Phillips Curve Part II: Adjusting Wages for Inflation

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A tenet of LEV workplace analysis is that profit-seeking firms, responding to information asymmetries that compromise the capacity of markets to price labor services, must construct intra-firm mechanisms of employer-employee price-mediated exchange. An important outcome of that mandate is the efficient design of wage-setting arrangements to account for product-price inflation.

There are two competing efficient-design strategies: (i) be forward-looking, adopting the expectations approach, or (ii) be backward-looking, using catch-up to inflation that has already occurred. Once selected in firm j, the strategy is assumed to be executed within the context of long-tenure employment. Wages are set for a fixed period, and the task is repeated with largely unchanged participants again and again.

Economic theorists have long rejected catch-up in favor of the forward strategy in modeling wage dynamics. Indeed, debate skipped over the choice of adjustment mechanism and focused on how workers and firms forecast inflation. In the contest between adaptive (based on the recent history of price inflation) and rational (based on all available information) expectations, victory was appropriately awarded to the latter. The use of Lucas-class expectations became a fundamental rule of engagement in the long-running dispute over the appropriate policy response to business cycles. Such broad acceptance has masked the fact that forward-looking labor-pricing arrangements have never been provided rational foundations.

What follows corrects that oversight, modeling rational choice between the two  strategies to adjust nominal wages for product-price inflation. It is divided into two parts. The first posits that the central bank’s inflation regime is credibly stationary. The second permits trend inflation to vary.

Stationary Inflation Regime

Recall that labor has been posited to be homogeneous until hired and trained, at which point the homogeneity becomes venue-specific. Employees share a constant discount rate (r), and are risk neutral. For wage adjustment in firm j, a worker’s nominal gain from using the expectations strategy instead of catch-up is:


where pķ denotes inflation over the catch-up period, W is the wage paid, and H is hours on the job.

Positing that pķ(t) has a stationary mean equal to pN, the present value of employee gross returns from using the expectations strategy rather than catch-up is:


Meanwhile, there are three types of worker costs involved in using the expectations strategy:

  • First is the expense of gathering and processing the information necessary to produce a reasonable and timely forecast of price inflation, denoted by Ğ(t).
  • Next are the costs of dissemination, persuasion and revision involved in achieving an effective consensus among relevant employees with respect to the inflation forecast (Č(t)).
  • Finally, there are the costs of negotiating agreement with management on the inflation forecast (Ň(t)), complicated by the parties’ differing objectives.

It is unsurprising that a process requiring forecasting, consensus-building, and successful negotiations between parties who inherently 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. Rational agents cannot ignore that executing the expectations strategy incurs nontrivial costs, while implementing catch-up does not.

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

                                  å pNWj(t)Hj(t)(1+ r)-t > å(Ğj(t)+Čj(t)+Ňj(t))(1+ r)-t.

In that cost-benefit context, two plausible circumstances motivate rational agents to choose catch-up instead of expectations as the means of periodically adjusting wages for inflation.   

First is the powerful free-rider problem, until now masked by the implicit assumption that the employees’ forecasting expenses are costlessly allocated to individual workers. Given that wage changes are paid to all employees, it cannot be ignored that there is no individual incentive to provide the time and effort to formulate, disseminate, persuade, and negotiate consensus expectations and then do it again and again. Employees can never use the expectations strategy in periodic wage adjustments absent a union or some other arrangement providing compensation for those who do the necessary work.

Second is the clincher. Responding to the relatively high cost of executing an expectations strategy, rational firms and workers search for wage-setting arrangements that make catch-up more mutually efficient. The analysis indicates the existence of two procedures that reduce the differential gross returns between the two strategies: (i) shortening the catch-up lag (ķ) and (ii) paying a compensating wage premium.

Catch-up lag.  The catch-up lag (ķ) is 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 product-price inflation is high. In a well-known example, Cecchetti (1984) examined wage-contracting arrangements in the union sector 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.

Wage premium. The hypothesized differential return to the expectations strategy is effectively erased by combining inflation catch-up with the payment of a premium over the base wage (Wj) that compensates for the adjustment lag (ķ):


   The difference between the paid premium and the base wages (WPj(t)Wj(t)) becomes an additional worker cost of using the expectations strategy instead of catch-up:

                     å pNWj(t)Hj(t)(1+r)-t≥ å((Ğj(t)+Čj(t)+Ňj(t))+(WPj(t)-Wj(t))Hj(t)))(1+r)-t.

Rearranging identifies the necessary condition for employees to prefer expectations to catch-up:

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

Workers can rationally choose the expectations strategy if and only if it is costless to implement. Zero cost of its implementation is, of course, not feasible.

For management, wage-setting arrangements that use catch-up and pay WP 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 more costly to implement than catch-up. Indeed, in the world of wage administration, firms’ expectations-strategy costs are understood to be onerous. The most significant problem is that using forecasts is more complex than catch-up, increasing the difficulty employees have comprehending the compensation plan and the incentives the firm wishes to promote. For wage policymakers, simple trumps complex. A long prominent wage administration text illustrates 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.” (Brennan, p.204)

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

Nonstationary Inflation Regime

In this short section, the monetary authority’s inflation regime can vary. The modification little alters the foregoing analysis. Rational arrangements continue to rely on catch-up. Expectations remain relatively costly, with insufficient corresponding benefits. Assume that the inflation-adjustment period (ķ) remains constant. Also posit that the monetary authority has a target trend inflation rate (pT), which can be immediately implemented and can vary over time. Altering the LEV wage model to account for the variable inflation regime requires only substituting nonstationary pT for  stationary pN in the earlier definition of the Wage Premium (WP) that compensates for catch up (ķ).  (Equation 4.6.) Inflation consequences for periodic wage setting from variable pT are efficiently captured by rational catch-up, pķ.

The overall message is robust. Given firm-specific human capital sufficient to make worker turnover costly, rational wage-setting arrangements require the use of catch-up to inflation that has already occurred. More to the point, catch-up replaces expectations in labor-price modeling. The gold-standard test of the wage-arrangements model now can be addressed. What method do LEV firms actually use? The answer is no secret. Catch-up is used; forecasts, no.  Making that much maligned aspect of EK thinking consistent with rational behavior will take some getting used to.

Illustrative of the difficult acclimation to the newfound rational behavior is the prominent textbook of Carlin and Soskice (2006, p.160): “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.” There is clearly much to unlearn. For starters, actual behavior should be cautiously, not confidently, dismissed as irrational.

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