# The Most Damaging Error in NK Macroeconomics

Students are typically introduced to macroeconomics via the New Keynesian (NK) 3-equation model rooted in friction-augmented general market equilibrium. This post features the version in the popular textbook, Macroeconomics, by Carlin and Soskice (C&S).  The first equation relates inflation-adjusted total output (X) and the real interest rate (r) and is divided into three parts:

X = A – b1r,

where b1 is a constant and A “is the sum of exogenous multiplied-up demands, thus including private and public sector exogenous demand”. C&S, p.82) the second part is;

XE =A – b1rS,

where XE is market equilibrium output and rS denotes the real interest rate that equates X and XE. The third part is named the output gap:

X – XE = b1(r – rS).

From C&S: “this equation makes clear that output will deviate from equilibrium to the extent that the interest rate differs from the stabilizing interest rate”.

The second equation is the famous inertia-augmented Phillips curve:

ΔP/P = (ΔP/P) -1 + b2(X – XE),

where P denotes product prices and Δ is a change operator. The third is the monetary-policy rule:

X – XE = -b3(ΔP/P – (ΔP/P)T),

where ΔPT is the central bank’s target inflation.

Let’s be blunt. The NK go-to model is useless. Relying on interest rates to drive spending decisions is fatally misaligned with how highly specialized economies behave. The hard fact is that the NK equations can neither guide effective stabilization policy nor adequately instruct students.

Mainstream theorists are committed to interest-rate criticality that they root in rational market exchange organized by the neoclassical tenets of optimization and equilibrium. The GEM Project demonstrates that view of interest rates is an artifact of restricting rational exchange to the marketplace. Once exchange is intuitively generalized to workplaces characterized by costly, asymmetric employee-employer information, neoclassical modeling reduces r to secondary status, making room for what practitioners know to be the important drivers of investment and consumption outlays. To repeat, the 3-equation model is useless. I cringe to think of all the students absorbing NK teaching that, if taken seriously, dooms their capacity to understand macro economies.

Investment outlays. Our deconstruction of the 3-equations approach  begins with a venerable model long important in NK toolbox. The Wicksell-Wicksteed (W&W) first-degree homogeneous two-factor income-distribution equation is a lynchpin of general-market-equilibrium analysis:

X=ƒ(H,Ҡ)=H(δX/δH)+Ҡ(δX/δҠ);

XP=HP(δX/δH)+ҠP(δX/δҠ)=WmH+PҠҠ,

where PҠ denotes the market price of physical capital Ҡ, X is production, H is labor hours, P and Wm stand for the market price of output and labor respectively. In the textbook market-centric model, neoclassical distribution theory powerfully links technology and optimizing marketplace exchange, deriving equality between rational payments to inputs and total revenue of the firm. There is no room for pure profit, i.e., the surplus paid to the owners of the firm’s capital (denoted by P).

Mainstream scholars, giving in to some Ptolemaic impulse, have for a long time simply ignored obvious interrelated problems rooted in large-scale production that sharply degrade the W&W capacity to describe modern economies. First, factor-market prices calibrated by labor and capital marginal productivities do not exist with respect to large, specialized firms. Second, constant returns to scale are, in most applications, an unacceptable assumption. Third, positing large-firm labor pricing equal to market opportunity cost is broadly inconsistent rules out facto rents and is inconsistent with the evidence.

Only the first problem may be sufficiently misunderstood by GEM Blog readers to require attention here. Large-scale production, ubiquitous after the Second Industrial Revolution, corrupts the analytic integrity of marginal productivities for both labor hours (δXjHj) and capital stock (δXjҠj), depriving the W&W model of key microfoundations. Generalized rational exchange imposes Hj=Έj/Źj on labor services, where Έj denotes labor input that is in 1:1 technical correspondence with production; δXjΈj is not measurable in the marketplace. Meanwhile, large-establishment capital stock (Ҡj) is both insufficiently divisible and excessively firm-specific to support Euler-theorem distribution. 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 (Ƙj) made available by the existing capital stock. That adjustment is consistent with layoffs.

The GEM Project provides a central place for capital services, distinct from capital stock, in the large-establishment technology space. Potential production (XjP) is described by a capacity function (XjP=ƒ(Ҡj)), where XjP is increasing in physical capital Ҡj and provides an upper bound on output (Xj(t)≤XjP(t)). Capital services (Ƙj), the measurement of which requires no knowledge of the contemporaneous interest rate, flow from the capital stock (such that ƘjP(t)=ƒ(Ҡj(t), ∆ƘjP/∆Ҡj>0, and Ƙj(t)≤ƘjP(t)). 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:

Xj(t)=ƒ(Έj(t),Ƙj(t));

Pj(t)Xj(t)=WnjHj(t)+řm(t)Ҡrj(t)+Pj(t); Pj(t) = Pj(t)Xj(t) – WnjHj(t) – řm(t)Ҡrj(t);

such that Έj(t)=Źj(t)Hj(t) and Ƙj(t)≤ƘjP(t)=ƒ(Ҡj(t)), while Wn denotes the efficiency wage, řm is the market interest rate, P is pure profit, and Ҡr is the capital stock net of its sunk component (Ҡr=ҠҠS), making the term (řm(t)Ҡr(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 the W-W 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 pure profit’s role as a residual claim by owners of sunk capital on firm revenue net of production-related outlays, Pj can be greater than, less than, or equal to zero, providing signals needed for the rational management of production capacity. As a determinant of investment spending, Pj dominates r – both theoretically and empirically.

Keynesian consumption. In the most important contribution to the fixed-wage general-equilibrium literature that received a great deal of attention in the 1970s, Robert Barro and Herschel Grossman (1971, 1976) posited nominal wage rigidity to anchor their careful investigation of the relationship between aggregate demand and involuntary job loss rooted in the interdependence of rationing in the labor and goods markets. The GEM Project microfounds B&G’s crucial assumption, reviving the stabilization-relevance of the FWGE school.

B&G sought to support the income-centric Keynesian consumption function. They showed that the strong relation between personal income and consumer spending, unmistakable in the data,  is a rational manifestation of wage-related disequilibrium in the labor market. Worker income, now representing the constrained effective demand for current output resulting from the excess market-supply of labor, centrally determines rational household spending. Interest rates, dominant in general-market-equilibrium analysis of consumption, play a relatively minor role.

Conclusion. The debilitating flaw of the C&S fundamental output-gap equation is now obvious. For highly specialized economies, it should read: XXE=AAE+b1(rrS), where AE is market-equilibrium total nominal spending. We know that A is critically influenced by expected pure profit and personal income. Microfounded meaningful wage rigidity reinforces the fact that A cannot be conveniently canceled out. No stabilization-relevant model makes aggregate demand exogenous.

Blog Type: New Keynesians Saint Joseph, Michigan