*Hybrid Phillips curve*. Mainstream theorists of my generation have been long exhausted by their 30-year microfoundations war. Enervation likely shaped a prominent macro theorist’s determined disinterest in the foregoing analysis: “… the debate [expectations versus catch-up] has to move to the data and can only be settled through empirical work.” (Correspondence from Olivier Blanchard to me.) Along the same lines, David Romer (2001, p.251) offered a free-parameter Phillips curve (PC) as the “natural compromise” between catch-up and expectations:

w(t)=a_{o}+a_{1}(U^{N}–U(t))+(1–ψ)p_{ķ}(t)+ψE_{t}p(t+1), s.t. ψ∈ [0,1],

where* ψ* governs the relative contributions of expectations and catch-up to nominal wage change. Romer exhibits creative exhaustion by relegating *ψ* to theoretic indeterminacy. It cannot be surprising that his market-centric guesswork differs from the GEM Phillips curve (see below), which is rooted in rational behavior. It is further unsurprising that, when Rudd and Whelan (2005) tested the hybrid approach, they found little support for forward-looking adjustments.

*Generalized exchange Phillips curve.* Two-venue generalization of rational exchange motivates a continuous-equilibrium entrant to the sprawling literature on single-equation wage modeling. The central baseline equation (the previous post), which features **Ҝ** durability and is confined to stationary aggregate demand disturbances, is consequently restricted by downward wage rigidity and chronic wage rent. To align the equation with the Phillips literature, posit that terms of trade remain unchanged (*p*^{J}=*p*^{K}=*p*^{I}), as do small-firm trend labor-productivity growth (Δ*γ*^{K}(t)=0), relative sector size (Δ*Φ*(t)=0), the natural rate of unemployment (Δ*U*^{N}(t)*=*0), and government intervention *(*Δ*μ*(t)*=*0). The simplified equation is the GEM variant of the Phillips curve:

w(t)=b_{o}+b_{1}(U^{N}−U(t))+b_{2}p_{ķ}(t), such that w^{J}(t)≥0 and W^{J}(t)>W^{m}(t).

Reiterating for emphasis, the GEM PC is constructed on inactive reference standards **Ҝ** that are consistent with stationary business cycles, the circumstances in which Phillips Curve analysis is typically conducted. Wages on average are downward sticky and LEV labor pricing is always greater than its SEV counterpart. In this wage model, labor-market conditions occupy a significant, albeit diminished, place. Price expectations disappear, an outcome supported by the evidence.

The GEM PC is constructed on (i) preferences and technology that are invariant with respect to the conduct of monetary policy and (ii) employer-employee decision-rule outcomes that are rationally informed by central-bank policies. The model happily replaces the arbitrary time-separation used by Early Keynesians to meld money neutrality and non-neutrality in the Neoclassical Synthesis. Given a reasonable take on the other branch of the wage-price nexus (Δ*p*(t)/Δ*w*(t)>0), inflation persistence is easily motivated: (Δ*p*(t)/Δ*w*(t))(Δ*w*(t)/Δ*p*_{ķ}(t))=Δ*p*(t)/ Δ*p*_{ķ}(t)>0. Inertial product-price inflation aligns with the evidence and is relevant to the proper design and implementation of stabilization policies.

*Other properties of the wage model*. Nonconvex WERs imposes a tight structure on *b*_{i} in the GEM PC that extends beyond DWR and PWR. The constant term (*b*_{o}=*Φr*^{n}+(1−*Φ*)*γ*^{K}) reflects the interaction of trend LEV real wage growth (*r*^{n}, embedded in **Ҝ**), small-firm trend productivity growth, and relative venue size. To the extent that any of those factors change during an estimation period, *b*_{o} will be unstable. A crucial, albeit infrequent, source of destabilization is **Ҝ** recalibration, which has been shown not to occur in stationary business cycles that provide the usual context for Phillips analysis. Also, the employment coefficient (*b*_{1}=(1−*Φ*(t))*a*_{1}) helps explain the relatively modest, albeit significant, estimates of the influence of contemporaneous joblessness on wage behavior.

The specifications of inflation catch-up (*p*_{ķ}(t)=*Φ*(t)*βσp*^{J}_{ķ}(t)+*Φ*(t)*β*(1−σ)*p*^{K}_{ķ}(t)+*Φ*(t)(1−β)*p*^{I}_{ķ}(t)) and LEV terms-of-trade dynamics (*þ*_{ķ}(t)=*βσp*^{J}_{ķ}(t)−*Φβ*(1−σ)*p*^{K}_{ķ}(t)−(1−β)*p*^{I}_{ķ}(t)) provide interesting restrictions on GEM single-equation specification. Domestic or international shifts in LEV labor’s terms of trade make *b*_{2} unstable. Consequently, the two-venue Phillips curve could not have adequately explained the stagflation that greatly challenged monetary policymaking in the 1970s and early 1980s. Finally, generalized-exchange Phillips macrodynamics underscores the significance of the implicit interaction between growth in LEV productivity (*γ*^{JT}) and the venue’s real wage (*r*^{n}). In the GEM model, Δ*γ*^{J}_{T}>Δ*r*^{n} exerts upward pressure on pure profit (*Π*^{J}), increasing common equity, capital investment, and aggregate income and spending while reinforcing **Ҝ** durability. If Δ*γ*^{J}_{T}<Δ*r*^{n}, there is downward pressure on profit, common equity, investment, income, and spending. Previous posts have showed how such circumstances eventually induce job downsizing, **Ҝ** recalibration, and wage givebacks.

*Making sense of the Phillps Curve.* Given the macro-war disparagement of the EK Phillips curve, its revival may look like karma. Any impression of wholesale rehabilitation, however, misleads. Phillips thinking consistent with the Neoclassical Synthesis differs fundamentally from single-equation modeling rooted in nonconvex WERs. Motivated by their righteous insistence on stabilization-relevance, Early Keynesians simply assumed wage stickiness sufficient to suppress recontracting in the short-term, morphing into market-driven full flexibility in the longer-run. The GEM story is much more developed, featuring labor pricing grounded in continuous decision-rule equilibrium informed by rational wage rigidities that suppress recontracting. The two-venue model resolves Keynes’ central problem of mass involuntary job loss. Optimizing market-centric models have never come close to producing joblessness of the size, location, and persistence needed to fit the available data.

While EK catch-up to past inflation has carried the day, that victory was largely accidental. Nonetheless, EK theorists (guided by evidence) did produce what turned out to be the only rational-behavior model in the Phillips literature. Alternatives rooted in inflation expectations are rejected, felled by the one-two punch of irrationality and inconsistency with the data. Does the comeback victory of the old order help build a stabilization-relevant Phillips Curve? That question forces thinking through a problem that is typically ignored. Attempting to construct rational, evidence-consistent Phillips curves, economists of all stripes must confront the necessity of microfounded wage rigidities.

Catch-up helps explain wage-price inertia and puts to rest destructive policy implications that Real Business Cycle theorists deduced from rational expectations. But catch-up does not suppress wage recontracting. The strategy can be rationally used in both Early and New Keynesian market-centric PCs, yet neither then motivates involuntary job loss. The rational-expectations PC revolution, even if we ignore its problematic wage-setting arrangements, has been greatly over-promised. In pushing forward useful modeling of macro instability, getting the inflation determinant of wages right turns out to be a relatively modest part of solving the overall problem. What most matters is making DWR and PWR consistent with rational behavior governed by general decision-rule equilibrium, fundamentally altering the neoclassical relation between wages and unemployment.

Blog type: New Keynesians

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