metadata: authors: 0: author: Clavijo, Fernando
1: author: Faini, Riccardo
docna: 0: docna: Differentiating cyclical and long-term
            income elasticities of import demand
docty: Policy Research Working Paper
subtopic: Trade Policy,International Trade and Trade Rules,Rules of Origin,Trade and Services,Natural Disasters,Trade and Multilateral Issues
teratopic: Poverty Reduction
abstracts: cdata!: Determining how imports react to
            cyclical and secular (long term) factors has been a
            recurrent theme in the empirical trade literature. The
            evidence suggests that cyclical income elasticities of
            import demand are generally higher than long term
            elasticities - particularly for basic materials and
            semi-manufactured goods. Traditional models generally
            underestimate the cyclical response in imports, and
            overestimate the long term response. For example, estimates
            of income elasticity using a traditional import model
            average 1.4 and 1.2 respectively. The authors' model
            suggests a cyclical elasticity averaging 2.6. This result
            suggests that the two elasticities may differ by an even
            larger factor for developing countries. Relative prices
            generally are more important in determining import demand in
            Latin America and Asian-Pacific countries, in this model,
            but seem to have little effect in the African and
            (surprisingly) Mediterranean countries. In countries for
            which both cyclical and long-term income elasticities are
            significantly different from zero, relative price
            coefficients are also significantly different than in
            countries for which income parameters are not significantly
            different from zero.
repnme: repnme: Differentiating cyclical and long-term
            income elasticities of import demand
display_title: Differentiating cyclical and
            long-term income elasticities of import demand
listing_relative_url: /research/1989/05/700524/differentiating-cyclical-long-term-income-elasticities-import-demand
topicv3: Trade m1326924 698,Trade in Services m1326928 780,Trade Policy and Integration m1327407 775,Trade Policy m1327640 776,Quantitative Restrictions m1504269 2564
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Poverty Reduction
origu: Policy Plan & Prog Review Dept
no_of_pages: 18
model_extractions: # **Plc,Planning, and Researckn**

# **Trade Policy**

How do imports react to cyclical and secular (long-term) factors? the evidence suggests that cyclical income elasticities of import demand are generally higher than long-term elasticities - particularly for basic materials and semimanufactured goods.

Traditional models for import demand generally underestimate the cyclical respcnse in imports, and overestimate the long-term response. This has important implications for forecasting short-term import flows in developing countries. For example, estimates of income elasticity using a traditional import model developed by Pritchett and Bahmani-Oskooee average 1.4 and 1.2 respectively.

Clavijo and Faini's model suggests a cyclical elasticity averaging 2.6. Khan and Ross foun2d for a sample of 14 industrial countries that cyclical income elasticity averaged about 40 percent higher than trend income elasticity. The authors' results suggest that the two elasticities may differ by an even larger factor for developing countries.

Relative prices generally are more important in determining import demand in Latin America and Asian-Pacific countries in Clavijo and Faini's sample, but seem to have I. Ie effect in the African and (perhaps surprisingly) Mediterranean countries. In countries for which both cyclical and long-term income elasticities are significantly different from zero, relative price coefficients are also significantly different than in countries for which income parameters are not significantly different from zero. Including the cyclical component in the model seems to improve not only the fit but also the performnance of the equation.

This paper is a product of the Trade Policy Division, Country Economics Department. Copies are available free from the World Bank, 1818 H Street NW, Washington DC 20433. Please contact Karla Cabana, room N8-065, extension 61539.

The PPR Working Paper Series disseminates **the** findings of work under way in the Bank's Policy, Planning, and Rcsearch Complex. An objective of the series is to get these findings out quickly, even if presentations are less than fully polished. The findings, interpretations, and conclusions in these papers do not necessarily represent official policy of the Bank.

Produced at the PPR Dissemination Center
# CYCLICAL AND SECULAR INCOME ELASTICITIES OF IMPORT DEMAND FOR DEVELOPING COUNTRIES

Fernando Clavijo (The World Bank)

# and

Riccardo Faini (Johns Hopkins University) The authors are very grateful to John Holsen for pointing nut the importance of differentiating cyclical and secular income elasticities of import demand and for recommending the analysis of this issue for the case of developing countries. We would also like to thank Jaime de Melo and Bela Balassa for their penetrating comments.
# CYCLICAL AND SECULAR INCOME ELASTICITIES OF IMPORT DEMAND FOR DEVELOPING COUNTRIES

# I. Introduction

Determining how imports react to cyclical (short-run) and secular (long-run) factors has been a recurrent theme in the empirical trade literature. The aggregate evidence for several countries shows that cyclical income elasticities of import demand are generally higher than secular elasticities (see Khan and Ross, 1975). This difference is particularly pronounced for basic materials and semimanufactured goods (see Marston 1971, and Deepler and Ripley 1978). More recently, using spectral analysis, Haynes and Stone (1983) provided further evidence that business cycle income demand elasticities generally exceed secular ones. These findings imply that the income elasticity of import demand will not be cor-stant but will vary over the business cycle. As Magee (1975) argues, traditional specifications of import equations by assuming income elasticity of import demand to be constant will generally produce biased estimates of both cyclical and secular elasticities.

