The supply and demand for exports of Pakistan: the polynomial distributed lag model (PDL) approach.

Atique, Zeshan ; Ahmad, Mohsin Hasnain

This study examines the individual (short-run) and cumulative (long-run) elasticities of determinants of export demand and supply using annual data over the period 1972-2000 by employing Almon Polynomial Distributed Lag Model. The main findings of the study are that Real Effective Exchange Rate (REER) is only significant but less elastic in the long run, and the world economic activity has individual and cumulative significant elastic effect in the case of export demand. On the other hand, domestic capacity utilisation has significant elastic effect on export supply. Relative prices and individual impact of wage rate are insignificant. However, cumulative effect of wage rate is significant but less elastic. The empirical results show a strong relationship between domestic capacity of production, the world economic activity, and export performance of Pakistan. The results also suggest that the cumulative effect of wage rate and REER is significant; however, its impact is relatively small on the export performance of Pakistan.

1. INTRODUCTION

In the global economy, the performance of any country will greatly depend on the performance of its exports. The trade performance determines the prospects of change. It helps countries win friends, and break the traditional mould of isolation and indifference. The performance of exports of countries depends on various price and non-price factors.

In international trade transactions it is important to recognise that these transactions require some amount of time that occurs between the decision to buy and actual delivery of the product from foreign country. In the Econometric modelling lag occupies a central role. It is recognised that due to psychological, technical and institutional reasons, a dependent variable may respond to explanatory variables with lapse of time, in particular when dealing with time-series trade models.

A number of studies have been conducted to examine the export performance of Pakistan. In the best of our knowledge, no study has been undertaken incorporating lags to examine the individual and cumulative impact of determinants of export performance of Pakistan.

Thus, the ultimate purpose of this paper is to estimate consistent individual (short run) and cumulative (long run) elasticities of both export demand and supply determinants using annual data over the period 1972-2000 by applying Almon approach. (l)

The plan of the paper is as follows: Section 2 presents literature review; while the data set and model are discussed in Section 3; the result and interpretations of these analyses are in Section 4 and conclusion and policy implications are summarised in the last.

2. LITERATURE REVIEW

Various studies have been conducted incorporating different determinants of export growth to evaluate the performance of the variables affecting exports and imports in different countries. Houthakker and Magee (1969) conducted pioneering study to determine export performance using time series data. Khan and Goldstein (1978) later examined elasticity of determinants of export demand and supply for the sample of eight countries by using simultaneous approach (2SLS). They found large export price elasticities of demand with medium term effect of independent variables on the adjustment of exports and also explained world income as a significant component of export demand. Goldar (1989) estimated the effect of productivity increase on India's export performance in engineering products and found out positive relationship between world demand and export performance of India's engineering sector. Roy (1991) also supported the finding of Goldar and found out world demand along with exchange rate as important factors in determination of export performance of Bangladesh. He found out that the devaluation has some positive impacts on export performance of Bangladesh. Ahmad (2000) by applying Cointegration Technique and Error Correction Model for the export supply of Bangladesh found the significant relationship between the export price, exchange rate, domestic capacity, and export supply of Bangladesh.

In the case of Pakistan the studies conducted during the last two decades used different techniques and incorporated different determinants for export performance. Initially studies were conducted assuming export demand as exogenous [Naqvi (1982) and (1983)]. Anwer (1985) used the simultaneous approach (2SLS) to examine export performance of Pakistan. He found the price elasticities are not significant while world income and domestic production significantly explain the demand and supply side of export respectively. For Pakistan Hasan and Khan (1994) carried out study and specified demand-side factors and supply-side factors for export performance of Pakistan. They also examined impact of exchange rate policy on Pakistan's trade balance by applying 3SLS technique. Their results showed that export demand is positively related with world demand and negatively related with relative export price in case of both primary and manufactured exports. The nominal exchange rate, on other hand, posited a positive and significant relationship between export demand in both cases. Another study for the determination of export demand and export supply factors conducted by Sajjad and Fauzia (2000) for Pakistan's economy, they examined the impact of exchange rate policy of Pakistan. They also determined the price and income impact on trade balance with respect to four major trade partners. They estimated Cobb-Douglas form equation using 3SLS technique.

