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Correcting for Endogeneity in Models with Bunching
We show that in models with endogeneity, bunching at the lower or upper boundary of the distribution of the treatment variable may be used to build a correction for endogeneity. We derive the asymptotic distribution of the parameters of the corrected model, provide an estimator of the standard errors, and prove the consistency of the bootstrap. An empirical application reveals that time spent watching television, corrected for endogeneity, has roughly no net effect on cognitive skills and a significant negative net effect on non-cognitive skills in children.
Should Children Do More Enrichment Activities? Leveraging Bunching to Correct for Endogeneity
We study the effects of enrichment activities such as reading, homework, and extracurricular lessons on children's cognitive and non-cognitive skills. We take into consideration that children forgo alternative activities, such as play and socializing, in order to spend time on enrichment. Our study controls for selection on unobservables using a novel approach which leverages the fact that many children spend zero hours per week on enrichment activities. At zero enrichment, confounders vary but enrichment does not, which gives us direct information about the effect of confounders on skills. ...
Better Bunching, Nicer Notching
We study the bunching identification strategy for an elasticity parameter that summarizes agents' response to changes in slope (kink) or intercept (notch) of a schedule of incentives. A notch identifies the elasticity but a kink does not, when the distribution of agents is fully flexible. We propose new non-parametric and semi-parametric identification assumptions on the distribution of agents that are weaker than assumptions currently made in the literature. We revisit the original empirical application of the bunching estimator and find that our weaker identification assumptions result in ...
Bunching Estimation of Elasticities Using Stata
A continuous distribution of agents that face a piecewise-linear schedule of incentives results in a distribution of responses with mass points located where the slope (kink) or intercept (notch) of the schedule changes. Bunching methods use these mass points to estimate an elasticity parameter, which summarizes agents' responses to incentives. This article introduces the command bunching, which implements new non-parametric and semi-parametric identification methods for estimating elasticities developed by Bertanha et al. (2021). These methods rely on weaker assumptions than currently made ...
A Dummy Test of Identification in Models with Bunching
We propose a simple test of the main identification assumption in models where the treatment variable takes multiple values and has bunching. The test consists of adding an indicator of the bunching point to the estimation model and testing whether the coefficient of this indicator is zero. Although similar in spirit to the test in Caetano (2015), the dummy test has important practical advantages: it is more powerful at detecting endogeneity, and it also detects violations of the functional form assumption. The test does not require exclusion restrictions and can be implemented in many ...