Much of the previous evidence applies only to developed countries. Little evidence is available for developing countries on the response of import flovs to cyclical and secular factors. Yet, the characteristics of the production structure in these countries make it likely that cyclical income elasticities will be relatively higher than in developed countries. These characteristics include, in general, a less integrated industrial structure, a lower supply responsiveness even under conditions of idle capacity due to the rigidities and distortions prevailing on those countries, as well as the presence of constraining bottlenecks in key sectors or steps in the production prucess. Other factors that also make
- 2 -

it likely that imports will react swiftly in the short run to increases in demand i!nclude the composition of imports, which is heavily weighted toward capital and intermediate goods, and the possibility that prices do not fully adjust to market disequilibria.

This paper draws on Khan and Ross (1975) to estimate an import demand equation in which secular and cyclical income elasticities of import demand are not constrained to be the same. Estimates were conducted for a sample of 43 developing countries. Section II presents the model and discusses the estimation technique. The econometric results are presented in section III followed by some conclusions that draw on the empirical evidence presented here.

# II. Model and Estimation Technique

Following Khan and Ross (1975) it is assumed that secular import demand is a function of trend income and relative prices, while cyclical demand for foreign goods also depands on actual income. If we also postulate a partial adjustment mechanism for short-run import demand, we are left with a system of two equations: M(t) - ao+al Yc(t) + a2(Y(t)-YC(t)] + a3 PM(t)_PD(t)J + a4H(t-l) +e(t) E1l Y(t) - YC(t) + 9(t) - X(t)p + 1(t). (21 (21 where all variables are in log, M denotes imports, Y and Yc denote respectively actual and trend output, and pM and pD represent respectively the prices of import and domestic substitutes. Equation 1 determines imports, while equation 2 describes output as a deviation from its trend,
-3-

with the trend in turn depending on a set of explanatory variables (still to be detailed), X(t).<sup>1</sup> An estimation problem arises because yc is unobserved. A procedure commonly used to deal with this problem (Barro 1977, 1978) and that adopted by Khan and Ross (1975) is to estimate equation 2 first, using the fitted values and the residuals from the regression of Y on X as a proxy for yc and y_yc respectively. A problem with this two-step procedure is that it will not lead to a consistent estimate of the coefficients' variance-covariance matrix (Pagan 1984, ch. 3).2 Only for the coefficient of the estimated residual, a2, does the two-step procedure allow for the recovery of a correct estimate of its standard error (Pagan 1984, ch. 7).

For the other coefficients, a different approach is needed. Substituting YC(t) - Y(t) - 1(t) in equation 1 yields: M(t) - aO+al(Y(t)-V(t)] + aZ 1(t) + a3(PH(t)_PD(t)] + a4M(t-l)+e(t) = aO+al Y(t) + a3(PM(t) PD(t)] + a4M(t-l)+e(t) + (a2-al)q(t) [3J Equation [3] resembles a fairly standard import demand equation. However, unless a1 - a2, plim T Y(t) 1(t) i 0 and equation 3 cannot be estimated by ordinary least-squares methods. A two-stage least-squares procedure with X(t), H(t-l), and PH(t) - 'D(t) as instruments must be used instead. This procedure obviously leads to a consistent estimate of the coefficients' variance-covariance matrix. It should be pointed out, towever, that the

- 1/ This is the approach taken by Artus (1973) and later by Khan and Ross (1975).

