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Testing for stochastic monotonicity

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  • Sokbae 'Simon' Lee

    ()
    (Institute for Fiscal Studies and University College London)

  • Oliver Linton

    ()
    (Institute for Fiscal Studies and London School of Economics)

  • Yoon-Jae Whang

    (Institute for Fiscal Studies and Seoul National University)

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 diffcult 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 infinite samples. We apply our test to the study of intergenerational income mobility.

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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP21/08.

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Date of creation: Jul 2008
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Handle: RePEc:ifs:cemmap:21/08

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  1. Ariel Pakes, 1986. "Patents as Options: Some Estimates of the Value of Holding European Patent Stocks," NBER Working Papers 1340, National Bureau of Economic Research, Inc.
  2. 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.
  3. Lorraine Dearden & Steve Machin & Howard Reed, 1995. "Intergenerational mobility in Britain," IFS Working Papers W95/20, Institute for Fiscal Studies.
  4. Einmahl, J.H.J. & Beirlant, J., 1996. "Maximal type test statistics based on conditional processes," Open Access publications from Tilburg University urn:nbn:nl:ui:12-125731, Tilburg University.
  5. Richard Blundell & Amanda Gosling & Hidehiko Ichimura & Costas Meghir, 2006. "Changes in the Distribution of Male and Female Wages Accounting for Employment Composition Using Bounds," CIRJE F-Series CIRJE-F-420, CIRJE, Faculty of Economics, University of Tokyo.
  6. Ivar Ekeland & James Heckman & Lars Nesheim, 2002. "Identification and estimation of hedonic models," CeMMAP working papers CWP07/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  7. Charles F. Manski & John V. Pepper, 1998. "Monotone Instrumental Variables: With an Application to the Returns to Schooling," Virginia Economics Online Papers 308, University of Virginia, Department of Economics.
  8. Pakes, A. & Ericson, R., 1990. "Empirical Implications Of Alternative Models Of Firm Dynamics," Papers 594, Yale - Economic Growth Center.
  9. 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.
  10. Solon, Gary, 1992. "Intergenerational Income Mobility in the United States," American Economic Review, American Economic Association, vol. 82(3), pages 393-408, June.
  11. Peter C.B. Phillips, 1987. "Conditional and Unconditional Statistical Independence," Cowles Foundation Discussion Papers 824R, Cowles Foundation for Research in Economics, Yale University, revised Dec 1987.
  12. Einmahl, J.H.J. & Keilegom, I. van, 2006. "Goodness-of-Fit Tests in Nonparametric Regression," Discussion Paper 2006-79, Tilburg University, Center for Economic Research.
  13. 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.
  14. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
  15. Gary Solon, 2002. "Cross-Country Differences in Intergenerational Earnings Mobility," Journal of Economic Perspectives, American Economic Association, vol. 16(3), pages 59-66, Summer.
  16. Peter Hall & Rodney C. L. Wolff & Qiwei Yao, 1999. "Methods for estimating a conditional distribution function," LSE Research Online Documents on Economics 6631, London School of Economics and Political Science, LSE Library.
  17. George S Olley & Ariel Pakes, 1992. "The Dynamics Of Productivity In The Telecommunications Equipment Industry," Working Papers 92-2, Center for Economic Studies, U.S. Census Bureau.
  18. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-406, November.
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Citations

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Cited by:
  1. 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.
  2. Victor Chernozhukov & Sokbae 'Simon' Lee & Adam Rosen, 2009. "Intersection Bounds: estimation and inference," CeMMAP working papers CWP19/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. Markus Jantti & Stephen P. Jenkins, 2014. "Income Mobility," Working Papers 319, ECINEQ, Society for the Study of Economic Inequality.
  4. Valentino Dardanoni & Mario Fiorini & Antonio Forcina, 2008. "Stochastic Monotonicity in Intergenerational Mobility Tables," Working Paper Series 156, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
  5. Berghaus, Betina & Bücher, Axel, 2014. "Nonparametric tests for tail monotonicity," Journal of Econometrics, Elsevier, vol. 180(2), pages 117-126.
  6. 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.
  7. Delgado, Miguel A. & Escanciano, Juan Carlos, 2012. "Distribution-free tests of stochastic monotonicity," Journal of Econometrics, Elsevier, vol. 170(1), pages 68-75.
  8. 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.

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