Everything’s not lost: revisiting TSTSLS estimates of intergenerational mobility in developing countries

This paper revisits the two-sample two-stage least squares (TSTSLS) method, commonly used to estimate intergenerational mobility measures without linked parent–child earnings data. First, we study the TSTSLS intergenerational earnings elasticity (IGE) by decomposing it into the IGE estimated via OLS with linked parent–child earnings data, a projection bias, and a variance bias. We propose a parsimonious procedure, the doubly corrected TSTSLS (DC-TSTSLS), to (i) eliminate the variance bias and (ii) reduce the prediction bias. Our method provides a lower bound for the IGE estimate via OLS with linked earnings data. Second, we formally study the rank-rank correlation estimated through TSTSLS by decomposing the estimator into the rank-rank correlation estimated through OLS with linked data and a projection bias. We deliver analytical conditions for when this estimate is a lower-bound of the OLS rank-rank correlation estimated using linked data. Finally, we use parent–child linked administrative data from a developing country to test our lower-bound method through an empirical Monte Carlo approach, confirming its validity. Our doubly corrected IGE and rank-rank TSTSLS estimators are informative lower bounds of their respective OLS intergenerational mobility estimates computed using linked data. Our results suggest that the following practices should be implemented when the TSTSLS method is used to estimate intergenerational mobility measures: (i) report the estimates of the rank-rank correlation computed through TSTSLS, and (ii) implement our lower-bound methodology when facing data constraints, (i.e., only a few controls are available to impute parental earnings).