KLEMS

From Hobson's Choice

Productive Factors in DGE Economics

KLEMS stands for "capital, labor, energy, materials, and services," a fuller list of productive factors than that commonly used in academic monographs. The KLEMS model is a system of econometrics that dates back to the original Kuznets figures of national accounts, and is used in much government research.

Among its advantages is separate treatment of materials and energy inputs.

Contents 1 Context 2 How KLEMS works 3 Criticism 4 Notes 5 External Links

Context

In economics texts it is 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, 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 = (Y_t-i - C_t-i)(1 - δ)_i. In the equation above, δ is the rate of capital depreciation; in each year of the past t - i, output was Y_t-i and consumption was C_t-i; so ∆K_t-i is always the difference between the two, and it will hereafter depreciate at (1 - δ)ⁱ where i is how many years ago ∆K_t-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?

How KLEMS works

An apparent alternative to the customary two-factor production function, at least for purposes of research, is the KLEMS methodology. KLEMS stands for capital, labor, energy, materials, and [business] services. It is used by government agencies to measure multifactor productivity growth; simply put:

The parts of this equation are:

• is the annual increase in total factor productivity;
• is the annual increment in output;
• is the annual increment in capital inputs;
• is the annual increment in labor inputs;
• is the annual increment in energy, materials, and business services.

In each case, the contribution is weighted (w) for the presumed contribution of each to actual output. The calculation of w_k, w_l, and w_ip is critical, and but quite simple: it is the average of the factor share of income for t and (t - 1). In other words, supposing labor's share was 32.3% in '03, and 31.9% in '02, then w_k would be 32.1% for calculating the growth of TFP in the period mentioned.

Using the Bureau of Economic Advisors' '05 Annual Industry Accounts , table 2, p.11, one can see that output is divided into actual value added (most recently, 55.8%), of which 31.9% was compensation of employees, 3.8% was net taxes, and 20.1% was "gross operating surplus" (or wk + profit—the two are not differentiated in KLEMS accounting). The remainder, 44.2% of GDP, was intermediate inputs of all kinds, including energy (1.9%), materials (17.2%), and purchased service inputs (25.1%).

I was frankly astonished at the low value of w_e, although it must be noted that much energy consumed would not appear in the ledger as an input; it's a consumer good (crude oil and PNG are material inputs when acquired by, say, an oil refinery; see p.2b).

KLEMS data has been collected on the US economy since 1947, and attracted some fascinating research in the EU (see EU KLEMS project linked below). As expected, this includes studies on the validity of standard production functions normally used in DGE models of the economy. Incidentally, production functions do not use the same method of calculating weights as does KLEMS. KLEMS simply assumes inputs contribute what they are paid. But formally, inputs to an economy will be reimbursed on the basis of their marginal revenue product; it is often the case that some industrial sectors will experience both a high degree of market concentration for output (oligopoly) and a similarly high degree of market concentration for input (oligopsony). When this happens, factor remuneration may be much lower than their contribution to output. While that's not likely to be a huge influence on factor pay for the entire economy, and not for very mobile factors, it does play a role in studies of capital-labor switching within economic sectors. Economists therefore use other methods for researching the contribution of factors to output, mainly through regression analysis of economic growth in different settings.^[1]

Criticism

According to Houseman (linked below), KLEMS is fundamentally flawed because of its assumption that factors are paid their actual contribution: Houseman cites the methods of data collection, which rely on employer surveys to measure expenditures on business services (the largest part of IP, above), then forces a match with census data on industry outputs for those same services. The inevitable deficit in expenditures was then distributed among all industrial sectors of the US economy based on the total output of each industrial sector. Moreover, KLEMS data breaks business services into six categories:

1. temporary help services
2. employee leasing services
3. security guards and patrol services
4. office administrative services
5. . facility support services,
6. nonresidential building cleaning services

To generate I-O estimates at a more disaggregated commodity level, it was assumed that industrial sectors utilized all contract labor services in the same proportion. For instance, if an industry was estimated to use 10 percent of all contract labor services, it was assumed to use 10 percent of each of the component contract services. The six categories are thus assigned in uniform proportions on the basis of industry output, despite the well-known fact that manufacturing is a heavy employer of temporary help (35-40% of all temps worked in manufacturing).

