Fixed vs Random: The Hausman Test Four Decades Later

Hausman (1978) represented a tectonic shift in inference related to the specification of econometric models. The seminal insight that one could compare two models which were both consistent under the null spawned a test which was both simple and powerful. The so-called ‘Hausman test’ has been applied and extended theoretically in a variety of econometric domains. This paper discusses the basic Hausman test and its development within econometric panel data settings since its publication. We focus on the construction of the Hausman test in a variety of panel data settings, and in particular, the recent adaptation of the Hausman test to semiparametric and nonparametric panel data models. We present simulation experiments which show the value of the Hausman test in a nonparametric setting, focusing primarily on the consequences of parametric model misspecification for the Hausman test procedure. A formal application of the Hausman test is also given focusing on testing between fixed and random effects within a panel data model of gasoline demand.