21 Also the two-step procedure is not always fully efficient in that it does not impose the restrictions that would arise from the joint estimation of equations 1 and 2.
cyclical income elasticity of import demand (a2) does not appear in the nonstochastic part of equation 3 and cannot therefore be estimated there. However, as already mentioned, the coefficient a2 can be estimated, together with a consistent estimate of its standard error, from the twostep procedure previously outlined. Applying separate estimation procedures for a, and a2 does not prejudge the possibility of testing whether cyclical and secular income elasticities are equal. A closer look at equation 3 reveals that a test of a1 . a2, under the maintained - assumption that COV ([(t), e(t)] 0, is equivalent to a test of independence between Y(t) and the error term. A standard Hausman-Wu procedure can be used for this purpose, which is the approach taken here.<sup>3</sup> The determinants X of Yc still need to be specified. Secular or trend GDP has been assumed to follow a segmented trend, with structural breaks occurring in 1974 and 1981.4 Hisspecification of this trend equation will result in inconsistent estimates of the coefficient a2, but will not affect the two-stage least-squares estimation of equation 3, except for an efficiency loss stemming from the choice of instrument.

- 3/ Our approach while drawing on Khan and Ross (1975) allows the recovery of a consistent estimate of the coefficient variancecovariance matrix. A different set-up such as that in Haynes and Stone (1983) would rely on spectral analysis, but the relatively small size of our sample precludes the use of this technique.

- 4/ A simple logarithmic function was used to generate the trend income variables. However, to allow for the impact of the external shocks that hit most developing countries during the estimation period, three subperiods were distinguished, each of them corresponding tentatively to a relatively constant growth rate. The first oil shock (1974) was taken as marking the beginning of the second period and the year following the 2-1/2 fold increase in oil prices (1981) as marking the beginning of the third period. The structural breaks in 1981 and 1974 were then found to be statistically significant for 90Z and 50Z, respectively, of our sample countries.
Measurement errors may be another source of inconsistency in our estimates. In particular the pervasiveness of quantitative restrictions and other import barriers in developing countries implies the need for a distinction between domestic and border prices of imports. Only the domestic price represents an accurate measure of import costs to domestic agents, but national account sourc.s usually rely on border prices information. This discrepancy in prices introduces an extra term into the error in equation 3 which, under a quota system, would be correlated with all the explanatory variables Y(t) and relative (border) prices, resulting again in inconsistent estimates.5 To assess the importance of this factor, two misspecification tests for dynamic simultaneous equation models, the Sargan (1964) and the Godfrey (1976) tests, were used. The Sargan test provides a statistical check on whether errors and instruments are independent, while the Godfrey test is for serial correlation of the error term.

# III. The Results

The model presented in the previous section was applied to a set of developing countries, using annual data for GDP, imports of goods and nonfactor services, and implicit prices for the period 1967-1987. The results are presented in table 1. The cyclical elasticity of income a2 was separately estimated using the two-step least-squares procedure. All the other coefflcients come from the two-stage least-squares (TSLS) estimation of equation 3.

- 5/ This can be easily seen as follows. Suppose that the supply of foreign exchange is not infinitely elastic. Then an increase in Yt will result in a higher domestic price of imports even if border prices remain unchanged.
- 6 -

An interesting result is that, even after a small sample correction, 27 of the 43 countries passed the misspecification tests, even though quantitative import restrictions are pervasive in developing countries. For the remaining sixteen countries the presence of serially correlated errors (coupled with a lagged dependent variable) and/or the endogeneity of some of the instruments are a source of inconsistent estimates, perhaps suggesting a significant effect of restrictive import policies. In what follows, results are reported only for the countries that passed both misspecification tescs.

The results in table 1 point to some important conclusions. Secular income appears to be a major determinant of import flows. Its coefficient _is_ statistically different from zero in 22 of the 27 countries. Excluding insignificant values, it ranges from 0.33 (for El Salvador) to 1.9 (for Uruguay). The mean of the 27 countries is 0.74, which is significantly lower than the means cited in Bahmani-Oskooee (1986) and in Pritchett (1987) who do not distinguish between secular and cyclical responses. Yet such a distinction is highly relevant. Among the countries that passed the misspecification tests, the values of the cyclical income coefficients average more than twice the values of the secular income coefficients when both elasticities are significantly different from zero. Cyclical income coefficients were higher from secular coefficients for 18 of the 27 countries. More formally the Hausman test indicates that secular income elasticities differ significantly from their cyclical counterparts for 13 countries, 11 of which show a higher value for cyclical elasticity.6 In interpreting these results, it must be recalled that they may reflect to 6/ To allow to some extent for the low power of the Hausman test, the critical value of the significance level is taken to be 20 percent.
some extent the low power of the Hausman test (Holly 1982). Failure to take this into account may lead to underestimation of the number of countries for which secular and cyclical income elasticities differ.<sup>7</sup> These results also illustrate how the traditional model may overestimate the secular response and underestimate the cyclical one, which has important implications for forecasting short-run import flows in developing countries. Thus, for example, estimates of income elasticity using a traditional import model developed by Pritchett (1987) and BahmaniOskooee (1986), average 1.4 and 1.2, respectively. The results presented here, however, suggest a cyclical elasticity averaging 2.6. It is not surprising therefore that imports are generally underestimated in shortterm projections of cyclical upturns in developing countries.

