Abstract

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

  • Three-way FE-Poisson Pseudo-Maximum Likelihood (PPML) is consistent in fixed-T settings for largely the same reasons the twoway models considered in Fernández-Val and Weidner (2016) are consistent, and we provide suitably modified versions of the regularity conditions and consistency results established by Fernández-Val and Weidner (2016) for the simpler two-way case

  • As we go on to discuss, the fixed effects Poisson Pseudo-Maximum Likelihood (FE-PPML) estimator that is most often used in this context has some special robustness against incidental parameter problems (IPPs), but this robustness does not hold for FE-PPML in general, especially once we deviate from the two-way gravity setting implied by (5)

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Summary

Introduction

Despite intense and longstanding empirical interest, the effects of bilateral trade agreements on trade are still considered highly difficult to assess. As emphasized in a recent practitioner's guide put out by the WTO (Yotov et al, 2016), many current estimates in the literature suffer from identifiable sources of bias (or “estimation challenges”). This is not for lack of awareness. One reason why some researchers may hesitate in embracing this estimator is the current lack of clarity regarding how the three fixed effects in the model may bias estimation, especially in the standard “fixed T” case where the number of time periods is small. To state our main results more precisely, in gravity settings where the number of countries (N) goes to infinity and T is small, we find the following: 1. Consistency of point estimates of FE-PPML: The point estimates produced by three-way FE-PPML estimator in gravity settings are asymptotically consistent

Asymptotic bias
Bias corrections improve inferences
Gravity models and IPPs
Fixed effects and gravity models
The incidental parameter problem
How FE-PPML is different
Results for the three-way gravity model
Consistency
Illustrating the bias using the T = 2 case
What if T is large? While
Downward bias in robust standard errors
Bias corrections for the three-way gravity model
Jackknife bias correction
Analytical bias correction
Bias-corrected standard errors
Other practicalities
Simulation evidence
What happens for larger values of T?
Empirical applications
Findings
Conclusion
Full Text
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