However, it is possible to use a variety of distributions, such as half-normal, truncated normal and
exponential to model the one-sided error term [Greene 1993b].23 In addition, the estimates from the
frontier model can be compared to linear production function estimates to test whether our index is
particularly sensitive to the distributional assumptions. The inconsistency of the efficiency estimator is
more difficult to circumvent in cross-sectional models.24 Fortunately, the estimator is unbiased and the
inconsistency is caused by the fact that the variance is independent of the sample size. The endogeneity
issues are dealt with in detail in the following two subsections.
Specification Issues I: Endogenous Inputs in the Production Frontier
The direct estimation of production functions has been criticized because inputs are typically jointly
determined with the output [Mundlak 1961]. In the production frontier, the parameters as well as technical
efficiency may be inconsistently estimated if technically efficiency is correlated with inputs [Kumbhakar
1987, Kalirajan 1990, Kumbhakar et. al 1991].
The literature has responded to this issue in two ways. Many studies have invoked the well-
known arguments of Zellner et. al [1966] to assume that input choices are exogenous in an stochastic
agricultural production environment.25 However, as Kumbhakar [1987] points out, this assumption holds
only if technical efficiency is unknown to the farmer. A solution to the endogeneity problem is the joint
estimation of the frontier and its first order conditions in a profit maximizing framework [Kumbhakar 1987,
like this fishery, several other factors can affect technical efficiency in a larger, more diverse data set.
23 Semi-parametric methods that are independent of functional assumptions have not yet been developed.
24 Battese and Coelli [1988] develops a consistent estimator for panel data.
25 Two recent examples are Battese and Coelli [1995] and Kirkley et. al. [1998]. Greene [1993] surveys some of the
earlier papers.
29
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