This paper explores the estimation of a class of life-cycle discrete choice intergenerational models. It proposes a new semiparametric estimator. It shows that it is root-n-consistent and asymptotically normally distributed. We compare our estimator with a modified version of the full solution maximum likelihood estimator (MLE) in a Monte Carlo study. Our estimator performs comparably to the MLE in a finite sample but greatly reduces the computational cost. The paper documents that the quantity-quality trade-offs depend on the household composition and specialization in the household. Using the proposed estimator, we estimate a dynastic model that rationalizes these observed patterns.