Labour Supply and Progressive Taxes

There are many studies in the literature involving the estimation of labour supply curves for individuals or families (Leuthold (1968), Kosters (1969), Christensen (1972), Hall (1973), Wales (1973, 1976), Wales and Woodland (1976, 1977)). Although most of these rely on the assumption of utility maximizing behaviour in their theoretical discussions, the empirical work is often based on an ad-hoc (often linear) reduced form equation relating hours of work to various determinants, such as the gross wage rate, non-labour income and socioeconomic variables. In some of these studies, however, the assumption of utility maximization carries through to the empirical work, resulting in a labour supply equation derived explicitly from a utility function (Leuthold (1968), Christensen (1972), Wales (1973, 1976), Wales and Woodland (1976, 1977)). At the macro level, on the other hand, there are many studies which explicitly use the utility function approach (Christensen (1968), Diewert (1974), Darrough (1975), Kiefer (1975), Abbott and Ashenfelter (1976), Donovan (1977)). Typically the treatment of taxes in empirical labour supply studies has been inadequate. Indeed in many cases information on taxes has not been available and consequently taxes have been ignored completely. When data are available the question arises of how to treat the piecewise-linear budget constraint implied by the progressive tax system. Several authors (Diewert (1971), Hall (1973), Wales (1973, 1976), Wales and Woodland (1976, 1977)) have proposed approximating this piecewise-linear constraint with a linear constraint passing through the observed point, thus yielding a net or after-tax wage rate to be used in place of the gross wage rate in the analysis. Although this procedure is appropriate for the non-stochastic case it introduces two problems in the stochastic case. First, the observed net wage rate that appears as an explanatory variable in the labour supply function is itself endogenous since it depends on the number of hours worked and is therefore correlated with the disturbance term. This endogeneity must be taken into account to avoid obtaining inconsistent estimates of the parameters.' The second problem involves a specification error. The basic difficulty is that although an individual may be observed to be on a given segment of a piecewise-linear constraint, this observed position is the sum of two components-his utility maximizing position plus a random disturbance. Hence it is entirely possible (particularly if the disturbances are large) that the individual's utility maximizing position may be on a segment of the piecewiselinear constraint other than the observed one. In this case the net after-tax wage rate that should be used in the labour supply equation is the one corresponding to the utility maximizing point, and not the observed one. Thus if the observed net wage rate is used in the estimation then for some individuals the appropriate net wage rate is measured with error while for others it is not. Further it is possible that an individual's utility maximizing position may be at one of the corners of the piecewise-linear constraint, rather than in the interior of a segment.