Model specification in regression analysis

Abstract

One of the most important but least understood issues in all of regression analysis concerns model specification. Model specification refers to the determination of which independent variables should be included in or excluded from a regression equation. In general, the specification of a regression model should be based primarily on theoretical considerations rather than empirical or methodological ones. A multiple regression model is, in fact, a theoretical statement about the causal relationship between one or more independent variables and a dependent variable. Indeed, it can be observed that regression analysis involves three distinct stages: the specification of a model, the estimation of the parameters of this model, and the interpretation of these parameters. Specification is the first and most critical of these stages. Our estimates of the parameters of a model and our interpretation of them depend on the correct specification of the model. Consequently, problems can arise whenever we misspecify a model. There are two basic types of specification errors. In the first, we misspecify a model by including in the regression equation an independent variable that is theoretically irrelevant. In the second, we misspecify the model by excluding from the regression equation anindependent variable that is theoretically relevant.