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Testing for stochastic monotonicity

  • Sokbae Lee

    ()

    (Institute for Fiscal Studies and cemmap and SNU)

  • Oliver Linton

    ()

    (Institute for Fiscal Studies and cemmap and Cambridge)

  • Yoon-Jae Whang

    ()

    (Institute for Fiscal Studies and SNU)

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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File URL: http://cemmap.ifs.org.uk/wps/cwp2108.pdf
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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 & Richard Ericson, 1989. "Empirical Implications of Alternative Models of Firm Dynamics," NBER Working Papers 2893, National Bureau of Economic Research, Inc.
  2. 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 S60-S109, February.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. Lorraine Dearden & Stephen Machin & H Reed, 1996. "Intergenerational Mobility in Britain," CEP Discussion Papers dp0281, Centre for Economic Performance, LSE.
  8. Gary Solon, 2002. "Cross-Country Differences in Intergenerational Earnings Mobility," Journal of Economic Perspectives, American Economic Association, vol. 16(3), pages 59-66, Summer.
  9. Ericson, Richard & Pakes, Ariel, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," Review of Economic Studies, Wiley Blackwell, vol. 62(1), pages 53-82, January.
  10. repec:att:wimass:9604 is not listed on IDEAS
  11. Solon, Gary, 1992. "Intergenerational Income Mobility in the United States," American Economic Review, American Economic Association, vol. 82(3), pages 393-408, June.
  12. 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.
  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. Phillips, Peter C. B., 1988. "Conditional and unconditional statistical independence," Journal of Econometrics, Elsevier, vol. 38(3), pages 341-348, July.
  16. 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.
  17. Ariel Pakes, 1984. "Patents as Options: Some Estimates of the Value of Holding European Patent Stocks," NBER Working Papers 1340, National Bureau of Economic Research, Inc.
  18. 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.
  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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