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Bootstrap Critical Values for Tests Based on the Smoothed Maximum Score Estimator

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Author Info
Joel L. Horowitz (Univ. of Iowa)

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Abstract

The smoothed maximum score estimator of the coefficient vector of a binary response model is consistent and asymptotically normal under weak distributional assumptions. However, the differences between the true and nominal levels of tests based on smoothed maximum score estimates can be very large in finite samples when first- order asymptotics are used to obtain critical values. This paper shows that the bootstrap provides finite-sample critical values that are more accurate than those obtained from first-order asymptotic theory. In a set of Monte Carlo experiments carried out to check numerical performance, the bootstrap essentially eliminates large finite- sample distortions of level that occur when asymptotic critical values are used.

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Paper provided by EconWPA in its series Econometrics with number 9603003.

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Length: 48 pages
Date of creation: 07 Mar 1996
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Handle: RePEc:wpa:wuwpem:9603003

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Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General
C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
C5 - Mathematical and Quantitative Methods - - Econometric Modeling
C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

References listed on IDEAS
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. J. L. Horowitz, . "Bootstrap Methods In Econometrics: Theory And Numerical Performance," Sonderforschungsbereich 373 1995-63, Humboldt Universitaet Berlin.
  2. Horowitz, Joel & Hardle, Wolfgang, 1994. "Direct Semiparametric Estimation of Single-Index Models With Discrete Covariates," Working Papers 94-22, University of Iowa, Department of Economics.
    Other versions:
  3. Osterwald-Lenum, Michael, 1992. "A Note with Quantiles of the Asymptotic Distribution of the Maximum Likelihood Cointegration Rank Test Statistics," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 461-72, August.
  4. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March. [Downloadable!] (restricted)
  5. Hall, Stephen G & Milne, Alistair, 1994. "The Relevance of P-Star Analysis to UK Monetary Policy," Economic Journal, Royal Economic Society, vol. 104(424), pages 597-604, May. [Downloadable!] (restricted)
  6. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November. [Downloadable!] (restricted)
  7. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March. [Downloadable!] (restricted)
  8. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, revised 05 Mar 1996. [Downloadable!]
  9. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238. [Downloadable!] (restricted)
    Other versions:
  10. Karl-Heinz Tödter & Hans-Eggert Reimers, 1994. "P-Star as a link between money and prices in Germany," Review of World Economics (Weltwirtschaftliches Archiv), Springer, vol. 130(2), pages 273-289, June. [Downloadable!] (restricted)
  11. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August. [Downloadable!] (restricted)
  12. Campos, Julia & Ericsson, Neil R. & Hendry, David F., 1996. "Cointegration tests in the presence of structural breaks," Journal of Econometrics, Elsevier, vol. 70(1), pages 187-220, January. [Downloadable!] (restricted)
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  13. Cosslett, Stephen R, 1983. "Distribution-Free Maximum Likelihood Estimator of the Binary Choice Model," Econometrica, Econometric Society, vol. 51(3), pages 765-82, May. [Downloadable!] (restricted)
  14. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May. [Downloadable!] (restricted)
  15. Breusch, Trevor S & Wickens, Michael R, 1987. "Dynamic Specification, the Long Run and the Estimation of Transformed Regression Models," CEPR Discussion Papers 154, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  16. Wickens, Michael R., 1996. "Interpreting cointegrating vectors and common stochastic trends," Journal of Econometrics, Elsevier, vol. 74(2), pages 255-271, October. [Downloadable!] (restricted)
  17. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July. [Downloadable!] (restricted)
  18. Sherman, Robert P, 1993. "The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, Econometric Society, vol. 61(1), pages 123-37, January. [Downloadable!] (restricted)
  19. H. L"Utkepohl & T. Ter"Asvirta & J. Wolters, . "Investigating Stability and Linearity of a German M1 Money Demand Function," Sonderforschungsbereich 373 1995-57, Humboldt Universitaet Berlin.
    Other versions:
  20. Horowitz, J.L., 1995. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Working Papers 95-10, University of Iowa, Department of Economics.
  21. Hallman, Jeffrey J & Porter, Richard D & Small, David H, 1991. "Is the Price Level Tied to the M2 Monetary Aggregate in the Long Run?," American Economic Review, American Economic Association, vol. 81(4), pages 841-58, September. [Downloadable!] (restricted)
  22. Hwang, Hae-shin, 1985. "Test of the Adjustment Process and Linear Homogeneity in a Stock Adjustment Model of Money Demand," The Review of Economics and Statistics, MIT Press, vol. 67(4), pages 689-92, November. [Downloadable!] (restricted)
  23. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September. [Downloadable!] (restricted)
  24. Miller, Stephen M, 1991. "Monetary Dynamics: An Application of Cointegration and Error-Correction Modeling," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 23(2), pages 139-54, May. [Downloadable!] (restricted)
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Cited by:
(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. Yoshihiko Nishiyama & Peter M Robinson, 2005. "The Bootstrap and the Edgeworth Correction for Semiparametric Averaged Derivatives," STICERD - Econometrics Paper Series /2005/483, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  2. Marcin Owczarczuk, 2008. "Maximum score type estimators," Working Papers 28, Department of Applied Econometrics, Warsaw School of Economics. [Downloadable!]
  3. Yannis Bilias & Michael Haliassos, 2004. "The Distribution of Gains from Access to Stocks," CSEF Working Papers 125, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy. [Downloadable!]
  4. Francisco Alvarez-Cuadrado, 2006. "Improving The Efficiency And Robustness Of The Smoothed Maximum Score Estimator," Departmental Working Papers 2004-01, McGill University, Department of Economics. [Downloadable!]
  5. Olivier Armantier & Amadou Boly, 2008. "Can Corruption Be Studied in the Lab? Comparing a Field and a Lab Experiment," CIRANO Working Papers 2008s-26, CIRANO. [Downloadable!]
  6. Y. Nishiyama & Peter Robinson, 2004. "The bootstrap and the Edgeworth correction for semiparametric averaged derivatives," CeMMAP working papers CWP12/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
    Other versions:
  7. Bergström, Pål, 1999. "Bootstrap Methods and Applications in Econometrics - A Brief Survey," Working Paper Series 1999:2, Uppsala University, Department of Economics. [Downloadable!]
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