Estimating the Intergenerational Elasticity of Expected Income with Short-run Income Measures: A Generalized Error-in-variables Model

• In Event: 3269 - Statistical Advances

Abstract

The intergenerational income elasticity (IGE), ubiquitously estimated in the economic mobility literature, has been misinterpreted as pertaining to the expectation of children’s income when it actually pertains to its geometric mean. The (implicit) reliance on the geometric mean to index conditional income distributions greatly hinders the study of gender and marriage dynamics in intergenerational processes, and leads to IGE estimates affected by substantial selection bias. For these reasons, it has been recently proposed that the conventional IGE be replaced by the IGE of the expectation as the workhorse intergenerational elasticity. To make this possible, mobility scholars need to have available a generalized error-in-variables model for the estimation of the latter IGE with short-run income measures. This paper derives a Taylor-series-based closed-form expression for the probability limit of the Poisson Pseudo Maximum Likelihood (PPML) estimator of the IGE of the expectation, and then uses this expression to develop the needed error-in-variables model. It also evaluates the model with data from the Panel Study of Income Dynamics. The results of the empirical analyses offer clear support for the account of lifecycle and attenuation biases provided by the model, and show that the strategy most commonly employed to estimate the conventional IGE by OLS can also be used for the estimation of the IGE of the expectation with the PPML estimator. The results also suggest that in order to eliminate the bulk of attenuate bias, survey-data estimates of the IGE of the expectation need to be based on parental measures averaging a least 13 years of income information.

Author

• Pablo Andres Mitnik, Stanford University