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Quantile treatment effects in difference in differences models under dependence restrictions and with only two time periods

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  • Callaway, Brantly
  • Li, Tong
  • Oka, Tatsushi

Abstract

This paper shows that the Conditional Quantile Treatment Effect on the Treated is identified under (i) a Conditional Distributional Difference in Differences assumption and (ii) a new assumption that the dependence (the copula) between the change in untreated potential outcomes and the initial level of untreated potential outcomes is the same for the treated group and untreated group. We consider estimation and inference with discrete covariates and propose a uniform inference procedure based on the exchangeable bootstrap. Finally, we estimate the effect of increasing the minimum wage on the distribution of earnings for subgroups defined by race, gender, and education.

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  • Callaway, Brantly & Li, Tong & Oka, Tatsushi, 2018. "Quantile treatment effects in difference in differences models under dependence restrictions and with only two time periods," Journal of Econometrics, Elsevier, vol. 206(2), pages 395-413.
  • Handle: RePEc:eee:econom:v:206:y:2018:i:2:p:395-413
    DOI: 10.1016/j.jeconom.2018.06.008
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    as
    1. Arindrajit Dube, 2019. "Minimum Wages and the Distribution of Family Incomes," American Economic Journal: Applied Economics, American Economic Association, vol. 11(4), pages 268-304, October.
    2. Fan, Yanqin & Yu, Zhengfei, 2012. "Partial identification of distributional and quantile treatment effects in difference-in-differences models," Economics Letters, Elsevier, vol. 115(3), pages 511-515.
    3. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
    4. Sergio Firpo, 2007. "Efficient Semiparametric Estimation of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 75(1), pages 259-276, January.
    5. Kato, Kengo & F. Galvao, Antonio & Montes-Rojas, Gabriel V., 2012. "Asymptotics for panel quantile regression models with individual effects," Journal of Econometrics, Elsevier, vol. 170(1), pages 76-91.
    6. repec:fth:prinin:382 is not listed on IDEAS
    7. Marianne P. Bitler & Hilary W. Hoynes & Thurston Domina, 2014. "Experimental Evidence on Distributional Effects of Head Start," NBER Working Papers 20434, National Bureau of Economic Research, Inc.
    8. Denis Chetverikov & Bradley Larsen & Christopher Palmer, 2016. "IV Quantile Regression for Group‐Level Treatments, With an Application to the Distributional Effects of Trade," Econometrica, Econometric Society, vol. 84, pages 809-833, March.
    9. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    10. Manuel Arellano & Stéphane Bonhomme, 2016. "Nonlinear panel data estimation via quantile regressions," Econometrics Journal, Royal Economic Society, vol. 19(3), pages 61-94, October.
    11. Christoph Rothe, 2012. "Partial Distributional Policy Effects," Econometrica, Econometric Society, vol. 80(5), pages 2269-2301, September.
    12. Alberto Abadie & Joshua Angrist & Guido Imbens, 2002. "Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings," Econometrica, Econometric Society, vol. 70(1), pages 91-117, January.
    13. Chernozhukov, Victor & Fernández-Val, Iván & Hoderlein, Stefan & Holzmann, Hajo & Newey, Whitney, 2015. "Nonparametric identification in panels using quantiles," Journal of Econometrics, Elsevier, vol. 188(2), pages 378-392.
    14. Alberto Abadie, 2005. "Semiparametric Difference-in-Differences Estimators," Review of Economic Studies, Oxford University Press, vol. 72(1), pages 1-19.
    15. Rivera Drew, Julia A. & Flood, Sarah & Warren, John Robert, 2014. "Making full use of the longitudinal design of the Current Population Survey: Methods for linking records across 16 months\m{1}," Journal of Economic and Social Measurement, IOS Press, issue 3, pages 121-144.
    16. Markus Frölich & Blaise Melly, 2013. "Unconditional Quantile Treatment Effects Under Endogeneity," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 346-357, July.
    17. Henry S. Farber, 1997. "The Changing Face of Job Loss in the United States, 1981-1995," Working Papers 761, Princeton University, Department of Economics, Industrial Relations Section..
    18. Marianne P. Bitler & Jonah B. Gelbach & Hilary W. Hoynes, 2006. "Welfare Reform and Children's Living Arrangements," Journal of Human Resources, University of Wisconsin Press, vol. 41(1).
    19. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
    20. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    21. Henry S. Farber, 1997. "The Changing Face of Job Loss in the United States, 1981-1995," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 28(1997 Micr), pages 55-142.
    22. V. Chernozhukov & C. Hansen, 2013. "Quantile Models with Endogeneity," Annual Review of Economics, Annual Reviews, vol. 5(1), pages 57-81, May.
