Modelling export prices and quantities in selected developing economies

Modelling Export Prices and Quantities in Selected Developing Economies

AUGUSTINE ARIZE*

I. Introduction

The use of simultaneous equation models to explain a country's export behavior is a major development in econometric analysis over recent years. See, for example, studies by Goldstein and Khan [1978], Dunlevy [1980], Haynes and Stone [1983(a)]. These and most other empirical studies in this area have, however, focused their attention largely on the United States' experience.

The primary purpose of this study is to examine the price responsiveness of both export demand and supply in eight African countries: Ivory Coast, Tunisia, Morocco, Kenya, Upper Volta, Zambia, Mauritius, and Matawi. Annual data on the aggregate exports of these countries have been gath- ered for the years 1960-82. These countries have been selected for two reasons: (1) Each has consistent data for the relevant variables over the entire period; and (2) Taken together, these countries are at similar developmental stages--most achieved their independence in the early 1960's.

The paper is organized into three sections. Section II describes the demand and supply functions for exports as estimated for each country. It also explains the stability test used in this paper. Section III discusses the results obtained from estimating these equations. The implications of the results and conclusions reached are set forth briefly in Section IV. The data for this study are from the International Financial Statistics Yearbook of 1983. That is, the end of period figures are used so that the actual sample period is 1959-60 through 1981-82. For

*East Texas State University. The author would like to thank Professors Joe Brocato, Dan Slottje, and Robert Pavur for helpful comments on earlier drafts of this paper. Thanks also go to an anonymous referee of this journal for valuable comments and suggestions on earlier drafts. The author is indebted to Cheryl McQueen and Marylyn King for excellent typing and competent research assistance.

brevity, this period is referred to as 1960-82 throughout the paper.

II. Functional Form

Demand Equation The world demand for the aggregate

exports of country i is specified in log-linear terms as follows9

lnX~t = lnao + al(lnPXit- lnWPt) + azlnWIt + Zt, ( l )

where: X~ is the real quantity of exports demanded of country i; PXi is the country's relevant export unit value; and WP is the alternative price faced by a prospective buyer of country i's exports. WP is measured by the world price level. WI is a measure of effective world purchasing power and is measured by the world real income.

Equation (1) can be rewritten as:

lnX~t = lnbo + btlnPXit + bzln WPt + b31nWTYt + b41nWCYt + Vt (2)

where, in addition to the symbols defined in equation (1), WTY is the world potential or trend income and WCY is the world capacity utilization. WCY is measured as deviation from potential income. 2 The V is an error term.

IThis exposition draws from Haynes and Stone [1983(a),(b)], Goldstein and Khan [1978], and Khan [1974].

2For a recent study of the effects of trend income and capacity utilization on the supply of exports for the United Kingdom and the United States, see Dunlevy [1980]. For the effects on the demand of the exports and a critique of the use of these variables to capture secular and cyclical income effects, see Haynes and Stone [1983(a)]. The cyclical and secular components were derived by regressing the log of real income on a time trend. The predicted values represent the trend (WTY) or (TY) and deviations from trend, the cyclical component (WCY) or (CY). However, the specification of the secular income may be rigid, and the cyclical variable might capture some of the secular effects. Other factors which affect the time trend of trade flows may be attributed to secular income changes. Experimentation with the Wilson and Takacs [1979, p. 270] method did result in similar estimates.

19

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The disequilibrium model for equation (2) is given as:

lnXit = Mnbo + )tbt lnPXit + )kb2 lnWPt + Xb3 lnWTYt + Xb4 lnWCYt + (1 -- X) lnX~,-~ + XVt. (2')

The symbol h in equation (2') is the coefficient of adjustment. The change in exports is related to the difference between the demand for exports in period t and the quantity of actual exports in period t - 1, as shown in equation (3):

lnXit - lnXit-i = X(lnX~t- lnXit-O , 0 < X < 1. (3)

