23 August 2007


An Introduction to KLEMS
(Part 1)

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 wk, wl, and wip is critical, and but quite simple: it's 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 wk would be 32.1% for calculating the growth of MFP in the period mentioned.

Using the Bureau of Economic Advisors' '05 Annual Industry Accounts (PDF), 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 we, 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

According to Houseman (PDF; linked in part 1), 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 eψu) 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 = eψuL
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.

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