The Ces Utility Function, Non-Linear Budget Constraints and Labour Supply. Results on Female Participation and Hours

Abstract

The most recent efforts in the study of labour supply decisions have concentrated on the estimation of explicit utility indices as a means to overcome the specification and endogeneity problems created by non-linear budget constraints. The presence of non-convexities and the interest in making welfare comparisons between individuals, are additional reasons that make the use of explicit utility functions, in either direct or indirect form, an essential requirement for labour supply studies. It is therefore important to consider carefully the available possibilities. From a utility index we want flexibility and ease of estimation. The StoneGeary function has proved its relative worth in consumption studies, but its performance has been disappointing when leisure is incorporated into the set of commodities. Abbot and Ashenfelter (I976) found that for part of their sample estimated available time was less than hours worked, and these results have pervasively reappeared in subsequent studies using this function.' Hausman (I980) has recently proposed a utility function which yields a linear hours function. This is an important contribution which facilitates the task of estimation enormously. This paper argues that the CES utility function, despite not generating a linear hours function, is also very convenient for estimation purposes. In fact it is shown below that to estimate the parameters of the utility function there is no need whatsoever for any explicit hours function. Labour supply responses by married women have been previously estimated with British data, but none of the available results has taken full account of the joint decision on participation and hours and of the non-linear shape of the budget constraint that the tax system generates. Layard et al. (I980) consider the joint decision in their estimation procedure but ignore the tax system. Greenhalgh (I980) takes into account the non-linearity of the budget constraint, but estimates labour supply responses by a method which treats participation and hours of work as separate and independent decisions. In the present paper, on the other hand, using an explicit utility index, we propose an estimation method which takes into account both the tax system and the joint hours-participation decision.