Production analysis with asymmetric noise

Abstract

Symmetric noise is the prevailing assumption in production analysis, but it is often violated in practice. Not only does asymmetric noise cause least-squares models to be inefficient, it can hide important features of the data which may be useful to the firm/policymaker. Here, we outline how to introduce asymmetric noise into a production or cost framework as well as develop a model to introduce inefficiency into said models. We derive closed-form solutions for the convolution of the noise and inefficiency distributions, the log-likelihood function, and inefficiency, as well as show how to introduce determinants of heteroskedasticity, efficiency and skewness to allow for heterogenous results. We perform a Monte Carlo study and profile analysis to examine the finite sample performance of the proposed estimators. We outline R and Stata packages that we have developed and apply to three empirical applications to show how our methods lead to improved fit, explain features of the data hidden by assuming symmetry, and how our approach is still able to estimate efficiency scores when the least-squares model exhibits the well-known “wrong skewness” problem in production analysis. The proposed models are useful for modeling risk linked to the outcome variable by allowing error asymmetry with or without inefficiency.