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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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    as
    1. Jean‐Pierre Dubé & Jeremy T. Fox & Che‐Lin Su, 2012. "Improving the Numerical Performance of Static and Dynamic Aggregate Discrete Choice Random Coefficients Demand Estimation," Econometrica, Econometric Society, vol. 80(5), pages 2231-2267, September.
    2. Carolina Caetano & Gregorio Caetano & Eric Nielsen, 2024. "Correcting for Endogeneity in Models with Bunching," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(3), pages 851-863, July.
    3. Soren T. Anderson & James M. Sallee, 2011. "Using Loopholes to Reveal the Marginal Cost of Regulation: The Case of Fuel-Economy Standards," American Economic Review, American Economic Association, vol. 101(4), pages 1375-1409, June.
    4. Joseph G. Altonji & Todd E. Elder & Christopher R. Taber, 2005. "Selection on Observed and Unobserved Variables: Assessing the Effectiveness of Catholic Schools," Journal of Political Economy, University of Chicago Press, vol. 113(1), pages 151-184, February.
    5. Clément de Chaisemartin & Xavier D'Haultfœuille, 2020. "Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects," American Economic Review, American Economic Association, vol. 110(9), pages 2964-2996, September.
    6. Gregorio Caetano & Josh Kinsler & Hao Teng, 2019. "Towards causal estimates of children's time allocation on skill development," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(4), pages 588-605, June.
    7. Carolina Caetano, 2015. "A Test of Exogeneity Without Instrumental Variables in Models With Bunching," Econometrica, Econometric Society, vol. 83(4), pages 1581-1600, July.
    8. Stéphane Bonhomme & Elena Manresa, 2015. "Grouped Patterns of Heterogeneity in Panel Data," Econometrica, Econometric Society, vol. 83(3), pages 1147-1184, May.
    9. Gregorio Caetano & Vikram Maheshri, 2018. "Identifying dynamic spillovers of crime with a causal approach to model selection," Quantitative Economics, Econometric Society, vol. 9(1), pages 343-394, March.
    10. Steve Berry & Oliver B. Linton & Ariel Pakes, 2004. "Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 613-654.
    11. Oeindrila Dube & Juan F. Vargas, 2013. "Commodity Price Shocks and Civil Conflict: Evidence from Colombia," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(4), pages 1384-1421.
    12. Emily Oster, 2019. "Unobservable Selection and Coefficient Stability: Theory and Evidence," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(2), pages 187-204, April.
    13. Ferreira, Daniel & Ferreira, Miguel A. & Mariano, Beatriz, 2018. "Creditor control rights and board independence," LSE Research Online Documents on Economics 84463, London School of Economics and Political Science, LSE Library.
    14. Bertanha, Marinho & McCallum, Andrew H. & Seegert, Nathan, 2023. "Better bunching, nicer notching," Journal of Econometrics, Elsevier, vol. 237(2).
    15. Harding, Matthew & Lovenheim, Michael, 2017. "The effect of prices on nutrition: Comparing the impact of product- and nutrient-specific taxes," Journal of Health Economics, Elsevier, vol. 53(C), pages 53-71.
    16. Chris Forman & Avi Goldfarb & Shane Greenstein, 2012. "The Internet and Local Wages: A Puzzle," American Economic Review, American Economic Association, vol. 102(1), pages 556-575, February.
    17. Caetano, Carolina & Rothe, Christoph & Yıldız, Neşe, 2016. "A discontinuity test for identification in triangular nonseparable models," Journal of Econometrics, Elsevier, vol. 193(1), pages 113-122.
    18. Kenneth E. Train & Clifford Winston, 2007. "Vehicle Choice Behavior And The Declining Market Share Of U.S. Automakers," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1469-1496, November.
    19. C de Chaisemartin & X D’HaultfŒuille, 2018. "Fuzzy Differences-in-Differences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(2), pages 999-1028.
    20. Susanne James-Burdumy, 2005. "The Effect of Maternal Labor Force Participation on Child Development," Journal of Labor Economics, University of Chicago Press, vol. 23(1), pages 177-211, January.
    21. Bleemer , Zachary, 2018. "The Effect Of Selective Public Research University Enrollment: Evidence From California," University of California at Berkeley, Center for Studies in Higher Education qt2b22k86h, Center for Studies in Higher Education, UC Berkeley.
    22. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, September.
    23. Erhardt, Eva Christine, 2017. "Microfinance beyond self-employment: Evidence for firms in Bulgaria," Labour Economics, Elsevier, vol. 47(C), pages 75-95.
    24. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    25. D’Haultfœuille, Xavier & Hoderlein, Stefan & Sasaki, Yuya, 2023. "Nonparametric difference-in-differences in repeated cross-sections with continuous treatments," Journal of Econometrics, Elsevier, vol. 234(2), pages 664-690.
    26. Scott A. Imberman & Adriana D. Kugler & Bruce I. Sacerdote, 2012. "Katrina's Children: Evidence on the Structure of Peer Effects from Hurricane Evacuees," American Economic Review, American Economic Association, vol. 102(5), pages 2048-2082, August.
    27. Nathan Nunn, 2008. "The Long-term Effects of Africa's Slave Trades," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(1), pages 139-176.
    28. Daniel Ferreira & Miguel A. Ferreira & Beatriz Mariano, 2018. "Creditor Control Rights and Board Independence," Journal of Finance, American Finance Association, vol. 73(5), pages 2385-2423, October.
    29. de Chaisemartin, Clement & D'Haultfoeuille, Xavier, 2014. "Fuzzy Changes-in Changes," CAGE Online Working Paper Series 184, Competitive Advantage in the Global Economy (CAGE).
    30. Lee, Lung-fei, 2007. "Identification and estimation of econometric models with group interactions, contextual factors and fixed effects," Journal of Econometrics, Elsevier, vol. 140(2), pages 333-374, October.
    31. Caetano, Gregorio & Maheshri, Vikram, 2019. "Gender segregation within neighborhoods," Regional Science and Urban Economics, Elsevier, vol. 77(C), pages 253-263.
    32. McCrary, Justin, 2008. "Manipulation of the running variable in the regression discontinuity design: A density test," Journal of Econometrics, Elsevier, vol. 142(2), pages 698-714, February.
    33. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    34. Arellano, M, 1987. "Computing Robust Standard Errors for Within-Groups Estimators," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 49(4), pages 431-434, November.
    35. Carolina Caetano & Gregorio Caetano & Eric R. Nielsen, 2020. "Should Children Do More Enrichment Activities? Leveraging Bunching to Correct for Endogeneity," Finance and Economics Discussion Series 2020-036, Board of Governors of the Federal Reserve System (U.S.).
    36. Bester, C. Alan & Conley, Timothy G. & Hansen, Christian B., 2011. "Inference with dependent data using cluster covariance estimators," Journal of Econometrics, Elsevier, vol. 165(2), pages 137-151.
    37. Bester, C. Alan & Conley, Timothy G. & Hansen, Christian B. & Vogelsang, Timothy J., 2016. "FIXED-b ASYMPTOTICS FOR SPATIALLY DEPENDENT ROBUST NONPARAMETRIC COVARIANCE MATRIX ESTIMATORS," Econometric Theory, Cambridge University Press, vol. 32(1), pages 154-186, February.
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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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