A contract curve model of working hours and geometric mean regression analysis

Abstract

The framework of supply curve of working hours is a main tool to explain how working hours aredetermined or how working hours respond to tax rate changes. However, the estimation task of thesupply curve is not complete yet.We constructed a new model of working hours incorporating both supply and demand curves of working hours. The constructed model demonstrates that (1) working hours (h) and wage earnings (E) are determined jointly at an equilibrium point on a contract curve where demand and supply of workers are equal, and (2) the contract curve passes through the intersection of the supply and demand curves of working hours. These results imply that (1) it is impossible to estimate the supply curve of working hours because equilibrium points are not usually located on a supply curve of working hours, and (2) a contract curve of working hours should be estimated to measure the wage elasticity of working hours. For the estimation of contract curves, geometric mean regression (GMR) is selected for three reasons. First, the constructed model is a type of measurement error model. That is, both variables (h and E) in the contract curve equations are measured with errors. Second, the GMR estimator is the maximum likelihood estimator. Third, the coefficient of determination (R2) of both variables is equal in the GMR. The estimated wage elasticity of working hours for four industry groups is between -0.13 and -0.23. The transportation group has a slightly higher elasticity than the others, and high school graduates have a slightly higher elasticity than college graduates. In GMR, there is a simple relation between the coefficient of determination (R^2) and correlation coefficient (r_xy) as follows: R^2= (1+|r_xy|)/2.