Estimating export equations

Abstract

Accurate estimates of the price and income elasticities of exports are valuable for growth policies based on trade promotion. However, not sufficient attention seems to have been paid to the specification of the relative price variable in some influential empirical works. This article estimates the export equation for Fiji, to show that inappropriate specification of the relative price variable may give underestimates of the price elasticity and overestimates of the income elasticity.

Notes

¹ There is a vast amount of empirical literature, too many to cite in the references, on testing the export-lead growth policies. A search for literature from the home page of Applied Economics, listed 75 references on this topic published in that journal and other sister journals of Applied Economics. A useful survey of the literature on export-lead growth is in Giles and Williams (2000a, b).

² Senhadji (1998) and Dutta and Ahmed (2004) have ignored E in their equations for exports and imports, respectively. Some exceptions to such limitations are Muscatelli et al . (1995), Abbott and De Vista (2002) and Nowak-Lehmann (2004). Abbott and De Vista is a particularly interesting study and takes into account the simultaneous equations bias and imposes over-identifying restrictions implied by the underlying theory. More on this study later in this article.

³ A formal econometric proof is complicated because we have used nonlinear estimation methods. The approximate bias in OLS estimates can be computed by estimating three equations: (A) is the correct specification, (B) is the mis-specified equation and (C) is an auxiliary regression:

Maddala (1992) shows that the expected values of the estimated coefficients from the misspecified Equation B are: and . Thus, the magnitude of this bias depends on the coefficients in the auxiliary equation.

⁴ We have used a VAR(1) model, after determining its optimal order with both AIC and SBC. However, we faced problems with the Johansen JML procedure. The null that there is at least one cointegrating vector for Equation 2 could be accepted only at the 90% level by the trace test. For Equation 3 this null is accepted by both the eigenvalue and trace tests at the 95% level.

⁵ In the Johansen JML, it was necessary to use a restricted intercept in the VAR. Therefore, we have estimated the GETS equations with NLLS to allow for this restriction. However, the intercept was significant only in (2).

⁶  SS is found be I(1) with a long lag structure of 7 periods in the ADF test.

⁷ The insignificant bias in the relative price elasticity is due to a small value of 0.046 for γ ₁ in the auxiliary regression. In contrast, the estimate of γ₂ is 0.370 implying that income elasticity could be overestimated, in the misspecified equation, by about 40%. See footnote 2.