No time to lose: time constraints and physical activity in the production of health

Abstract

Although individuals are all endowed with the same time budgets—1,440 minutes per day—time use patterns differ owing to heterogeneity in preferences and in other constraints. In today’s health policy arena there is considerable discussion, but little conclusive strategy, about how to improve health outcomes by increasing levels of physical activity. In this paper, we explore how individuals with different levels of human capital (educational attainment) allocate time to physically-demanding activities that we characterize as health-producing behaviors. Our hypothesis is that many individuals are confronted with significant constraints on their allocation of time to exercise, and that these constraints differ importantly by level of human capital (e.g., educational attainment). However, the prediction of how human capital influences time allocated to physical activity is ambiguous because there are both substitution and wealth effects at work: since the shadow price of non-labor time use is relatively greater for high-wage individuals, they may spend less time engaged in health-promoting activities (as has been documented for activities like sleep); yet individuals who have amassed high levels of human capital are both more able to afford health-producing behaviors and more likely to prefer greater levels of produced health. We explore a set of empirical questions suggested by this framework using data from the American Time Use Survey (ATUS), administered by the U.S. Bureau of Labor Statistics. We focus on respondents ages 25–64 using the combined 2005 and 2006 ATUS data. The ATUS data are based on daily time use diaries completed by individuals aged 15 and older, including information on a large number of detailed physical activity time uses. We compare time allocated to physical activity to time allocated to sleep, household and personal activities, care for others, work, and non-exercise leisure activities. Since the ATUS time use categories are mutually exclusive and exhaustive (i.e. “multitasking” is not accommodated) we employ econometric share equation techniques to enforce the adding-up requirement that time use is constrained to 1,440 minutes per day. Our findings largely bear out the hypothesis that different levels of human capital endowment (educational attainment) result in different manifestations of how time is used in ways that may produce different health outcomes. While more-educated individuals tend to sleep much less than less-educated individuals and to work more hours, they are more likely to allocate time to physical activity in their leisure time. Our application of economic share equation techniques allows us to extend the literature by demonstrating not only how educational status is associated with time allocated to physical activity, but also where the other minutes of the day are allocated to and from.

Appendix: Estimation details

Appealing to the estimation methods described by Papke and Wooldridge for the univariate case, one can set up a multinomial logit-like criterion function $Q({\boldsymbol \beta } ) = \prod_{\text i = 1}^{\text N} {\prod_{{\text{m}} = 1}^{\text M} {\mu_{\rm im}^{{}} \left(\mathbf {x} \right)^{{{\text{y}}_{\text im} }} } }$ whose log is ${\hbox{J}}(\boldsymbol{\beta } ) { = }\sum\nolimits_{\text{i = 1}}^{\text{\text N}}{\sum\nolimits_{\text{m = 1}}^{\text{M}} {{\text {y}}_{\text{im}}\times \log \left( {\mu_{\text{im}} \left( \mathbf {x} \right)}\right)} }$, where $\boldsymbol {\beta }$ is either a kx(M-1) matrix or k(M-1)x1 vector depending on the particular reference. The corresponding estimating or score equations are:

$$ {\frac{{\partial \text{J}(\boldsymbol {\beta })}}{{\partial {\boldsymbol{\beta}}_{\text{m}} }}} = \sum\limits_{\text i = 1}^{\text N} {\mathbf {x}_{\text i}^{,} } \left[ {{\text y_{im}} - \left( {{\frac{{\exp (\mathbf {x}_{\text i} \boldsymbol{\beta }_{\text{m}} )}}{{1 + \sum\nolimits_{\text k = 2}^{\text M} {\exp (\mathbf{x}_{\rm i} \boldsymbol{\beta }_{\text k} )} }}}} \right)} \right],\quad {\text{j}} = 2, \ldots ,{\text{M}}, $$

which are obviously the same solution equations as those corresponding to a standard multinomial logit estimator; note, however, that in this case the y_im are not binary.¹¹ Consistency of the resulting $\widehat{\boldsymbol{\beta }}$ follows from standard arguments, in particular that ${\hbox{E}}\left[ {{\frac{{\partial {\rm J}(\boldsymbol{\beta })}}{{\partial \boldsymbol{\beta }_{\text{m}} }}}} \right] = {\rm E}_{\mathbf{x}} {\rm E}|\left[ {{\frac{{\partial {\rm J}(\boldsymbol{\beta })}}{{\partial \boldsymbol{\beta }_{\text{m}} }}}\left| \mathbf{x} \right.} \right] = \mathbf{0}$.

It should be noted that although estimating the model using MNL-type pseudo-likelihood methods will provide consistent estimates of the $\boldsymbol{\beta }_{\text{M}}$ parameters, the corresponding MNL covariance matrix will not be a consistent estimator of the true covariance matrix so long as Pr(y_im ∈ (0,1)|x _i) > 0, which is to be expected in the time use data. In particular, the data in such cases will exhibit underdispersion relative to a maintained multinomial probability structure. It can be demonstrated formally (Mullahy 2007) that the difference between the MNL covariance estimator obtained as the negative inverse expected Hessian and the expected standard robust “sandwich” estimator is positive semidefinite so that, e.g., standard errors obtained using the MNL covariance estimator will tend to be too large relative to actual standard errors (a result opposite that more commonly found in the literature on overdispersion).