In summary the world income is one of the most important determinants of export demand, whereas, the exchange rate (2) shows statistically mixed results on export performance. Empirical studies showed domestic capacity utilisation as a significant determinant on supply side, while; relative prices do not reach the traditional level of significance in all studies.

3. THE MODEL AND DATA SOURCE

In order to realise aim of the study, world demand for Pakistan goods is specified in log-linear form. The demand function can be expressed in the following form:

Ln Xd = [alpha].sub.0] + [[alpha].sub.1] + LnREER + [[alpha].sub.2] Ln EA + [u.sub.1] (1)

It is expected that [alpha].sub.1] will be negative and [[alpha].sub.2] positive

Xd = Quantity of Export Demanded

EA = World Economic Activities

REER = Real Effected Exchange Rate

In this study world economic activity is represented by industrial production index of industrial countries (IPI). (3)

Since the above equation is specified in log-linear [[alpha].sub.1] and [[alpha].sub.2] are the elasicities of demand of export with respect explanatory variables. The Supply of export is specified as follows

Ln Xs = [[beta].sub.0 + [[beta].sub.1] Ln (RP) + [[beta].sub.2] Ln Y + [[beta].sub.3] Ln Wr + [u.sub.2] (2)

Where it is expected [[beta].sub.1], [[beta].sub.2]> 0 and [[beta].sub.2<]0, similarly as mention above [[beta].sub.1], [[beta].sub.2] and [[beta].sub.3] are the elasicities of supply of export with respect explanatory variables

Xs = quantity of supply of export

RP = ([UVE.sub.pak]/[CPI.sub.pak]) relative prices, the unit value of export ([UVE.sub.pak]) of Pakistan to domestic prices of Pakistan ([CPI.sub.pak])

Y = Domestic Production Capacity

Wr = Wage Rate per Worker (4)

Predicted values of real GDP (1980=100) used as a proxy variable for domestic production capacity of economy.

In order to estimate the distributed lag model, Equations (1) and (2) remodeled as follows. (5)

The export equation becomes

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

The supply equation becomes

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

Equations (3) and (4) were estimated using the Almon lag procedure with K=3 (6) and the degree of polynomial were 2 with no end constraint.

Before going on data few words are in order about the data. The estimation was performed using annual data for years 1972-2000, all the data are annual and taken from the following sources:

1. International Financial Statistic (IFS).

2. Economic Survey (ES), various issues.

3. Statistical Year Book (SYB).

Data for unit value of export (UVX), volume of export (VEX), consumer price index (CPI) of Pakistan and world consumer price index (WCPI), Industrial production index (IPI) exchange rate (ER) of selected export partner countries of Pakistan (7) are taken from (IFS). Data for wage rate is taken from (SYB) and data for export of selected countries, real GDP of Pakistan are taken from (ES). This data is further used for estimation of variables. (8)

4. EMPIRICAL RESULTS

The estimated export demand equation is satisfactory with respect to sign, high adjusted [R.sup.2], no autocorrelation and particularly significance of long run coefficients of both explanatory variables. The current and lagged one, two and three of REER is insignificant at 5 percent level, but cumulative effect is significant at 5 percent level.

Thus, results indicate that a 1 percent decrease in REER would increase the quantity of export demanded by 0.49 percent in current year, 0.36 percent in second year, 0.53 percent and 0.003 percent in third and fourth years respectively. Similarly, 1 percent devaluation or depreciation of Rupees will increase the export demand by 0.39 percent in long run.

The result shows that the elasticity of demand for export with respect to real effective exchange rate is inelastic short run (individually) as well as in long run (cumulatively).

The elasticity of demand for export with respect to IPI index is inelastic for individual years except forth year. Their cumulative effect in long run is elastic, the sum of elasticity is greater than one that is, 2.9 and significant at 1 percent level.

