  We study linear panel regression models in which the unobserved error term is
an unknown smooth function of two-way unobserved fixed effects. In standard
additive or interactive fixed effect models the individual specific and time
specific effects are assumed to enter with a known functional form (additive or
multiplicative). In this paper, we allow for this functional form to be more
general and unknown. We discuss two different estimation approaches that allow
consistent estimation of the regression parameters in this setting as the
number of individuals and the number of time periods grow to infinity. The
first approach uses the interactive fixed effect estimator in Bai (2009), which
is still applicable here, as long as the number of factors in the estimation
grows asymptotically. The second approach first discretizes the two-way
unobserved heterogeneity (similar to what Bonhomme, Lamadon and Manresa 2021
are doing for one-way heterogeneity) and then estimates a simple linear fixed
effect model with additive two-way grouped fixed effects. For both estimation
methods we obtain asymptotic convergence results, perform Monte Carlo
simulations, and employ the estimators in an empirical application to UK house
price data.
