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 approaches popular in empirical research, including linear, two-way fixed effects, and discrete choice models. We apply the test to the estimation of the effect of a mother's working hours on her child's skills in a panel data context (James-Burdumy 2005)