Although the intergenerational income elasticity (IGE) has long been the workhorse measure of economic mobility, this elasticity has been widely misinterpreted as pertaining to the conditional expectation of children’s income when 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 measures of income. This paper contributes to this aim. It advances a “bracketing strategy” for the estimation of the IGE of the expectation that is equivalent to that used to bracket 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. To achieve its goal the paper develops two generalized error-in-variables models for the IV estimation of the IGE of the expectation, and compares them to the corresponding model underlying the IV estimation of the conventional IGE. By considering the bracketing strategies from the perspective of the partial-identification approach to inference, the paper also specifies how to construct confidence intervals for the IGEs from the bounds estimated with those strategies. Lastly, using data from the Panel Study of Income Dynamics, the paper 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.