Grouped Data Estimation and Testing in Simple Labor Supply Models

Labor supply research has not yet produced a clear statement of the size of the labor supply elasticity nor how it should be measured. Measurement error in hourly wage data and the use of inappropriate identifying assumptions can account for the poor performance of some empirical labor supply models. I propose here a generalization of Wald's method of fitting straight lines that is robust to measurement error, imposes mild testable identifying assumptions, and is useful for the estimation of life-cycle labor supply models with panel data. A convenient Two-Stage Least Squares (TSLS) equivalent of the generalized Wald estimator is presented and a TSLS over-identification test statistic is shown to be the test statistic for equality of alternative Wald estimates of the same parameter. These results are applied to labor supply models using a sample of continuously employed prime-age males. Labor supply elasticities from the two best-fitting models that pass tests of over-identifying restrictions range from 0.6 to 0.8 . A test for measurement error based on the difference between generalized Wald and Analysis of Covariance estimators is also proposed. Application of the test indicates that measurement error can account for low or negative Analysis of Covariance estimates of labor supply elasticities.