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We study a nonlinear two-way fixed effects panel model that allows for unobserved individual heterogeneity in slopes and flexibly specified link function. The former is relevant when the researcher is interested in the distributional causal effects of covariates, and the latter mitigates potential misspecification errors due to restrictions imposed on the link function. We show that the fixed effects parameters and the link function can be identified when both individual and time dimensions are large. We propose a novel iterative Gauss-Seidel estimation procedure that overcomes the practical challenge of dimensionality in the number of fixed effects when the dataset is large. We revisit two empirical studies in trade (Helpman et al., 2008) and innovation (Aghion et al., 2013), and find non-negligible unobserved dispersion in trade elasticity across countries and the effect of institutional ownership on innovation across firms. These exercises emphasize the usefulness of our method in capturing flexible heterogeneity in the causal relationship of interest that may have important implications for the subsequent policy analysis. This is joint work with Ao Wang (University of Warwick).
