalent to excluding the sample point corresponding to
the unique event and estimating the equation without the unique event
dummy. It is, therefore, important to note the implications of the two
unique event dummies W and S (for the years 1965-66 and 1971-72) present
in the estimated import demand functions. Due to the identically zero value of regression residuals for the sample points corresponding to the
two unique events the values of R-square and F-statistic are inflated
upward. Further, in the presence of unique event dummies the regression
equation has essentially been estimated using discontinuous time series
with two missing observations and, hence, the value of D. W. statistics
require some adjustment. It may be noted, however, that the authors did
not use any unique event dummy in their main analysis on the
determination of the timing and nature of shift in the import demand
function.
Eatzaz Ahmad
Quaid-i-Azam University
Islamabad.
Authors' Note: We are grateful to Mr M Rafiq and Mr Masood
Ishfaq for valuable computer programming, and Syed Zaheer Abbas Shah for
his excellent typing. Of course, we alone bear responsibility for any
shortcomings of the paper.
REFERENCES
Goldfeld, S. M., and R. E. Quandt (1973) The Estimation of
Structural Shifts by Switching Regressions. Annals of Economic and
Social Measurement. 2 : 475-485.
Johnston, J. (1984) Econometric Methods. New York: McGraw-Hill Book
Company.
Khan, Ashfaque H. (1980) The Demand for Money in Pakistan. Some
Further Results. The Pakistan Development Review 19 : 1 25-50.
Naqvi, Syed Nawab Haider, and Ashfaque H. Khan (1989) Inflation and
Growth: An Analysis of Recent Trends in Pakistan. Islamabad: Pakistan
Institute of Development Economics.
Quandt, Richard E. (1958) The Estimation of the Parameters of a
Linear Regression System Obeying two Separate Regimes. Journal Of the
American Statistical Association 53 : 873-880:
Sarmad, Khwaja (1989) Determinants of Import Demand in Pakistan.
World Development. 17 : 10 1619-1625.
(1) [Sarmad (1989), p. 1623].
(2) However there have been a few studies in other areas. For
instance, Khan (1980) studies the issue of structural change during the
1959-60 to 1977-78 in demand for money for Pakistan. He finds that the
estimated coefficient of the expected rate of inflation is insignificant
for the period 1959-60 to 1970-71 while it becomes statistically
significant during 1971-72 to 1977-78. This suggests that there had been
a single structural change in 1970-71.
(3) In fact, as discussed later in this section, we restricted the
SR based search to the 1970-71-1972-1973 time period on grounds of a
priori information.
(4) For instance, the political turmoils of 1969-70, start of civil
war in March 1971 and ultimately war with India and separation of East
Pakistan in December 1971 after.
(5) LS did not give satisfactory results since for most cases, H0
of 'no first order autocorrelation in error terms' could not
be rejected. In order to correct for this we decided to use AR(1) ML
rather than the more commonly used iterative Cochrane-Orcutt since (a)
we needed ML estimates for the Quandt Likelihood test (Equation (2),
Methodology Section) and (b) as [Johnston (1984), pp.326] points out,
AR(1) ML may be a relatively superior way to correct for AR(1) in the
error term.
(6) Sarmad (1989) reports output elasticity of 0.63 and the price
elasticity of -0.669 for the same variables and notes the output
elasticity to be 'too low'. However, the time period for his
study is 1960-86. Also his specification includes Ln FR.
(7) The respective log likelihood values were 29.38, 30.51 and
26.12, respectively for [t.sup.*] = 1970-71, 1971-72, 1972-73
respectively.
(8) Assuming independence of the coefficient estimates across the
regimes the test statistic is t = ([[beta].sub.2] -
[[beta].sub.1])/[(Var[[beta].sub.2]/[n.sub.2]+
Var[[beta].sub.1]/[n.sub.1]).sup.1/2] with ([n.sub.1] + [n.sub.2]) d.f.
where [n.sub.1] and [n.sub.2] are respective sample sizes for the two
regimes.
Tayyeb Shabbir is Senior Research Economist and Riaz Mahmood is
Research Economist at the Pakistan Institute of Development Economics,
Islamabad.
Variable's
Name Definition (Source)
Ln TI Natural logarithm of real imports demanded in year t as given
by the value of imports calculated at constant 1959-60
prices. (Source: Foreign Trade Statistics of Pakistan:
Various Issues.)
