We propose a model to study economic convergence in the tradition of neoclassical growth theory. We employ a novel stochastic set-up of the Solow (1956) model with shocks to both capital and labor. Our novel approach identifies the speed of convergence directly from estimating the parameters which determine equilibrium dynamics. The inference on the structural parameters is done using a maximum-likelihood approach. We estimate our model using growth and population data for China's provinces from 1980 to 2009. We report heterogeneity in the speed of convergence both across provinces and time. The Eastern provinces show a higher tendency of convergence, while there is no evidence of convergence for the Central and Western provinces. We find empirical evidence that the speed of convergence decreases over time for most provinces.