Abstract
In this article, we compare three data-driven procedures to determine the bunching window in a Monte Carlo simulation of taxable income. Following the standard approach in the empirical bunching literature, we fit a flexible polynomial model to a simulated income distribution, excluding data in a range around a prespecified kink. First, we propose to implement methods for the estimation of structural breaks to determine a bunching regime around the kink. A second procedure is based on Cook’s distances aiming to identify outlier observations. Finally, we apply the iterative counterfactual procedure proposed by Bosch, Dekker, and Strohmaier which evaluates polynomial counterfactual models for all possible bunching windows. While our simulation results show that all three procedures are fairly accurate, the iterative counterfactual procedure is the preferred method to detect the bunching window when no prior information about the true size of the bunching window is available.
Highlights
ObjectivesWe aim to provide recommendations for practitioners how these procedures can be used to make the specification of the counterfactual model less reliant on researchers’ subjective decisions
The results show that across all specifications, BP () produces the smallest number of false negatives with the exception of specifications with the smallest binwidth and largest standard deviations. Both a small binwidth and a large standard deviation result in a widespread distribution of bunching individuals around the threshold. This in turn leads to the problem that the data no longer show structural deviations from their projected values and BP fails to detect a structural break in these settings
When the bunching window is normally distributed around the threshold, Cook’s D and BDS performed best with slight advantages of BDS over Cook’s D if standard deviations were large or sample sizes were small
Summary
We aim to provide recommendations for practitioners how these procedures can be used to make the specification of the counterfactual model less reliant on researchers’ subjective decisions
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