A generalized Uzawa growth theorem and capital-augmenting technological change

We prove a generalized, multi-factor version of the Uzawa steady-state growth theorem. The theorem implies that neoclassical growth models need at least three factors of production to be consistent with empirical evidence on both the capital-labor elasticity of substitution and the existence of capital-augmenting technical change. We also build and calibrate a three-factor endogenous growth model with directed technical change and show that it converges to a balanced growth path that is consistent with the empirical evidence. Our results indicate that natural resources including land and directed technical change play a central role in explaining balanced growth.