A quantile-based nonadditive fixed effects model

TL;DR

This paper introduces a novel quantile-based nonadditive fixed effects panel model that captures heterogeneous causal effects with less restrictive assumptions, providing identification, estimation, and empirical application insights.

Contribution

It develops a flexible fixed effects model allowing nonseparable unobserved heterogeneity and stable rank dependence, extending panel quantile regression capabilities.

Findings

Model achieves uniform consistency and asymptotic normality.

Simulations demonstrate good finite-sample performance.

Application reveals causal effects of oil wealth on military spending.

Abstract

I propose a quantile-based nonadditive fixed effects panel model to study heterogeneous causal effects. Similar to standard fixed effects (FE) model, my model allows arbitrary dependence between regressors and unobserved heterogeneity, but it generalizes the additive separability of standard FE to allow the unobserved heterogeneity to enter nonseparably. Similar to structural quantile models, my model's random coefficient vector depends on an unobserved, scalar ''rank'' variable, in which outcomes (excluding an additive noise term) are monotonic at a particular value of the regressor vector, which is much weaker than the conventional monotonicity assumption that must hold at all possible values. This rank is assumed to be stable over time, which is often more economically plausible than the panel quantile studies that assume individual rank is iid over time. It uncovers the heterogeneous causal effects as functions of the rank variable. I provide identification and estimation results, establishing uniform consistency and uniform asymptotic normality of the heterogeneous causal effect function estimator. Simulations show reasonable finite-sample performance and show my model complements fixed effects quantile regression. Finally, I illustrate the proposed methods by examining the causal effect of a country's oil wealth on its military defense spending.