Mitnik, Pablo.
Forthcoming. “Intergenerational Income Elasticities, Instrumental Variable
Estimation, and Bracketing Strategies.” *Sociological Methodology*.

**Abstract**

The
fact that the intergenerational income elasticity (IGE)—the workhorse measure
of economic mobility—is defined in terms of the geometric mean of children’s
income generates serious methodological problems. This has led to a call to
replace it with the IGE of the expectation, which requires developing the
methodological knowledge necessary to estimate the latter with short-run
measures of income. This article contributes to this aim. The author advances a
“bracketing strategy” for the set estimation of the IGE of the expectation that
is equivalent to that used to set estimate (rather than point estimate) the
conventional IGE with estimates obtained with the ordinary least squares and
instrumental variable (IV) estimators. The proposed bracketing strategy couples estimates generated with the Poisson pseudo–maximum
likelihood estimator and a generalized method of moments IV estimator of the
Poisson or exponential regression model. The author develops a generalized
error-in-variables model for the IV estimation of the IGE of the expectation
and compares it with the corresponding model underlying the IV estimation of
the conventional IGE. By considering both bracketing strategies from the
perspective of the partial-identification approach to inference, the author specifies
how to construct confidence intervals for the IGEs, in
particular when the upper bound is estimated more than once with
different sets of instruments. Finally, using data from the Panel Study of
Income Dynamics, the author shows that the bracketing strategies work as
expected and assesses the information they generate and how this information
varies across instruments and short-run measures of parental income. Three
computer programs made available as companions to the article make the set
estimation of IGEs, and statistical inference, very simple endeavors.