This paper proposes a variant of the classical HAUSMAN specification test commonly employed to decide whether the estimation of a random-effects model is a viable alternative to estimating fixed effects. Whereas the classical test probes the equality of fixed- and random effects, the proposed variant focuses on the equality of between-groups and fixed-effects coefficients. While both test procedures lead to the same conclusions, the panel model specification underlying our testing strategy facilitates the simultaneous estimation of the fixed- and between-groups effects. As a consequence, we are able to examine both the equality of the whole range of coefficients as well as that of individual variables. The usefulness of the test is illustrated using a panel of household travel data for Germany.