Dynamic models of structural transformation are often non-stationary, precluding balanced growth path (BGP) analysis. We develop a generalization of the BGP concept that we call a Stable Transformation Path (STraP). The STraP characterizes the medium-term dynamics of the economy in a turnpike sense; it is the non-stationary path toward which the economy (quickly) converges from an arbitrary initial capital stock. Calibrated simulations demonstrate that these medium-term dynamics have important quantitative implications for structural transformation, investment, and growth, including slow convergence. Medium-term dynamics alone account for the observed 40% secular decline in average growth rates across stages of development.