Abstract
We study the incidental parameter problem for the “three-way” Poisson Pseudo-Maximum Likelihood (“PPML”) estimator recently recommended for identifying the effects of trade policies and in other panel data gravity settings. Despite the number and variety of fixed effects involved, we confirm PPML is consistent for fixed T and we show it is in fact the only estimator among a wide range of PML gravity estimators that is generally consistent in this context when T is fixed. At the same time, asymptotic confidence intervals in fixed-T panels are not correctly centered at the true parameter values, and cluster-robust variance estimates used to construct standard errors are generally biased as well. We characterize each of these biases analytically and show both numerically and empirically that they are salient even for real-data settings with a large number of countries. We also offer practical remedies that can be used to obtain more reliable inferences of the effects of trade policies and other time-varying gravity variables, which we make available via an accompanying Stata package called ppml_fe_bias.
Highlights
Despite intense and longstanding empirical interest, the effects of bilateral trade agreements on trade are still considered highly difficult to assess
The results show that fixed effects Poisson Pseudo-Maximum Likelihood (FE-PPML) clearly suffers from an incidental parameter problem (IPP) in this example
To recap the sequence of results just described, we know that FE-PPML estimates with one fixed effect do not suffer from an IPP
Summary
Despite intense and longstanding empirical interest, the effects of bilateral trade agreements on trade are still considered highly difficult to assess. Aside from the bias in point estimates, another (not unrelated) issue that affects the three-way model is a general downward bias in the cluster-robust sandwich estimator typically used to compute standard errors This latter bias is similar to one that has been found in the simpler two-way gravity model by several recent studies (Egger and Staub, 2015; Jochmans, 2016; Pfaffermayr, 2019) and arises for the same reason: because the origin-time and destination-time fixed effects in the model each converge to their true. Turning to three-way models, Hinz, Stammann, and Wanner (2019) have recently developed bias corrections for dynamic three-way probit and logit models based on asymptotics suggested by Fernández-Val and Weidner (2018) where all three panel dimensions grow at the same rate Though widely applicable, this approach is not appropriate for our setting because of the different role played by the time dimension when the estimator is FE-PPML..
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