The Estimation of Labor Supply Over Kinked Budget Constraints: Some New Econometric Methodology

Most programs of taxation and income maintenance imply that the tax rate faced by an individual changes at different levels of labor supply. As a result, the individual's budget constraint is kinked which presents problems for the empirical study of labor supply. This paper develops econometric methodology for estimating labor supply in the presence of taxes. Equations for market wage and shadow price are used to describe labor supply choices over a kinked budget constraint This approach makes a distinction between the discrete choice of which segment or corner of the kinked constraint to work on and the selection of the actual number of hours of work along linear segments. A consistent procedure is derived that uses all the tax rates faced by the individual and relies on no more structure than has been used in the previous literature on labor force participation. This procedure summarizes the individual's kinked budget constraint by calculating the expected value of variables that assume different values on the sections of the constraint. Techniques for estimating the model based on a probit analysis of the decision to work above or below certain corners of the budget constraint are presented. Maximum likelihood estimation is also discussed.