IDEAS home Printed from https://ideas.repec.org/p/kyo/wpaper/948.html
   My bibliography  Save this paper

Nonparametric tests for the effect of treatment on conditional variance

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP948.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. 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.
    6. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, April.
    7. Richard B. Freeman, 1980. "Unionism and the Dispersion of Wages," ILR Review, Cornell University, ILR School, vol. 34(1), pages 3-23, October.
    8. 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.
    9. Andrews, Donald W.K. & Shi, Xiaoxia, 2014. "Nonparametric inference based on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 179(1), pages 31-45.
    10. 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).
    11. 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.
    12. 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.
    13. 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.
    14. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-1159, September.
    15. 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.
    16. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    17. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    18. repec:cwl:cwldpp:1840rr is not listed on IDEAS
    19. 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.
    20. Qiongxia Song & Lijian Yang, 2009. "Spline confidence bands for variance functions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(5), pages 589-609.
    21. 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.
    22. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. David Card & Thomas Lemieux & W. Craig Riddell, 2020. "Unions and wage inequality: The roles of gender, skill and public sector employment," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 53(1), pages 140-173, February.
    2. Susan Hayter & Bradley Weinberg, 2011. "Mind the Gap: Collective Bargaining and Wage Inequality," Chapters, in: Susan Hayter (ed.), The Role of Collective Bargaining in the Global Economy, chapter 6, Edward Elgar Publishing.
    3. Susan Hayter, 2015. "Unions and collective bargaining," Chapters, in: Janine Berg (ed.), Labour Markets, Institutions and Inequality, chapter 4, pages 95-122, Edward Elgar Publishing.
    4. Töngür, Ünal & Elveren, Adem Yavuz, 2014. "Deunionization and pay inequality in OECD Countries: A panel Granger causality approach," Economic Modelling, Elsevier, vol. 38(C), pages 417-425.
    5. Jonathan E. Booth & John W. Budd & Kristen M. Munday, 2010. "Never Say Never? Uncovering the Never‐Unionized in the United States," British Journal of Industrial Relations, London School of Economics, vol. 48(1), pages 26-52, March.
    6. Sergio Firpo, 2007. "Efficient Semiparametric Estimation of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 75(1), pages 259-276, January.
    7. Albert Jan Hummel & Bas Jacobs, 2018. "Optimal Income Taxation in Unionized Labor Markets," Tinbergen Institute Discussion Papers 18-064/VI, Tinbergen Institute.
    8. Ying-Ying Lee, 2014. "Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models," Economics Series Working Papers 706, University of Oxford, Department of Economics.
    9. Donald, Stephen G. & Hsu, Yu-Chin, 2014. "Estimation and inference for distribution functions and quantile functions in treatment effect models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 383-397.
    10. Callaway, Brantly & Collins, William J., 2018. "Unions, workers, and wages at the peak of the American labor movement," Explorations in Economic History, Elsevier, vol. 68(C), pages 95-118.
    11. Hummel, Albert Jan & Jacobs, Bas, 2023. "Optimal income taxation in unionized labor markets," Journal of Public Economics, Elsevier, vol. 220(C).
    12. Ganesh Karapakula, 2023. "Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap," Papers 2301.05703, arXiv.org, revised Jan 2023.
    13. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    14. Addison, John T. & Bailey, Ralph & Siebert, W. Stanley, 2009. "Wage Dispersion in a Partially Unionized Labor Force," IZA Discussion Papers 4202, Institute of Labor Economics (IZA).
    15. Christian M. Dahl & Daniel le Maire & Jakob R. Munch, 2013. "Wage Dispersion and Decentralization of Wage Bargaining," Journal of Labor Economics, University of Chicago Press, vol. 31(3), pages 501-533.
    16. Fernando Rios-Avila & Barry T. Hirsch, 2014. "Unions, Wage Gaps, and Wage Dispersion: New Evidence from the Americas," Industrial Relations: A Journal of Economy and Society, Wiley Blackwell, vol. 53(1), pages 1-27, January.
    17. Ensar Yilmaz & Sayin San, 2017. "Wage gap and dispersion in a partially unionized structure in Turkey," Empirical Economics, Springer, vol. 52(2), pages 577-597, March.
    18. Kerr, Andrew & Wittenberg, Martin, 2021. "Union wage premia and wage inequality in South Africa," Economic Modelling, Elsevier, vol. 97(C), pages 255-271.
    19. David Card & Thomas Lemieux & W. Craig Riddell, 2003. "Unionization and Wage Inequality: A Comparative Study of the U.S, the U.K., and Canada," NBER Working Papers 9473, National Bureau of Economic Research, Inc.
    20. Jorge Eduardo Camusso & Ana Inés Navarro, 2021. "Asymmetries in aggregate income risk over the business cycle: evidence from administrative data of Argentina," Asociación Argentina de Economía Política: Working Papers 4447, Asociación Argentina de Economía Política.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kyo:wpaper:948. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Makoto Watanabe (email available below). General contact details of provider: https://edirc.repec.org/data/iekyojp.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.