Disaggregated import demand functions for Pakistan.
Sarmad, Khwaja ; Mahmood, Riaz
This paper estimates demand elasticities of relative prices and,
those with respect to the activity variable for selected imports of
Pakistan at different levels of aggregation for the 1969-70--1983-84
period. The relative price elasticities, adjusted for tariffs, are found
to be quite small and distinctly different from those estimated for
developed countries. Elasticities with respect to the activity variable
are on the higher side which may reflect the increased outward
orientation of the economy during this period. We have also found
evidence which supports the argument that import substitution of
consumer and capital goods has led to increased import dependence on
inputs.
INTRODUCTION
In the field of international trade, little systematic information
on disaggregated trade elasticities is available for the developing
countries. (1) The primary reason for this is the unavailability of
adequate data pertaining to prices of different categories of imports
and exports. The empirical determination of the relationship between
imports, relative prices and economic activity at the disaggregated
level is important for policy decisions relating to changes in the level
of tariffs and domestic taxes, exchange rate, etc., as well as for
estimating the effect of relative price changes on production and
employment in specific sectors and industries. (2)
This study examines the behaviour of selected imports of Pakistan
at both the aggregate and disaggregated levels for the period from
1969-70 to 1983-84 and provides elasticity estimates for seventeen
different categories of imports at the three-digit level and for more
aggregate levels. (3)
THE IMPORT FUNCTION
In empirical economic literature, the demand for imports has been
estimated by relating the quantity of imports to a domestic economic
activity variable and to the ratio of the price of imports to domestic
prices. When relative prices are adjusted by tariffs, the function can
be written in logarithm form as follows: (4)
log [M.sup.d.sub.it] = [alpha] + [beta] log (1 + [t.sub.it])
[RP.sub.it] + [gamma] log [Y.sub.t] + [u.sub.it] ... ... (1)
where
[M.sup.d.sub.it] = quantity of goods i imported;
[t.sub.it] = tariff rate on the ith import;
[RP.sub.it] = ratio of the unit value of the ith import to its
domestic price;
[Y.sub.t] = activity variable; (5)
[beta], [gamma] = elasticities with respect to relative price and
activity variable; and
[u.sub.it] = a random disturbance term such that [u.sub.it] NID (0,
[x.sup.2.sub.u]).
In general, the relative price elasticity [beta] is expected to be
non-positive ([beta] < 0) while the elasticity with respect to the
activity variable may be either greater or less than one, reflecting the
fact that domestic production can increase more or less than consumption
of importables as the level of income rises. (6)
Equation (1) is estimated with the assumptions that, firstly,
importers are always in equilibrium ([M.sup.d.sub.it] = [M.sub.it]) (7)
; secondly, there is an infinite supply elasticity of imports with
respect to price so that import prices are determined exogenously (8);
and, thirdly, prices of domestic goods and the real activity variable
are exogenous. (9)
RESULTS
The estimates of price and income elasticities obtained from
estimating Equation (1) are given in Table 1. In several cases, there
was evidence of first-order autocorrelation in the residuals. For these
cases, the elasticities were re-estimated by removing auto-correlation
using the Cochrane-Orcutt iterative technique for a first-order
autoregressive scheme. The fit of the equations is good in many cases
and fair in others.
The results show that in all the cases the price elasticities have
the expected negative sign and, like the income elasticities, the vast
majority of them are significantly different from zero at the 10-percent
level. A number of other interesting observations can also be made:
Firstly, the (absolute) price elasticities are on the lower side with
only import elasticities of paper products, iron and steel ingots, and
electric equipment (PSTC 642, 672 and 725) having a value of more than
one. Secondly, the sizes of the price elasticities at the three-digit
level are significantly different from those of developed countries.
(10) This is also true for the one-digit and aggregate levels. These
comparisons conform with theoretical expectations about the different
response to relative price changes in the developing and developed
countries. (11) Thirdly, the absolute price elasticities are, in
general, also lower than those obtained by Khan [3] and Melo and Vogt
[8] for Venezuela. Khan's estimates of price elasticities, -2.042
and -1.176 for food and agriculture products, are similar to those
obtained by Melo and Vogt, as against our estimates, -0.740 and -0.816
for imports of food products and crude materials (PSTC 0 and 2).
