[Paper Review] Bounds on Average Effects in Discrete Choice Panel Data Models

Cavit Pakel, Martin Weidner|arXiv (Cornell University)|Sep 17, 2023

Spatial and Panel Data Analysis4 citations

TL;DR

This paper proposes computationally simple outer bounds on the identified set of average effects in discrete choice panel data models with fixed effects, enabling parametric-rate estimation and asymptotically valid confidence intervals even in short panels with continuous covariates. The method avoids the curse of dimensionality and provides robust inference when average effects are only partially identified due to incidental parameter problems.

ABSTRACT

In discrete choice panel data, estimation of average effects is crucial for quantifying the effect of covariates, and for policy evaluation and counterfactual analysis. However, in short panels with individual-specific effects, challenges arise due to partial identification and the incidental parameter problem. In particular, estimating the sharp identified set on average effects becomes impractical when covariates have large support sets, such as when they are continuous. This paper proposes a method for estimating outer bounds on the identified set of average effects, which are easy to construct, converge at the parametric rate, and remain computationally feasible even for moderately large samples. Asymptotically valid confidence intervals are also provided.

Motivation & Objective

• To address the challenge of estimating average effects in short panel data models with individual-specific effects, where standard methods face the incidental parameter problem and partial identification.
• To develop a computationally efficient alternative to sharp identified set estimation, which suffers from the curse of dimensionality in realistic sample sizes.
• To provide outer bounds on average effects that are easy to compute, converge at the parametric rate, and remain valid regardless of whether covariates are discrete or continuous.
• To construct asymptotically valid confidence intervals for the identified set, improving inference robustness in finite samples.
• To demonstrate the method's performance through simulations and an empirical application to female labor force participation.

Proposed method

• The method constructs outer bounds on the sharp identified set of average effects using a uniform linear programming approach, which simplifies the high-dimensional optimization required for sharp set estimation.
• It leverages the fact that average effects depend on both the structural parameter β and the distribution of unobserved heterogeneity π, and derives bounds that are conservative but computationally feasible.
• The approach uses a semiparametric model where f(Y_i|Z_i) is a mixture of conditional distributions f(Y_i|Z_i, A_i; β) weighted by π(A_i|Z_i), with β point-identified and π left unrestricted.
• Outer bounds are derived by solving a linear program over the support of covariates, ensuring convergence at the parametric rate even when π is nonparametric.
• Asymptotically valid confidence intervals are constructed using a normal approximation to the sampling distribution of the outer bounds, as formalized in Theorem 1.
• The method is applicable to both static and dynamic models and handles both discrete and continuous covariates without requiring discretization.

Experimental results

Research questions

• RQ1 Can we construct outer bounds on the identified set of average effects in discrete choice panel models that are computationally feasible and converge at the parametric rate?
• RQ2 How does the proposed method perform in finite samples compared to existing methods when covariates are continuous or high-dimensional?
• RQ3 Can we construct asymptotically valid confidence intervals for the average effect using outer bounds, even when the sharp identified set is infeasible to compute?
• RQ4 How does the method compare to point-identification methods (e.g., BC logit, probit) in terms of coverage and robustness when the true effect varies across individuals?
• RQ5 What is the empirical performance of the method in a real-world application, such as female labor force participation with continuous income and education covariates?

Key findings

• The proposed outer bounds are computationally simple and converge at the parametric rate, even when the number of support points of the covariates is large, avoiding the curse of dimensionality.
• In simulations, the method performs well in finite samples and provides informative bounds that reflect heterogeneity in treatment effects, such as varying impacts of young children on labor force participation.
• For the labor force participation application, all methods agree that having a child under three reduces participation, but the outer bounds produce wider confidence intervals that reflect unobserved heterogeneity in the effect across individuals.
• The outer bounds' confidence intervals are wider than those from point-identification methods, but they are more robust and valid under partial identification, especially when individual effects vary.
• In the second empirical illustration with richer covariates, the outer bounds' confidence intervals are narrower than those of alternative methods in some cases, indicating improved efficiency and coverage under model uncertainty.
• The method’s confidence intervals for the average effect of education are mostly positive, consistent with other methods, while those for spouse income are ambiguous but mostly negative, with outer bounds capturing this uncertainty more reliably.