Thursday, May 21, 2015

A Theory of Production

Economists often use the word "technology" to mean the relationship between output and factors of production such as capital and labor.  The Cobb-Douglas production function, which is a ubiquitous description of technology has its origin in a 1928 AER article, "A Theory of Production," by Charles Cobb and Paul Douglas.

Using C to denote capital, L for labor and P for production, the production function makes its first appearance:
Although the description of technology is a theoretical contribution, much of the article is empirical in nature, as they construct indexes of capital and labor in order to test their model.  They compare the production implied by their function and estimates of capital and labor, P', with a measure of actual production.
To a contemporary macroeconomist reader, the striking thing about the article is the extent to which it anticipates how we analyze business cycles today.  Cobb and Douglas, separate out cyclical and trend components (using 3 year moving averages) and show that the deviations of actual production and the production implied by changes in capital and labor are procyclical.
The article includes a chronology of business cycles which aligns with the NBER chronology; the NBER recessions during this period are
  • June 1899 - Dec. 1900
  • Sept. 1902 - Aug. 1904
  • May 1907 - June 1908
  • Jan. 1910 - Jan. 1912
  • Jan. 1913 - Dec. 1914
  • Aug. 1918 - Mar. 1919
  • Jan. 1920 - July 1921
Cobb and Douglas' estimates are annual, but several of these do line up with points where P' (implied production) exceeds actual production, P.

Today these deviations of actual output from the amount implied by changes in factors of production are known as "Solow residuals" after work by Robert Solow in the 1950s and interpreted as measures of technological progress (i.e., our ability to wring more output out of given amounts of capital and labor).  Although Solow was mainly concerned with long-run growth trends, in the 1980's, Real Business Cycle theorists interpreted short-run fluctuations as "technology shocks".  In Real Business Cycle models these shocks drive economic fluctuations, and the same pattern identified by Cobb and Douglas - using postwar data and newer detrending techniques - was cited in support of this theory.  One weakness of this argument is that short run movements in the Solow residual are at least partly due to utilization - "factor hoarding" - rather than changes in technology.  This, too, was anticipated by Cobb and Douglas:
The index does not of course measure the short-time fluctuations in the amount of capital used.  Thus, no allowance is made for the capital which is allowed to be idle during periods of business depression nor for the greater than normal intensity of use int he form of second shifts etc., which characterizes the periods of prospertity.
Overall, this article would fit very well into a syllabus for a current course on business cycle theory.  Hmm...


The Arthurian said...


Thanks so much for the link to the Cobb-Douglas PDF. I glanced my way through it once; I think I can read and understand it.

By no means an even trade, but here's a link to Creating a Macroeconomic Model Using Real Economic Data, from Rodney Smith at the University of Minnesota.

Again -- interesting post.

Anonymous said...

Thanks. I'll give that a look. - Bill C