The current industrial production index is significant at 5 percent up to 2 lags. This suggests that IPI would take 3 years to have full impact on quanity of export demanded.

In particular, 1 percent increase in industrial index would increase the export of Pakistan by 0.33 percent in current year, 0.69 percent in second year, 0.68 percent in third year and 1.5 percent in forth year.

The results of export supply equation are significant with respect to sign and high-adjusted [R.sup.2] and no autocorrelation.

The coefficient of relative price has correct sign but insignificant, predicted values of real GDP and cumulative effect of wage rate have emerged as significant determinant of export supply function.

The performance of (LY) is according with theory; with coefficient being significant the (LY) elasticity is elastic with respect to export supply and also significant. The result suggests that 1 percent increase in domestic capacity of the economy will increase the export supply by 3.7 percent.

The coefficient of wage rate is insignificant individually at 5 percent but significant at 5 percent at cumulative level, elasticity of export supply with respect to wage rate is inelastic. Results suggest that 1 percent increase in wage rate the export supply will decrease by .7 percent. Our result is in the line of structuralist economists that reduction in real wage without increasing productivity does not increase output and employment [Taylor (1990) and Trap (1993)]

5. CONCLUSION AND POLICY IMPLICATIONS

The empirical results suggest that the world economic activity and real effective exchange rate are the important determinants of export demand of Pakistan. However significant and inelastic coefficient of REER on demand side in the long run points out towards an interesting policy implication that devaluation or depreciation may not be an effective source of export growth in Pakistan.

The significant and elastic coefficient of world economic activity shows colossal dependence of Pakistan's export on trading pattern in the world economies. The results indicate that the government should monitor the business cycles of its trade partners in order to target expanding exports during their periods of cyclical booms. Government should make it a priority in its policy agenda to expand exports to major trade partners by diversification of exports with better quality products and high value added components.

On the supply side the wage rate is although insignificant in the short run but its cumulative effect is significant and less elastic. Our result is in the line of structuralist economists that institutions (economic and political) do matter. The coefficient of domestic production capacity is significant and elastic that shows greater role of domestic production in determination of export of Pakistan. These results suggest need of policies for greater utilisation of productive capacity of the economy. While insignificant relative price coefficient suggests that it is not statistically important determinant of export supply in case of Pakistan.

Despite the importance of above mentioned factors non price factors such as product differentiation, trade promotion, facilities at ports, infrastructural facilities, etc. may also produce greater influence on export performance and government should also consider non price factors in future policy formulation to promote export.

APPENDIX

Real Effective Exchange Rate

In this section, we shall briefly explain the calculation of Pakistan's rupees real effective exchange rate based on export weighted exchange rate. For export weighted exchange rate, the trade partners were chosen on the basis of exports are more than 1 percent in total exports in 1990.

Let [X.sup.p.sub.0] be the value of exports to the pth trading partner in the base period (0), expressed in that partner's currency. Let [e.sup.p.sub.1] and [e.sup.p.sub.0] be the dollar values ($/currency) of one unit of the pth partner's currency in period 1 and in the base period (0), respectively, and [e.sup.r.sub.1] and [e.sup.r.sub.1] be the dollar values ($/currency) of one unit of the reporting country's currency in period 1 and in the base period (0), respectively. Then, to compare the change in the values of the base period's export earnings (from all partners) owing to exchange rate movements, the following ratio is formed

E = [summation over (p)] [X.sub.o.sup.p] ([e.sup.p.sub.1] / [e.sup.r.sub.1]) / [summation over (p)] [X.sub.o.sup.p] ([e.sup.p.sub.o] / [e.sup.p.sub.o]) * 100 (1)

Where, subscripts refer to the time period and superscripts to the country. The price and quantity components [X.sup.p.sub.0] of the value of export receipts are held constant only the relative exchange rates are changed. Through simple manipulation,

Equation (1) can written in a form readily recognisable from the effective exchange rate literature

E = [summation over (p)] [W.sup.p.sub.0] / [summation] [W.sup.p.sub.0] ([e.sup.p.sub.1] / [e.sup.p.sub.0] / [e.sup.r.sub.1] / [e.sup.r.sub.0] * 100 (2)

