Mitnik, Pablo. 2017.
“Two-Sample Estimation of the Intergenerational Elasticity of Expected
Income.” Stanford Center on Poverty and
Inequality Working Paper.

**Abstract**

The
intergenerational income elasticity (IGE)—the workhorse measure of economic
mobility—has very often been estimated with short-run income measures drawn
from two independent samples and using the Two-Sample Two-Stage Least Squares
estimator. The IGE conventionally estimated in the literature, however, has
been widely misinterpreted: While it is assumed that it pertains to the
conditional expectation of children’s income, it actually
pertains to its conditional geometric mean. This has led to a call to
replace it by the IGE of the expectation, which requires developing the
methodological knowledge necessary to estimate the latter with short-run income
measures drawn from two independent samples. This paper contributes to this aim
in three ways. First, it advances a two-sample Generalized Method of Moments
estimator of the exponential regression model, which can be used to estimate
the IGE of the expectation. Second, it develops a generalized
error-in-variables model for the estimation of the IGE of the expectation with
that estimator and short-run income measures. Lastly, the paper uses data from
the Panel Study of Income Dynamics to estimate the IGE of the expectation with
the instruments typically available to mobility scholars. The empirical results
are consistent with the predictions of the formal analysis and show that, if
the income measures are obtained when parents and children are close to 40
years old, the estimates generated by the two-sample estimator need to be
interpreted as upper-bound estimates and vary substantially across instruments.
This suggests that mobility scholars should estimate the IGE with a variety of
instruments, and then select the estimate that provides the tightest bound as
the preferred upper-bound estimate.