Identification and Inference in General Bunching Designs

TL;DR

This paper introduces a comprehensive econometric framework for identifying and inferring parameters in general bunching designs, extending existing methods to include covariates and broader distribution classes.

Contribution

It develops point and partial identification methods under analyticity assumptions, incorporating covariates, and proposes the generalized polynomial strategy for counterfactual estimation.

Findings

The proposed method outperforms traditional polynomial estimators in simulations.

Application to Saez (2010) data yields substantially different results.

The framework broadens the class of distributions and covariate inclusion in bunching analysis.

Abstract

This paper develops an econometric framework and tools for the identification and inference of a structural parameter in general bunching designs. We present point and partial identification results, which generalize previous approaches in the literature. The key assumption for point identification is the analyticity of the counterfactual density, which defines a broader class of distributions than many commonly used parametric families. In the partial identification approach, the analyticity condition is relaxed and various inequality restrictions can be incorporated. Both of our identification approaches allow for observed covariates in the model, which has previously been permitted only in limited ways. These covariates allow us to account for observable factors that influence decisions regarding the running variable. We provide a suite of counterfactual estimation and inference methods, termed the generalized polynomial strategy. Our method restores the merits of the original polynomial strategy proposed by Chetty et al. (2011) while addressing several weaknesses in the widespread practice. The efficacy of the proposed method is demonstrated compared to the polynomial estimator in a series of Monte Carlo studies within the augmented isoelastic model. We revisit the data used in Saez (2010) and find substantially different results relative to those from the polynomial strategy.