Quantile Regression Analysis of Asymmetrically Distributed Residuals in Consumer Demand Equations

Abstract

Apart from examining for autocorrelation and heteroscedasticity, applied econometricians seldom give much attention to the properties of the stochastic terms of their regression models. Most of the time, least-squares estimation (in some form or another) is employed, based upon a belief (often no more than implicit) that the conditions needed for the validity of the Gauss-Markov and Classical Normal Central-Limit Theorems are ever present. In fact, there are a lot of reasons as to why real-world error terms may not behave in ways that these conditions require. Residuals from Engel curves and demand functions estimated from data from the BLS quarterly consumer expenditure surveys provides a rather striking instance of this, in that the distribution of these residuals are almost invariably asymmetrical and fat-tailed. The focus of the present exercise is on the use of quantile regression as a robust corrective.