Adjusting Wages for Inflation, Part II

This is the final installment of the three-part summary of the GEM Project’s reconstruction of the Phillips curve to be both properly microfounded and stabilization-relevant. Last week’s post demonstrated that, given a stationary central-bank inflation regime, employers and employees rationally choose catch-up to periodically adjust nominal wages to inflation. Stationary mean inflation is a reasonable assumption in the circumstances of a one-time monetary shock. But, in many other contexts, the inflation regime does change; and self-interested workers and firms must pay attention. In this section, the wage-arrangements model allows the monetary authority’s inflation regime (p^N) to vary, increasing its explanatory power without altering the conclusions summarized in the two earlier posts.

Nonstationary inflation regime. For ease of presentation, assume that the wage-adjustment period (ķ) remains constant. Also posit that the monetary authority has at time t a target inflation regime (p^N(t)), which it can implement immediately: p^T(t) = p^N(t). Wage adjustment for inflation is now analytically separable into two parts: (a) the influence of price change given the inflation regime and (b) the influence of changes in the inflation regime.

For the first channel of influence, the use of expectations was shown last week to be suboptimal. It is relatively costly, with no corresponding benefits, to produce and implement inflation forecasts in support of regularly scheduled compensation adjustments. There is no doubt that for rational agents catch-up to past inflation is the superior strategy. For the second channel, the efficient calibration of wage-setting arrangements (W_P) requires a rationally constructed forecast of changes in the inflation regime, necessarily playing close attention to credible monetary policy. Here, the costs of the expectations approach are mitigated by a relatively low frequency of regime shifts and, when they do occur, the degree to which the central bank provides credible forewarning.

In the blog appearing two weeks ago, a consistent large-establishment nominal wage-dynamics model was shown  to be w_j(t)= a_o+ a₁(U^N(t)–U(t))+ p_ķ(t)+ E_t p^N(t+1)–E_t-1 p^N(t), where lower-case variables denote rates of change and U is the jobless rate, U^N the natural rate, and E_t the expectations operator conditional on information available at time t. (Chapter 4) Three distinct expectations configurations comprise the model’s wage-setting environment. First, the inflation regime is credibly unchanged, E_tp^N(t+1)–E_t-1  p^N(t) =0, implying uncomplex labor-price dynamics reminiscent of Early Keynesian thinking:

w_j(t)=a_o+a₁(U^N(t)−U(t))+p_ķ(t).

The influence of expectations is eliminated; wage-price dynamics are motivated wholly by catch-up to inflation that has already occurred. This is the definitional case in the aftermath of a one-time monetary shock. Catch-up crowds out expectations whenever the existing inflation regime is credibly unchanged.

Second is  a credible change in the inflation regime, Δp^N(t)=E_t  p^N(t+1)−E_t-1 p^N(t) ≠0, implying:

w_j(t)=a_o+a₁(U(t)–U(t))+p_ķ(t)+Δp^N(t).

Rational wage-setting procedures still assign a central role to catch-up. Expectations are activated but return to being dormant after a one-time W_P recalibration (ΔW_P=Δp^N).

Finally, there are continuing errors in agent forecasts of the inflation regime, ε_j(t)= Δp^N(t)(E_tp^N(t+1)−E_t-1p^N(t))≠0, implying:

w_j(t)=a_o+a₁(U^N(t)–U(t))+p_ķ(t)+Δp^N(t)−ε_j(t).

Stubbornly incorrect regime forecasts do not alter the structural role of catch-up, which is embedded in efficient wage-setting arrangements. They do, however, change the role of expectations, which become more active. As long as forecast errors persist, agents keep searching for the appropriate calibration of the wage premium. Rationally constructed expectations, however, prevent the errors from being serially correlated and imply that the more active influence of expectations in the aftermath of a misunderstood inflation-regime change produces no systematic effect on the dynamic path of labor pricing or use. When wage setting is properly restricted to be rational, inflation-expectations play a much more modest role than in mainstream models.

Summing up. Given sufficient firm-specific human capital to make worker turnover costly, optimizing labor-pricing arrangements mandate that catch-up always be an integral part of periodic wage adjustments, while expectations are restricted to a more latent role. The rational role of inflation catch-up in periodic wage determination is badly understood, even by New Keynesians. Carlin and Soskice (2006, p.160) are illustrative: “The key point to highlight is that although the inertial or backward-looking Phillips curve matches the empirical evidence concerning inflation persistence, it has a major shortcoming. Because it rests on ad hoc assumptions – in particular about the inflation process – rather than being derived from an optimizing micro model of wage or price setters’ behaviour, it does not allow a role for ‘credibility’ in the way monetary policy affects outcomes.”

During credibly anticipated shifts in inflation regimes, the two strategies must be used in combination. Catch-up continues to link wage adjustments to past inflation while expectations recalibrate the size of the wage premium or the length of the adjustment period in response to the new regime, largely ratifying the intuition of the Early Keynesians. Throughout, the analysis remains rooted in the formal economic method rightly prized by modern theorists.

The implications of restricting real Phillips-curve effects from central-bank credibility to the particular circumstances of expected regime change deserve emphasis. Operationally, central banks typically attempt to establish credibility by committing to an inflation target. A credible transition to such a regime produces a one-time effect on wages, via a change in W_P. After wage-setting arrangements have been recalibrated, expectations again become dormant in labor pricing. Indeed, an important benefit to effectively committing to a price objective is short-circuiting the influence of inflation expectations on labor compensation. Price inflation will vary around the targeted mean, and central banks want such deviations to trigger only catch-up, not more destabilizing incorrect anticipations of an altered price regime.

Most significant, however, is the point that New Keynesians ignore. Coherent mainstream modeling, with its inherent wage recontracting, demonstrates the necessity of meaningful labor-price rigidity (MWR) for the Phillips curve to produce interesting results. Catch-up by itself helps confines inflation expectations to a latent role and explains wage-price inertia, not MWR. Catch-up is rational in both mainstream and GEM model classes and, absent MWR, easily accommodates the nominal labor-price reductions required by recontracting in the context of an adverse disturbance in nominal demand.

Blog Type: Wonkish Saint Joseph, Michigan