6 - Production Functions: The Search for Identification

Summary

We have here one of those cases - so frequent in economic practice - where it can be “proved” by abstract reasoning that a solution is not possible, but where life itself compels us nevertheless to find a way out.

Frisch (1934, p. 274)

Introduction

Econometric production functions, as we know them today, originated in the work of Douglas (Cobb and Douglas, 1928). They started out as tools for testing hypotheses about the workings of marginal-productivity theory and the competitiveness of labor markets, using macroeconomic data. After a number of withering attacks by critics, this line of work shifted from macroeconomic data to microeconomic data, especially in agriculture (e.g.,Tintner, 1944; Mundlak, 1961; Heady and Dillon, 1961), where the assumptions necessary for estimating something sensible appeared to be more plausible. The increasing interest in growth and technological change brought production functions back as a measurement framework for productivity at the macroeconomic level. An important “dual” literature on cost functions, factor-demand systems, and flexible functional forms emerged somewhat later, but we shall comment on it only in passing here; see Jorgenson (1986) for a review. Both approaches have undergone significant econometric questioning, focused primarily on whether or not the relationship of interest has really been identified or is even identifiable with the data at hand.