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A Dummy Test of Identification in Models with Bunching

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Abstract

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).

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  • Carolina Caetano & Gregorio Caetano & Hao Fe & Eric R. Nielsen, 2021. "A Dummy Test of Identification in Models with Bunching," Finance and Economics Discussion Series 2021-068, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgfe:2021-68
    DOI: 10.17016/FEDS.2021.068
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    Cited by:

    1. Nicole Black & Danusha Jayawardana & Gawain Heckley, 2023. "Children’s Time Allocation and the Socioeconomic Gap in Human Capital," Papers 2023-06, Centre for Health Economics, Monash University.

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    More about this item

    Keywords

    Bunching; Discrete-choice models; Endogeneity; Identification test; Linear models; Two-way fixed effects;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models

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