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Testing for Stochastic Monotonicity

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  • Sokbae Lee
  • Oliver Linton
  • Yoon-Jae Whang

Abstract

We propose a test of the hypothesis of stochastic monotonicity. This hypothesis is of interest in many applications in economics. Our test is based on the supremum of a rescaled U-statistic. We show that its asymptotic distribution is Gumbel. The proof is difficult because the approximating Gaussian stochastic process contains both a stationary and a nonstationary part, and so we have to extend existing results that only apply to either one or the other case. We also propose a refinement to the asymptotic approximation that we show works much better in finite samples. We apply our test to the study of intergenerational income mobility. Copyright 2009 The Econometric Society.

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  • Sokbae Lee & Oliver Linton & Yoon-Jae Whang, 2009. "Testing for Stochastic Monotonicity," Econometrica, Econometric Society, vol. 77(2), pages 585-602, March.
  • Handle: RePEc:ecm:emetrp:v:77:y:2009:i:2:p:585-602
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    1. Dearden, Lorraine & Machin, Stephen & Reed, Howard, 1997. "Intergenerational Mobility in Britain," Economic Journal, Royal Economic Society, vol. 107(440), pages 47-66, January.
    2. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
    3. Ivar Ekeland & James J. Heckman & Lars Nesheim, 2004. "Identification and Estimation of Hedonic Models," Journal of Political Economy, University of Chicago Press, vol. 112(S1), pages 60-109, February.
    4. Hall, Peter & Wolff, Rodney C. L. & Yao, Qiwei, 1999. "Methods for estimating a conditional distribution function," LSE Research Online Documents on Economics 6631, London School of Economics and Political Science, LSE Library.
    5. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-1406, November.
    6. Einmahl, J.H.J. & Beirlant, J., 1996. "Maximal type test statistics based on conditional processes," Other publications TiSEM d031d073-2eea-4770-9bee-a, Tilburg University, School of Economics and Management.
    7. Gary Solon, 2002. "Cross-Country Differences in Intergenerational Earnings Mobility," Journal of Economic Perspectives, American Economic Association, vol. 16(3), pages 59-66, Summer.
    8. Phillips, Peter C. B., 1988. "Conditional and unconditional statistical independence," Journal of Econometrics, Elsevier, vol. 38(3), pages 341-348, July.
    9. Solon, Gary, 1999. "Intergenerational mobility in the labor market," Handbook of Labor Economics,in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 29, pages 1761-1800 Elsevier.
    10. Richard Blundell & Amanda Gosling & Hidehiko Ichimura & Costas Meghir, 2007. "Changes in the Distribution of Male and Female Wages Accounting for Employment Composition Using Bounds," Econometrica, Econometric Society, vol. 75(2), pages 323-363, March.
    11. Olley, G Steven & Pakes, Ariel, 1996. "The Dynamics of Productivity in the Telecommunications Equipment Industry," Econometrica, Econometric Society, vol. 64(6), pages 1263-1297, November.
    12. Solon, Gary, 1992. "Intergenerational Income Mobility in the United States," American Economic Review, American Economic Association, vol. 82(3), pages 393-408, June.
    13. Pakes, Ariel S, 1986. "Patents as Options: Some Estimates of the Value of Holding European Patent Stocks," Econometrica, Econometric Society, vol. 54(4), pages 755-784, July.
    14. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
    15. Richard Ericson & Ariel Pakes, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," Review of Economic Studies, Oxford University Press, vol. 62(1), pages 53-82.
    16. Horowitz, Joel L., 2001. "The Bootstrap," Handbook of Econometrics,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 52, pages 3159-3228 Elsevier.
    17. Alexandra L. Minicozzi, 2003. "Estimation of sons' intergenerational earnings mobility in the presence of censoring," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(3), pages 291-314.
    18. Pakes, Ariel & Ericson, Richard, 1998. "Empirical Implications of Alternative Models of Firm Dynamics," Journal of Economic Theory, Elsevier, vol. 79(1), pages 1-45, March.
    19. repec:dau:papers:123456789/6486 is not listed on IDEAS
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    Cited by:

    1. Takashi Kamihigashi & John Stachurski, 2014. "Partial Stochastic Dominance," Discussion Paper Series DP2014-23, Research Institute for Economics & Business Administration, Kobe University.
    2. Abdelaati Daouia & Hohsuk Noh & Byeong U. Park, 2016. "Data envelope fitting with constrained polynomial splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 3-30, January.
    3. Valentino Dardanoni & Mario Fiorini & Antonio Forcina, 2012. "Stochastic monotonicity in intergenerational mobility tables," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(1), pages 85-107, January.
    4. Takashi Kamihigashi & John Stachurski, 2011. "Existence, Stability and Computation of Stationary Distributions: An Extension of the Hopenhayn-Prescott Theorem," Discussion Paper Series DP2011-32, Research Institute for Economics & Business Administration, Kobe University.
    5. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
    6. Misha Beek & Hennie Daniels, 2014. "A Non-parametric Test for Partial Monotonicity in Multiple Regression," Computational Economics, Springer;Society for Computational Economics, vol. 44(1), pages 87-100, June.
    7. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    8. Lee, Tae-Hwy & Tu, Yundong & Ullah, Aman, 2014. "Nonparametric and semiparametric regressions subject to monotonicity constraints: Estimation and forecasting," Journal of Econometrics, Elsevier, vol. 182(1), pages 196-210.
    9. Jantti, Markus & Jenkins, Stephen P., 2013. "Income mobility," ISER Working Paper Series 2013-23, Institute for Social and Economic Research.
    10. Ibarra, Raul, 2013. "A spatial dominance approach to evaluate the performance of stocks and bonds: Does the investment horizon matter?," The Quarterly Review of Economics and Finance, Elsevier, vol. 53(4), pages 429-439.
    11. Sokbae (Simon) Lee & Ryo Okui & Yoon-Jae Whang, 2016. "Doubly robust uniform confidence band for the conditional average treatment effect function," CeMMAP working papers CWP03/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. Gutknecht, Daniel, 2016. "Testing for monotonicity under endogeneity," Journal of Econometrics, Elsevier, vol. 190(1), pages 100-114.
    13. Berghaus, Betina & Bücher, Axel, 2014. "Nonparametric tests for tail monotonicity," Journal of Econometrics, Elsevier, vol. 180(2), pages 117-126.
    14. Qu, Zhongjun & Yoon, Jungmo, 2015. "Nonparametric estimation and inference on conditional quantile processes," Journal of Econometrics, Elsevier, vol. 185(1), pages 1-19.
    15. Arden Finn & Murray Leibbrandt & Vimal Ranchhod, 2016. "Patterns of persistence: Intergenerational mobility and education in South Africa," SALDRU Working Papers 175, Southern Africa Labour and Development Research Unit, University of Cape Town.
    16. Aradillas-López, Andrés & Gandhi, Amit & Quint, Daniel, 2016. "A simple test for moment inequality models with an application to English auctions," Journal of Econometrics, Elsevier, vol. 194(1), pages 96-115.
    17. Delgado, Miguel A. & Escanciano, Juan Carlos, 2012. "Distribution-free tests of stochastic monotonicity," Journal of Econometrics, Elsevier, vol. 170(1), pages 68-75.
    18. Maribel Jiménez, 2016. "Movilidad Intergeneracional del Ingreso en Argentina. Un Análisis de sus Cambios Temporales desde el Enfoque de Igualdad de Oportunidades," CEDLAS, Working Papers 0203, CEDLAS, Universidad Nacional de La Plata.
    19. Armstrong, Timothy B. & Chan, Hock Peng, 2016. "Multiscale adaptive inference on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 194(1), pages 24-43.
    20. Daniel Gutknecht, 2013. "Testing for Monotonicity under Endogeneity An Application to the Reservation Wage Function," Economics Series Working Papers 673, University of Oxford, Department of Economics.
    21. 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.

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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