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We incorporate forward-looking capital accumulation into a dynamic discrete choice model of migration. We characterize the steady-state equilibrium; generalize existing dynamic exact-hat algebra techniques to incorporate investment; and linearize the model to provide an analytical characterization of the economy's transition path using spectral analysis. We show that capital and labor dynamics interact to shape the economy's speed of adjustment towards steady-state. We implement our quantitative analysis using data on capital stocks, populations and bilateral trade and migration flows for U.S. states from 1965-2015. We show that this interaction between capital and labor dynamics plays a central role in explaining the observed decline in the rate of income convergence across U.S. states and the persistent and heterogeneous impact of local shocks.