Regularized conditional estimators of unit inefficiency in stochastic frontier analysis,with application to electricity distribution market

In stochastic frontier analysis, the conventional estimation of unit inefficiency is based on the mean/mode of the inefficiency, conditioned on the composite error. It is known that the conditional mean of inefficiency shrinks towards the mean rather than towards the unit inefficiency. In this paper, we analytically prove that the conditional mode cannot accurately estimate unit inefficiency, either. We propose regularized estimators of unit inefficiency that restrict the unit inefficiency estimators to satisfy some a priori assumptions, and derive the closed form regularized conditional mode estimators for the three most commonly used inefficiency densities. Extensive simulations show that, under common empirical situations, e.g., regarding sample size and signal-to-noise ratio, the regularized estimators outperform the conventional (unregularized) estimators when the inefficiency is greater than its mean/mode. Based on real data from the electricity distribution sector in Sweden, we demonstrate that the conventional conditional estimators and our regularized conditional estimators provide substantially different results for highly inefficient companies.

     

On the median regression for SURE models with applications to 3-generation immigrants data in Sweden

In this paper we generalize the median regression method to be applicable to system of regression equations, in particular SURE models. Giving the existence of proper system wise medians of the residuals from different equations, we apply the weighted median regression with the weights obtained from the covariance matrix of the equations obtained from ordinary SURE method. The benefit of this model in our case is that the SURE estimators utilise the information present in the cross regression (or equations) error correlation and hence more efficient than other estimation methods like the OLS method. The Seemingly Unrelated Median Regression Equations (SUMRE) models produce results that are more robust than the usual SURE or single equations OLS estimation when the distributions of the dependent variables are not normally distributed or the data are associated with outliers. Moreover, the results are also more efficient than is the cases of single equations median regressions when the residuals from the different equations are correlated. A theorem is derived and indicates that even if there is no statistically significant correlation between the equations, using SUMRE model instead of SURE models will not damage the estimation of parameters.