Helping a Great Economist: Robert Lucas

The overriding objective of Robert Lucas’s theoretical contributions was to restore the primacy of rational behavior to macroeconomics. In his modeling, agents are coherently self-interested. In particular, they make cost-effective use of available information to inform their choices. The GEM Project also insists that macro theory be grounded in optimization and equilibrium. Substantial experience demonstrates that models carefully motivated by rational behavior better explain and predict macro activity. Lucas and the Project are natural allies. It is in effectuating that natural alliance that the formidable theorist is offered a Helping Hand.

Original Great Idea

In the 1970s, Lucas famously argued that adaptive expectations left information on the table and, therefore, could not be consistent with optimization. Lucas’ special target was the Early-Keynesian use of catch-up adjustment for inflation in their Phillips Curve (PC). In his alternative wage equation, Lucas substituted rational expectations, which reasonably requires the cost-effective use of available information. Lucas’ RE Phillips variation was in the vanguard of the macro-theory insurgency that eventually banished EK thinking from mainstream discussion and debate.

Lucas’s PC gathered almost panicked attention by then-mainstream theorists. Excitement was understandable, since RE appeared to blow up mainstream macro theory’s stabilization relevance. producing a “curve” that is vertical at the natural rate of unemployment. Discretionary monetary policy now had no real-side effects, i.e., the “Policy Ineffectiveness Proposition”. Many macro theorists believed that rational expectations was the coup de grace for EK modeling. That belief has been a deeply damaging error – a wrong turn that resulted from Lucas’s reliance on an irrational model of wage-setting arrangements.

GEM Helping Hand

Many of the Blog’s Helping Hands, enhancing great ideas in macroeconomics, involve the rational introduction of either downward nominal wage rigidity and/or chronic labor-price rents. For the RE Phillips curve, however, the improvement is more generally rooted in the Project’s construction of intra-firm decision rules in circumstances of costly, asymmetric workplace information. The focus here is on how to model rational wage-setting arrangements.

Macro theorists choose between two competing strategies in understanding arrangements that enable the rational adjustment of labor compensation for price inflation. Be forward-looking, adopting the expectations approach, or be backward-looking, adopting the catch-up approach. Since Lucas, economists have rejected catch-up, using the forward-looking strategy when thinking about wage dynamics. Indeed, active debate simply skipped over the construction of the adjustment mechanism and focused on how workers and firms can best 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. Lucas made rational expectations a central rule of engagement in research on the nature of business cycles. Broad acceptance rapidly coalesced, despite the fact that forward-looking labor-pricing arrangements have never been provided rational foundations.

GEM framework. For periodic wage adjustments in firm j, employees’ gross nominal gain from using the expectations strategy instead of catch-up is: p_ķj(t)W_j(t)H_j(t), where p is the rate of price inflation over the catch-up period (ķ) from time t to t+1, W is the wage rate, and H is hours on the job. Assuming that, over time, p_ķ(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: åp^MW_j(t)H_j(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 expense of gathering and processing the information necessary to produce a reasonable and timely rational 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 their acceptable 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.

Workers reject the catch-up strategy in favor of expectations if the latter’s benefits exceed its costs:

å p^MW_j(t)H_j(t)(1+r)^-t≥(G_oj+C_oj+N_oj)+å((Ğ_j(t)+Č_j(t)+Ň_j(t))(1+r)^-t.

There are circumstances that motivate rational agents to choose catch-up instead of expectations to periodically adjust wages for inflation. Workers and firms respond to the relatively costly execution of the 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) shorten the catch-up lag (k) and (ii) pay 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. Firms and workers most efficiently reduce 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 (ķ) noted above: W^P_j(t)=W_j(t)(1+p^M). The difference between the premium and the base wages (W^P_j(t)–W_j(t)) becomes an additional worker cost of using the expectations strategy instead of catch-up:

å p^MW_j(t)H_j(t)(1+r)^-t≥(G_oj+C_oj+N_oj)+å((Ğ_j(t)+Č_j(t)+Ň_j(t))+(W^P_j(t)-W_j(t))H_j(t)))(1+r)^-t.

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

(Ģ_oj+Ç_oj+Ņ_oj)+ ∑(Ğ_j(t)+Č_j(t)+Ň_j(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, over time, labor compensation equal to using the rational expectations strategy.  Consequently, employers 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 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/she] must be able to calculate earnings with little difficulty. Complex plans should be avoided because employees distrust those which they cannot understand.”

Sharing a characteristic with effective wage plans, the analysis has not been complex. It shows that, in the aftermath of a one-time monetary shock, catch-up must be used to rationally adjust wages; forward-looking expectations are unacceptable.  Outside economics, none of this is new.  Backward-looking adjustments for inflation have been characteristic of wage administration since the beginning of wage administration.

Is the Game Worth the Candle?

The Phillips curve has long been an important macroeconomic tool, especially in the classroom. Unfortunately, Lucas’s RE variant provides badly misleading guidance to students as well as to policymakers and model-builders. The Project identifies its problem to be inattention to rational behavior. The Helping Hand corrects that fundamental flaw, clearly making the game worth the candle. Also candle-worthy is the GEM extension of the wage-arrangements model, producing the same results, in which p^M can vary. Lucas may not be happy with the help, but I suspect the consummate theorist will accept it.

Cumulative score: Worth it: 6, Not worth it: 0. As the score builds, keep in mind the major objection of mainstream theorists to generalized-exchange macroeconomics: Adding a second (workplace) venue of rational exchange is too much work. Its benefits are not worth the effort.

Blog Type: Wonkish Chicago, Illinois