Jay Stewart (2009)
"Tobit or Not Tobit?"
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.
Last Modified Date: February 5, 2010