A general approach for estimating the translog function in the presence of zero-value agruments

The transcendental logarithmic (translog) function is a familiar choice in applied econometric work. It has been shown to exhibit superior approximations to unknown direct and indirect economic objective functions (Driscoll; Guilkey, Knox Lovell and Sickles; Stem). Fitting the translog function to consumer or firm level micro-data can encounter zero values for some function arguments. For example, a subset of consumers may not purchase strictly positive quantities of all goods in a choice set, or firms may be observed to employ a subset of available inputs in production. Because the natural logarithm is undefined at zero, the translog function cannot be estimated directly. To facilitate the logarithmic transformation, researchers typically modify zero-value arguments by either replacing them with arbitrarily small values or by applying the Box-Cox transformation.