The results presented in table 1 indicate that relative prices generally play an important role in determining import demand in the Latin American and Asian-Pacific countries in our sample, but appear to be of little consequence in the African and (perhaps surprisingly) Mediterranean countries of our sample. It is interesting to note that for all countries for which both cyclical and secular income elasticities are significantly different from zero, relative price coefficients are also significantly

- 7/ Results using spectral analysis as in Haynes and Stone (1982) and Marquez (1988) illustrate that the ambiguity of the interpretation of both cyclical and secular income elasticities cannot be fully overcome when using income trend and deviation from trend as proxies for secular and cyclical income. In addition, the well-known Monte Carlo experiments showed long ago that spectral analysis requires long time seiles data in order to be reliable. This sample size precludes the use of spectral analysis in the case of most developing countries because although quarterly and/or monthly trade flows are usually available, the unavailability of prices is generally a binding contraint.
different from zero, whereas when income parameters are not significant, relative price parameters are also not significant. Interestingly, a comparison of the results presented here with those of a traditional import demand equation (see Pritchett 1987) shows that price elasticities generally appear to be higher when both cyclical and secular income elasticities are significantly different from zero, suggesting perhaps that the inclusion of the cyclical component improves not only the fit but also the performance of the equation.

Finally, it is instructive to compare these results with the evidence for developed countries. Khan and Ross (1975) found for a sam' of 14 industrial countries that the cyclical income elasticity was on average about 40 percent higher than the trend income elasticity. The findings presented here suggest that the two elasticities may differ by a even larger factor for developing countries. It should be noted, however, that our results, while not strictly comparable because of different methodologies, are not much different quantitatively from the results presented in Haynes and Stone (1983), whose special analysis produced estimates of cyclical income elasticities for U.S. imports that are roughly double their secular estimates.

# IV. Conclusions

This examination of the response of imports in developing countries to cyclical and secular fluctuations in income found that observational errors and serially correl-ted residuals will often lead to inconsistent and thus unreliabl **e** stimates. Both problems may be traced to
-9-

the restrictive trade regime prevailing in many developing countries.8 As a result, careful testing is essential for assessing the reliability of the estimated coefficients.

On a more substalAtive note, for two-thirds of our sample countries the cyclical income elasticity is higher than the secular one and that for more than one-third of the sample the difference is statistically significant. Only for two countries is the secular income elasticity of import d-mand significantly higher than the cyclical one. This provides encouraging evidence for the claim that import demand in developing countries is relatively more responsive to short-run fluctuations in income.

On the issue of the influence of relative prices on import demand, the results show some regional differences, with relative prices playing an important role in Latin American and Asian-Pacific countries in the sample but having little effect in the African and Mediterranean countries. Countries for which both cyclical and secular income elasticities are significantly different from zero also have relative price coefficients that are significantly different from zero, while relative price parameters are not significant in countries for which income parameters are not significantly different from zero.

8/ Khan (1974) has argued that a restrictive trade regime may lead to serially correlated errors. Also, as mentioned earlier, the presence of quantitative restrictions on imports will introduce a wedge between border and domeatic prices of imports and, if only the first variable is observed, reault in an error-in-variable problem.
TABLE 1: IMPORT PARAMETERS

|Region/<br>Country|Price<br>Elasticity|Secular<br>Income<br>7lastic"'ty|Cyclical<br>Income<br>Elasticity|import<br>t-l|12|SE|Sargan|Godfrey|Rnsu=n|
|---|---|---|---|---|---|---|---|---|---|
|Latin Ame<br>&Caribb|rica<br>ean|||||||||
|ARG|-7.54<br>-(6.62)|1.403<br>(6.86)|1.638<br>(2.80)|.233<br>(2.40)|.89|.147|2.44|2.379|.30|
|COL|-. 499<br>-(2.44)|1.263<br>(9.15)|2.391<br>(2.82)|-|.95|.17|2.54|1.83|1.33|
|CRI|-. 514<br>-(6.15)|.424<br>(2.78)|1.224<br>(3.18)|.561<br>(4.78)|.97|.07|3.42|3.39|3.59|
|ECU|.385<br>-(1.12)|-. 152<br>-(.39)|.717<br>(1.36)|.962<br>(3.11)|.91|.27|3.76|.07|2.13|
|JAM|-. 314<br>-(5.68)|1.232<br>(7.59)|1.289<br>(6.37)|-|.86|.08|1.72|.98|.98|
|MEX|-1.044<br>-(7.60)|1.213<br>(16.51)|.477<br>(.75)|-|.93|.24|3.59|3.59|.41|
|PER|-. 646<br>-(3.03)|.522<br>(1.90)|2.309<br>(2.93)|.530<br>(3.41)|.66|.323|6.56|4.27|2.71|
|PRY|-. 478<br>-(1.80)|.672<br>(1.97)|.985<br>(2.13)|.549<br>(2.78)|.98|.158|2.32|.22|1.18|
|SLV|-. 286<br>-(1.03)|.328<br>(.72)|1.382<br>(4.02)|.713<br>(2.64)|.83|.19<br>a|1.95|.71|2.50|
|URY|-. 368<br>-(4.71)|1.864<br>(7.62)|.991<br>(2.62)|.160<br>(1.48)|.95|.083|5.04|5.00|1.70|
TABLE 12 IMPORT PARAMETERS (cont.)

