Generalized-Exchange Phillips Curve

Get ready for the wonkiest blog yet. It is based on my 2009 paper, “Getting Serious about Understanding the Phillips Curve”, which is available on the Research-Exchange page of this Website. “Getting Serious” has two parts. First, it corrects a fundamental error in Robert Lucas’s use of Muth’s rational expectations to discredit and replace the Early-Keynesian “adaptive expectations” Phillips curve. Today’s consensus belief that the rational-expectations Phillips curve is actually rooted in rational behavior is demonstrated to be false. (A summary of this analysis will appear next week.) Second, two-venue generalized exchange is used to construct a substantially improved Phillips-class reduced-form wage model, which is summarized in this post.

Two-Venue Wage Modeling

Small-establishment venue (SEV). Firms characterized by effective direct supervision of on-the-job behavior populate the small-establishment (kth) venue. Rational worker choice is restricted to the marketplace, and profit-seeking firms accept market pricing of labor hours that equals labor opportunity costs. Wage dynamics are familiar from textbook descriptions of optimization in competitive markets:

w^m_k(t)=r^m_k(t)+p^m_k(t),

where w^m is the growth rate of the market wage, r^m denotes the growth in firm marginal labor productivity, and p^m is the firm’s product-price inflation. Management decision-making is restricted to adjusting labor hours, thereby influencing r^m. There is no firm-endogenous influence on w^m, which is determined in the marketplace.

The GEM model fills out the SEV wage analysis by positing coherent price-discovery frictions, familiar government constraints, and tractably aggregated labor pricing in the small-establishment venue:

w^m_K(t)=γ^m_K(t)+p^m_K(t)+a₁(U^N–U(t))+a₂Δμ_t, such that a₁>0, a₂>0,

where γ^m denotes marginal labor-productivity growth (γ^m_K(t)=r^m_K(t)), U is the jobless rate, U^N denotes the natural rate, and Δμ represents calibrated change in government labor-market intervention (e.g., wage minimums). In the labor-pricing literature, short response lags to altered market conditions are typically attributed to price-discovery costs, rooted in costly market information or administrative charges.

Large-establishment venue (LEV). Workplace-equilibrium innovations in labor-pricing economics are confined to large, specialized establishments, subject to costly, asymmetric workplace information and routinized jobs. Rational employer-employee interaction makes labor productivity (Ź_j) endogenous to the firm, mandating wages that variably exceed labor’s market opportunity costs. (Chapters 2 and 3) LEV firms are home to optimizing labor-pricing decision rules, constraints, and mechanisms of exchange that differ fundamentally from the rules, constraints, and exchange mechanisms that govern choice in the marketplace. All this is not new. Practitioners crucially learned long ago that employees resent being treated as a commodity governed by the arbitrary interaction of supply and demand. They want, instead, to be treated fairly and have sufficient on-the-job latitude to enforce that preference. In practice, fair treatment is manifest in workplace reference standards, which the GEM model denotes with Ҝ_j. (Chapter 2)

Getting Serious demonstrates that baseline LEV (durable-Ҝ) continuous-equilibrium is consistent with the following discrete-time wage dynamics:

wⁿ_J(t)=rⁿ_J+p^c_ķ(t)+E_tp^N(t+1)−E_t-1p^N(t).

The growth rate of the nominal reference wage is denoted by wⁿ; rⁿ is the real-wage growth rate consistent with Ҝ_j dynamics; p^c is consumer price inflation; and J denotes the tractably aggregated workplace venue; p^N is the perceived central-bank inflation target. The rational price-adjustment portion of the baseline wage equation (p^c_ķ(t)+E_tp^N(t+1)–E_t-1p^N(t)) is the subject of next week’s blog.

To better utilize the equation’s capacity to introduce structure into wage determination and the propagation of macro shocks, further define price inflation: p(t)=βp^D(t)+(1−β)p^I(t), where D represents the prices of domestically produced goods and services, I is imports, and β is the relative weight of domestic products in the index of total consumer prices; and p^D(t)=σpⁿ(t)+(1−σ)p^m(t), where σ denotes the relative weight of LEV product prices in overall domestic prices. For ease of presentation, p also represents consumer prices. Along the same lines, define the sectoral composition of trend productivity growth: γ(t)=Φ(t)γⁿ_T(t)+(1−Φ(t))γ^m_T(t), where Φ represents the relative size of the large-establishment venue.

