A data-driven procedure to determine the bunching window: an application to the Netherlands

Abstract

We extend the bunching approach introduced by Saez (Am Econ J Econ Policy 2:180-212, 2010) by proposing an intuitive, data-driven procedure to determine the bunching window. By choosing the bunching window ad hoc, researchers throw away informative data points for estimating the counterfactual income distribution in the absence of the kink. Assuming a descending bunching mass to both sides of the threshold, the proposed algorithm produces a distribution of lower and upper bounds for the bunching window. In each iteration, the bunching window is defined as all contiguous bin midpoints around the threshold that lie outside of the confidence band resulting from running a local regression through all data points outside of the excluded region. Monte Carlo simulations provide evidence that our data-driven procedure outperforms larger bunching windows in terms of bias and efficiency. In our application for the Netherlands, we find clear evidence of bunching behaviour at all three thresholds of the Dutch tax schedule with a precisely estimated elasticity of 0.023 at the upper threshold, which is driven by self-employed, women and joint tax filers.

A Comparison of Different Data-driven Procedures to Determine the Bunching Window

“…Cook’s distances have difficulties determining the true bunching window especially with small sample sizes, large standard deviations, and when the bunching mass is not spread symmetrically around the threshold. Therefore, we find that the procedure by Bosch, Dekker, and Strohmaier (2020) performs best for determining the size of the bunching window although Cook’s distances run it a close second, especially when considering its ease of implementation. Secondary analyses, relating the elasticity estimates to a baseline scenario without optimization frictions, support the finding that the method proposed by Bosch, Dekker, and Strohmaier (2020) is superior in extreme cases.…”

“…However, additional problems exist within the standard bunching framework itself, that is, before the estimate of the excess mass is translated into the ETI. For example, Blomquist and Newey (2017) criticize the dependence on functional form assumptions and Bosch, Dekker, and Strohmaier (2020) argue that relying on eyeballing when determining the counterfactual model should be replaced by a data-driven procedure. We focus on improving the conventional bunching method as such and investigate the performance of different procedures to select the bunching window.…”

“…The bulk of studies implementing the bunching approach relies on eyeballing to determine the bunching window and hedges against any concerns that this might drive results by altering the bunching window in robustness checks. We argue, in the spirit of Bosch, Dekker, and Strohmaier (2020), that the choice of the (only) appropriate bunching window is crucial to the unbiasedness of the bunching estimator and therefore requires a sound data-driven technique to identify it. The bunching window is directly linked to the estimation of the counterfactual model which helps to identify the relative excess mass ( b ).…”

“…To circumvent this problem, we discuss two new data-driven procedures and compare them to the data-driven procedure derived in Bosch, Dekker, and Strohmaier (2020). First, we propose to implement methods for the estimation of structural breaks following Bai and Perron (1998, 2003).…”

“…We identify the Cook’s distances—scaled deviations from the least squares projected value—and say that the bunching window is made up of adjacent data points around the threshold that have a significantly positive distance. Third, we apply the iterative counterfactual procedure proposed by Bosch, Dekker, and Strohmaier (2020) which tests all possible combinations of excluded regions within a predetermined interval. The procedure returns a bunching window for each excluded region, from which the mode is taken to determine the bunching window that is to be used for the estimation of the relative excess mass.…”