[Paper Review] probitfe and logitfe: Bias corrections for probit and logit models with two-way fixed effects

Mario Cruz‐Gonzalez, Iván Fernández‐Val+1 more|arXiv (Cornell University)|Oct 24, 2016

Monetary Policy and Economic Impact4 citations

TL;DR

This paper introduces Stata commands probitfe and logitfe that implement analytical and jackknife bias corrections for probit and logit models with two-way fixed effects, addressing the incidental parameter problem in nonlinear panel models. The method delivers consistent estimates of coefficients and average partial effects even when both N and T are moderately large, significantly improving finite-sample accuracy over standard fixed-effect estimators.

ABSTRACT

We present the Stata commands probitfe and logitfe, which estimate probit and logit panel data models with individual and/or time unobserved effects. Fixed effect panel data methods that estimate the unobserved effects can be severely biased because of the incidental parameter problem (Neyman and Scott, 1948). We tackle this problem by using the analytical and jackknife bias corrections derived in Fernandez-Val and Weidner (2016) for panels where the two dimensions ($N$ and $T$) are moderately large. We illustrate the commands with an empirical application to international trade and a Monte Carlo simulation calibrated to this application.

Motivation & Objective

• To address the incidental parameter problem in nonlinear panel models with two-way fixed effects, which biases standard fixed-effect estimators of probit and logit models.
• To develop and implement bias-corrected estimators for model coefficients and average partial effects in binary response models with individual and time effects.
• To provide the first Stata commands offering analytical and jackknife bias corrections for nonlinear panel models with two-way fixed effects.
• To improve estimation accuracy in moderately large panels (N and T moderately large), especially when time effects are included and conditional likelihood methods are inapplicable.
• To enable reliable inference on average partial effects, which are often the primary estimands in empirical applications.

Proposed method

• Uses analytical bias corrections derived from Fernandez-Val and Weidner (2016) to adjust the fixed-effect estimators of probit and logit models with individual and time effects.
• Applies jackknife-based bias corrections (SPJ and Hahn-Newey methods) to reduce bias in coefficient estimates, particularly in finite samples.
• Computes corrected estimates of average partial effects (APEs) using bias-corrected coefficient estimates and empirical moments of the covariates.
• Employs a finite population correction term in standard errors to account for sampling from finite N and T populations.
• Derives standard errors for both uncorrected and corrected estimators using the inverse of the observed Fisher information matrix and robust variance estimators.
• Implements the corrections through Stata ado-files that support both one-way (individual or time only) and two-way fixed effects models.

Experimental results

Research questions

• RQ1 How can the incidental parameter problem be effectively mitigated in probit and logit models with two-way fixed effects?
• RQ2 What is the finite-sample performance of bias-corrected estimators compared to standard fixed-effect estimators in nonlinear panel models?
• RQ3 Can analytical and jackknife bias corrections be reliably implemented in Stata for probit and logit models with two-way fixed effects?
• RQ4 How do the bias-corrected estimates of average partial effects compare to those from uncorrected estimators in empirical applications?
• RQ5 What is the impact of including time effects on the magnitude of incidental parameter bias in logit and probit models?

Key findings

• The analytical and jackknife bias corrections significantly reduce finite-sample bias in coefficient estimates for probit and logit models with two-way fixed effects.
• The commands probitfe and logitfe produce consistent estimates of average partial effects, which are often the primary estimands in empirical work.
• Monte Carlo simulations calibrated to an international trade application show that bias corrections substantially improve estimator accuracy, especially when T is moderate.
• The jackknife corrections (SPJ and Hahn-Newey) outperform uncorrected estimators in terms of root mean squared error and coverage rates in finite samples.
• Standard errors are computed with a finite population correction, improving inference quality when N and T are finite.
• The method is applicable to a wide range of panel data structures, including traditional micro panels, country-level panels, and square pseudo-panels of trade flows.