Where,

[W.sup.p.sub.0] = [X.sup.p.sub.0] [e.sup.p.sub.0] / [e.sup.r.sub.0]

In formulation (2), the index is shown to be simply the bilateral export weighted index of the nominal effective exchange rate described by the Rhomberg

[(1976), p. 95]. The result [e.sup.p.sub.1] /[e.sup.p.sub.0] and [e.sup.r.sub.1] / [e.sup.r.sub.0] are the indices changes from the base period

in p's and r's numeraire exchange rates, respectively.

Nominal Effective Exchange Rate--Adjustment for Inflation Differentials

Consider the nominal index rate derived in formulations (1) and (2). Deflating equation (1) by the ratio of price changes from the base period in the partner countries to that in the reporting country gives, after a number of mathematical manipulations,

R = [summation over (p)] [Z.sup.p] ([e.sup.pr.sub.1] / [e.sup.pr.sub.0] / [e.sup.pr.sub.1] / [e.sup.pr.sub.0] (3)

where, [Z.sub.p] = [W.sup.p.sub.0] / [summation over (p)] [W.sup.p.sub.0] is the bilateral export share; [e.sup.pr.sub.0] = [e.sup.pr.sub.0] / [e.sup.r.sub.0] and

[e.sup.pr.sub.1] = [e.sup.p.sub.1] [e.sup.r.sub.1] are bilateral exchange rates of the partner countries to those of the

reporting country at time 0 and time 1, respectively; and [p.sup.pr.sub.0] = [p.sup.p.sub.0] / [p.sup.r.sub.0] and

[p.sup.pt.sub.1] = [p.sup.p.sub.1] / [p.sup.r.sub.1] are the ratios of export process of the partner countries to those of reporting country at time 0 and time 1.

Equation (3) can, in turn, be easily expressed in a more reduced, mathematically equivalent form, that is,

R = [summation over (p)] [Z.sub.p] (r.sup.p.sub.1] / [r.sup.p.sub.0] (4)

Where [r.sup.p.sub.1] = [e.sup.pr.sub.1] / [p.sup.pr.sub.1] and [r.sup.p.sub.1] = [e.sup.pr.sub.0] / [p.sup.pr.sub.0] so that R is a weighted sum of real exchange rates.

Production Capacity of Economy

For production capacity of economy, the Predicted value of real GDP (1990=-100) used as proxy of real GDP [See Khan and Goldstein (1978) and Abroad (2000)].

Comments

I would like to congratulate the young authors on a worthwhile effort in understanding and modelling aggregate exports of Pakistan. Unfortunately, I only received the paper a few days ago, and could not give it the attention that it deserved. The paper offers us a number of intriguing puzzles, resolution of which is likely to improve the paper, and our understanding of the nature of Pakistan's exports, substantially.

The first puzzle: The authors claim that the Hausman test shows that there is no simultaneity problem between the supply and demand equation for Pakistani Exports. As Supply and Demand is the classic case of simultaneity, we wonder how this could be so. Of course, it is well-known that simultaneity tests often have low power, and so this could be a case of type II error--there is simultaneity, but the tests failed to detect. If we give the test the benefit of the doubt, and assume that the result is valid, then we must explain how it is that the price of exports is exogenous to the system. On reflection, this is only possible if Pakistan is too small an exporter to influence the price of its exports. In this case, the price of Pakistani exports would be determined on the world market. The quantity of Pakistani exports would then be determined PURELY by the supply equation. There would be no demand for Pakistani exports as such--Pakistani exports would be a small part of the world market, and the world demand would be for the goods. To see this, consider a farmer growing a crop in a competitive market. There is no demand for farmer X's crop or farmer Y's crop; there is only an aggregate demand which all farmers together fulfil in equilibrium. Let us call this case A:

Case A: Pakistan is a small supplier of exports, and does not influence world prices. In this case, the supply function will completely determine exports. There will be no demand for Pakistani exports as such. There will be a world demand function, but it will be demand for all world equivalents of Pakistani exports, from whatever country of origin.

