Import and Export Demand in Developing Countries

Both the import demand of developing countries and the world demand for their exports have generally been assumed in the literature to be determined by nonmarket forces. Therefore, products imported and exported by these countries have been considered to be relatively insensitive to changes in prices. The evidence for this view can be seen in the models of trading behavior of developing countries that have been constructed by Chenery and Strout (1966) and by Maizels (1968).

Abstract

Both the import demand of developing countries and the world demand for their exports have generally been assumed in the literature to be determined by nonmarket forces. Therefore, products imported and exported by these countries have been considered to be relatively insensitive to changes in prices. The evidence for this view can be seen in the models of trading behavior of developing countries that have been constructed by Chenery and Strout (1966) and by Maizels (1968).

Both the import demand of developing countries and the world demand for their exports have generally been assumed in the literature to be determined by nonmarket forces. Therefore, products imported and exported by these countries have been considered to be relatively insensitive to changes in prices. The evidence for this view can be seen in the models of trading behavior of developing countries that have been constructed by Chenery and Strout (1966) and by Maizels (1968).

Individual country studies have in certain cases included price variables as determinants of imports and exports but these studies, while certainly useful, do not allow one to generalize easily across developing countries. One recent study by Houthakker and Magee (1969) did consider the trading patterns of a few developing countries, and in a certain sense the present paper can be considered as an extension of that study to cover developing countries more comprehensively.

The essential aim of this paper is to provide estimates of import and export demand functions for 15 countries that can be characterized as “developing” and to test the hypothesis of whether changes in prices of traded and nontraded goods exert any significant influence on the trade flows of these countries. In addition, an attempt is made to demonstrate how the role of quantitative restrictions on trade can be approximated and incorporated into the estimates. This is necessary because (1) on the import side of the trade accounts, controls have been regarded as commonplace in developing countries; and (2) on the export side, considerable attention has focused on imposition of quotas and other restrictions on the flow of exports by the buyer countries. Although the precise role of quantitative restrictions may actually be nonquantifiable, it will be shown that, under certain assumptions, approximations are possible and tests can be made to evaluate their importance.

The 15 countries covered in this paper are Argentina, Brazil, Chile, Colombia, Costa Rica, Ecuador, Ghana, India, Morocco, Pakistan, Peru, the Philippines, Sri Lanka, Turkey, and Uruguay. The period of study was 1951–69 on an annual basis. The countries were selected for two reasons: (1) taken together they represented a fairly wide geographical coverage and thus would provide some generalization, and (2) each had consistent data for the relevant variables over the entire period.

Section I of this paper describes the demand functions for imports and exports that will be estimated. Section II discusses the results obtained from estimating these equations. The implications of the results and the conclusions reached are set forth briefly in Section III. Data sources are listed in the Appendix.

I. Import and Export Demand Functions

import function

The simplest formulation of an aggregate import demand equation relates the quantity of imports demanded by country i to the ratio of import prices to domestic prices (assuming a degree of substitutability between imports and domestic goods) and to domestic real income, all in period t.1 In log-linear terms the estimating equation has the following form:

logMdit = α0 + α1log (PMiPDi)t + α2logYit + ui(1)

where

Mi = quantity of imports of country i,

PMi = unit value of imports of country i,

PDi = domestic price level of country i,

Yi = real gross national product of country i.

ut is an error term, and the superscript d refers to demand.

Since the equation is specified in logarithms, α1 and α2 are the relative price and income elasticities, respectively. The signs are expected to be: 2

α1<0;α2>0.

There are two reasons why the equation is specified in logarithms: (1) it allows imports to react in proportion to a rise and fall in the explanatory variables; and (2) on the assumption of constant elasticities, it avoids the problem of drastic falls in the elasticity as imports rise.3

Two particular assumptions are made when one estimates an equation such as equation (1), abstracting from problems of aggregation and measurement errors. First, it is implicitly assumed that importers are always on their demand function, that is, Mdi = Mi. Second, if equation (1) is estimated as a reduced form equation by ordinary least-squares, an assumption is made that supply price elasticities are infinite (or at least large), so that the price of imports can be properly treated as exogenous.

