This paper analyzes the dynamics of the distributions of per capita Gross Domestic Product (GDP), the infant mortality rate, and the adult literacy rate across states in Mexico during the period 1940-2000. It also analyzes the hypothesis of convergence to a common level of per capita income, infant mortality, and adult literacy among states. The approach used here exploits both the time-series and cross-section dimensions of the data by tracking the evolution over time of the entire cross-section distributions. Through the estimation of transition matrices for each of these welfare indicators, we are able to analyze changes in the external shapes of the distributions as well as the intra-distribution mobility of states. This allows us to analyze the long-run distributions by computing the invariant or ergodic distributions implied by the estimated transition matrices. The results show there is higher persistence over time in the positions states occupy in the distribution of per capita income than in the case of infant mortality and adult literacy. Furthermore, the results show there is convergence to a common level of adult literacy, but not to a common level of per capita income or infant mortality among Mexican states.