Inference on Counterfactual Transition Matrices (with Brantly Callaway, Job Market Paper)
Abstract: Transition matrices provide a very useful way to summarize the dependence between two random variables; for example, the dependence between parents’ income and child’s income. This paper considers estimation and inference techniques for (i) conditional transition matrices – transition matrices that are conditional on some vector of covariates, (ii) counterfactual transition matrices – transition matrices that arise from holding fixed conditional transition matrices but adjusting the distribution of the covariates, and (iii) transition matrix average partial effects. Estimating conditional transition matrices is closely related to estimating conditional distribution functions, and we propose new semiparametric distribution regression estimators that may be of interest in other contexts as well. We also derive uniform inference results for transition matrices that allow researchers to account for issues such as multiple testing that naturally arise when estimating a transition matrix. We use our results to study differences in intergenerational mobility for black families and white families. In the application, we document large differences between the transition matrices of black and white families. We also show that these differences are partially, but not fully, explained by differences in the distributions of other family characteristics.
[Semiparametric Estimation of Local Intergenerational Elasticities] (status: working paper)