Consistent method of moments estimation of the true fixed effects model

- We propose method of moment estimation of 'True' fixed effects models.
- We show consistency of the estimators of the normal-half-normal and the normal-gamma models.
- We derive asymptotic normality results.
- Monte Carlo simulations support the theoretical findings.

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.