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The Tobit model with a non-zero threshold


  • Richard T. Carson
  • Yixiao Sun


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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    References listed on IDEAS

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    21. 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.
    22. I. Bateman & R. Brouwer & S. Ferrini & M. Schaafsma & D. Barton & A. Dubgaard & B. Hasler & S. Hime & I. Liekens & S. Navrud & L. De Nocker & R. Ščeponavičiūtė & D. Semėnienė, 2011. "Making Benefit Transfers Work: Deriving and Testing Principles for Value Transfers for Similar and Dissimilar Sites Using a Case Study of the Non-Market Benefits of Water Quality Improvements Across E," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 50(3), pages 365-387, November.
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    25. Kim, Younhee & Yang, Bongmin, 2011. "Relationship between catastrophic health expenditures and household incomes and expenditure patterns in South Korea," Health Policy, Elsevier, vol. 100(2), pages 239-246.

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