Similarly, for the imports of machinery, paper and cardboard, and
chemical goods Khan's estimates range from -0.765 to -1.277 as
compared with our estimates, -0.450, -0.730 and -0.720 for imports of
machinery and transport equipment, manufactured goods, and chemicals
(PSTC 7, 6 and 5), which are higher than the price elasticities -0.456
and -0.200 for imports of chemicals and manufactures reported by Melo
and Vogt. Fourthly, the high aggregate price elasticity is due, in large
part, to the influence of the inelastic demand for petroleum imports. A
higher aggregate price elasticity (-0.540) is obtained when petroleum
imports are excluded from total imports. Fifthly, the higher price
elasticities within the seventeen import groups are associated, in
general, with products which are either consumer goods or capital goods,
(12) e.g. food products and crude materials (PSTC 022, 051 and 2)have
price elasticities ranging from -0.739 to -0.941. Similarly, the price
elasticities of machinery and transport equipment (PSTC 714 and 725),
which are capital goods, are -0.706 and -1.059. With a few exceptions,
the price elasticities for the rest of the import groups, which are raw
materials for consumer and capital goods, are lower than -0.700.13
Sixthly, import groups within the same industry have more or less
similar sensitivity to relative price changes. (14) Among the imports of
food and crude materials (PSTC 0 and 2) elasticities range from -0.739
to -0.941. For imports of animal and vegetable otis (PSTC 4) and
chemical imports (PSTC 5) the variance is similar or even less. However,
price elasticities vary slightly more for imports of manufactured goods
(PSTC 6), ranging from -0.319 to -1.153. These results reinforce the
argument made above that development policy has influenced the growth of
specific import-substitution industries, namely consumer goods and
capital goods, to the neglect of others. However, within the import
group for manufactured goods (PSTC 6), it is more appropriate to talk of
neglected commodities than of industries.
Aggregation Bias
Distribution elasticities were calculated to investigate the extent
of the aggregation error which arises from the use of the direct
estimate of price elasticity instead of estimates based on disaggregate elasticities. (15) (See Table 2.)
An aggregation error results when either or both of the following
two conditions hold: (i) price changes at the disaggregated level are
not uniform, and (ii) such changes are correlated with the product of
the corresponding elasticities and weights [6].
The derived aggregate price elasticity was calculated as the sum of
the products of the individual elasticities, the corresponding
distribution elasticities and the average share of individual imports in
total imports. The results (reported in Table 3) show an upward
aggregation bias for the relative price elasticity. (16) When no
adjustment is made for the distribution elasticity, the absolute derived
estimate of the relative price elasticity is higher but the upward
aggregation bias is still present, even though the extent of the bias is
much reduced.
CONCLUSION
Estimates of the elasticities with respect to the relative price,
adjusted for tariffs, and the activity variable for selected imports at
different levels of aggregation have been obtained for the period
extending from 1969-70 to 1983-84. The absolute relative price
elasticities are low and distinctly different from those estimated for
developed countries. The higher elasticities with respect to the
activity variable may be an evidence of an increase in the import/income
ratio reflecting a greater outward orientation of Pakistan's
economy during this period.
In some cases, the higher absolute relative price elasticities
suggest that, while progress has been made in import-substitution in
specific industries, it has led to a precarious dependence on imported
inputs.
Like Khan [3] and Melo and Vogt [8] we have found an upward
aggregation bias for the relative price variable.
REFERENCES
[1.] Boylan, T. A., M. P. Cuddy and I. O'Muircheartaigh.
"The Functional Form of the Aggregate Import Demand Equation".
Journal of International Economics. Vol. 10. 1980. pp. 561-566.
[2.] Hamilton, C. "Import Elasticities at a Disaggregate
Level. The Case of Sweden". Scandanavian Journal of Economics. Vol.
4. 1980. pp. 449-463.
[3.] Khan, M. S. "The Structure and Behaviour of Imports of
Venezuela". Review of Economics and Statistics. May 1975. pp.
221-224.
[4.] Khan, M. S., and K. Z. Ross. "The Functional Form of the
Aggregate Import Demand Equation". Journal of International
Economics. Vol. 7. 1977. pp. 149-160.
[5.] Kreinin, M. E. "Disaggregated Import Demand Functions:
Further Results". Southern Economic Journal. Vol. 40. July 1973.
pp. 19-25.
[6.] Magee, S.P. "Prices, Incomes and Foreign Trade". In
P. B. Kehan (ed.), International Trade and Finance: Frontiers for
Research. Cambridge: Cambridge University Press. 1975.
[7.] Mahmood, R. Growth and Structure of Imports of Pakistan
(1959-60 to 1978-79). Islamabad: Pakistan Institute of Development
Economics. 1980. (Statistical Paper Series, No. 3)
[8.] Melo, O., and M. G. Vogt. "Determinants of the Demand for
Imports of Venezuela". Journal of Development Economics. Vol. 14.
1984. pp. 351-358.
