An important question is whether underdeveloped countries will converge to the per-capita income level of developed countries. Economists have used the disequilibrium adjustment property of growth models to justify the view that convergence should occur. Unfortunately, the empirical literature does not obey the "Lucas" admonition of estimating the structural parameters of a growth model that has the conditional convergence property and then computing the speed of convergence implied by the estimated structural parameters. In this paper, we use U.S. time-series data to estimate the structural parameters of a stochastic neoclassical growth model and compute the speed of conditional convergence in the non-stochastic model from the structural parameter estimates. We follow an approach used to econometrically estimate business cycle models via maximum likelihood. We obtain a speed of conditional convergence of 12.8 percent per-year for logarithmic consumer preferences and find that the data rejects the hypothesis of the 2 percent per-year speed of conditional convergence obtained in the empirical literature.