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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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  7. Dearden, Lorraine & Machin, Stephen & Reed, Howard, 1997. "Intergenerational Mobility in Britain," Economic Journal, Royal Economic Society, vol. 107(440), pages 47-66, January.
  8. 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.
  9. Phillips, Peter C. B., 1988. "Conditional and unconditional statistical independence," Journal of Econometrics, Elsevier, vol. 38(3), pages 341-348, July.
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  18. Solon, Gary, 1992. "Intergenerational Income Mobility in the United States," American Economic Review, American Economic Association, vol. 82(3), pages 393-408, June.
  19. 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.
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Cited by:
  1. Delgado, Miguel A. & Escanciano, Juan Carlos, 2012. "Distribution-free tests of stochastic monotonicity," Journal of Econometrics, Elsevier, vol. 170(1), pages 68-75.
  2. Victor Chernozhukov & Sokbae 'Simon' Lee & Adam Rosen, 2012. "Intersection bounds: estimation and inference," CeMMAP working papers CWP33/12, 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. Victor Chernozhukov & Iván Fernández-Val & Blaise Melly, 2012. "Inference on counterfactual distributions," CeMMAP working papers CWP05/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. 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, 01.
  6. 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.
  7. Misha Beek & Hennie Daniels, 2014. "A Non-parametric Test for Partial Monotonicity in Multiple Regression," Computational Economics, Society for Computational Economics, vol. 44(1), pages 87-100, June.
  8. Berghaus, Betina & Bücher, Axel, 2014. "Nonparametric tests for tail monotonicity," Journal of Econometrics, Elsevier, vol. 180(2), pages 117-126.
  9. 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.
  10. Raúl Ibarra-Ramírez, 2011. "Stocks, Bonds and the Investment Horizon: A Spatial Dominance Approach," Working Papers 2011-03, Banco de México.
  11. repec:ese:iserwp:2013-23 is not listed on IDEAS
  12. 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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