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Nonparametric tests for the effect of treatment on conditional variance

Author

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  • Yanchun Jin

    (Graduate School of Economics, Kyoto University)

Abstract

This paper proposes nonparametric tests for the null hypothesis that a treatment has a zero effect on conditional variance for all subpopulations defined by covariates. Rather than the mean of outcome, which measures to what extent treatment changes the level of outcome, researchers are also interested in how the treatment affects the dispersion of outcome. We use variance to measure the dispersion and estimate the conditional variances by series method. We give a test rule comparing a Wald-type test statistic with the critical value from chi-squared distribution. We also construct a normalized test statistic that is asymptotically standard normal under the null hypothesis. We illustrate the usefulness of the proposed test by Monte Carlo simulations and an empirical example that investigates the effect of unionism on wage dispersion.

Suggested Citation

  • Yanchun Jin, 2016. "Nonparametric tests for the effect of treatment on conditional variance," KIER Working Papers 948, Kyoto University, Institute of Economic Research.
  • Handle: RePEc:kyo:wpaper:948
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    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP948.pdf
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    References listed on IDEAS

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    1. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, March.
    2. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2008. "Nonparametric Tests for Treatment Effect Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 389-405, August.
    3. DiNardo, John & Fortin, Nicole M & Lemieux, Thomas, 1996. "Labor Market Institutions and the Distribution of Wages, 1973-1992: A Semiparametric Approach," Econometrica, Econometric Society, vol. 64(5), pages 1001-1044, September.
    4. Johnson, George E, 1975. "Economic Analysis of Trade Unionism," American Economic Review, American Economic Association, vol. 65(2), pages 23-28, May.
    5. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    6. David Card & Thomas Lemieux & W. Craig Riddell, 2004. "Unions and Wage Inequality," Journal of Labor Research, Transaction Publishers, vol. 25(4), pages 519-562, October.
    7. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, December.
    8. Qiongxia Song & Lijian Yang, 2009. "Spline confidence bands for variance functions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(5), pages 589-609.
    9. Richard B. Freeman, 1980. "Unionism and the Dispersion of Wages," ILR Review, Cornell University, ILR School, vol. 34(1), pages 3-23, October.
    10. Thomas Lemieux, 1993. "Unions and Wage Inequality in Canada and the United States," NBER Chapters, in: Small Differences That Matter: Labor Markets and Income Maintenance in Canada and the United States, pages 69-108, National Bureau of Economic Research, Inc.
    11. Andrews, Donald W.K. & Shi, Xiaoxia, 2014. "Nonparametric inference based on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 179(1), pages 31-45.
    12. Guido W. Imbens & Whitney Newey & Geert Ridder, 2005. "Mean-square-error Calculations for Average Treatment Effects," IEPR Working Papers 05.34, Institute of Economic Policy Research (IEPR).
    13. David Card, 2001. "The Effect of Unions on Wage Inequality in the U.S. Labor Market," ILR Review, Cornell University, ILR School, vol. 54(2), pages 296-315, January.
    14. Francis Vella & Marno Verbeek, 1998. "Whose wages do unions raise? A dynamic model of unionism and wage rate determination for young men," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(2), pages 163-183.
    15. Gosling, Amanda & Machin, Stephen, 1995. "Trade Unions and the Dispersion of Earnings in British Establishments, 1980-90," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 57(2), pages 167-184, May.
    16. Abadie A., 2002. "Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 284-292, March.
    17. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-1159, September.
    18. Yu, K. & Jones, M.C., 2004. "Likelihood-Based Local Linear Estimation of the Conditional Variance Function," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 139-144, January.
    19. Fan, Jianqing & Yao, Qiwei, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
    20. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    21. repec:cwl:cwldpp:1840rr is not listed on IDEAS
    22. Myoung‐jae Lee, 2009. "Non‐parametric tests for distributional treatment effect for randomly censored responses," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 243-264, January.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    treatment effect; conditional variance; series estimation;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • 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

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