__Rational-Expectations Phillips Curve__

Robert Lucas and his colleagues kicked off the famous macro wars by using the stagflation decade to motivate their anti-Keynesian insurgency. From Lucas (1981):“Keynesian orthodoxy or the neoclassical synthesis *is* in deep trouble, the deepest kind of trouble in which an applied body of theory can find itself: It appears to be giving seriously wrong answers to the most basic questions of macroeconomic policy. Proponents of a class of models which promised 3-1/2 to 4-1/2 percent unemployment to a society willing to tolerate annual inflation rates of 4 to 5 percent have some explaining to do after a decade as we have just come through.” (p.559)

From the decades-later perspective of the GEM Project, the “explaining” is not difficult. The Early Keynesians were led astray in the 1970s by their arbitrary assumption of convenience about the nature of meaningful wage rigidity. MWR is properly defined by its capacity to rationally suppress wage recontracting and is necessary for macro theory to be both stabilization relevant and consistent with the neoclassical tenets of optimization and equilibrium – two characteristics much prized by Lucas, his fellow anti-Keynesians, and the Project.

*Early Keynesians.* The EK off-target guess about wage determination that adequately supports MWR had two consequential problems: the use of a homogeneous nominal wage that was catching up to homogeneous price inflation and, more generally, relying on a specification constructed on irrational behavior. Both issues damage the EK Phillips curve:

w(t)=α_{o}+α_{1}U(t)+α_{2}p_{ķ}(t),

where lower-case variables denote rates of change, *U* is the jobless rate, and *p* the product-price inflation rate over the catch-up period (*ķ*) at time* t*. The wage equation became the keystone of Samuelson’s Neoclassical Synthesis. In response to the terms-of-trade shocks adverse to labor that occurred in force at the beginning of the stagflation decade, EK theorists quickly enriched their description of product prices, improving the fit of their Phillips relation. But they did not solve the more significant problem of wage heterogeneity rooted in the ubiquity of workplaces in which employer-employee information is restricted by costly, asymmetric information. Nor did they solve the problem of misleading model-building guidance that is characteristic of irrational-behavior theories. Early Keynesians were flying with faulty instruments in the stagflation crisis.

*Anti-Keynesians.* Lucas and his colleagues chose the early-version Phillips curve and its failure to explain stagflation as their point of attack on EK orthodoxy. Interestingly, the insurrectionists were also flying blind. Lucas’s rational-expectations wage modeling, which quickly became the lynchpin of anti-Keynesian thinking, similarly lacks rational-behavior foundations. It is not surprising that their stagflation explanation, captured in Lucas’s “rational-expectations” (sic) Phillips variation, and monetary-policy advice are so damagingly wrong:

w(t)=ɑ_{o}+ɑ_{1}(U^{N}(t)–U(t))+E_{t}p(t+1),

*U*^{N} is the natural rate of unemployment and *E*_{t} the expectations operator conditional on information available at time *t*. Expectations are restricted to the cost-effective use of available information. Central-bank behavior, of course, critically informs such expectations.

The post demonstrates, from the perspective of generalized price-mediated exchange, that the textbook expectations-oriented Phillips Curve is deeply flawed. The analysis has two parts. The first investigates the periodic adjustment of wages for inflation, a surprisingly misunderstood process. Much of the early Phillips-curve controversy is related to the inclusion of product prices as an explanatory variable, the specification of which has been used to model the effects of nominal disturbances on employment and output. Careful modeling of wage-price dynamics recalibrates the significance of the famous Lucas innovation. It falsifies his rejection of the rationality and structural nature of wage catch-up to product-price inflation that has already occurred. The second part, postponed to next week, specifies a useful rational-behavior Phillips curve.

__Irrational vs Rational Inflation Expectations__

In modeling wage-setting arrangements, macro theorists choose between two competing strategies to adjust nominal compensation for price inflation: Be forward-looking, adopting the expectations approach, or be backward-looking, adopting the catch-up approach. Led by Lucas, economists have, for a long time, rejected catch-up, adopting the forward-looking strategy in thinking about wage dynamics. Indeed, active debate simply skipped over the choice of adjustment mechanism in order to focus on how workers and firms predict price inflation. In a forecasting contest between adaptive (based on inflation history) and rational (based on all available information) expectations, victory surely goes to the latter. Rational expectations became a central rule of engagement in mainstream research on the nature of business cycles. Given such broad acceptance, it is surprising that forward-looking labor-pricing arrangements have never been provided rational foundations.

What follows looks at the optimizing choice between the forward-looking and backward-looking strategies. It is divided into two parts. The first posits that the central bank’s inflation regime is credibly stationary; the second, appearing next week, permits trend inflation to vary.