If either of these two assumptions is not satisfied, estimates of α1 obtained from equation (1) would be biased and inconsistent.4

The possible problems created by these assumptions are well known and have been discussed extensively in the literature (Magee, 1973). In the context of developing countries a further source of misspecification occurs in the estimation of equation (1) when no account is taken of quantitative restrictions that are imposed on import flows; and, again, there is a possibility of obtaining biased and inconsistent elasticity estimates of α1 and α2.5

The approach adopted in this paper in attempting to take into account these potential sources of bias is to introduce the possibility of behavior out of equilibrium by specifying a partial adjustment mechanism for imports, in which the change in imports is related to the difference between the demand for imports in period t and actual imports in period t – 1:

ΔlogMit = γ[logMdit − logMit1]0γ1(2)

where ΔlogMit = logMitlogMit–1

When applied to imports of country i, this type of adjustment function implies that the price of imports relative to the domestic price level is exogenous to the importing country i, usually being determined in the overseas market, with quantities being adjusted domestically. A rationale of equation (2) can be made on the basis that there are costs involved in the adjustment of imports to a desired flow and that only part of the adjustment is achieved within the period.6 A further rationale is that many imports are linked to contracts extending over a period of time and thus cannot respond promptly to changes in demand (Malinvaud, 1966, p. 622). This partial adjustment framework introduces a geometric lag structure into the determination of imports.

Substitution of equation (1) in equation (2), and then solving for imports in period t, yields

logMit = γα0 + γα1log(PMiPDi)t + γα2logYit+(1 − γ)logMit1 + γut(3)

where γα1 and γα2 are the short-run price and income elasticities, respectively.

An objection to the use of ordinary least-squares to estimate equations (1) and (3) is that one must assume that there is no possibility of a supply relationship between prices and quantities. If this supply relationship is less than infinitely price elastic, the estimated price elasticity in the demand equation would be a weighted average of a positive supply elasticity and a negative demand elasticity, and thus the estimate would be biased and inconsistent. In order to allow for the simultaneous relationship between the quantity and the price of imports, a supply function for imports can be specified and consistent estimates can be obtained for α1 and γα1 by using the two-stage least-squares method.

For the equilibrium case, the demand function can be rewritten as

logMit = α0 + α1[logPMit − logPDit] + α2logYit + ut(4)

The supply of imports to country i is specified as a log-linear function of the price of imports, the world price level (PW), and world income (W):

logM8it = a0 + a1logPMit + a2logPWt + a3logWt(5)

This can be written in inverse form as

logPMit = a0 + a1logMit − a2logPWt − a3logWt(5)

Equation (4) is estimated by using PDi, Yi, PW and W as instruments, with the linear constraint that α1 is the same elasticity for PMi and PDi.

The disequilibrium import equation can be written as

logMit = γα0 + γα1[logPMit − logPDit] + γα2logYit+(1 − γ)logMit1 + γut(6)

The price of imports is assumed to adjust to excess supply:

ΔlogPMit = γ[logM8it − logMit](7)

Substitution of equation (5) in equation (7), and solving for log PMit, yields

logPMit = A0 + A1logPWt + A2logWt + A3logMit+A4logPMit1(8)
A0 = γa01 − γa1A1 = γa21 − γa1A2 = γa31 − γa1A3 = γ1 − αa1A4 = 11 − γa1

Equation (6) is estimated by using PDit, Yit, PWt, Wt, Mit–1 and PMit–1 as instruments.

In order to account for the role of quantitative restrictions, most studies—for example, those by Dutta (1964), Islam (1961), Turnovsky (1968)—have included measures such as the level of international reserves, of export receipts, and of overseas assets in the import equation. The assumption behind the use of these alternative measures is that the authorities vary restrictions inversely with the country’s capacity to import, and this capacity can be measured by one of the above proxies. The use of these proxies does reduce the degree of bias in the estimates as compared with the complete omission of the nonquantifiable variable (McCallum, 1972; Wickens, 1972).

Even if restrictions are not correlated with the explanatory variables, if their effect varies systematically over time (that is, that restrictions are serially correlated, as the use of the proxies would imply), it cannot any longer be assumed that the error terms in the estimating equations are independent. However, one can approximate the effect of restrictions by assuming an autoregressive process in the error term and by considering the coefficient of autocorrelation as an indicator of restrictions. It must be noted that this would be a relevant indicator only on the assumption that the simple equations (4) and (6) are the “true” equations and that misspecification occurs only through the omission of the role of restrictions. In a more general sense, adjustment for autocorrelation, irrespective of the cause, will correct for bias in the coefficients and their standard errors when equations (4) and (6) are estimated.

Therefore, a first-order autoregressive process for the error terms in equations (4) and (6) is specified, as follows:

ut =ρ1ut1 + ε1tγut =ρ2(γut1) + ε2t|ρ1|< 1;|ρ2|< 1.

