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 biases. 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, and uses it 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 Ordinary Least Squares can also be used for the estimation of the IGE of the expectation with the PPML estimator.