(1) With the important exception of, e.g., Khan [3] and Melo and
Vogt [8].
(2) An obvious problem with aggregate elasticities (even those
estimated at the one-digit level of the SITC) is that different product
groups are treated as a homogeneous commodity even when there is no
justification for assuming that relative prices do not vary, with a
common elasticity estimate being applied to all commodity subgroups.
(3) The data for this purpose have been compiled from six-digit
value and quantity data reported in the Foreign Trade Statistics of
Pakistan. From 1981-82 onwards, the data are reported at the seven-digit
level.
(4) The log-linear formulation of the import demand function is
most common in empirical economic work; see e.g. Khan [4], Magee [6],
Hamilton [2], Boylan et al. [1] and Melo and Vogt [8]. The choice of the
functional form was made by comparing standard goodness-of-fit criteria
for linear and lo-linear formulations. It is much more convenient to use
the log-linear specification as it constrains the elasticity estimates
to be constant over the estimation period, which precludes the
possibility of a secular fall in the elasticities with respect to price
and the activity variables when the dependent variable rises faster than
the independent variable. The predictive power of the model may be
affected by inclusion of variables that reflect the rigidities of the
system, but adequate time-series data for these variables are not
available.
(5) A number of activity variables were tried in the import
functions. For total and aggregated imports, real Gross Domestic Product
(GDP) gave the best results; for imports of Milk, Milk Products and
Fruits, real consumption expenditure was used as the activity variable;
for other imports at the three-digit level, real value added in the
manufacturing sector yielded the best results in terms of
goodness-of-fit criteria.
(6) For total imports and imports of consumer goods--Milk and Cream
(022), Milk Products and Fruits (051)--Equation (1) was re-estimated
including the variable real foreign exchange reserves. In all the cases,
the foreign-exchange reserves variable was found to be statistically
Insignificant even at the 85-percent level. The estimated coefficients
are not affected significantly and there is a slight decrease in the
value of R-squared (with the exception of imports of Milk Products in
which case the R-squared is the same). This suggests that during the
period from 1969-70 to 1983-84 foreign-exchange availability did not act
as a constraint to imports, which may partly be explained by the large
inflow of foreign remittances during this time.
(7) The results of estimating a partial-adjustment mechanism for
imports show that while the disequilibrium model holds for a few cases,
in general, adjustment was made within the year. For developing
countries Khan [3] and Melo and Vogt [8] and for developed countries
Kreinen [5] have also found an insignificant lag structure at the
disaggregated level.
(8) The simultaneous relationship between the quantity of imports
demanded and import price may be considered untenable in the case of
Pakistan because of its small effect, so that as long as tariffs are the
only trade barriers the OLS estimates of relative price and income
elasticities can be considered unbiased.
(9) The disadvantage of using the domestic price of goods as the
measure of the price of domestically produced tradable goods is that it
includes imported goods and non-tradable domestically produced goods.
However, it is the best available measure of the price of domestic
goods. Assuming that the domestic price is a weighted average of the
import price and the true price of domestically produced goods, it is a
simple matter to show that
[eta] [p.sup.t.sub.m] = [eta] [p.sup.o.sub.m] (1--w)
[p.sup.t.sub.d]/[p.sup.o.sub.d]
where [eta]/[p.sup.t.sub.m] is the true price elasticity of demand for imports, [eta][p.sup.o.sub.m] is the observed price elasticity and
(1--w) [p.sup.t.sub.m]/[p.sup.o.sub.d] is the weight of the true price
of domestic goods in the observed price of goods. The extent of the bias
in the estimated price elasticity of demand for imports depends on the
latter factor.
(10) This observation can be only of a very general nature because
of differences in aggregation and estimating equations in, e.g., Kreinin
[5] and Hamilton [2].
(11) Developing countries' demand for imports is generally
believed to be inelastic as compared with that of the developed
countries.
(12) For the classification of Pakistan's imports into
consumer goods, raw materials for consumer goods, capital goods and raw
materials for capital goods, see Mahmood [7].
(13) These results tend to confirm the view that import
substitution of consumer and capital goods has led, in general, to
greater import dependence on inputs of these industries.
(14) This is contrary to the results obtained for developed
countries. Hamilton [2] has found large variance of price elasticities
within import groups for Sweden.
(15) Distribution elasticities have been estimated from the
equation
[DELTA] log [P.sub.it] = [beta] [DELTA]log [P.sub.t] + [V.sub.t]
where [P.sub.t] is the relative price variable adjusted for
tariffs, [P.sub.t] = [summation] [P.sub.i], [[beta].sub.i]s are the
distribution elasticities and [V.sub.t] is a random disturbance term.
