Heteroskedasticity-robust elasticities in logarithmic and two-part models

Abstract

Logarithmic models are widely used to study highly skewed positive outcomes, either alone or in combination with an equation that first distinguishes between zero and nonzero values (the two-part model). A well-known drawback of such models is that to obtain marginal effects that pertain to the arithmetic mean, rather than the mean of logs, we must exponentiate, and this retransformation is complicated in the presence of heteroskedasticity. This article presents a simple method for correcting estimated elasticities for the effects of heteroskedasticity, in both log-linear and log-log (constant elasticity) equations. An example, drawing on Bulgarian farm survey data, demonstrates that this correction leads to significantly different estimates of the elasticity of expenditures on agricultural inputs with respect to land area and the age of the household head.

Notes

¹ This is the elasticity of the expected number of (say) households that will have positive expenditures, with respect to x_k .