# Adjusting Wages for Inflation, Part I

As promised, this week’s post takes a critical look at Robert Lucas’s use of rational expectations in wage modeling. That innovation fundamentally transformed the Early Keynesian Phillips curve and, ultimately, macroeconomics. It is surprisingly easily shown to be fundamentally wrong.

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. Economists have, for a long time, rejected catch-up, adopting the forward-looking strategy in their analysis of wage dynamics.  Indeed, active debate simply skipped over the choice of adjustment mechanism and focused 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 business-cycle research. Given such broad acceptance, it is shocking 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. (For the complete model, see Chapter 4.)

Analytic framework. For periodic wage adjustments in firm j, workers’ gross nominal gain from using the expectations strategy instead of catch-up is: pķj(t)Wj(t)Hj(t), where p denotes price inflation over the catch-up period (ķ) from time t to t+1, W is the wage rate, and H hours on the job. Assuming that pķ(t) has a stationary mean equal to pM, the present value of employee gross returns from using the expectations strategy rather than catch-up is: ∑pMWj(t)Hj(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 rational and timely forecast of price inflation. Such costs are separable into fixed investment in forecasting capacity (Go) 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 (Co and Č(t)).
• Finally, there are the fixed and variable costs of negotiating agreement with management on the inflation forecast (No and Ň(t)), complicated by the parties’ differing objectives.

It is not surprising that a process requiring forecasting, consensus-building, and successful negotiations between parties who typically disagree is complex.  By contrast, if the calculation of the consumer price index is a public good, the catch-up approach is simple, easily understood, and virtually costless to implement.

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

∑ pMWj(t)Hj(t)(1+r)-t≥(Goj+Coj+Noj)+∑(Ğj(t)+Čj(t)+Ňj(t))(1+r)-t.

The GEM Project documents circumstances that motivate rational agents to choose catch-up instead of expectations in the periodic adjustment of wages for inflation. Most notably, workers and firms rationally respond to the relatively costly execution of an expectations strategy by searching for wage-setting arrangements that make catch-up more efficient. Two procedures 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. The evidence shows, not surprisingly, that workers become most interested in shortening the catch-up lag when inflation is high. Cecchetti (1984), for example, examined wage-contracting arrangements in unionized firms in the United States.  In the 1950s and 1960s, when mean inflation was low, the average period between discretionary wage changes was seven quarters.  By contrast, in the 1970s, when mean inflation was relatively high, the average dropped to four quarters.  The incidence of indexing also increased in the 1970s, a period when the rational-expectations Phillips curve was taking hold.

Wage premium. Firms and workers most effectively 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): WPj(t)=Wj(t)(1+pM). The difference between the premium and the base wages (WPj(t)-Wj(t)) becomes an additional worker cost of using the expectations strategy instead of catch-up:

∑ pMWj(t)Hj(t)(1+r)-t≥(Goj+Coj+Noj)+∑((Ğj(t)+Čj(t)+Ňj(t))+(WPj(t)-Wj(t))Hj(t)))(1+r)-t.

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

ojojoj)+ ∑(Ğj(t)+Čj(t)+Ňj(t))(1+r)-t≤0.

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

For management, wage-setting arrangements that pay WP and use catch-up produces, over time, 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 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, this post’s 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; relying on forward-looking expectations is clearly irrational.  Outside economics, none of this is new.  Backward-looking adjustments for inflation have been characteristic of wage administration since the beginning of wage administration. It must be a pretty big deal that Lucas’s famous reformulation of the Early Keynesian Phillips curve lacks rational foundations. That conclusion is extended beyond a one-time shock in next week’s blog.

Blog Type: Wonkish Chicago, Illinois