(16) Khan [3] and Melo and Vogt [8] also give evidence of an upward
aggregation bias for the relative price elasticity.
KHWAJA SARMAD and RIAZ MAHMOOD *
* The authors ate, respectively, Senior Research Economist and
Staff Economist at the Pakistan Institute of Development Economics,
Islamabad. They would like to express their gratitude to Professor Syed
Nawab Haider Naqvi, Director, Pakistan Institute of Development
Economics, for his constant encouragement and very helpful comments.
They also gratefully acknowledge the help extented to them by Syed Hamid
Hasan Naqavi in making editorial changes and stylistic improvements in
the paper.
Table 1
Estimates of Price and Income Elasticities
PSTC * Price Income
Commodity Group Equivalent Elasticity Elasticity
(1) (2) (3) (4)
Total Imports -0.230 1.290
(-3.290) (-8.350)
Total Imports excluding -0.540 1.630
Petroleum Imports (-2.200) (8.100)
Food Products 0 -0.740 3.160
(-1.580) (3.130)
Milk and Cream 22 -0.941 3.198
(-2.060) (5.043)
Milk Products -0.828 3.146
(-1.688) (5.138)
Fruits 51 -0.739 -0.276
(-4.650) (-0.357)
Crude Materials 2 -0.816 1.444
(1.961) (2.325)
Fuels 3 -0.051 0.736
(-0.856) (5.154)
Animal and 4 -0.580 2.530
Vegetable Oils (-3.590) (11.910)
Animal Oils 411 -0.461 1.416
(-2.128) (9.251)
Vegetable Oils 421 -0.495 2.145
(-2.294) (8.883)
Chemicals 5 -0.720 2.020
(-2.860) (6.360)
Inorganic Chemicals 514 -0.651 1.910
(-1.639) (5.522)
Cleansing 554 -0.877 2.067
Preparations (-2.020) (5.510)
Plastic Materials 581 -0.660 1.399
(-2.099) (3.582)
Manufactured Goods 6 -0.730 -3.07
(-1.820) (-3.980)
Articles of Rubber 629 -0.319 2.126
(-1.681) (3.229)
Articles of Paper 642 -1.151 -3.943
(-1.907) (-3.145)
Iron and 672 -1.028 -2.885
Steel Ingots (-0.944) (-3.447)
Aluminium Products 684 -0.910 2.269
(-1.912) (7.084)
Tin Products 687 -0.753 -2.932
(-2.919) (-4.288)
Machinery and 7 -0.450 4.140
Transport Equipment (-0.190) (6.260)
Office Mechines 714 -0.706 0.741
(-3.406) (1.430)
Electric Equipment 725 -1.059 4.711
(-3.206) (3.121)
[[bar.R]
Commodity Group .sup.2] D. W. S.E.
(1) (5) (6) (7)
Total Imports 0.890 1.930 0.089
Total Imports excluding 0.830 1.530 0.220
Petroleum Imports
Food Products 0.430 1.680 0.470
Milk and Cream 0.638 1.495 0.598
Milk Products 0.645 1.433 0.583
Fruits 0.602 1.412 0.240
Crude Materials 0.755 1.858 0.585
Fuels 0.744 1.945 0.113
Animal and 0.920 2.360 0.220
Vegetable Oils
Animal Oils 0.873 2.032 0.204
Vegetable Oils 0.863 2.032 0.300
Chemicals 0.820 2.200 0.190
Inorganic Chemicals 0.773 2.088 0.233
Cleansing 0.729 1.729 0.195
Preparations
Plastic Materials 0.452 1.836 0.285
Manufactured Goods 0.520 2.000 0.550
Articles of Rubber 0.775 2.267 0.198
Articles of Paper 0.518 2.195 1.008
Iron and 0.565 1.806 0.809
Steel Ingots
Aluminium Products 0.836 2.227 0.422
Tin Products 0.697 1.734 0.728
Machinery and 0.770 1.640 0.250
Transport Equipment
Office Mechines 0.453 1.761 0.248
Electric Equipment 0.568 1.675 0.610
Note: * Pakistan Standard Trade Classification.
The figures in brackets are t-values.
Table 2
Distribution Elasticities
PSTC Distribution
Commodity Group Equivalent Elasticity
Food Products 0 0.9218
Crude Materials 2 1.4765
Fuels 3 1.3330
Animal and Vegetable Oils 4 0.1918
Chemicals 5 0.6901
Manufactured Goods 6 1.1259
Table 3
Derived Aggregate Import Elasticities
Weighted
Average
including
Weighted Distribution
Average Elasticities
Price Elasticity -0.222 -0.140