Growth, Capital Shares, and A New Production Function

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

ABSTRACT PROPOSAL NUMBER: 0242000 INSTITUTION: University of California at Berkeley NSF PROGRAM: ECONOMICS PRINCIPAL INVESTIGATOR: Jones, Charles I PROPOSAL TITLE: Growth, Capital Shares, and A New Production Function Four stylized facts, taken together, constitute a puzzle in modem growth theory: (1) some countries can grow at a relatively stable average rate for a long time, (2) contrary to conventional wisdom, factor payments as a share of GDP are not constant over time in most countries and typically exhibit large trends for several decades, (3) estimates of the elasticity of substitution between capital and labor are often less than unity, (4) the price of capital equipment relative to that of consumption is falling, suggesting that some technical change is embodied in equipment capital, a phenomenon often called investment-specific technical change. For a neoclassical growth model to exhibit a steady state, either technical change must be entirely labor augmenting in the long run, or the production function must be Cobb-Douglas. To get steady growth in the presence investment-specific technical change, the production function should be Cobb-Douglas; however, this is inconsistent with Facts 2 and 3. This research consists of three projects that document and resolve this puzzle. The first project will create a new dataset on factor payments to capital and labor for a large number of countries, both at the aggregate and industry levels, over as long a time as possible. This is important because Fact 2 runs counter to the conventional wisdom: it is commonly accepted that capital shares are relatively constant over time. The second project proposes a new production function that is consistent with all four stylized facts. Factor shares and estimates of the elasticity of substitution are driven by short-run properties of the production function. However, requirements for steady-state growth involve the shape of the long-run production function. The production function proposed here exploits this difference. The short-run elasticity of substitution responsible for factor pricing is less than one. In the long run, additional substitution possibilities arise and production occurs with a Cobb-Douglas structure. The third project explores the microfoundations for this new production function. A production technique, with a low elasticity of substitution, may be appropriate for a given input mix. To produce with a very different input mix, a new production technique may be required. The shape of a given technique governs the short-run elasticity of substition, while the long- run elasticity of substitution is determined by the distribution of newly discovered techniques. A necessary condition for steady growth is that new techniques are distributed according to a Pareto distribution. This same distributional assumption generates a long-run production function that takes the Cobb-Douglas form. This research will resolve some of pressing puzzles in growth theories that seem to be inconsistent with the observed facts.