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Testing for Stochastic Monotonicity

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Author Info
Sokbae Lee
Oliver Linton
Yoon-Jae Whang

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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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File URL: http://hdl.handle.net/10.3982/ECTA7145
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Publisher 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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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
  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. [Downloadable!]
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  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. [Downloadable!] (restricted)
  4. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
  5. Solon, Gary, 1992. "Intergenerational Income Mobility in the United States," American Economic Review, American Economic Association, vol. 82(3), pages 393-408, June. [Downloadable!] (restricted)
  6. Pakes, A. & Ericson, R., 1990. "Empirical Implications Of Alternative Models Of Firm Dynamics," Papers 594, Yale - Economic Growth Center.
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  7. 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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  8. 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. [Downloadable!] (restricted)
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  9. Gary Solon, 2002. "Cross-Country Differences in Intergenerational Earnings Mobility," Journal of Economic Perspectives, American Economic Association, vol. 16(3), pages 59-66, Summer. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
  11. 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. [Downloadable!] (restricted)
  12. Einmahl, John H.J. & Van Keilegom, Ingrid, 2006. "Goodness-of-fit tests in nonparametric regression," Discussion Paper 79, Tilburg University, Center for Economic Research. [Downloadable!]
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  13. Phillips, Peter C. B., 1988. "Conditional and unconditional statistical independence," Journal of Econometrics, Elsevier, vol. 38(3), pages 341-348, July. [Downloadable!] (restricted)
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  14. 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. [Downloadable!] (restricted)
  15. 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. [Downloadable!] (restricted)
  16. 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. [Downloadable!]
  17. 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. [Downloadable!] (restricted)
  18. Dearden, Lorraine & Machin, Stephen & Reed, Howard, 1997. "Intergenerational Mobility in Britain," Economic Journal, Royal Economic Society, vol. 107(440), pages 47-66, January. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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 22 Nov 2007. [Downloadable!]
  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. [Downloadable!]
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