Fixed Effects Estimation of Binary Choice Models with Three-Dimensional Panels: Theory and Application

Category: Quantitative Economic Policy Seminar
When: 22 January 2024
, 14:15
 - 15:15
Where: RuW 207

Talk based on:

Debiased Fixed Effects Estimation of Binary Logit Models with Three-Dimensional Panel Data


Naive maximum likelihood estimation of binary logit models with fixed effects leads to unreliable inference due to the incidental parameter problem. We study the case of three-dimensional panel data, where the model includes three sets of additive and overlapping unobserved effects. This encompasses models for network panel data, where senders and receivers maintain bilateral relationships over time, and fixed effects account for unobserved heterogeneity at the sender-time, receiver-time, and sender-receiver levels. In an asymptotic framework, where all three panel dimensions grow large at constant relative rates, we characterize the leading bias of the naive estimator. The inference problem we identify is particularly severe, as it is not possible to balance the order of the bias and the standard deviation. As a consequence, the naive estimator has a degenerating asymptotic distribution, which exacerbates the inference problem relative to other fixed effects estimators studied in the literature. To resolve the inference problem, we derive explicit expressions to debias the fixed effects estimator.


and State Dependence and Unobserved Heterogeneity in the Extensive Margin of Trade (joint with Julian Hinz and Joschka Wanner)


We study the role and drivers of persistence in the extensive margin of bilateral trade. Motivated by a stylized heterogeneous firms model of international trade with market entry costs, we consider dynamic three-way fixed effects binary choice models and study the corresponding incidental parameter problem. The standard maximum likelihood estimator is consistent under asymptotics where all panel dimensions grow at a constant rate, but it has an asymptotic bias in its limiting distribution, invalidating inference even in situations where the bias appears to be small. Thus, we propose two different bias-corrected estimators. Monte Carlo simulations confirm their desirable statistical properties. We apply these estimators in a reassessment of the most commonly studied determinants of the extensive margin of trade. Both true state dependence and unobserved heterogeneity contribute considerably to trade persistence and taking this persistence into account matters significantly in identifying the effects of trade policies on the extensive margin.