The errors єit are assumed to be normal and independent, with zero means and constant variances—that is:

ε1tNID(0,σ2ε1);ε2tNID(0,σ2ε2).

The equations will be estimated subject to these nonlinear restrictions.

export function

The world demand for the ith country’s aggregate exports is specified in log-linear terms as

logXdit = β0 + β1log (PXiPW)t + β2logWt + vt(9)

where

Xi = quantity of exports of country i,

PXi = unit value of exports of country i,

PW = world price level (prices reported by the Organization for Economic Cooperation and Development (OECD)),

W = real world income (OECD real gross national product).

β1 and β2 are the price and income elasticities respectively, with the expected signs (recalling that the sign of the income elasticity is ambiguous).

β1<0;β2>0.

Simple export demand functions such as equation (9) have been estimated by Houthakker and Magee (1969) for a number of developing countries. Again, as in the case of imports, one can test for incorrect specification—due to estimation of an equilibrium relationship when the true relationship is a disequilibrium—by specifying an adjustment function relating the change in exports to the difference between the demand for exports in period t and actual exports in the previous period (t–1).

ΔlogXit = γ[logXdit − logXit1](10)0λ1

where λ is the coefficient of adjustment. This adjustment function assumes that prices of exports are generally determined in the home country i and that quantities are adjusted abroad.

Substitution of equation (9) in equation (10), and solving for exports in period t yields

logXit = γβ0 + γβ1log(PXiPW)t + γβ1logWt+(1 − λ)logXit1 + λvt(11)

where λβ1 and λβ2 are the short-run price and income elasticities, respectively.

The simultaneity between the quantity and the price of imports can be accounted for by specifying supply relationships similar to the ones in the case of imports.

Equation (9) can be rewritten as

logXdit = β0 + β1[logPXit − logPWt] + β3logWt + vt(12)

The supply of exports of country i is specified as a log-linear function of the price of exports, the domestic price level, and domestic real income:

logX8it = b0 + b1logPMit + b2logPDit + b3logYit(13)

Written in inverse form (assuming X8it = Xit), this yields

logPXit = b0 + b1logXit − b2logPDit − b3logYit(13)

Equation (10) is estimated by the two-stage least-squares method, using PDi, Yi, PW, and W as instruments, with the linear constraint of β1 being the export price elasticity and also the domestic price elasticity.

The disequilibrium export equation is specified as

logXit = γβ0 + γβ1[logPXit − logPWit] + γβ2logWit + (1 − γ)logXit − 1 + γvt(14)

The price of exports is specified as adjusting to excess supply:

ΔlogPXit = λ[logX8it − logXit](15)

Substitution of equation (13’) in equation (15), and solving for logPXit, yields

logPXit = B0 + B1logPDit + B2logYit+B3logXit + B4logPXit1(16)
B0 = λb01 − λb1B1 = λb21 − λb1B2 = λb31 − λb1B3 = λ1 − λb1B4 = 11 − λb1

Equation (14) is estimated by using PDit, Yit, PWt, Wt, Xit-1, and PXit-1 as instrumental variables.

There still remains a problem with quantitative restrictions placed on the exports of developing countries by the buyers. The obvious example of these is the quotas placed on the import of primary and primary-based products by industrial countries.

A test for the importance of these restrictions in the determination of exports will be made in the same way as was discussed for imports—that is, by specifying a first-order autoregressive process for the error terms in equations (12) and (14):

vt =ρ3vt1 + ω1tλvt =ρ4(λvt1) + ω2t|ρ3|<1,|ρ4|<1,andtheωi,shave the propertiesω1tNID(0,σω12),ω2tNID(0,σω22)

II. Results of the Estimations

The import equations (4) and (6) and the export equations (10) and (12) were estimated subject to the errors following a first-order autoregressive process. There are several ways of estimating equations with autoregressive errors under the assumption that the ε’s and ω’s are normal and independent. One can obtain consistent, but not efficient, estimates by using instrumental variables or, if consistent estimates of the error variance matrices are available, by using Aitken’s generalized least-squares method. Maximum-likelihood methods will also yield consistent, asymptotic efficient estimates.7

The results from estimating the equations by the two-stage least-squares method 8 are shown in Table 1 for imports and in Table 2 for exports. The simple import and export formulations (4) and (12) are referred to as “equilibrium equations,” and (6) and (14) are referred to as “disequilibrium equations.” In the tables, ρi (i= 1, …, 4) is the coefficient of autocorrelation and the chi-squared statistic is based on – 2 Log (L), where L is the likelihood ratio. The chi-squared statistic tests the hypothesis that ρi = 0. This test, due to Sargan (1964), with a chi-squared value for one degree of freedom, is asymptotically equivalent to a t test on the ρi.

