Jensen’s Modern Income-Distribution Model

Thomas Piketty’s recent polemic on labor-versus-capital shares of national income excited a flurry of public debate on the venerable issue. Greater attention here is a good thing. While the Piketty analysis is easily dismissed, the GEM Project more significantly demonstrates that consensus macro thinking on factor-income distribution is deeply flawed. The elegant Wicksell-Wicksteed approach endures in textbooks but, for more than a hundred years, has not been an adequate general theory. Fortunately, a replacement already exists in the literature: Michael Jensen’s (2000) intuitive residual-claims distribution model. If macroeconomists truly aspire to support effective policymaking, Jensen must become the go-to model in mainstream textbooks.

Neoclassical income distribution. Knut Wicksell and Philip Wicksteed were among the great 19^th-century theorists pioneering marginal analysis, transforming how economics is done. Their focus on optimizing exchange organized by general market clearing crowded out the surplus-oriented classical analysis, accepted since Ricardo, of distributive shares. The neoclassical Euler-theorem treatment of relative factor incomes within the market-centric single-venue general-equilibrium (SVGE) framework pretty much exhausts what modern macro theorists have to say on the topic. Factor inputs are paid their marginal-product and opportunity cost of time, which exhausts first-degree homogeneous production. The model is viewed by many as the apogee of SVGE welfare analysis, providing ethical justification for the market distribution of income.

In the long aftermath of Walrasian and marginalist revolutions, mainstream macro models have been ever more carefully constructed within the coherent SVGE framework. In the modern consensus version cobbled together by New Classical, RBC and New Keynesian theorists, a representative household solves an intertemporal expected-utility maximization problem in the context of competitive markets, rational expectations, and the restriction of optimizing exchange to the marketplace. The familiar Wicksell-Wicksteed first-degree homogeneous two-factor equation plays a central role in modern thinking:

X=ƒ(H,Ҡ)=H(δX/δH)+Ҡ(δX/δҠ);

PX=PH(δX/δH)+PҠ(δX/δҠ)=W^mH+RҠ,

where R denotes the market price of physical capital Ҡ, X is production, H is labor hours, P and W^m stand for the market price of output and labor respectively. In the textbook model, neoclassical distribution theory powerfully links the technology space and optimizing marketplace exchange, mandating that rational payments to inputs exhaust total revenue. Deep down, however, everybody must know that Wicksell-Wicksteed is unsuited to that building-block role.

Mainstream scholars, giving in to some Ptolemaic impulse, have for a long time simply ignored obvious problems rooted in large-scale production that sharply degrade the Wicksell-Wicksteed capacity to describe modern economies. First, factor-market prices calibrated by labor and capital marginal productivities do not exist for large, specialized firms. Second, constant returns to scale are, in many applications, an unacceptable assumption. Third, positing large-firm labor pricing equal to market opportunity cost is broadly inconsistent with the evidence. Fourth, again contrary to the evidence and deeply damaging in policy-relevant application, Wicksell-Wicksteed implies the non-existence of pure profit.

Only the first problem is sufficiently misunderstood to deserve attention here. Large-scale production, ubiquitous after the Second Industrial Revolution, corrupts the analytic integrity of marginal productivities for both labor hours (δX/δH) and capital stock (δX/δҠ), depriving Wicksell-Wicksteed of crucial microfoundations. Generalized rational exchange imposes H=Έ/Ź on labor services, where Έ denotes labor input that is in 1:1 technical correspondence with production; δX/δΈ is not measurable in the marketplace. (Chapter 2) Meanwhile, large-establishment capital stock (Ҡ) is both insufficiently divisible and excessively firm-specific to support Euler-theorem distribution. (Chapter 3) Given indivisibility, portions of capital cannot be withdrawn in response to relatively small reductions in output, as illustrated by the absence of small-lot capital-stock liquidations in cyclical downturns. What is instead marginally withdrawn, with a cut in output, is some utilization of capital services (Ƙ) that are made available by the existing capital stock.

The GEM Project provides a central place for capital services, distinct from capital stock, in the large-establishment technology space. Potential production (X^P) is described by a capacity function (X^P=ƒ(Ҡ)), where X^P is increasing in physical capital Ҡ and provides an upper bound on output (X≤X^P). Capital services (Ƙ), the measurement of which requires no knowledge of the contemporaneous interest rate, flow from the capital stock (such that Ƙ^P(t)=ƒ(Ҡ(t), ∆Ƙ^P/∆Ҡ>0, and Ƙ≤Ƙ^P). Physical-capital indivisibilities in combination with optimizing workplace exchange must be accounted for in the specification of the large establishment’s production function and consequent factor-income distribution:

X(t)=ƒ(Έ(t),Ƙ(t));

P(t)X(t)=WⁿH(t)+ř^m(t)Ҡ^r(t)+G(t),

such that Έ=ŹH and Ƙ≤Ƙ^P=ƒ(Ҡ), while Wⁿ denotes the efficiency wage, ř^m is the market interest rate, G is pure profit, and Ҡ^r is the capital stock net of its sunk component (Ҡ^r=Ҡ–Ҡ^S), making the term (ř^m(t)Ҡ^r(t)) the market opportunity cost of the firm’s capital stock. (Chapter 3) Generalized-exchange modeling has established that, in large-scale production, neither labor hours nor capital services can be efficiently priced in the marketplace, breaking down the Wicksell-Wicksteed market mechanism that eliminates pure profit. The GEM Project’s technological space also accommodates increasing returns to scale, further enriching the capacity of the residual-claim distribution model to accommodate critical determinants of economic growth. Given profit’s role as a residual claim by owners of sunk capital on firm revenue net of production-related outlays, G can be greater than, less than, or equal to zero, providing signals needed for the rational management of production capacity.

The inherent nature of large-scale production disallows reliance on textbook Euler-equation modeling of factor-income distribution in modern applications. It is, therefore, good news is that the GEM Project microfounds Ricardian distribution along the lines pioneered by Michael Jensen (2000). His residual-claims model class, easily and coherently introduced into generalized-exchange macroeconomics, solves the debilitating problems cited above. It has been identified as one of the important, overlooked theories the connectivity of which with a broad range of intuitive models is revealed in the Workplace-Marketplace Synthesis. Jensen is invited to join the GEM Project.

Blog Type: Wonkish Saint Joseph, Michigan