14 August 2007


Productive Factors in DGE Economics

In economics classes and the vast majority of monographs I've read on recent economic theory, it's common to refer to two factors of production: capital (K) and labor (L). In the late 19th century, this was very important since there was a lot of polemics over the correct theory of value, with the conservatives of the day insisting on the utility theory of value. Much more recently, we have seen the Solow-Swan Classical Growth Theory, in which the Keynesian theories of the business cycle were supplemented with, then replaced by, a comprehensive model of capital and technology (A) accumulation.

This has typically been disappointing to me precisely because it seemed to me that a model of the economy in which there was a single universal production function Y = f(A, K, L) would yield only certain results. Bear in mind that we're always interested in output per worker (Y/L, or y), which is always assumed to be a function of capital per worker (K/L, or k). Some modern theories of economic growth are described as exogenous, such as Solow's; they are "exogenous" in the sense that they believe the main determinant of economic growth, A, is something outside of the economic model. "Endogenous growth theory," in contrast, focuses on the tendency of capital accumulation to cause A directly. Both theories ran into serious problems with respect to international comparisons. Exogenous growth implied that the difference between countries was the result of capital accumulation, but capital accumulation in the richest nations of the OECD is actually not much larger than that of low-income countries such as the Philippines or India. Nor was this an anomaly of the present day; today, of course, saving and investment in the least-developed countries (LDC's) surpasses that of, say, the USA (where net saving is negative).

Conversely, endogenous growth theory merely consisted of assuring us that there were increasing returns to scale of capital investment; by allowing any exponent on capital that would fit the data, the endogenous growth theorists came up with the most Panglossian view imaginable of economic development. They suffered from the logical dilemma that small, island nations like Singapore often responded better to capital accumulation than large, integrated regions (like Western Europe). While Western Europe, taken as a unit, is very affluent, and K is huge, its network spillovers ought to be larger than Singapore's. As everyone knows, the opposite is true; not only that, but investors in Europe and Japan are keen on exporting capital as if they—i.e., "the market" for investment opportunities—knew better.

Also, I was well aware that some dissident economists had objected to the obsession with human inputs to the industrial economy. Labor is superabundant; economists are usually expected to make sure the supply of that is utilized. Capital is always treated as a component of prior output, or,
K = ∑(Yt-i - Ct-i)(1 - δ)i, for i = 1 --> ∞.
In the equation above, δ is the rate of capital depreciation; in each year of the past t - i, output was Yt-i and consumption was Ct-i; so ∆Kt-i is always the difference between the two, and it will hereafter depreciate at (1 - δ)i where i is how many years ago ∆Kt-i occurred. While i may be as large as ∞, (1 - δ)i would make any capital accumulated before 1968 worth about 1% of its real value in '68.

A problem, though, is that this implies that nothing bad can happen to the economy, provided the immense stock of capital survives (and the world population doesn't shrink). What about peak oil? What about significant changes in climate that reduce farm output? And, for workers, what about corner solutions in which the full employment of all non-labor resources (renewables, energy, and capital) leaves much labor unemployed?

(Part 2)

ADDITIONAL READING & SOURCES: Susan Houseman "Outsourcing, Offshoring, and Productivity Measurement in Manufacturing" (PDF), Upjohn Institute Staff Working Paper No. 06-130 (June 2006); Harold Cole & Lee Ohanian, "The Great Depression in the United States from a Neoclassical Perspective" (PDF), Federal Reserve Bank of Minneapolis (1999);

On the labor theory of value: Albert C. Whitaker, "History and Criticism of the Labor Theory of Value in English Political Economy" (PDF) Stanford University (1904); for an introduction to the utility theory of value, I have to recommend William Stanley Jevons, The Theory of Political Economy (5th edition), IV (complete text). As you can see, Whitaker's work of 1904 was a piece of historical research; Jevons introduced the alternative "utility theory" in 1870. The whole issue of value theory is hence pretty antiquarian. Or so you'd think; but Joseph A. Schumpeter, in his History of Economic Analysis, III.6.2, seems to think it's the basis of any system of economic analysis. Polemically, it means a lot to him, although he argues that one should not draw any polemical conclusions from any theory of value!

Schumpeter is correct when he says one ought not to draw any polemical conclusions from one's theory of value; but the logical corollary is that one therefore ought to use theories of values like domain-specific programming languages, a proposition that would no doubt cause Schumpeter to turn several different shades of magenta.

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