Mitnik, Pablo. 2017. “Two-Sample Estimation of the Intergenerational Elasticity of Expected Income.” Stanford Center on Poverty and Inequality Working Paper.
The intergenerational income elasticity (IGE)—the workhorse measure of economic mobility—has very often been estimated with short-run income measures drawn from two independent samples and using the Two-Sample Two-Stage Least Squares estimator. The IGE conventionally estimated in the literature, however, has been widely misinterpreted: While it is assumed that it pertains to the conditional expectation of children’s income, it actually pertains to its conditional geometric mean. This has led to a call to replace it by the IGE of the expectation, which requires developing the methodological knowledge necessary to estimate the latter with short-run income measures drawn from two independent samples. This paper contributes to this aim in three ways. First, it advances a two-sample Generalized Method of Moments estimator of the exponential regression model, which can be used to estimate the IGE of the expectation. Second, it develops a generalized error-in-variables model for the estimation of the IGE of the expectation with that estimator and short-run income measures. Lastly, the paper uses data from the Panel Study of Income Dynamics to estimate the IGE of the expectation with the instruments typically available to mobility scholars. The empirical results are consistent with the predictions of the formal analysis and show that, if the income measures are obtained when parents and children are close to 40 years old, the estimates generated by the two-sample estimator need to be interpreted as upper-bound estimates and vary substantially across instruments. This suggests that mobility scholars should estimate the IGE with a variety of instruments, and then select the estimate that provides the tightest bound as the preferred upper-bound estimate.