The intergenerational income elasticity (IGE) conventionally estimated in the mobility literature has been widely misinterpreted as pertaining to the conditional expectation of children’s income, when in fact it pertains to its conditional geometric mean. In line with recent work, this article focuses on the estimation of the IGE of expected income. It proposes that, in the one-sample context, estimation of this IGE be based on the Poisson Pseudo Maximum Likelihood estimator, or on a Generalized Method of Moments (GMM) instrumental variable estimator of the Poisson or exponential regression model, depending on the parental information available. These estimators can also be used together to generate a set estimate of the IGE of the expectation. In the two-sample context, the article proposes that estimation be based on a recently advanced two-sample GMM estimator of the exponential regression model. The article explains how to use official Stata commands to estimate the IGE of the expectation with the first two estimators, and how to construct confidence intervals for the partially identified IGE when their estimates are combined to generate a set estimate. It also explains how to use the user-written Stata command igetwos to estimate the IGE of the expectation with the third estimator in the two-sample context.