Ln GNP Natural logarithm of real Gross National Product in year t
calculated at constant 1959-60 prices. (Source: Economic
Survey 1989-90.)
Ln P Natural logarithm of the relative price of imports in year t
calculated as the ratio of the index of unit value of imports
to the domestic wholesale
price index. This ratio has been adjusted for the aggregate
rate of tariff. (Source: Various Issues of the Pakistan
Statistical Year Book and the Monthly Statistical Bulletin.)
Ln FR Natural logarithm of the real foreign exchange reserves in
year t measured in constant 1959-60 prices. (Source: Annual
Reports, State Bank of Pakistan; Various Issues.)
W Dichotomous (O,1) dummy variable which is equal unity for
1965-66 to account for the possible effects of the September
1965 war with India.
S Dichotomous (O,1) dummy variable which equals unity for
1971-72 to account for the East Pakistan separated from the
Federation in December 1971.
Table 1
Mean (X) and Standard Deviation (SD) of Variables
1959-60-198/-88 1959-60-1971-72
Whole-sample Sub-sample 1
N = 29 N = 13
X SD X SD
Variables
Ln TI 3.57 0.33 3.32 0.25
Ln GNP 10.56 0.50 10.10 0.24
Ln P 0.66 0.45 0.19 0.11
Ln FR 7.18 0.60 6.68 0.38
TI 37.30 12.05 28.44 7.14
GNP 43655.10 21697.61 24946.23 5888.13
P 2.12 0.89 1.22 0.14
FR 1556.48 1003.33 851.62
1972-73-1987-88
Sub-sample 2
N = 16
X SD
Variables
Ln TI 3.77 0.25
Ln GNP 10.94 0.30
Ln P 1.04 0.15
Ln FR 7.58 0.41
TI 44.49 10.34
GNP 58856.06 17356.22
P 2.86 0.44
FR 2129.19 1006.51
Table 2
AR(1) Maximum Likelihood Estimates for the Aggregate
Import Demand Function
(1959-60 to 1987-88)
Variables
1 2
Dependent
Variable = Ln TI
Constant -8.73 * -9.32 *
(-4.53) (-5.74)
Ln GNP 1.20 * 1.26 *
(6.23) (7.84)
Ln P -0.72 * -0.83 *
(-3.53) (-5.20)
Ln FR
W
S -0.34 *
(-4.37)
Adjusted [R.sup.2] 0.69 0.82
DW 1.92 1.81
SE 0.13 0.09
N 29 29
Variables 3 4
Dependent
Variable = Ln TI -8.43 * -8.43 *
Constant (-5.08) (-4.68)
1.17 * 1.17 *
Ln GNP (7.09) (6.81)
-0.69 * -0.69 *
Ln P (-4.08) (-3.59)
0.0004
Ln FR (0.009)
-0.16 * -0.16 **
W (-1.97) (-1.93)
-0.33 * -0.33 *
S (-4.53) (-4.18)
Adjusted [R.sup.2] 0.84 0.83
DW 1.58 1.58
SE 0.09 0.09
N 29 29
* Significant at 95 percent level; 2-tailed t- test
(t-statistics are in the parentheses).
** Significant at 90 percent level for 2-tailed t-test yet
significant at 95 percent level for 1-tailed t-test.
Table 3
AR(1) Maximum Likelihood Estimates for the
Import Demand Equation
(Breakpoint 1971-72)
1959-60 to 1959-60 to 1972-73 to
1987-88 1971-72 1987-88
Whole-sample Sub-sample 1 Sub-sample 2
Variables
Constant -8.73 * -4.12 -9.03 *
(-4.53) (-1.58) (-3.46)
Ln GNP 1.20 * 0.76 * 1.20 *
(6.23) (2.91) (4.79)
Ln P -0.72 * -1.61 * -0.52 **
(-3.53) (-3.58) (-1.83)
Adjusted
[R.sup.2] 0.69 0.90 0.92
DW 1.92 1.56 1.67
SE 0.13
0.11 0.10
N 29 13 16
* Significant at 95 percent level; 2-tailed t-test
(t-statistics are in the parentheses).
** Significant at 90 percent level for 2-tailed t-test yet
significant at 95 percent level for 1-tailed t-test.