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

Abstract

Time use researchers frequently debate whether it is more appropriate to fit censored regression (Tobit) models using maximum likelihood estimation or linear models using ordinary least squares (OLS) to explain individuals' allocations of time to different activities as recorded in time-diary data. One side argues that estimation of Tobit models addresses the significant censoring (i.e., large numbers of zeros) typically found in time-diary data and that OLS estimation leads to biased and inconsistent estimates. The opposing side argues that optimization occurs over a longer period than that covered by the typical time diary, and thus that reported zeros represent measurement error rather than true non-participation in the activity, in which case OLS is preferred. We use the Australian Time Use Surveys, which record information for two consecutive diary days, to estimate 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. We find a moderate amount of measurement error when we use the 24-hour window compared to the 48-hour window, but a large number of zeros in the shorter window remain zeroes when we double the window length. Most of the qualitative conclusions we draw are similar for the two windows of observation and the two estimation methods, although there are some slight differences in the magnitudes and statistical significance of the estimates. Importantly, Tobit estimates appear to be more sensitive to window length than OLS estimates.

Time Spent on Child Care by Fathers in Leadership Positions: The Role of Work Hours and Flextime

“…According to the MacKelvey and Zavoina pseudo R 2 , the model accounts for only a small part of the variation in father involvement. This is not uncommon, however, for models of father involvement (e.g., Foster & Kalenkoski, 2013;Hook & Wolfe, 2012;Raley et al, 2012;Sousa-Poza et al, 2001). The main reason seems a large error variance in the models due to the method of surveying time use: The question refers to 1 day only, which introduces much randomness into the estimate of involvement (e.g., if the father happened to be on a trip or ill).…”

“…Although Tobit models are fairly common practice for time use variables (e.g., Craig, 2006b;Sayer et al, 2004;Sousa-Poza et al, 2001;Yeung et al, 2001), their use has not gone unquestioned. Because the zeroes can result from a reference period mismatch (e.g., the father may be usually involved but may have gone on a business trip on the diary day) rather than from being "truly uninvolved," some have advocated using ordinary least squares (OLS) models (Foster & Kalenkoski, 2013). Because this issue is unresolved, the analysis was conducted in parallel with a Tobit and an OLS model, without any important difference.…”

Health inequality and the uses of time for workers in Europe: policy implications

“…5 There can be some controversy regarding the selection of alternative models, such as that of Tobin (1958), given the high proportion of non-participation in some activities such as non-market work. Foster and Kalenkoski (2013) compare the use of Tobit and linear models in the analysis of the time devoted to childcare activities, finding that the qualitative conclusions are similar for the two estimation methods. 6 We do not include the labour status of respondents (e.g., part-time or full-time), as it may lead to endogeneity problems since the labour status of individuals probably influences the time devoted to all activities.…”

Total work time in Spain: evidence from time diary data

“…Foster and Kalenkoski (2013) compare the use of tobit and OLS models in the analysis of the time devoted to childcare activities, finding that the qualitative conclusions are similar for the two estimation methods. We estimate the following equation by OLS regressions:…”