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A Multi-factor Uzawa Growth Theorem and Endogenous Capital-Augmenting Technological Change

Gregory Casey () and Ryo Horii

No 1458, 2019 Meeting Papers from Society for Economic Dynamics

Abstract: We prove a generalized, multi-factor version of the Uzawa steady state growth theorem. In the two-factor case, the theorem implies that a neoclassical growth model cannot be simultaneously consistent with empirical evidence on both capital-augmenting technical change and the elasticity of substitution between labor and reproducible capital. In the multi-factor case, balanced growth with capital-augmenting technical change is possible as long as capital has a unitary elasticity of substitution with any single non-reproducible factor, significantly increasing the likelihood that neoclassical models can be consistent with empirical findings. To illustrate the importance of this result, we also build a three-factor growth model with endogenous and directed technical change and show that is has a locally stable balanced growth path with a strictly positive rate of capital-augmenting technical change.

Date: 2019
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