Regressions from Samples Having Different Characteristics

Abstract

Economists are sometimes interested in explaining variation in parameters estimated from samples having different characteristics. In this REVIEW Russell (1967) has explained Houthakker's (1957) country income elasticity of demand estimates by regressing these estimates on such country characteristics as consumption per capita and relative prices. Similarly, Wachter (1970) demonstrates that high wage, noncompetitive industries (by contrast with low wage, competitive industries) have a positive relation between their relative wages and unemployment by regressing the estimated coefficient of the unemployment term in a relative wage regression on concentration ratios and unionization variables. Elsewhere, Williamson (1971) explains differences in the sectoral speed of adjustment parameter with a regression using sectoral elasticities, sectoral capital growth rates and a time dummy, while Lave and Lave (1970) account for differences in individual hospital cost function parameters by regressing these parameters on a variety of time-invariant characteristics of individual hospitals. Regression analyses such as these raise at least two issues. First, a kind of a priori information is available on the dependent variables in these regressions. How can this information best be incorporated into the estimation procedure? Second, what is the meaning of the two-step procedure implicitly adopted by the above authors? How does this approach compare with methods that would estimate the observations on the dependent variable and simultaneously provide an explanation of their variation?