It has recently been argued that the intergenerational income elasticity (IGE) ubiquitously estimated in the economic mobility literature should be replaced by the IGE of expected income. This article derives an approximate closed-form expression for the probability limit of the Poisson Pseudo-Maximum Likelihood (PPML) estimator of constant elasticities and uses it to advance a generalized error-in-variables model for the estimation of the latter IGE with short-run income measures. Empirical analyses with data from the Panel Study of Income Dynamics offer clear support for the account of lifecycle and attenuation biases the model provides. Together, the model and the associated empirical evidence supply a methodological justification for the estimation of the IGE of the expectation with the PPML estimator and proxy income variables that satisfy some conditions. This eliminates the main obstacle for making this IGE the workhorse elasticity of the economic mobility field, which would (a) dissolve the selection-bias problem generated by the current expedient of dropping children with zero income from samples in order to make estimation of the conventional IGE possible, and (b) greatly stimulate the study of gender and marriage dynamics in intergenerational processes, something that the reliance on the conventionally estimated IGE essentially precludes.