The other objection Houseman has is that the the equation at the top of the entry reflects a stable equilibrium model, not the dynamic general equilibrium (DGE) model. As she explains in pp.13ff, a shift to outsourced labor (either Ford's use of temps and Cisco's use of Chinese R&D) results in a prolonged but transitional effect of reduced labor productivity, but since the now-outsourced labor is measured as an intermediate service, the loss of labor productivity is suppressed. Put another way, outsourcing is a method of substituting low-cost labor (especially that with a low value of e^ψu) for capital, but instead of appearing on the ledger as lower labor productivity, less labor is reported being used. Productivity of labor, as reported, will depend on the arbitrary matter of the institutional relationship.

I was also very disappointed in the limited role of energy utilization in measuring efficiency. My entire interest was to examine US adaptation to soaring prices of non-renewables, but when energy inputs are handled as <2%,>

Notes

1. ↑ The estimation of factor shares is a hot-button issue, partly because of the semantics of human capital. My source on growth accounting with human capital is Charles I. Jones, Introduction to Economic Growth, W.W. Norton & Co. (1998), chapter 3.1: "The Solow Model with Human Capital," which is mainly based on Mankiw, Romer, and Weil's "A Contribution to the Empirics of Economic Growth" (1992).
   
   Usually the baseline of analysis is either the Swan-Solow Classical Growth model; immediately after introduction, professors teaching this model nearly always divide Y (GDP) by labor L to get the intensive form y of the equation. Then all attention is focused on estimating how much of y is caused by technology (A) and how much by capital (K/L = k). In Mankiw, et. al., we get introduce the term H (skilled labor), which is
   H = e^ψuL
   where u is the amount of time spent learning a skill and ψ is an empirically determined natural log of return to time spent assimilating that skill. According to Mankiw, et. al., including this in a regression of comparative international data leads to a very good fit.

External Links

• Susan Houseman "Outsourcing, Offshoring, and Productivity Measurement in Manufacturing" , Upjohn Institute Staff Working Paper No. 06-130 (June 2006);
• Bureau of Economic Analysis, "Guide to the Interactive GDP-by-Industry Accounts Tables" (2007)
• EU KLEMS Working Paper Series, esp. Marcel P. Timmer, Mary O’Mahony, & Bart van Ark, "EU KLEMS Growth and Productivity Accounts: An Overview"
• Erich H. Strassner, Gabriel W. Medeiros, & George M. Smith, "Annual Industry Accounts Introducing KLEMS Input Estimates for 1997–2003" , Bureau of Economic Analysis (2005)
• John R. Baldwin, Guy Gellatly & Tarek Harchaoui, "The Role of Analysis in Delivering Information Products" , Statistics Canada, Microeconomics Analysis Division—see p.8 (July 2004)
• Robert J. Vigfusson, "The Delayed Response To A Technology Shock: A Flexible Price Explanation" International Finance Discussion Papers, FRS (2004); in light of Susan Houseman's study, I am a little skeptical of Vigfusson's rosy conclusions. Vigfusson uses BLS KLEMS data and a flexible price model to argue that, when positive technology shocks are serially correlated, there is a delayed response of labor markets to respond with increased labor.
• staff, "What Is Productivity?" The Ledger, Federal Reserve Bank of Boston (2004)
• John Haltiwanger, "Measuring Plant-Level Total Factor Productivity and Decomposing the Aggregate" ( p.22) Review, Federal Reserve Bank of St. Louis (1997)

James R MacLean (15:17, 18 September 2007 (PDT))