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Tobit or Not Tobit?


  • Stewart, Jay

    () (U.S. Bureau of Labor Statistics)


Time-use surveys collect very detailed information about individuals' activities over a short period of time, typically one day. As a result, a large fraction of observations have values of zero for the time spent in many activities, even for individuals who do the activity on a regular basis. For example, it is safe to assume that all parents do at least some childcare, but a relatively large fraction report no time spent in childcare on their diary day. Because of the large number of zeros Tobit would seem to be the natural approach. However, it is important to recognize that the zeros in time-use data arise from a mismatch between the reference period of the data (the diary day) and the period of interest, which is typically much longer. Thus it is not clear that Tobit is appropriate. In this study, I examine the bias associated with alternative estimation procedures for estimating the marginal effects of covariates on time use. I begin by adapting the infrequency of purchase model, which is typically used to analyze expenditures, 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 (1971) two-part model, and OLS – under a number of alternative assumptions about the data-generating process. I find that the estimated marginal effects from Tobits are biased and that the extent of the bias varies with the fraction of zero-value observations. The two-part model performs significantly better, but generates biased estimated in certain circumstances. Only OLS generates unbiased estimates in all of the simulations considered here.

Suggested Citation

  • Stewart, Jay, 2009. "Tobit or Not Tobit?," IZA Discussion Papers 4588, Institute for the Study of Labor (IZA).
  • Handle: RePEc:iza:izadps:dp4588

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    References listed on IDEAS

    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Blundell, Richard & Meghir, Costas, 1987. "Bivariate alternatives to the Tobit model," Journal of Econometrics, Elsevier, vol. 34(1-2), pages 179-200.
    9. 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.
    10. Joseph Price, 2008. "Parent-Child Quality Time: Does Birth Order Matter?," Journal of Human Resources, University of Wisconsin Press, vol. 43(1).
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    More about this item


    time use; Tobit;

    JEL classification:

    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • J22 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Time Allocation and Labor Supply

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