Table 1.

Imports

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The discussion of the estimates in Table 1 and Table 2 will be within the framework of testing the following three hypotheses, namely that:

  • (1) relative prices influence trade flows of developing countries;
  • (2) the errors in these models are serially independent; and
  • (3) the data are generated by an equilibrium rather than disequilibrium system.
Table 2.

Exports

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The equations for imports and exports will be discussed separately. It should be noted that the theory for interpreting equations subject to autocorrelation, dynamics, and simultaneity has not been well worked out, and the discussion will thus be on a somewhat heuristic level.9

imports

In Table 1, presenting the estimates derived from the import equations for each of the countries, t-values are shown in parentheses below the estimated coefficients. The equilibrium results show that the estimated price elasticities are generally high and therefore indicate that relative prices have a significant effect on the imports of developing countries; α1^ is significantly different from zero at the 5 per cent level and has the expected negative sign in the results for Brazil, Colombia, Costa Rica, Ecuador, India, Pakistan, Peru, the Philippines, Sri Lanka, Turkey, and Uruguay. With the exceptions of Colombia and Pakistan, where the estimated price elasticity is fairly small, all estimated price elasticities that are significantly different from zero are also close to or greater than unity. This does not confirm the commonly expressed view that developing countries have a price-inelastic demand for import goods. Except for the results for Argentina, Chile, Ghana, India, Turkey, and Uruguay, all of the estimated income elasticities are significantly different from zero at the 5 per cent level and have positive signs. The coefficient of autocorrelation is significantly different from zero at the 5 per cent level in the estimates for eight countries—Argentina, Chile, Costa Rica, Ecuador, Ghana, Pakistan, and Turkey. This could be taken as indicative of incorrect specification owing to omission of the role of restrictions, but it could also be simply due to the fact that static equations such as equation (4) do not capture the true dynamics of demand (Houthakker and Magee, 1969).

In the disequilibrium estimates shown in Table 1 the short-run price elasticities are significantly different from zero and have the correct signs in the equations for Brazil, Colombia, Costa Rica, Ecuador, Pakistan, and Sri Lanka. With the exception of Chile, for which the estimated coefficient of lagged imports was significant, in all other cases this short-run elasticity is also the equilibrium elasticity.10 The income elasticities are significantly different from zero at the 5 per cent level and have positive signs in the results for Brazil, Colombia, Ecuador, and Pakistan. The elasticity estimates for the Philippines and Sri Lanka become insignificant when a lagged dependent variable is added, perhaps because of multicollinearity. The coefficient of autocorrelation is significantly different from zero for Argentina, Brazil, Chile, Costa Rica, Pakistan, and Turkey; it appears, therefore, that the simple equation is incorrectly specified in only these cases.

exports

The results obtained from estimating by equation (12), the equilibrium export equation, are given in Table 2. The estimated price elasticities are significantly different from zero at the 5 per cent level and have the correct negative signs in the equations for Chile, Costa Rica, Ecuador, Ghana, Morocco, Pakistan, Peru, the Philippines, and Turkey; the price elasticity for Uruguay is also significantly different from zero but has an incorrect positive sign. The implication of this general result is that although these countries are primary commodity exporters, they do not necessarily face an inelastic demand schedule, and price variations would affect the quantity of exports demanded.

The income elasticities are positive and significant in the estimated equations for Argentina, Brazil, Chile, Ecuador, Pakistan, Peru, the Philippines, and Uruguay. Apart from the result for Pakistan, these income elasticities are less than unity. The coefficient of autocorrelation is significant in the equations for Chile, Costa Rica, and Turkey, although for Chile and Uruguay it is negative. This general result could be interpreted as indicative of restrictions or simply represent the coefficient’s reflection of the dynamics of adjustment of exports.