*Analytic framework.* For firm *j*’s periodic wage adjustments in market-clearing general equilibrium, workers’ gross nominal gain from using the expectations strategy instead of catch-up is: *p*_{k}(t)*W*(t)*H*(t), where *p* is the rate of price inflation over the catch-up period (*k*) from time* t* to *t+1*, *W* is still the wage rate equal to the market labor price (*W*^{M}), and *H* is hours on the job. Assuming that, over time, *p*_{k}(t) has a stationary mean equal to *p*^{M}, the present value of employee gross returns from using the expectations strategy rather than catch-up is: å*p*^{M}*W*(t)*H*(t)(1+*r*)^{-t}, where the quantities are summed over the life of the work relationship.

There are three types of employee costs involved in using the expectations strategy:

- First is the gathering and processing the information necessary to produce a timely forecast of price inflation. Such costs are separable into fixed investment in forecasting capacity (
*G*_{o}) and the variable expense associated with each forecast exercise (*Ğ*(t)). - Next are the dissemination, persuasion, and revision costs involved in achieving an effective consensus among workers with respect to the inflation forecast, also separable into fixed and variable components (
*C*_{o }and*Č*(t)). - Finally, there are the fixed and variable costs of negotiating agreement with management on the inflation forecast (
*N*_{o}and*Ň*(t)), complicated by the parties’ differing objectives.

It is unsurprising that a process requiring forecasting, consensus-building, and successful negotiations between parties who typically disagree is complex. By contrast, if the calculation of a consumer price index is a public good, the catch-up approach is simple, easily understood, and virtually costless to implement.

The firm’s workers must reject the catch-up strategy in favor of expectations if the latter’s relative benefits exceed its relative costs:

SUM p^{M}W(t)H(t)(1+r)^{-t}≥(G_{o}+C_{o}+N_{o})+å((Ğ(t)+Č(t)+Ň(t))(1+r)^{-t}.

It is becoming clear that there are circumstances motivating rational agents to choose catch-up instead of expectations to periodically adjust wages for inflation. Most notably, workers and the firm rationally respond to the relatively costly execution of an expectations strategy by searching for wage-setting arrangements that make catch-up more efficient. There are at least two procedures that reduce the differential gross returns between the two strategies: (i) shortening the catch-up lag (*k*) and (ii) paying a compensating wage premium.

*Catch-up lag*. The catch-up lag (*ķ*) can be shortened by more frequent wage adjustments, reducing the differential returns generated by the expectations strategy. The best-known application of this strategy is short-period automatic cost-of-living escalators.

*Wage premium*. The firm and its workers can effectively eliminate the differential return to the expectations strategy by combining inflation catch-up with the payment of a premium over the base wage that compensates for the adjustment lag (*k*): *W*^{P}(t)=*W*^{m}(t)(1+*p*^{M}). The difference between the premium and the base (market) wages (*W*^{P}(t)*-W*^{m}(t)) becomes an additional worker cost of using the expectations strategy instead of catch-up:

SUM p^{M}W(t)H(t)(1+r)^{-t}≥(G_{o}+C_{o}+N_{o})+SUM ((Ğ(t)+Č(t)+Ň(t))+(W^{P}(t)-W(t))H(t)))(1+r)^{-t}.

Rearranging identifies the necessary condition, given the inflation regime, for employees to prefer expectations to catch-up:

(G_{o}+C_{o}+N_{o})+∑(Ğ(t)+Č(t)+Ň(t))(1+r)^{-t}≤0.

Workers rationally choose the expectations strategy only when it is costless to implement. Assigning zero cost to its implementation, however, is indefensible.

For management, wage-setting arrangements that pay *W*^{P} and use catch-up produces labor compensation equal to using the rational expectations strategy. Consequently, the firm must also reject the forward-looking approach. It yields no relative benefits and must be costlier than catch-up. Indeed, wage administrators have generally concluded that expectations-strategy costs are substantial. Most significantly, using expectations is more complex than catch-up, increasing the difficulty employees have understanding the compensation plan and the incentives the firm wishes to promote. For wage policymakers, simple trumps complex. The following from Charles Brennan’s respected wage administration text is illustrative of the general view: “The [wage] plan must be kept simple. The plan must be kept as free as possible of intricate involvements which would prevent the employee from understanding it. He must be able to calculate his earnings for himself with little difficulty. Complex plans should be avoided because employees distrust those which they cannot understand.”

__Conclusion__

Sharing a characteristic with effective wage plans, the foregoing analysis has not been complex. It shows that catch-up, not expectations, rationally motivates the periodic adjustment of wages. Outside economics, that conclusion does not surprise. Backward-looking adjustments for inflation have been characteristic of wage administration since the beginning of wage administration. But for economists, it’s a pretty big deal that Lucas’s famous reformulation of the Early Keynesian Phillips curve lacks rational foundations. His “rational-expectations” approach badly misleads any serious attempt to explain the stagflation decade.

Blog Type: Wonkish Saint Joseph, Michigan

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