DO ECONOMIC VARIABLES FOLLOW SCALE OR LOCATION-SCALE DISTRIBUTIONS?

Economics researchers often assume that random variables are drawn from distributions that are members of scale or location-scale families of distributions. This article generalizes earlier results in the literature on the bias in least squares estimates of multiplicative error models, and uses those results to construct a test of the scale and location-scale hypotheses. A Monte Carlo simulation shows that the test is powerful in large samples. The empirical relevance of these findings is illustrated with estimates of a supply function for U.S. wheat production. Implications for applied economics research are discussed. Key words: bias test, location-scale, multiplicative error, scale, wheat production. JEL codes: C12, C51. Throughout the applied economics literature, researchers often assume that random vari-ables are drawn from distributions that are members of scale or location-scale families of distributions.1 Why are these distributional assumptions so popular? One reason is that a multiplicative error is a convenient way to impose nonnegativity on a dependent variable such as a quantity produced or demanded. Scale and location-scale distributions are often parsimonious and convenient for theoretical as well as empirical analysis. The log-normal dis-tribution, a member of a scale family, often fits economic data well, and has been used exten-sively in applied economic research to repre-sent production functions, demand functions, and various other relationships. Perhaps the mostwidely used functional form in economics, the constant elasticity or Cobb- Douglas func-tion,is conveniently estimated in log formusing linear least squares or themaximum likelihood methodwhenamultiplicative error is assumed. Of course, the normal distribution is probabl