Assessment: How realistic is this? Most of Pakistan exports are commodities, like wheat, rice, cotton, etc. In some of these markets, Pakistan is a big exporter on world markets and may have some influence on the price. In other cases, Pakistan is small, and has no effect on the world price. It would require more detailed analysis to assess the realism of this assumption. For suitable models, it may be advisable to disaggregate exports into these two types, as suitable exogeneity assumptions are different in the two types of models. In case A, however, the demand equation is clearly misspecified.

Clarification: If any of these variables on the RHS of either equation are endogenously determined, then there will be simultaneity bias. There is no simultaneity bias if and only if all variables on the right hand side are exogenous. But if all RHS variables are exogenous then there are two different equations, both of which determine the same variable. This is impossible--two different independent equations cannot both determine the same quantity unless there is some variable on the RHS which adjusts to equilibrate (and hence is endogenous).

Case B: Pakistan is a big exporter and does influence world price for Pakistani exports. In this case, there will definitely be a simultaneity problem. There are two other problems which need to be considered. (B1) If Pakistani exports are considered as a unique good, with Pakistan as a sole supplier, then we have a monopoly exporter. In this case, the demand curve is properly specified, but there is no supply curve as such. The quantity of Pakistani exports would be determined by the demand equation together with the cost curves and profit maximisation for the monopolist. This appears to be unrealistic. (B2) For items like wheat, cotton, and rice, Pakistan is a big exporter, but not the only exporter. Here we have an oligopolistic market. Pakistan can influence world prices, and now must use strategic considerations to decide on its supply. The demand curve would not be suitably modelled as a demand for Pakistani exports, but as an aggregate demand for world supply of the good which is being supplied by Pakistan. Determination of Pakistan's supply would require a deeper analysis of market structure and the policies of our government in this regard, as well as the policies of other major suppliers. A simple demand and supply equation does not seem adequate in this complex case. It seems likely to me that a sophisticated analysis of this type would be quite valuable to the Government in determining suitable policies regarding our exports. If the authors wish to undertake such analysis in the future, I would suggest that they disaggregate the exports into major categories. This will make it more possible to get realistic estimates on the basis of market structure.

Finally, I would like to indicate the Almon's Polynomial Distributed Lag technique has been virtually abandoned. I know of no empirical study using this technique published within the last ten years. The main reason for this is the influence of Hendry's methodology, described in detail in the important text Dynamic Econometrics. I will only provide a sketch of his critique here. Consider Almon's model:

S(t) = a + a0(t) O(t-1) + a1 O(t-1) + a2 O(t-2) + ... + ak O(t-k)

The supply (shipments) at time t is a distributed lag based on previous orders. This is a special case of the general ARMA (k, k) model, which would also have lagged variables S(t-1) to S(t-k) on the right hand side. Hendry makes a strong case for general-to-simple modelling, which involving starting with the most general ARMA (k, k) model and then simplifying to special cases. In the Almon model, we would want to start by putting these omitted variables on the RHS. We can exclude these variables only after we test the coefficients of the shipments and find that the null hypothesis that they are zero cannot be rejected. In fact, I asked a graduate student to carry out this exercise with the Almon data, and found that this null is strongly rejected. On reflection, it is clear that lagged values of shipments are very important variables. It is the UNFILLED orders from the previous periods which affect current shipments. We found that by putting in lagged shipments, we could construct very simple models which outperformed Almons best PDL models by large factors of accuracy.

Asad Zaman

International Institute of Islamic Economics, International Islamic University, Islamabad.

REFERENCES

Ahmed, Naseeruddin (2000) Export Response to Trade Liberalisation in Bangladesh: A Co-integration Analysis. Applied Economics 32, 1077-1084.

Anwer, Sajjad (1985) Export Function for Pakistan: A Simultaneous Equation Approach. Pakistan Journal of Applied Economics 4:1, 29-34.

Goldar, Bishwanath (1989) Determinants of India's Export Performance in Engineering Products, 1960-79. Developing Economics 27:1.

