Intergenerational Income Elasticities, Instrumental Variable Estimation, and Bracketing Strategies

The fact that the intergenerational income elasticity (IGE)—the workhorse measure of economic mobility—is defined in terms of the geometric mean of children’s income generates serious methodological problems. This has led to a call to replace it with the IGE of the expectation, which requires developing the methodological knowledge necessary to estimate the latter with short-run measures of income. This article contributes to this aim. The author advances a “bracketing strategy” for the set estimation of the IGE of the expectation that is equivalent to that used to set estimate (rather than point estimate) the conventional IGE with estimates obtained with the ordinary least squares and instrumental variable (IV) estimators. The proposed bracketing strategy couples estimates generated with the Poisson pseudo–maximum likelihood estimator and a generalized method of moments IV estimator of the Poisson or exponential regression model. The author develops a generalized error-in-variables model for the IV estimation of the IGE of the expectation and compares it with the corresponding model underlying the IV estimation of the conventional IGE. By considering both bracketing strategies from the perspective of the partial-identification approach to inference, the author specifies how to construct confidence intervals for the IGEs, in particular when the upper bound is estimated more than once with different sets of instruments. Finally, using data from the Panel Study of Income Dynamics, the author shows that the bracketing strategies work as expected and assesses the information they generate and how this information varies across instruments and short-run measures of parental income. Three computer programs made available as companions to the article make the set estimation of IGEs, and statistical inference, very simple endeavors.