    23. Ozkan Eren & Serkan Ozbeklik, 2014. "Who Benefits From Job Corps? A Distributional Analysis Of An Active Labor Market Program," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(4), pages 586-611, June.
    24. Ivan A. Canay, 2011. "A simple approach to quantile regression for panel data," Econometrics Journal, Royal Economic Society, vol. 14(3), pages 368-386, October.
    25. Susan Athey & Guido W. Imbens, 2006. "Identification and Inference in Nonlinear Difference-in-Differences Models," Econometrica, Econometric Society, vol. 74(2), pages 431-497, March.
    26. Abrevaya, Jason & Dahl, Christian M, 2008. "The Effects of Birth Inputs on Birthweight," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 379-397.
    27. Khan, Shakeeb & Ponomareva, Maria & Tamer, Elie, 2016. "Identification of panel data models with endogenous censoring," Journal of Econometrics, Elsevier, vol. 194(1), pages 57-75.
    28. Bryan S. Graham & Jinyong Hahn & Alexandre Poirier & James L. Powell, 2015. "Quantile regression with panel data," CeMMAP working papers CWP12/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    29. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, December.
    30. James Heckman & Hidehiko Ichimura & Jeffrey Smith & Petra Todd, 1998. "Characterizing Selection Bias Using Experimental Data," Econometrica, Econometric Society, vol. 66(5), pages 1017-1098, September.
    31. Victor Chernozhukov & Iván Fernández‐Val & Jinyong Hahn & Whitney Newey, 2013. "Average and Quantile Effects in Nonseparable Panel Models," Econometrica, Econometric Society, vol. 81(2), pages 535-580, March.
    32. Bitler, Marianne P. & Gelbach, Jonah B. & Hoynes, Hilary W., 2008. "Distributional impacts of the Self-Sufficiency Project," Journal of Public Economics, Elsevier, vol. 92(3-4), pages 748-765, April.
    33. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-694, July.
    34. Rosen, Adam M., 2012. "Set identification via quantile restrictions in short panels," Journal of Econometrics, Elsevier, vol. 166(1), pages 127-137.
    35. Henry S. Farber, 1997. "The Changing Face of Job Loss in the United States, 1981-1995," Working Papers 761, Princeton University, Department of Economics, Industrial Relations Section..
    36. Djebbari, Habiba & Smith, Jeffrey, 2008. "Heterogeneous impacts in PROGRESA," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 64-80, July.
    37. Riddell, W. Craig & Song, Xueda, 2011. "The impact of education on unemployment incidence and re-employment success: Evidence from the U.S. labour market," Labour Economics, Elsevier, vol. 18(4), pages 453-463, August.
    38. Antonio F. Galvao & Kengo Kato, 2014. "Estimation and Inference for Linear Panel Data Models Under Misspecification When Both n and T are Large," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 285-309, April.
    39. Gronau, Reuben, 1974. "Wage Comparisons-A Selectivity Bias," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1119-1143, Nov.-Dec..
    40. Sergio Firpo & Nicole M. Fortin & Thomas Lemieux, 2009. "Unconditional Quantile Regressions," Econometrica, Econometric Society, vol. 77(3), pages 953-973, May.
    41. Marianne Bertrand & Esther Duflo & Sendhil Mullainathan, 2004. "How Much Should We Trust Differences-In-Differences Estimates?," The Quarterly Journal of Economics, Oxford University Press, vol. 119(1), pages 249-275.
    42. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
    43. Antonio F. Galvao & Carlos Lamarche & Luiz Renato Lima, 2013. "Estimation of Censored Quantile Regression for Panel Data With Fixed Effects," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 1075-1089, September.
    44. Brantly Callaway & Tong Li, 2019. "Quantile treatment effects in difference in differences models with panel data," Quantitative Economics, Econometric Society, vol. 10(4), pages 1579-1618, November.
    45. Xavier D'Haultfoeuille & Stefan Hoderlein & Yuya Sasaki, 2013. "Nonlinear Difference-in-Differences in Repeated Cross Sections with Continuous Treatments," Boston College Working Papers in Economics 839, Boston College Department of Economics.
    46. Tue Gorgens & Chirok Han & Sen Xue, 2016. "Moment restrictions and identification in linear dynamic panel data models," ANU Working Papers in Economics and Econometrics 2016-633, Australian National University, College of Business and Economics, School of Economics.
    47. Li, Tong & Oka, Tatsushi, 2015. "Set identification of the censored quantile regression model for short panels with fixed effects," Journal of Econometrics, Elsevier, vol. 188(2), pages 363-377.
    48. Chernozhukov, Victor & Hansen, Christian, 2006. "Instrumental quantile regression inference for structural and treatment effect models," Journal of Econometrics, Elsevier, vol. 132(2), pages 491-525, June.
    49. Arindrajit Dube & T. William Lester & Michael Reich, 2010. "Minimum Wage Effects Across State Borders: Estimates Using Contiguous Counties," The Review of Economics and Statistics, MIT Press, vol. 92(4), pages 945-964, November.
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    Cited by:

