The interpretation of multiple dummy variable coefficients: an application to industry effects in wage equations

Abstract

The traditional textbook approach to avoiding the dummy trap problem is to delete a category from each qualitative variable. This paper illustrates an alternative constraint which can be used to transform conventional dummy variable coefficients. This constraint serves to simplify their interpretation when the regression equation contains several qualitative variables and allows the computation of a coefficient for the deleted class. Using this constraint the intercept term can be written as the mean Y macron and the coefficients for the dummy variables are now interpreted as differences from the mean of the dependent variable rather than the deleted class. Computation of a standard error for the estimated coefficient of the deleted class is also discussed. An application to examine the importance of industry wage affiliation in explaining relative wages is presented.