The results of the disequilibrium export equations are also given in Table 2. The estimated short-run price elasticities are significant and have the correct signs in the equations for Chile, Ecuador, Ghana, India, Pakistan, and Turkey. Since the coefficient of adjustment was significantly different from unity in only the equations for Ecuador, Pakistan, and Uruguay, these price elasticities are also the long-run or equilibrium elasticities for the rest of the countries.11 The estimated income elasticities are significant and have positive signs in the equations for Chile and Ecuador only. In all other countries, although the sign is positive, the elasticities are themselves not significant. This could be due to multicollinearity between lagged exports and world income caused by the fact that both follow a common trend. The coefficient of autocorrelation shows no evidence of positive autocorrelation in the estimates, and negative autocorrelation is evident in the estimate for Pakistan.

summary of results

The results have shown that for both import and export equations a simple equilibrium formulation appears to be adequate. Both imports and exports appear to adjust within a year (the period of observation) to changes in demand. One can therefore consider the implications of the simple equation results. Price elasticities of imports and exports tend to be much larger than perhaps would have been generally expected. Interestingly, they also tend to be similar in a number of cases. Income elasticities are on the low side for both imports and exports and also are fairly similar in a number of countries. In general it was found that the degree of autocorrelation (as measured by the number of cases where the coefficient of autocorrelation was significant) was greater in the import equations than in the export equations.12 If, as suggested here, the degree of autocorrelation is an indicator of quantitative restrictions having been omitted, this result tends to confirm the view that restrictions are more important in the determination of imports than of exports. Other than this interpretation, there does not seem to be any easy economic rationale as to why import equations suffer from more specification error than do simple export equations.13

III. Conclusion

The basic conclusion of this paper is that it appears that prices do play an important role in the determination of imports and exports of developing countries. As far as the size of the estimated price elasticities is concerned, they were found to be fairly high for most of the 15 countries studied. This implies that in a number of developing countries the Marshall-Lerner condition for successful devaluation would be easily satisfied—a result similar to that obtained by Houthakker and Magee (1969) for industrial countries. Further, the estimates in this paper indicate that on an annual basis a static equilibrium model may be justified.

Broadly speaking, the results have been good in the sense that common equations were able to explain imports and exports of a group of countries. It is conceivable that the results could be considerably improved if special features of the countries, such as their state of development or characteristics of their trade structure, as well as special circumstances during the period of study, were incorporated into the equations.

APPENDIX Data Sources

All import and export quantity and unit value data were obtained from the International Monetary Fund, International Financial Statistics, various issues, except for two countries. For Argentina, the source of data was the Central Bank of the Republic of Argentina, Comercio Exterior; for Pakistan, unpublished data were obtained from the Pakistan Institute of Development Economics.

Nominal gross national product (GNP) data were taken from International Financial Statistics; real GNP data, from the United Nations, Statistical Yearbook, various issues. The implicit deflator was generated.

World income and prices are defined as real GNP reported by the Organization for Economic Cooperation and Development (OECD) and the OECD GNP deflator, respectively. Data were taken from OECD, Main Economic Indicators.

All data are in terms of U. S. dollars. Where a series was only available in domestic currency, it was converted by use of the current official exchange rate. In cases of multiple rates, an implicit rate for conversion was constructed by use of the trade balance in domestic and in foreign currency.

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*

Mr. Khan, an economist in the Financial Studies Division of the Research Department, holds degrees from the London School of Economics and Columbia University. In addition to colleagues in the Fund, the author is greatly indebted to D. F. Hendry, H. G. Johnson, and C. R. Wymer for their comments and suggestions.

2

The sign of α2 could be negative, since imports are the difference between consumption and production. For a discussion of this, see Magee (1973) and Khan and Ross (1974a).

3

Evidence on the appropriate functional form of the import demand equation is contained in Khan and Ross (1974b).

4

In the case of the assumption of equilibrium, a misspecification bias in the estimates would occur if in fact the data were generated by a disequilibrium system. If the assumption of infinite price elasticities of supply was not met, the result would be simultaneous equation bias.

5

If quantitative restrictions are correlated with either of the explanatory variables, the estimated elasticities would be biased and inconsistent. This would be the case of specification error due to an omitted variable. See Ramsey (1969).

6

See Griliches (1967). For an application to the case of imports, see Turnovsky (1968).

7

The program used yields asymptotic maximum-likelihood estimates. The technique used is from Sargan (1964).

8

All variables are defined in constant 1958 dollars. For data sources, see the Appendix.

9

For an analytic approach that covers some of the issues, see Hendry (1972).

10

The long-run price elasticity would be calculated as γα11 − (1 − γ). If 1 – γ = 0, then γ = 1 and adjustment of imports to a desired level is instantaneous (that is, within a year).

11

In the case of Ecuador, the sign of 1 – λ is negative, implying λ > 1.

12

There were eight such cases in the equation results for imports, versus two for exports.

13

Alternative explanations in terms of exchange rate changes or of incorrect specification of the lag structure would have to show why differential impacts occur in imports and exports.