Endogenous Saving in a Model of Factor-Eliminating Technical Change

Virtually all theoretical studies satisfy the requirement for economic growth via the augmentation of non-reproducible factors of production. Peretto and Seater (2009), however, satisfy the requirement using a different mechanism. They develop an endogenous theory of factor elimination, whereby the non-reproducible factors of production are eliminated from the production process. They allow factor intensities to change endogenously via spending on R&D, and this serves as the catalyst for growth. In this paper, I extend the theory developed by Peretto and Seater by incorporating endogenous saving. Peretto and Seater assume that households save a fixed fraction of their total income. The general equilibrium dynamics in their model have two possible outcomes. If the exogenous saving rate is high enough, the economy’s production function becomes AK in the limit thereby supporting perpetual growth. If the saving rate is not sufficiently high, the economy goes to a Solow steady state with no growth and a standard production function with fixed factor intensities. My model yields the same testable implications pertaining to cross-country factor shares, offers the same insight into the transition from a primitive to an advanced economy and provides the same resolution to the linearity critique as that of Peretto and Seater. However, the equilibrium dynamics in my model have only one possible outcome—the economy achieves perpetual growth. Consumer optimization alters the model so that the possibility of a Solow Steady state is eliminated; all equilibrium paths lead to a production function that asymptotically becomes AK. This extension, which is analogous to moving from the Solow model to the Cass model, enriches the theory. The primary new finding is that the saving rate, when chosen by optimizing households, is always high enough to support perpetual growth. The inclusion of consumer optimization also lays the foundation for the model to be extended in the future to analyze government policies because government policies, in general, impact the incentive to save.