This paper proposes a fully nonparametric model to investigate the dynamics of intergenerational income mobility. In our model, an individual’s income class probabilities depend on parental income in a manner that accommodates nonlinearities and interactions among various individual characteristics and parental characteristics, including race, education, and parental age at childbearing. Consequently, we offer a generalization of Markov chain mobility models. We employ kernel techniques from machine learning and further regularization for estimating this highly flexible model. Utilizing data from the Panel Study of Income Dynamics (PSID), we find that race and parental education play significant roles in determining the influence of parental income on children’s economic prospects.