Testing procedures for detection of linear dependencies in efficiency models

The validity of many efficiency measurement methods rely upon the assumption that variables such as input quantities and output mixes are independent of (or uncorrelated with) technical efficiency, however few studies have attempted to test these assumptions. In a recent paper, Wilson (2003) investigates a number of independence tests and finds that they have poor size properties and low power in moderate sample sizes. In this study we discuss the implications of these assumptions in three situations: (i) bootstrapping non-parametric efficiency models; (ii) estimating stochastic frontier models and (iii) obtaining aggregate measures of industry efficiency. We propose a semi-parametric Hausman-type asymptotic test for linear independence (uncorrelation), and use a Monte Carlo experiment to show that it has good size and power properties in finite samples. We also describe how the test can be generalized in order to detect higher order dependencies, such as heteroscedasticity, so that the test can be used to test for (full) independence when the efficiency distribution has a finite number of moments. Finally, an empirical illustration is provided using data on US electric power generation.