The Complete Goods-activities Framework to Model Time Assignment, Consumption and Discrete Choices

The Complete Goods-activities Framework to Model Time Assignment, Consumption and Discrete Choices


Sergio R. Jara-Diaz, University of Chile, CL


A system of equations representing activities duration, goods consumption and discrete choices is derived from a general microeconomic framework. Properties (values of work and leisure) are highlighted and empirical experience is summarized.


Forty years of contributions to the understanding of time in consumer?s behaviour theory can be synthesized in a model that takes into account:
-all activities and all goods as sources of utility;
-a money budget constraint;
-a time budget constraint;
-technical constraints on goods and activities.

On the other hand, discrete choice models rest on the estimation of a conditional indirect utility function (CIUF) that represents the maximum an individual can achieve for each of the available alternatives. Within the transport field, this was proposed by Train and McFadden (1978) within a consumer?s behaviour framework that includes only goods and leisure as sources of utility in an aggregated manner.

Applying the discrete choice approach to the general model proposed above necessarily requires obtaining the conditional demands both for time assigned to all discretionary activities and for goods consumption. Once these are replaced back in utility, a generalized version of the CIUF is obtained. Most importantly, this function and the conditional demands have to be compatible.

By giving direct utility a Cobb-Douglas form and including the three types of constraints mentioned above, we have derived explicit equations for time assigned to work (an individual labour supply equation), for time assigned to discretionary activities, for goods consumption (or for the associated expenditures) and for the CIUF. The independent variables are the total time assigned to mandatory (time constrained) activities, total expenses on mandatory (constrained) goods, the wage rate, and the cost and time of the discrete alternatives. From these equations, the value of leisure, the value of time assigned to work and the value of time assigned to that activity modelled as a discrete choice, can be calculated.

At this point it should be realized that one can add as many discrete choice models as constrained activities or no discrete model at all. Therefore, the analyst has the choice to model a subset of the activity and consumption equations, including or not discrete choice models. In this paper the complete model is presented and the empirical experience so far is summarized, including systems of activity equations and joint activity-travel systems.


Association for European Transport