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We consider method-of-moments fixed effects (FE) estimation of technical inefficiency. When dealing with a large number of cross-sectional observations, N, it is possible to obtain consistent moment estimators of the inefficiency distribution. It is well known that the classical FE estimator may be seriously upward biased when N is large and T, the number of time observations, is small. The method-of-moments FE estimators do not suffer from this type of bias in large-N settings. The proposed methodology bridges classical FE and maximum likelihood estimation, leading to a reduction in bias without making the random effects assumption.

The fixed effects (‘FE’) estimator of technical inefficiency performs poorly when N (the ’number of firms’) is large and T (the ‘number of time observations’) is small. We propose kernel estimators, which includes the FE estimator as a special case. In terms of criteria based on collective conditional ‘mean square error’, it is demonstrated that some kernel estimators are more efficient than the FE estimators of firm effects and inefficiencies in finite sample settings. Monte Carlo simulations support our theoretical findings, and we use an empirical example to show how FE estimation and kernel estimation lead to very different conclusions about technical inefficiency among Indonesian rice farmers.

This is a note about proxy variables and instruments for identification of structural parameters in regression models. We have experienced that in the econometric textbooks these two issues are treated separately, although in practice these two concepts are very often combined. Usually, proxy variables are inserted in instrument variable regressions with the motivation they are exogenous. Implicitly meaning they are exogenous in a reduced form model and not in a structural model. Actually if these variables are exogenous they should be redundant in the structural model, e.g. IQ as a proxy for ability. Valid proxies reduce unexplained variation and increases the efficiency of the estimator of the structural parameter of interest. This is especially important in situations when the instrument is weak. With a simple example we demonstrate what is required of a proxy and an instrument when they are combined. It turns out that when a researcher has a valid instrument the requirements on the proxy variable is weaker than if no such instrument exists

About a decade ago William H. Greene introduced the so-called ‘True fixed effects’ (TFE) model, which is intended to discriminate between heterogeneity and efficiency in stochastic frontier analysis. We would say that the TFE model has had a huge impact on applied stochastic frontier analysis. One problem with the original TFE estimator, is its inconsistency in cases with finite time observations, at least for the variance components. For the normal-half-normal model, this problem was solved by Chen et al. (2014) based on maximum likelihood estimation of the within-transformed model. In this study, we illustrate the possibilities offered by method of moments estimation. This approach is more flexible than the MLE proposed by Chen et al. (2014), since the method of moments estimators are not so closely dependent on the distributional assumptions and do not hinge on an explicit distribution of the random error. We only assume symmetry, as well as a fixed fourth-order cumulant for more complicated models. Greene’s methodology can, and has been, generalized to other models than the normal-half-normal model. However, the method of moments estimators proposed here are consistent.