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The Tobit model with a non-zero threshold

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  • Richard T. Carson
  • Yixiao Sun

Abstract

The standard Tobit maximum likelihood estimator under zero censoring threshold produces inconsistent parameter estimates, when the constant censoring threshold γ is non-zero and unknown. Unfortunately, the recording of a zero rather than the actual censoring threshold value is typical of economic data. Non-trivial minimum purchase prices for most goods, fixed cost for doing business or trading, social customs such as those involving charitable donations, and informal administrative recording practices represent common examples of non-zero constant censoring threshold where the constant threshold is not readily available to the econometrician. Monte Carlo results show that this bias can be extremely large in practice. A new estimator is proposed to estimate the unknown censoring threshold. It is shown that the estimator is superconsistent and follows an exponential distribution in large samples. Due to the superconsistency, the asymptotic distribution of the maximum likelihood estimator of other parameters is not affected by the estimation uncertainty of the censoring threshold. Copyright Royal Economic Society 2007

Suggested Citation

  • Richard T. Carson & Yixiao Sun, 2007. "The Tobit model with a non-zero threshold," Econometrics Journal, Royal Economic Society, vol. 10(3), pages 488-502, November.
  • Handle: RePEc:ect:emjrnl:v:10:y:2007:i:3:p:488-502
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    14. Xinyu Zhang & Alan T. K. Wan & Sherry Z. Zhou, 2011. "Focused Information Criteria, Model Selection, and Model Averaging in a Tobit Model With a Nonzero Threshold," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 132-142, June.
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    19. Carson, Richard T. & Louviere, Jordan J., 2014. "Statistical properties of consideration sets," Journal of choice modelling, Elsevier, vol. 13(C), pages 37-48.
    20. Heimer, Rawley Z., 2014. "Friends do let friends buy stocks actively," Journal of Economic Behavior & Organization, Elsevier, vol. 107(PB), pages 527-540.
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    22. Emin M. Dinlersoz & Mehmet Yorukoglu, 2012. "Information and Industry Dynamics," American Economic Review, American Economic Association, vol. 102(2), pages 884-913, April.
    23. Daniel Ordoñez-Callamand & Mauricio Villamizar-Villegas & Luis F. Melo-Velandia, 2016. "Foreign Exchange Intervention Revisited: A New Way of Estimating Censored Models," Borradores de Economia 972, Banco de la Republica de Colombia.
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    25. Darius Lakdawalla & Wesley Yin, 2009. "Insurer Bargaining and Negotiated Drug Prices in Medicare Part D," NBER Working Papers 15330, National Bureau of Economic Research, Inc.

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