Tobit or OLS? An empirical evaluation under different diary window lengths

Abstract

Researchers analysing time-use data often estimate limited dependent variable models because time spent must be nonnegative and cannot be more than the total amount of time in a given observation period. While the traditional empirical technique applied to such cases is maximum likelihood estimation of a Tobit (censored regression) model, recent debate has questioned whether linear models estimated via Ordinary Least Squares (OLS) are preferable. On the one hand, Tobit models are deemed necessary to address the significant censoring (i.e. large numbers of zeroes) typically found in time-use data, in the face of which OLS estimators would be biased and inconsistent. Yet, optimization occurs over a longer period than that covered by the typical time diary (often a day), and thus some argue that reported zeroes represent a measurement problem rather than true nonparticipation in the activity, in which case OLS would be preferred. We provide direct empirical evidence on this question using the Australian Time Use Surveys, which record time-use information for two consecutive diary days, by estimating censored and linear versions of a parental child care model for both 24-hour and 48-hour windows of observation in order to determine the empirical consequences of estimation technique and diary length.

Keywords:

• time-diary data
• Tobit
• OLS
• child care
• Australia

JEL Classification::

• J22
• J13
• D13
• B41

Notes

¹ Kalenkoski et al. (2011) propose an event-history model as a third alternative for modelling censored dependent variables. We do not evaluate this estimation option in the present article.

² This problem does not occur only with zero responses. For example, an individual may spend an average of 3.5 hours per day in child care but spend 6 hours on 1 day and one on the next. If we only observe one of those 2 days, then we have mis-measured that person's daily use of time.

³ In their unpublished paper, Gershuny and Egerton (2007) engage in a comparison of Tobit and OLS models but incorrectly compare OLS coefficients to Tobit coefficients, rather than to Tobit marginal effects. Stewart's (2009) working paper provides useful comparative simulations for censored and linear models, but does not apply different estimation methods to real data.

⁴ Diary incompleteness, in the sense of respondents not reporting activities for the full 48-hour diary window, is of minimal concern in this sample. The average number of minutes of unrecorded time is between 2 and 4 minutes per day depending on the sample and the year. Less than 5% of the sample of diary days is incomplete by even one minute.

⁵ An indicator for weekend is also included in the 24-hour models that include a weekend day and a weekday.

⁶ In this model, due to the discrete categorization of observations into three types based on observed Y, greater mis-measurement implies spurious changes in the categorization of observations, rather than reflecting underlying changes in latent Y* for the period over which individuals are actually optimizing.

⁷ For the censored Tobit models, all marginal effects are calculated in comparison to the omitted category for the relevant dummy array. With respect to the selected results shown in these tables, the omitted categories are: married, under 25 years old, speaking English at home, not Australian, has not completed high school, no other adults in the household, age of youngest child in household is less than 2 years, no disabled adults or children in the household, child care is not difficult to find, household is located in a metropolitan urban area, household has one dependent child, and (for samples that include weekend days) the diary day was a weekday.