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We study linear panel regression models in which the unobserved error term isan unknown smooth function of two-way unobserved fixed effects. In standardadditive or interactive fixed effect models the individual specific and timespecific effects are assumed to enter with a known functional form (additive ormultiplicative). In this paper, we allow for this functional form to be moregeneral and unknown. We discuss two different estimation approaches that allowconsistent estimation of the regression parameters in this setting as thenumber of individuals and the number of time periods grow to infinity. Thefirst approach uses the interactive fixed effect estimator in Bai (2009), whichis still applicable here, as long as the number of factors in the estimationgrows asymptotically. The second approach first discretizes the two-wayunobserved heterogeneity (similar to what Bonhomme, Lamadon and Manresa 2021are doing for one-way heterogeneity) and then estimates a simple linear fixedeffect model with additive two-way grouped fixed effects. For both estimationmethods we obtain asymptotic convergence results, perform Monte Carlosimulations, and employ the estimators in an empirical application to UK houseprice data.

Linear Panel Regressions with Two-Way Unobserved Heterogeneity