The endogenous direction of technological change in a discrete-time Ramsey model

The relative price of capital (or equipment) goods with respect to consumption goods is strongly, negatively correlated with income per capita in cross-sections of countries. This stylized fact suggests that economic growth takeoffs are associated with changes in the direction of technical change. It also suggests that increases in productivity that are embodied in capital goods lead to relatively quicker growth. The goal of this paper is to explore the message of the discrete-time Ramsey model with logarithmic utility, augmented with endogenous direction of technical change. We suppose that the representative agent, while initially at steady state, is offered the possibility to increase either labor-augmenting productivity or investment-specific productivity. We derive the marginal increase in utility from each option. We find that when the elasticity of substitution, the capital share and the rate of impatience lie within the usual ranges, investment-specific technological change is relatively undervalued, because its fruits take relatively more time to materialize. This approach reflects some interesting ideas on the macroeconomics of structural change. However, its predictions stand at odds with cross-country evidence as well as with the early British growth experience (~1770–1913). We argue that the fixity of the production function constitutes a major obstacle for a consistent theory of the direction of technological changes on neoclassical bases.