Hasan, M. Aynul, and Ashfaque H. Khan (1994) Impact of Devaluation on Pakistan's External Trade: An Econometric Approach. The Pakistan Development Review 33:4, 1205-1215.

Houthakker, H. S., and S. P. Magee (1969) Income and Price Elasticities in World Trade. Review of Economics and Statistics 51:2.

Hausman, J. A. (1976) Specification Tests in Econometrics. Econometrica 46, 1251-1271.

Khan, Mohsin S., and M. Goldstein (1978) The Supply and Demand for Exports: A Simultaneous Approach. Review of Economics and Statistics May: 257-286.

Naqvi, S. N. H., et al. (1983) The P. I. D. E Macro Econometric Model of Pakistan's Economy. Islamabad: Pakistan Institute of Development Economics.

Rohmberg, Robert R. (1976) Indices of Effective Exchange Rages. Staff Papers 23, 88-112.

Roy, Dilip Kumar (1991) Determination of Export Performance of Bangladesh. The Bangladesh Development Studies 19:4.

Sajjad, and Fauzia (2000) Pakistan Trade Performance via-h-via its Major Trading Partner. 1, 37-50.

Taylor, L. (1990) Socially Relevant Policy Analysis: Structuralist Compatible General Equilibrium Models for Developing Countries. Cambridge, MA: MIT Press.

Trap, F. (1993) Stabilisation and Structural Adjustment: Macroeconomic Frameworks for Analysing Sub-Saharan Africa. London: Routlege

(1) Almon technique has a distinct advantage over the Koyck method because the latter has some serious estimation nrnhlems. Moreover Koyck will not work when assumption of [beta] coefficient decline,

(2) Different studies used different types of exchange rates (nominal, real, and effective).

(3) Industrial production index of industrial countries is taken as a proxy of world economic activity because more than 60 percent of export of Pakistan goes to industrial countries.

(4) Wage rate as proxy of cost of production is first time used in export supply equation of Pakistan.

(5) We check the simultaneity problem between export demand and supply equation by employing Huasman Specification Test. We found that there is no simultaneous problem exists between export demand and supply equations.

(6) The number of lags included was determined using Akaike Information Criteria (AIC), indicating that optimal lag is 3.

(7) Share of export of trade partner more than 1 percent in total export in 1990.

(8) Estimation procedure of real effective exchange rate and production capacity of economy is given in Appendix.

Zeshan Atique is Faculty Member, Shaheed Zulfikar Ali Bhutto Institute of Science and Technology, Karachi, and Lecturer in Economics at the University of Karachi, Karachi. Mohsin Hasnain Ahmad is Project Economist, Applied Economics Research Centre, University of Karachi, Karachi.

The Export Demand Equation

Lagged Explanatory Estimated
 Variables Coefficient T-Ratio

Constant -6.86 -4.26 *
REER (0) -0.49 -1.57
REER (-1) -0.36 -1.49
REER (-2) -0.53 -1.07
REER (-3) -0.03 -0.01
IPI (0) 0.38 2.47 **
IPI (-1) 0.69 2.24 **
IPI (-2) 0.68 2.27 **
IPI (-3) 1.58 1.77
[3.summation over (i=0)] REER(i) -0.39 -2.12 **
[3.summation over (i=0)] IPI (i) 2.93 12.3 *
Adjusted [R.sup.2] 0.92
D.W 2.06

* and ** indicate significant at 1 percent and 5 percent respectively.

The Export Supply Equation

Explanatory Estimated
 Variables Coefficient T-Ratio

Constant -37.51 -5.16 *
LRP 0.42 0.99
LY 3.67 4.97
Wr (0) -0.25 -1.29
Wr (-1) -0.05 -1.43
Wr (-2) -0.08 -0.52
Wr (-3) -0.31 -1.58
[3.summation over (i=0)] REER(i) -0.70 -2.56 *
Adjusted [R.sup.2] 0.92
D.W 2.13

* and ** indicate significant at 1 percent and 5 percent respectively.