In the first chapter, we consider GMM estimation when there are more moment conditions than observations. Due to the singularity of the estimated variance matrix of the moment conditions, the quick solution of using the generalized inverse, although temping, is shown to be unfruitful.

In the second and third chapters, we consider the problem of point estimation of technical inefficiency in a simple stochastic frontier model with panel data.

In the second chapter, we wish to correct the bias of the estimates of technical inefficiency based on fixed effects estimation that previously shown to be biased upward. Previous work has attempted to correct this bias using the bootstrap, but in simulations the bootstrap correct only part of the bias. The usual panel jackknife is based on the assumption that the bias is of order T^-1 and is similar to the bootstrap. We show that when there is a tie or a near tie for the best firm, the bias is of order T^-1/2, not T^-1, and this calls for a different form of the jackknife. The generalized panel jackknife is quite successfully in removing the bias. However, the resulting estimates have a large variance.

In the third chapter, we focus on how we could decrease the variance and MSE of a jackknife-type estimate of the frontier intercept found in the previous chapter. We consider the split-sample jackknife proposed by Dhaene, Jochmans and Thuysbaert (2006), which is simply two times the original estimate based on the whole sample minus the average of the two half-sample estimates, and the "generalized" version proposed by Satchachai and Schmidt (2008), which is relevant in the case of an exact tie or a near tie. Although these estimators also successfully remove the bias, their variance is still large. We also consider whether or not there is an "optimal" split-sample jackknife estimator that has small variance and/or small MSE. For a special case of N = 2, we derive the "optimal" weights for the original estimate and the half-sample estimates. Although the "optimal" split-sample jackknife has even smaller variance and MSE, it does not properly remove the bias, and it appears that there is not much gain in terms of mean square error from applying the jackknife procedure.