Repairing and Endogenizing the Solow Model

Abstract

Uzawa (1961) proves and Samuelson (1965) explains how Solow’s 1956 contribution to growth theory requires “purely labor-augmenting” steady-state technical change, a condition fundamentally inconsistent with observable reality. This paper uncovers Solow and Uzawa’s error – a misapplied unaugmented capital-output ratio that overturns the critical property of constant returns to scale for the Hicks invention-neutral function, Y= AF(K,L), thereby confounding the distinction between Hicks and Harrod-neutral change and creating unbalanced capital-labor growth. A benefit of the repaired Solow model is that it opens the door to a nearly unbounded set of varieties of factor-biased technical change, which invites a more robust interpretation of the nature of technical change. To contextualize the Solow-Uzawa error and provide a more systemic interpretation of technical change, the paper reinterprets Samuelson’s characterization of “natural units” of change. Contrasted with Samuelson’s characterization of capital as dollars and labor as unskilled labor, our reformulation centers on the symmetric units that frame the three principles of technical change: technical change requires natural units of augmentable undeveloped land and unskilled labor that function as platforms for new technologies; augmentation results from the recombinant innovation of molecular compounds to create objects and neural networks to create ideas; and the inseparable processes of factor accumulation and augmentation require the balancing of invention-neutral induced physical- and human-capital investment. With this reformulation, Solow 1956 transforms from a model requiring repeated exogenous additions of labor-augmenting change to a parsimonious model of continuous recursive invention-neutral technical change and economic growth.