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Accounting for time-varying unobserved heterogeneity poses a fundamental challenge for empirical finance research. We show how grouped fixed effects (GFE) models capture such heterogeneity and illustrate their merits over conventional panel data models used in finance applications. We propose a new Hausman-type specification test to select among fixed effects models, and show that it differs from standard Hausman statistics precisely due to the presence of the time-varying group heterogeneity, which jointly depends on groups and time. We also develop an empirical design using a natural experiment to empirically explain the GFE group membership estimates. The empirical importance of GFE in finance is illustrated via a study on the relation between CEO characteristics and firm innovation.