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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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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 77 (2009)
Issue (Month): 2 (03)
Pages: 585-602

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Handle: RePEc:ecm:emetrp:v:77:y:2009:i:2:p:585-602

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References

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  1. Lorraine Dearden & Steve Machin & Howard Reed, 1995. "Intergenerational mobility in Britain," IFS Working Papers W95/20, Institute for Fiscal Studies.
  2. 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.
  3. 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.
  4. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
  5. Ekeland, Ivar & Heckman, James J. & Nesheim, Lars, 2003. "Identification and Estimation of Hedonic Models," IZA Discussion Papers 853, Institute for the Study of Labor (IZA).
  6. Einmahl, J.H.J. & Keilegom, I. van, 2004. "Goodness-of-fit Tests in Nonparametric Regression," Discussion Paper 2004-12, Tilburg University, Center for Economic Research.
  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. Pakes, Ariel S, 1986. "Patents as Options: Some Estimates of the Value of Holding European Patent Stocks," Econometrica, Econometric Society, vol. 54(4), pages 755-84, July.
  9. Phillips, Peter C. B., 1988. "Conditional and unconditional statistical independence," Journal of Econometrics, Elsevier, vol. 38(3), pages 341-348, July.
  10. 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.
  11. 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.
  12. 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.
  13. Ariel Pakes & Richard Ericson, 1989. "Empirical Implications of Alternative Models of Firm Dynamics," NBER Working Papers 2893, National Bureau of Economic Research, Inc.
  14. G. Steven Olley & Ariel Pakes, 1992. "The Dynamics of Productivity in the Telecommunications Equipment Industry," NBER Working Papers 3977, National Bureau of Economic Research, Inc.
  15. 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.
  16. Solon, Gary, 1992. "Intergenerational Income Mobility in the United States," American Economic Review, American Economic Association, vol. 82(3), pages 393-408, June.
  17. 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.
  18. Olley, G Steven & Pakes, Ariel, 1996. "The Dynamics of Productivity in the Telecommunications Equipment Industry," Econometrica, Econometric Society, vol. 64(6), pages 1263-97, November.
  19. Hall, Peter & Wolff, Rodney C. L. & Yao, Qiwei, 1999. "Methods for estimating a conditional distribution function," Open Access publications from London School of Economics and Political Science http://eprints.lse.ac.uk/, London School of Economics and Political Science.
  20. 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.
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Citations

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Cited by:
  1. 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.
  2. 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.
  3. Delgado, Miguel A. & Escanciano, Juan Carlos, 2012. "Distribution-free tests of stochastic monotonicity," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/15031, Universidad Carlos III de Madrid.
  4. Victor Chernozhukov & Sokbae 'Simon' Lee & Adam Rosen, 2011. "Intersection bounds: estimation and inference," CeMMAP working papers CWP34/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Marmer, Vadim & Shneyerov, Artyom & Xu, Pai, 2007. "What Model for Entry in First-Price Auctions? A Nonparametric Approach," Micro Theory Working Papers marmer-07-11-22-02-26-44, Microeconomics.ca Website, revised 18 Feb 2011.

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