Galtonian regression of intergenerational income linkages: biased procedures, a new estimator and mean-square error comparisons

Because the permanent incomes of parents and children are typically unobserved, the estimation of the intergenerational correlation via the use of proxy variables entails an errors-in-variables bias. By solving a system of moment equations for income observed at a given year, and a T-period average of this variable, we derive an analytical form for the signal to total variance ratio. In turn, we propose a simple estimator of the intergenerational elasticity via division of the OLS estimator of this quantity. Estimates of the intergenerational elasticity derived from a PSID sample range between 0.34 and 0.69. The averaging estimator provides intermediary values between OLS and the proposed estimator. Persistence is higher for family income measures than labor market outcomes. Estimates generally increase for moving average specifications in comparison to the assumption that measurement errors are uncorrelated. The three estimators are further examined in the light of their mean-square errors (square bias plus variance).