Equation (3) is the adjustment mechanism outlined by Houthakker and Taylor [1970]. It assumes that prices of exports are generally determined in the home country i and that the quantity of exports is adjusted abroad [Goldstein and Khan, 1978]. The average time lag in the adjustment of exports can be calculated from the parameters of equation (2') and 1/(1 -- )~).3

It has been suggested by Browne [1982] that export demand equations, like (2'), are misspecified by the use of equation (3), especially when dealing with small, open economies in which exporters are regarded as price acceptors, not as price setters. Browne [1982, p. 346] suggests that the appropriate adjustment mechanism is that in which excess demand determines the change in the price of exports, as shown in the equation below:

l n P X i t - l n P X i t - 1 = e(lnX~et - - l n X i t ) ,

e > 0. (4)

To examine this specification, equation (2) is substituted into equation (4) to give:

lnPXit = elnc0 + ecdn WPt + ec21n WTYt + ec31nWCYt + elnXit + (1 - e) lnPXit-~. (5)

3The long run price elasticity would be calculated as Xa~/ l - - ( t - - h ) . If l - X = 0 , then h = l and the adjustment of expor ts to a desired level is instantaneous (that is, within a year).

If equation (5) is more appropriate, Browne suggests that the absolute value of the ratio of the estimated coefficient of In WP to that of lnX;~ should be large relative to the long run elasticity of PX in (2'). Such a case would show that as perfect competitors on the world markets, these countries may have little or no long-term monopoly power in international trade.

Supply Equations

Since a supply relationship between prices and quantities can exist, and since such a supply relationship might not be perfectly price elastic, a simultaneous relationship between the quantity and the price of exports is taken into account by using the two-stage, least-squares method. This method permits consistent estimates of the price ratio or export price to be obtained from the demand equations.

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

lnX~, = lndo + dllnPXit + d21nPDit + d31nYit + st. (7)

Rewriting equation (7) to take into account country i's potential income and capacity utilization [Haynes and Stone, 1983(a)] results in a new equation:

lnX~t = lnj? +ftlnPXit + J~lnPDit +filnTI~],t +fllnCYi~ + et, (8 )

where, TYi is country i's trend income and CY represents its capacity utilization (deviation from trend income).

Following Goldstein and Khan [1978], the supply adjustment mechanism that relates the price of exports to the conditions of excess supply as written as:

l n P X i t - - l n P X i t - i = 0 ( l n X ~ t - - lnXit), 0 > 0. (9)

Substituting (8) into equation (9) and solving for lnPX yields:

ARIZE: MODELLING EXPORT PRICES 21

lnPXit : 0 lnd 0 + 0 d~ lnPDit + 0 dzlnTY~t + 0 d31nCY~, + Od'41nXit + (1 - O)lnPXit-1 + Out. (10)

Browne [t982] has shown that for small, open economies the appropriate adjustment mechanism is not equation (9), but one in which export quantities adjust toward sup- pliers' desired values, as shown in equation (11):

lnXit -- lnXit-i = (~(lnX~ -- lnXit-~ ), 0. (11)

Substituting equation (8) into equation (11) and solving for lnX yields the following supply equation:

lnX , = ¢lnJ; + ¢lnJ PX , + ¢lnJ2PD,t + ¢lnJ;rY~t

+ (~lnJ4CY~, + (1-- O)lnXit-l. (12)

If equation (12) is more appropriate, Browne [1982] suggests a low value for the estimated coefficient on PX~ because the non-traded sector of the economy is small relative to the total economy. Hence, a change in export prices does not elicit a large supply response since factors of production from the non-traded sector may not be available.

The theories underlying these models have been extensively discussed in the literature [Houthakker and Magee, 1969; Goldstein and Khan, 1978; Browne, 1982; Haynes and Stone, 1983(a), (b); Ali, 1984]. They need not be repeated here.

