Tobit or Not Tobit?
by
Jay Stewart
(November 2009)
forthcoming in: Journal of Economic and Social Measurement
Abstract:
Timeuse 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 timeuse 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 timediary 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 timediary data – Tobit, the Cragg (1971) twopart model, and OLS – under a number of alternative assumptions about the datagenerating process. I find that the estimated marginal effects from Tobits are biased and that the extent of the bias varies with the fraction of zerovalue observations. The twopart model performs significantly better, but generates biased estimated in certain circumstances. Only OLS generates unbiased estimates in all of the simulations considered here.
Text: See Discussion Paper No. 4588
