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Tobit or not Tobit?

Author

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  • Stewart, Jay

    (U.S. Bureau of Labor Statistics, 2 Massachusetts Ave., NE, Washington, DC 20212, USA)

Abstract

Time-diary surveys collect detailed information about individuals’ activities over a short period of time, typically one day. Thus, it is common to see zero time spent in many activities, even for individuals who regularly do the activity. Because of the large number of zeros, Tobit would seem to be the natural approach. However, once it is recognized that these zeros arise not from censoring, but from a mismatch between the reference period of the data (the diary day) and the period of interest (typically much longer than a day), it is not clear that Tobit is appropriate. I examine the bias associated with alternative procedures for estimating the marginal effects of covariates on time use. I begin by adapting the infrequency of purchase model to time-diary data and showing that OLS estimates are unbiased. Next, using simulated data, I examine the bias associated with three procedures that are commonly used to analyze time-diary data – Tobit, the Cragg [11] two-part model, and OLS. I find that the estimated marginal effects from Tobit are biased and that the bias increases with the fraction of zero-value observations. The two-part model performs significantly better, but generates biased estimates when the number of zeros is a function of the covariates. Only OLS generates unbiased estimates in all of the simulations considered here

Suggested Citation

  • Stewart, Jay, 2013. "Tobit or not Tobit?," Journal of Economic and Social Measurement, IOS Press, issue 3, pages 263-290.
    • Handle: RePEc:ris:iosjes:0004
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    References listed on IDEAS

    as
    1. Sven-Olov Daunfeldt & Jörgen Hellström, 2007. "Intra-household Allocation of Time to Household Production Activities: Evidence from Swedish Household Data," LABOUR, CEIS, vol. 21(2), pages 189-207, June.
    2. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
    3. Lennart Flood & Urban Gråsjo, 2001. "A Monte Carlo simulation study of Tobit models," Applied Economics Letters, Taylor & Francis Journals, vol. 8(9), pages 581-584.
    4. Joseph Price, 2008. "Parent-Child Quality Time: Does Birth Order Matter?," Journal of Human Resources, University of Wisconsin Press, vol. 43(1).
    5. Cragg, John G, 1971. "Some Statistical Models for Limited Dependent Variables with Application to the Demand for Durable Goods," Econometrica, Econometric Society, vol. 39(5), pages 829-844, September.
    6. Alfonso Sousa-Poza & Hans Schmid & Rolf Widmer, 2001. "The allocation and value of time assigned to housework and child-care: An analysis for Switzerland," Journal of Population Economics, Springer;European Society for Population Economics, vol. 14(4), pages 599-618.
    7. McDonald, John F & Moffitt, Robert A, 1980. "The Uses of Tobit Analysis," The Review of Economics and Statistics, MIT Press, vol. 62(2), pages 318-321, May.
    8. Harley Frazis & Jay Stewart, 2011. "How does household production affect measured income inequality?," Journal of Population Economics, Springer;European Society for Population Economics, vol. 24(1), pages 3-22, January.
    9. Blundell, Richard & Meghir, Costas, 1987. "Bivariate alternatives to the Tobit model," Journal of Econometrics, Elsevier, vol. 34(1-2), pages 179-200.
    10. Keen, Michael, 1986. "Zero Expenditures and the Estimation of Engel Curves," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 1(3), pages 277-286, July.
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    More about this item

    Keywords

    Tobit; two-step estimation; OLS; time-use data;

    JEL classification:

    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models

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