Quantitative theory uses simple, abstract economic models together with a small amount of economic data to highlight major economic mechanisms. To illustrate the methods of quantitative theory, we review studies of the production function by Paul Douglas, Robert Solow, and Edward Prescott. Consideration of these studies takes an important research area from its earliest days through contemporary real business cycle analysis. In these quantitative theoretical studies, economic models are employed in two ways. First, they are used to organize economic data in a new and suggestive manner. Second, models are combined with economic data to display successes and failures of particular theoretical mechanisms. Each of these features is present in each of the three studies, but to varying degrees, as we shall see.
These quantitative theoretical investigations changed how economists thought about the aggregate production function, i.e., about an equation describing how the total output of many firms is related to the total quantities of inputs, in particular labor and capital inputs. Douglas taught economists that the production function could be an important applied tool, as well as a theoretical device, by skillfully combining indexes of output with indexes of capital and labor input. Solow taught economists that the production function could not be used to explain long-term growth, absent a residual factor that he labeled technical progress. Prescott taught economists that Solow's residual was sufficiently strongly procyclical that it might serve as a source of economic fluctuations. More specifically, he showed that a real business cycle model driven by Solow's residuals produced fluctuations in consumption, investment, and output that broadly resembled actual U.S. business cycle experience.
In working through three key studies by Douglas, Solow, and Prescott, we focus on their design, their interrelationship, and the way in which they illustrate how economists learn from studies in quantitative theory. This learning process is of considerable importance to ongoing developments in macroeconomics, since the quantitative theory approach is now the dominant research paradigm being used by economists incorporating rational expectations and dynamic choice into small-scale macroeconomic models.
Quantitative theory is thus necessarily akin to applied econometric research, but its methods are very different, at least at first appearance. Indeed, practitioners of quantitative theory--notably Prescott (1986) and Kydland and Prescott (1991)--have repeatedly clashed with practitioners of econometrics. Essentially, advocates of quantitative theory have suggested that little is learned from econometric investigations, while proponents of econometrics have suggested that little tested knowledge of business cycle mechanisms is uncovered by studies in quantitative economic theory.
This article reviews and critically evaluates recent developments in quantitative theory and econometrics. To define quantitative theory more precisely, Section 1 begins by considering alternative styles of economic theory. Subsequently, Section 2 considers the three examples of quantitative theory in the area of the production function, reviewing the work of Douglas, Solow, and Prescott. With these examples in hand, Section 3 then considers how economists learn from exercises in quantitative theory.
One notable difference between the practice of quantitative theory and of econometrics is the manner in which the behavioral parameters of economic models are selected. In quantitative theoretical models of business cycles, for example, most behavioral parameters are chosen from sources other than the time series fluctuations in the macroeconomic data that are to be explained in the investigation. This practice has come to be called calibration. In modem macroeconometrics, the textbook procedure is to estimate parameters from the time series that are under study. …