    1. Brantly Callaway & Tong Li, 2019. "Quantile treatment effects in difference in differences models with panel data," Quantitative Economics, Econometric Society, vol. 10(4), pages 1579-1618, November.
    2. Brantly Callaway & Pedro H. C. Sant'Anna, 2018. "Difference-in-Differences with Multiple Time Periods and an Application on the Minimum Wage and Employment," DETU Working Papers 1804, Department of Economics, Temple University.
    3. Brantly Callaway & Pedro H. C. Sant'Anna, 2018. "Difference-in-Differences with Multiple Time Periods," Papers 1803.09015, arXiv.org, revised Dec 2020.
    4. Jessica Ya Sun, 2020. "Welfare consequences of access to health insurance for rural households: Evidence from the New Cooperative Medical Scheme in China," Health Economics, John Wiley & Sons, Ltd., vol. 29(3), pages 337-352, March.
    5. David Bounie & Youssouf Camara, 2020. "Card-Sales Response to Merchant Contactless Payment Acceptance," Post-Print hal-02296302, HAL.
    6. Afrouz Azadikhah Jahromi & Brantly Callaway, 2019. "Heterogeneous Effects of Job Displacement on Earnings," DETU Working Papers 1901, Department of Economics, Temple University.
    7. Bounie, David & Camara, Youssouf, 2020. "Card-sales response to merchant contactless payment acceptance," Journal of Banking & Finance, Elsevier, vol. 119(C).
    8. Pedro H. C. Sant'Anna, 2016. "Program Evaluation with Right-Censored Data," Papers 1604.02642, arXiv.org.
    9. Saibal Ghosh, 2020. "Bank Lending and Monetary Transmission: Does Politics Matter?," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 18(2), pages 359-381, June.
    10. Soichiro Yamauchi, 2020. "Difference-in-Differences for Ordinal Outcomes: Application to the Effect of Mass Shootings on Attitudes toward Gun Control," Papers 2009.13404, arXiv.org.
    11. Masayuki Sawada, 2019. "Noncompliance in randomized control trials without exclusion restrictions," Papers 1910.03204, arXiv.org, revised Feb 2020.
    12. David Bounie & Youssouf Camara, 2019. "Card-Sales Response to Merchant Contactless Payment Acceptance: Causal Evidence," Working Papers hal-02296302, HAL.
    13. Gonçalves, S. & Rodrigues, T.P. & Chagas, A.L.S., 2020. "The impact of wind power on the Brazilian labor market," Renewable and Sustainable Energy Reviews, Elsevier, vol. 128(C).

    More about this item

    Keywords

    Quantile treatment effects; Copula; Panel data;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: 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
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

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