Stability Test

The formal stability test employed in this paper is that established by Farley, et al [1970, 1975]. In this test, the coefficients t hough t to be unstable are treated as linear functions of time. Thus, if coefficient a~ is thought to be unstable, it is modeled as follows:

ai = a i + hit (13)

where, t---= 1,..., n, and where n is the

number of observations in the sample. The test adds to the basic equation variables of the form tx, where x is a variable whose coefficient is suspected to be unstable. The coefficients (hi) on these added variables are jointly tested for significance from zero.

Under the null hypothesis that the coefficients are zero, an F test is appropriate. For example, if the coefficient on the export price in equation (2) is suspected to be unstable, then the equation:

lnXit = lnao + allnXit-1 + a21nPX~t + M(tlnPXiO + aAn WPt + aslnWTYt + a61nWCYt + ct (14)

is estimated, and the significance of M on the interaction variable (tlnPXit) is tested.

Since the author had no strong prior beliefs as to which coefficients were unstable, each coefficient was separately treated as unstable. A joint test of instability was performed using the F test as follows:

F = [(RSS2 - - R S S , ) / m ] / ( R S S 1 / N - k), d f = m, N - k (15)

residual sum of squares of the unrestricted regression, which is Ha;

RSS2 = residual sum of squares of the restricted regression, which is H0;

m = number of linear restrictions; k = number of parameters in the unre-

stricted regression; and N = number of observations.

Then the equation follows the F distribu- tion with m and N - k degrees of freedom.

If the computed F value is statistically insignificant, one may accept the null hypothesis of structural stability. Note that this test assumes that the parameter shift point is unknown.

III. Results

The equilibrium and disequilibrium models outlined in the previous section were estimated for the eight countries under study. The estimator used was two-stage

where: RSS1 =

22 A T L A N T I C E C O N O M I C J O U R N A L

TABLE 1

Estimated Long Run Demand Elasticities (Total Exports: Annual Data, 1960-1982)

Count ry PX PX/ WP WP WTY WC Y WI

Ivory Coast - . 0 8 2 - . .64* .37 - . 9 1 " - - Tunisia --. 11 - - 1.58" 1.54" 1.13 - - Morocco - . 8 2 * - - 1.12' - - - - .18 Kenya +.15 - - .94* 1.65" 1.2" - - Upper Volta - - --2.1" - - - - - - .30 Zambia +.08 - - .48* - - - - .66* Maurit ius - - - .04 . . . . .47* Malawi - . 4 8 * - - 2.08* 1.99" ,65 - -

*Significant at the l0 percent level.

least squares (TSLS), with correct ion for first-order autocorrela t ion where necessary.

In order to evaluate and compare the empirical relevance of equat ions (2'), (5), (10), and (12), one must determine the criteria by which to rate them. First, stability test results must be examined. Second, if all the equat ions are stable, the long run elasticities as claimed by Browne [1982, p. 346] must be examined.

T a k i n g e q u a t i o n (5) first, the results obta ined are inconsis tent with Browne 's suggestions: in Ivory Coast, Kenya, Zambia, and Matawi the d e m a n d equa t i ons are statistically unstable over the sample period. In Morocco , the lagged export variable is negative and statistically significant at the 10 percent level. This may suggest that the adjustment mechanism is misspecified. In Tunisia, with a large demand elasticity of 13.3, the lagged expor t var iable is not statistically significant. In Maurit ius, the demand elasticity is a mere 1.52 (Browne, us ing I r e l and as an example , ob t a ined demand and supply elasticities o f 16.16 and 1.14, respectively). The remaining results are based on the data in Tables 1 and 2.

The data in Table 1 are the estimated long run elasticities of equat ion (2) or its variants. As can be seen, in three of the eight countries

s t ud i ed - -Morocco , Upper Volta, and Ma- lawi- - the estimated demand price elasticity is statistically different f rom zero at the 90 percent level of conf idence? The world price level is pos i t ive and s ign i f i can t in all countries. The trend or potential income is statistically significant in Tunisia, Kenya, and Malawi. In Zambia, the world income va r i ab le car r ies a pos i t ive s ign and is statistically significant at the 90 percent level o f conf idence . In Maur i t ius , the world income variable is negative and statistically significant. 5

These results conf i rm a widely held view that developing countries face low prices and income elasticities for their exports. For example , D u t t a [ t 9 6 5 ] has f o u n d tha t

4Learner and Stern [1970] note that the use of an aggregate price index may understate the true elasticity since goods with relatively low elasticity may exhibit the largest variation in price and the effect of such variation lies primarily in its relative importance in the construc- tion of the aggregate price index. This limitation should be kept in mind.

