The “wrong skewness” problem in stochastic frontier models: A new approach

Abstract

Stochastic frontier models are widely used to measure, e.g., technical efficiencies of firms. The classical stochastic frontier model often suffers from the empirical artefact that the residuals of the production function may have a positive skewness, whereas a negative one is expected under the model, which leads to estimated full efficiencies of all firms. We propose a new approach to the problem by generalizing the distribution used for the inefficiency variable. This generalized stochastic frontier model allows the sample data to have the wrong skewness while estimating well-defined and non-degenerate efficiency measures. We discuss the statistical properties of the model and we discuss a test for the symmetry of the error term (no inefficiency). We provide a simulation study to show that our model delivers estimators of efficiency with smaller bias than those of the classical model even if the population skewness has the correct sign. Finally, we apply the model to data of the U.S. textile industry for 1958-2005, and show that for a number of years our model suggests technical efficiencies well below the frontier, while the classical one estimates no inefficiency in those years.

Asymmetries in Business Cycles and the Role of Oil Prices

“…Lee (1993) showed that, in this case, the likelihood ratio statistic asymptotically follows a mixture of a χ 2 distribution with one degree of freedom and a point mass of 1/2 at zero. In the case of the extended model (5), Hafner et al (2016) show that, despite the fact that the information matrix is still singular at µ u = 0, the likelihood ratio statistic follows a standard χ 2 distribution because the parameter µ u is no longer on the boundary under the null hypothesis.…”

“…In practice, when the residuals have positive skewness, the maximum likelihood estimator will either fail to converge or will converge to a local maximum. A solution to this problem is proposed in Hafner et al (2016), which we adapt to our setting. We extend the distribution of u t to allow for negative values and extend its parameter µ u to lie in R. To be specific, when µ u < 0 we define the density of u t to be an exponential distribution mirrored onto the negative axis by reflecting it at zero.…”

“…We adapt it to estimate the extent of asymmetry in aggregate time series. Furthermore, we extend the model to allow for arbitrary signs of skewness following the approach suggested in Hafner et al (2016). We compare the restricted model without asymmetries to the unrestricted model using a likelihood ratio test.…”

The ‘wrong skewness’ problem: a re-specification of stochastic frontiers

“…To overcome this issue, several authors have proposed the use of distribution functions with negative asymmetry for inefficiency component. In partic-ular, Carree (2002) uses the Binomial probability function, Tsionas (2007) More recent attempts to obtain the desired direction of residual skewness are Feng et al (2013) where authors propose a finite sample adjustment to existing estimators and Hafner et al (2013) where authors use an artificial truncation.…”

The Impacts of Telecommuting on The Time-Space Distribution of Daily Activities

“…It is worth noting that recent work has been attempting to overcome the datarelated issues when using stochastic frontier analysis to estimate the morning terminal vertex as well as the evening origin vertex (Hafner, et al, 2015;Almanidis and Sickles, 2012).…”