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Conditional Moment Tests for Parametric Duration Models

  • James E. Prieger

This paper develops and compares specification tests for parametric duration models estimated with censored data. The tests are based on generalized residuals (the integrated hazard), which is exponentially distributed if the model is correctly specified. I present several conditional moment tests based on the generalized residuals: a raw moments test, a test based on Laguerre polynomials, and a Lagrange multiplier (LM) test. The LM test extends Lancaster’s (1985) test by allowing an arbitrarily precise approximation of the likelihood under the alternative. The raw moments test implemented via an auxiliary regression is examined using both asymptotic and bootstrap critical values. Monte Carlo evidence indicates that no one test dominates the others in all situations in terms of size, power, and ease of use. When the data are not censored, the Laguerre test appears to be the best choice. When there is censoring in the data, the Laguerre test is still at least as powerful as the other tests, but the raw moment test may be more convenient to perform. For the convenience of the practitioner the explicit forms of the tests for exponential and Weibull duration models are presented.

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Paper provided by California Davis - Department of Economics in its series Department of Economics with number 00-10.

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Handle: RePEc:fth:caldec:00-10
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  1. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September.
  2. Gourieroux, Christian & Monfort, Alain & Renault, Eric & Trognon, Alain, 1987. "Generalised residuals," Journal of Econometrics, Elsevier, vol. 34(1-2), pages 5-32.
  3. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
  4. Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April.
  5. Kiefer, Nicholas M., 1985. "Specification diagnostics based on Laguerre alternatives for econometric models of duration," Journal of Econometrics, Elsevier, vol. 28(1), pages 135-154, April.
  6. Sunil Sharma, 1987. "Specification Diagnostics for Econometric Models of Duration," UCLA Economics Working Papers 440, UCLA Department of Economics.
  7. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March.
  8. Jaggia, Sanjiv & Thosar, Satish, 1995. "Contested Tender Offers: An Estimate of the Hazard Function," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 113-19, January.
  9. Pagan, Adrian & Vella, Frank, 1989. "Diagnostic Tests for Models Based on Individual Data: A Survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(S), pages S29-59, Supplemen.
  10. Joel L. Horowitz, 1999. "Semiparametric Estimation of a Proportional Hazard Model with Unobserved Heterogeneity," Econometrica, Econometric Society, vol. 67(5), pages 1001-1028, September.
  11. Sanjiv Jaggia, 1997. "Alternative Forms of the Score Test for Heterogeneity in a Censored Exponential Model," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 340-343, May.
  12. Jaggia, Sanjiv, 1991. "Tests of moment restrictions in parametric duration models," Economics Letters, Elsevier, vol. 37(1), pages 35-38, September.
  13. Horowitz, Joel L & Neumann, George R, 1989. "Specification Testing in Censored Regression Models: Parametric and Semiparametric Methods," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(S), pages S61-86, Supplemen.
  14. Lancaster, Tony, 1985. "Generalised residuals and heterogeneous duration models : With applications to the Weilbull model," Journal of Econometrics, Elsevier, vol. 28(1), pages 155-169, April.
  15. Chesher, Andrew & Spady, Richard, 1991. "Asymptotic Expansions of the Information Matrix Test Statistic," Econometrica, Econometric Society, vol. 59(3), pages 787-815, May.
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