51t should be noted that the sign of the real income elasticity is usually assumed to be positive; however, Goldstein and Khan [1978], Magee [1975], and Khan and Ross [ 1975] have shown that it need not necessarily be so. If the export level of a country is simply a residual demand by the rest of the world, then the sign of the income elasticity would be negative.

ARIZE: M O D E L L I N G EXPORT PRICES 23

TABLE 2

Estimated Export Price Elasticities of Supply (Total Exports: Annual Data, 1960-1982)

Country Supply Price Elasticity

Ivory Coast +.92 (+.51) Tunisia +.65 (+.78) Morocco +.34 (+.52) Kenya +2.2 (+2.3) Upper Volta + ~ ( + ~ ) a

Zambia + 1.5 (+.99) Mauritius +.86 (+.50) Malawi +.66 (+.80)

Notes: Estimates (not in parentheses) are the long run supply price elasticities calculated for each country for the estimated coefficients of equation (I0). Those in parentheses have been calculated from the estimated coefficients of equation (12)--these estimates from Browne's equation do not change the basic conclusion of this paper. The supply estimates are from statistically stable equations. aN = infinity.

relative price has no effect on the world demand for Indian exports. The Houthakker and Magee [1969] study shows demand price elasticities of- - .09 , - - .18 , - .70 , and +83 for Chile, Columbia, Peru, and Venezuela, respectively. Khan [1974] reports demand price elasticities o f - . 4 4 for Ghana. For Morocco, Khan reports an estimate of -.70, which is similar to the estimate in Table 1 above. Gafer [1981, p. 161] has obtained a demand price elasticity of - .30 and an income elasticity of .58 for Jamaica.

In a recent study, Bahmani-Oskooe [1984, p. 16t] obtained insignificant demand price elasticities for the three countries examined in that study, namely, +.267 for Korea, - . t 1 for South Africa, and - .32 for Thailand. The study concludes that relative prices, on the average, have a weak effect on the exports of these countries.

The data in Table 2 are the estimated long run supply price elasticities of equations (10) and (12). These estimates also yield useful information. The estimated coefficient of exports, (X~t), is positive and significantly different from zero in seven of the eight

countries in Table 2, implying a positively sloped supply function for exports in each of these countries. The exception is Upper Volta, where the estimated coefficient on exports is not significantly different from zero--a finding that can be interpreted as suggesting that Upper Volta's export production is infinitely elastic with respect to export prices.

An estimate of the aggregate export supply with respect to price was calculated as the inverse of the estimated coefficient on X, As can be seen, these elasticities show a rather wide variation across countries as in Goldstein and Khan [1978]. For example, if Upper Volta is excluded, the elasticities range from a low of .34 for Morocco to a high of 2.2 for Kenya.

Unfortunately, there is only one estimate of export supply elasticity for a third world country that is available in the literature with which to compare the estimates in Table 2. Ali [t984] reports a long run supply price elasticity of +1.8 for India, a result consistent with the estimates in Table 2.

24 ATLANTIC ECONOMIC JOURNAL

IV. Conclusion

Previous studies on the behavior of exports have tended to ignore the simultaneous relationship between the quantity of exports and their prices [Goldstein and Khan, 1978]. In this study, an explicit account of this simultaneity has been made by specifying statistically stable, well-defined models of export demand and supply.

