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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. 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.
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  13. Lorraine Dearden & Stephen Machin & H Reed, 1996. "Intergenerational Mobility in Britain," CEP Discussion Papers dp0281, Centre for Economic Performance, LSE.
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Citations

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Cited by:
  1. 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.
  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. repec:ese:iserwp:2013-23 is not listed on IDEAS
  4. Victor Chernozhukov & Ivan Fernandez-Val & Blaise Melly, 2008. "Inference On Counterfactual Distributions," Boston University - Department of Economics - Working Papers Series wp2008-005, Boston University - Department of Economics.
  5. Jäntti, Markus & Jenkins, Stephen P., 2013. "Income Mobility," IZA Discussion Papers 7730, Institute for the Study of Labor (IZA).
  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. 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.
  8. 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.
  9. Delgado, Miguel A. & Escanciano, Juan Carlos, 2012. "Distribution-free tests of stochastic monotonicity," Journal of Econometrics, Elsevier, vol. 170(1), pages 68-75.
  10. 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.
  11. Raúl Ibarra-Ramírez, 2011. "Stocks, Bonds and the Investment Horizon: A Spatial Dominance Approach," Working Papers 2011-03, Banco de México.
  12. Berghaus, Betina & Bücher, Axel, 2014. "Nonparametric tests for tail monotonicity," Journal of Econometrics, Elsevier, vol. 180(2), pages 117-126.

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