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Panel data models often use fixed effects to account for unobserved heterogeneities. These fixed effects are typically incidental parameters and their estimators converge slowly relative to the square root of the sample size. In the maximum likelihood context, this induces an asymptotic bias of the likelihood function. Test statistics derived from the asymptotically biased likelihood, therefore, no longer follow their standard limiting distributions. This causes severe distortions in test sizes. We consider a generic class of dynamic nonlinear models with two-way fixed effects and propose an analytical bias correction method for the likelihood function. We formally show that the likelihood ratio, the Lagrange-multiplier, and the Wald test statistics derived from the corrected likelihood follow their standard asymptotic distributions. A bias-corrected estimator of the structural parameters can also be derived from the corrected likelihood function. We evaluate the performance of our bias correction procedure through simulations and an empirical example.

Statistical and structural modeling represent two distinct approaches to data analysis. In this paper, we propose a set of novel methods for combining statistical and structural models for improved prediction and causal inference. Our first proposed estimator has the doubly robustness property in that it only requires the correct specification of either the statistical or the structural model. Our second proposed estimator is a weighted ensemble that has the ability to outperform both models when they are both misspecified. Experiments demonstrate the potential of our estimators in various settings, including fist-price auctions, dynamic models of entry and exit, and demand estimation with instrumental variables., Comment: arXiv admin note: substantial text overlap with arXiv:2004.12601

We propose a novel method for modeling data by using structural models based on economic theory as regularizers for statistical models. We show that even if a structural model is misspecified, as long as it is informative about the data-generating mechanism, our method can outperform both the (misspecified) structural model and un-structural-regularized statistical models. Our method permits a Bayesian interpretation of theory as prior knowledge and can be used both for statistical prediction and causal inference. It contributes to transfer learning by showing how incorporating theory into statistical modeling can significantly improve out-of-domain predictions and offers a way to synthesize reduced-form and structural approaches for causal effect estimation. Simulation experiments demonstrate the potential of our method in various settings, including first-price auctions, dynamic models of entry and exit, and demand estimation with instrumental variables. Our method has potential applications not only in economics, but in other scientific disciplines whose theoretical models offer important insight but are subject to significant misspecification concerns.