In many developing economies, govern- ments need considerable information in order to review their export pricing and support policies. This paper presents evi- dence from aggregate export demand and supply for a number of African countries. It is found that for a majority of the countries, the export or relative price variable has the expected negative sign; however, the variable was statistically significant in only three out of the eight countries. The implication of this general result is that these primary commod-

ity exporters face an inelastic demand schedule and that, for the most part, price variations do not affect the quantity of exports demanded by the rest of the world.

On the supply side, there is a fairly large positive response in the quantity of exports to changes in export prices. The implication that emerges from this positively sloped supply function is that the relative profitabil- ity of producing for the export market is the constraint for export supply. A package of changes may elicit a quite different response from farmers than a price change alone.

The findings of this paper suggest that the supply price elasticities facing an individual country may not be infinite. In that context, simultaneous estimation takes on an added significance. The aggregate nature of the paper and the paucity of the number of observations constitute the major shortcom- ings.

REFERENCES

Ifzal Ali, "Estimating the Determinants of Export Supply in India," The lndian Economic Journal, 3t, 1984, pp. 1-12.

Moshen Bahmani-Oskooee, "On the Effect of Effective Exchange Rates On Trade Flows," Indian Journal of Economics, LXV, July 1984, pp. 57-67.

Francis X. Browne, "Modeling Export Prices and Quantities In a Small Open Economy," Review of Economics and Statistics', LXIV, May 1982, pp. 346-7.

James A. Dunlevy, "A Test of the Capacity Pressure Hypothesis Within a Simultaneous Equations Model of Export Performance," Review of Economics and Statistics, 62, February 1980, pp. 131-5.

M. Durra, "Measuring the Role of Price in Interna- tional Trade: Some Further Tests," Econometrica, 3, 1965, pp. 600-07.

J. U. Farley and M. J. Hinich, "A Test for a Shifting Slope Coefficient in a Linear Model," Journal of American Statistical Association, 65, 1970, pp. 1320-29.

J. U. Farley, M. J. Hinich, and T. W. McGuire, "Some Comparisons of Tests For a Shift in the Slope of a Multivariate Linear Time Series Model," Journal of Econometrics, 3, 1975, pp. 297-318.

John Gafer, "Devaluation and the Balance of Payments Adjustment In a Developing Economy: An Analysis Relating to Jamaica: 1954-1972," Applied Economics, June 1981, pp. 151-65.

Morris Goldstein and Mohsin Khan, "The Supply and Demand for Exports: A Simultaneous Approach," Review of Economics and Statistics, 60, May t978, pp. 275-86.

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of U.S. Trade to Income: An Evaluation of Traditional Models," Review of Economics and Statistics, 65, February 1983(a), pp. 87-95.

_ _ , "Specification of Supply Behavior in International Trade," Review of Economics and Statistics, 65, 1983(b), pp. 626-3 I.

Hendrik S. Houthakker and Stephen Magee, "In- come and Price Elasticities in World Trade," Review of Economics and Statistics, 51, 1969, pp. t 11-25.

Hendrik S. Houthakker and Lester Taylor, Consumer Demand in the United States, Cambridge: Harvard University Press, 1970.

M. S. Khan, "Imports and Export Demand in Developing Countries," IMF Staff Papers, 2t, t974, pp. 412-18.

_ _ and Knud Z. Ross, "Cyclical and Secular Income Elasticities of the Demand for Imports," Review of Economics and Statistics, 57, 1975, pp. 357-61.

Edward E. Leamer and Robert Stern, Quantitative International Economics, Boston: Allyn and Bacon, Inc., 1970.

S . P: Magee, "Prices, Income, and Foreign Trade: A Survey of Recent Economic Studies," in P. B. Kenen, ed., International Trade and Finance: Frontiers for Research, Cambridge: Cambridge University Press, 1975, pp. 175-252.

J. F. Wilson and Wendy Takacs, "Differential Responses to Price and Exchange Rate Influence in the Foreign Trade of Selected Industrial Countries," Review of Economics and Statistics, 61, May 1979, pp. 267-79.

Documents

Modelling export prices and quantities in selected developing economies