|Country|Price<br>Elasticity|Secular<br>Income<br>Elasticity|Cyclical<br>Income<br>Elasticity|Import<br>t-|12|SE|Sargan|Godfrey|Hausmmn|
|---|---|---|---|---|---|---|---|---|---|
|Africa||||||||||
|BENIN|.068<br>(.15)|-. 114<br>-(.32)|1.640<br>(1.43)|.831<br>(5.63)|.84|.49|4.36|.95|1.63|
|CAP|-. 947<br>-(4.97)|.628<br>(3.20)|.048<br>(.08)|-|.71|.17|1.95|.056|1.23|
|GMB|-1.034<br>-(3.21)|1.283<br>(4.14)|.775<br>(1.55)|.299<br>(1.68)|.77|.15|.013|.013|.86|
|SEN|-. 282<br>-(1.29)|1.307<br>(2.74)|1.381<br>(1.49)|.460<br>(2.35)|.87|.14|7.67|.49|.35|
|Mediterrane|an|||||||||
|EGY|.518<br>(2.96)|.563<br>(4.17)|-. 478<br>-(.99)|-|.90|.11|2.87|1.55|1.86|
|GRC|-. 028<br>-(.14)|1.404<br>(21.79)|1.415<br>(4.54)|-|.98|.07|5.93|3.37|.025|
|ISR|-. 195<br>-(.85)|.344<br>(.98)|.944<br>(1.79)|.686<br>(2.72)|.96|.14|3.20|.42|1.48|
|LBY|-1.194<br>-(19.47)|1.004<br>(5.26)|.485<br>(2.42)||.97|.15|2.13|2.13|1.48|
|MAR|-. 267<br>-(.93)|.510<br>(1.12)|-. 761<br>-(.74)|.638<br>(2.56)|.89|.25|5.89|1.03|.05|
|SYR|.104<br>(.61)|1.480<br>(26.21)|1.312<br>(3.22)|-|.98|.21|3.83|.018|.02|
|YUG|-. 777<br>-(6.63)|1.044<br>(10.81)|1.572<br>(2.43)|-|.85|.12|3.76|3.75|1.16|
# TABLE 1: IMPORT PARAMETERS (cont.)

|Country|Price<br>Elasticity|Secular<br>Income<br>Elasticity|Cyclical<br>Income<br>Elasticity|Import<br>t-l|1<sup>2</sup>|SE|Sargan|Godfrey|Hausuan|
|---|---|---|---|---|---|---|---|---|---|
|Asia Paci|fic|||||||||
|BGD|-.084<br>-(.32)|1.385<br>(4.81)|2.515<br>(3.86)|-|.69|.74|1.45|1.45|1.62|
|IND|-.325<br>-(1.82)|1.067<br>(4.71)|.045<br>(.03)|-|.62|.15|.48|.48|.68|
|KOR|-.405<br>-(2.11)|.407<br>(2.05)|1.291<br>(2.16)|.644<br>(5.32)|.99|.09|1.24|1.24|1.60|
|MYS|-.428<br>-(1.35)|.623<br>(2.96)|2.288<br>(5.67)|.541<br>(3.51)|.98|.128|1.65|1.28|3.48|
|PAK|-.556<br>-(5.53)|.997<br>(7.33)|2.715<br>(2.55)|-|.73|.22|2.59|2.59|1.23|
|PHL|-.250<br>-(1.54)|1.012<br>(10.70)|1.824<br>(5.68)|-|.92|.14|2.43|2.08|2.90|

Note: t statistics are in parentheses.