Pedro Torres

 

Empirical research often relies on combining information from multiple datasets when key variables are not jointly observed. A widely used solution is the two-sample two-stage (TSTS) procedure, which imputes missing variables from a donor dataset and then estimates relationships using the imputed values. While TSTS enables otherwise infeasible analyses, it introduces two sources of bias: variance bias, due to reduced variability in imputed variables, and projection bias, stemming from Berkson measurement error. These biases affect estimands differently depending on whether the imputed variable is used as a regressor or as an outcome. Existing correction methods typically address only one source of bias—either restoring variance through stochastic imputation or correcting projection bias via rescaling—leaving the other unresolved. This paper proposes a novel quantile-based imputation approach that simultaneously targets both biases by adjusting first-stage predictions at the quantile level. The method fully restores the variance of the imputed variable and partially recovers the covariance lost during imputation, thereby improving the consistency of second-stage estimates.