Tobit or not Tobit?

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.