Combining the definitions yields nominal wage dynamics, given a credibly unchanged inflation regime, in the LEV sector:

wⁿ_J(t)=rⁿ_J+βσpⁿ_ķJ(t)+β(1−σ)p^m_ķK(t)+(1−β)p^I_ķ(t).

Venue Synthesis

Combining labor pricing in large- and small-establishment venues identifies the determinants of baseline nominal compensation growth:

w(t)=Φ(t)rⁿ_J+Φ(t)βσpⁿ_ķJ(t)+ Φ(t)β(1−σ)p^m_ķK(t)+ Φ(t)(1−β)p^I_J(t)+ Φ(t)(E_tp^N(t+1)−E_t-1p^N(t))
+(1−Φ(t))(γ^m_K(t)+ p^m(t))+ (1−Φ(t))(a₁(U^N(t)− U(t))+ (1−Φ(t))a₂Δμ(t)_.

Posit that terms of trade remain unchanged (pⁿ=p^m=p^I), as do small-firm trend labor-productivity growth (Δγ^m(t)=0), relative venue size (ΔΦ(t)=0), the natural rate of unemployment (ΔU^N(t)=0), and government intervention (Δμ(t)=0):

w(t)=b_o+b₁(U^N−U(t))+b₂p_Ł(t)+ b₃(E_tp^N(t+1)−E_t-1p^N(t))+ε(t),

where Ł the price-inflation lag structure (t-ķ to t) and ε is an error term.

That simplified reduced-form wage equation, confined to stationary disturbances and thereby characterized by Ҝ durability, is named the Generalized-Exchange Phillips Curve. It is constructed on preferences and technology that are invariant with respect to the conduct of monetary policy as well as employer-employee decision-rules that are rationally informed by central-bank policies. The model replaces the time-separation arbitrarily used by Early Keynesians to meld money neutrality and non-neutrality in the Neoclassical Synthesis. Moreover, a reasonable specification of the other branch of the wage-price nexus (Δp(t)/Δw(t)>0) yields inflation persistence: (Δp(t)/Δw(t))(Δw(t)/Δp_Ł(t))=Δp(t)/Δp_Ł(t)>0.

The GEM Phillips relation imposes a tight structure on b_i. The constant term (b_o=Φrⁿ+(1−Φ)γ^m) reflects the interaction of trend LEV real wage growth (rⁿ_J, 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. Also, the employment coefficient (b₁=(1−Φ(t))a₁) helps explain the surprisingly small estimated influence of joblessness on aggregate wage behavior.

The specification of inflation catch-up (p_Ł(t)= Φ(t)βσpⁿ_ķ(t)+ Φ(t)β(1−σ)p^m_ķ(t)+ Φ(t)(1−β)p^I_ķ(t)) and LEV terms-of-trade dynamics (þ_Ł(t)= βσpⁿ_ķ(t)− Φβ(1−σ)p^m_ķ(t)− (1−β)p^I_ķ(t)) provide important restrictions. Domestic or international shifts in labor’s terms of trade make b₂ unstable. The enhanced Phillips curve, with its simplifying assumptions, would have been understood to be incapable of predicting or explaining the stagflation of the 1970s and early 1980s. The GEM specification also usefully restricts the role of price expectations, which are now limited to anticipated shifts in the central bank’s inflation regime and only affect large-establishment labor pricing (b₃=Φ(t)). Well-specified models of wage dynamics must include both inflation-regime expectations and catch-up.

Finally, generalized-exchange Phillips dynamics reveal the significance of the interaction between the rates of growth in large-establishment nonstationary productivity (γⁿ_T) and the real wage (rⁿ). In GEM analysis, Δγⁿ_T>Δrⁿ exerts upward pressure on LEV profit (Π_J), increasing equity prices, capital investment, and aggregate spending and income while reinforcing Ҝ durability. If Δγⁿ_T<Δrⁿ, there is downward pressure on profit, equity valuation, investment, income, and spending. Such circumstances eventually induce job downsizing and Ҝ recalibration.

Blog Type: Wonkish Saint Joseph, Michigan