This paper is based on a long-term research program with Rachel Kranton on the implications of identity

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The absence of wage indexation in union contracts is a fifth tell-tale of problems with

natural rate theory.  Economists have advanced reasons why indexation will not be complete. 

But the reasons that have been advanced for incomplete indexation, are also reasons why wage

bargainers will not act as if they first come to an agreement over a real wage in current prices,

and then add in inflationary expectations.  If wages are set as indicated by natural rate

theorists—with bargains first determined in real terms and nominal wages and prices determined

by adjustment for expected inflation—firms and workers with risk aversion will both have their

welfare improved by contracts with wages indexed to inflation.  Wage indexation, even in the

unionized sector, is remarkably rare.  Christofides and Peng (2004) analyzed a sample of almost

12,000 Canadian union contracts from 1976 to 2000.  The mean length of these contracts was

slightly more than two years (25 months).  Yet only 19 percent of these contracts were indexed. 

And even in those with indexation, price increases were considerably less than fully covered (at

only 58 percent) (Christofides and Peng (2004, Table 1, p. 38)).  

Jo Anna Gray (1978) offers a theoretical explanation why wage indexation would be less

than complete.  The CPI, which is the measure of inflation used in most indexed contracts, is not

only correlated with shocks to the money supply, which should not affect relative prices, but also

correlated with real supply shocks, which do affect relative prices.  In this case optimal

indexation will be determined by the relative importance of demand shocks and supply shocks. 

Card (1986) and Ehrenberg, Danziger, and San (1983) have demonstrated that the facts fit the

theory: at the microeconomic level correlations between input and output prices and the

consumer price index are related, as predicted, to levels of indexation in union contracts. 

But empirical findings still suggest that contracts are under-indexed.  Christofides and

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Ehrenberg, Danziger and San (1983, p. 222) compute a formula for the degree of indexation, which they

call 

,

.  In their elegant 1-period model they find that neither 

,

 nor the fraction of contracts engaged in indexation

will vary with the level of expected inflation. See Table 1, p, 223.

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See, for example, Ehrenberg, Dantziger, San (1983, p. 239).  An indicator of the frequency of such

provisions in such contracts is provided by Christofides and Peng (2004, p. 11): in roughly 1/3 of the indexed

contracts in their investigation the COLA clause was never triggered.   Another possible anomaly is that many

contracts have caps in the amount of contingent wage adjustment that can be generated.

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There is a further anomaly.  Since CPI-inflation may be correlated with real changes, wage contracts

should not just be dependent on the aggregate CPI, but should also be based on industry-specific shocks to demand

and supply.  Why are unions and firms not more creative in indexing wages also to market-specific indicators of

changes in demand?  Card ( 1986, p. S150) asks: “Why not index-link wages directly to market-specific prices?”   

35

Peng (2004) construct measures of the variance of relative supply shocks and the variance of

relative demand shocks.  Given the previous findings of Card and Ehrenberg et al it is not

surprising that indexation, contract length and the nominal wage adjustment depend on these

variances, as the theory predicts.  But, Christofides and Peng also find that indexation is

correlated with the expected level of inflation, even with controls for the size of real shocks to

supply and demand.

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  The theory had not predicted this result.  In the language regarding

consumption and investment behavior: these results suggest excess sensitivity of wage

indexation to inflationary expectations.

48

  

In addition, indexed contracts contain yet another anomaly.  Many such contracts have

COLA adjustment, but only after inflation has passed some trigger level.

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 It is difficult to

explain such a provision under the assumption that wage contracts are made only with concerns

about real variables.

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A sixth observation, regarding estimates of the Phillips Curves themselves, suggests yet

another type of problem with natural rate theory.  While some Phillips Curve estimates produce

coefficients of unity on lagged inflation, others do not.  William Brainard and George Perry

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The tests with direct measures of expectations do not suffer from econometric bias due to endogeneity of

price expectations.  Some econometric bias remains because of measurement error in inflationary expectations, but

the estimated values of the coefficients are so very far from one, especially in the wage equations, that the

discrepancy is unlikely to be explainable by econometric bias.  Further study should be made of the likely size of this

bias. 

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(2000) made estimates of Phillips Curves allowing for the possibility of time variation in the

distributed lag on past inflation.  The sum of these lag coefficients was not constantly one,  as

would be the case with natural rate theory with adaptive expectations.  Instead it varied

considerably.  

There is a systematic difference between times when the coefficients sum to unity and the

times when they are considerably lower.  William Dickens, George Perry and myself (2000)

estimated Phillips Curves for the United States for periods of high inflation and for periods of

low inflation.  When inflation is high, the sum of coefficients on lagged inflation in both price

and wage equations is close to one.  But, in contrast, when inflation is low, that sum is close to

zero for wage equations; for price equations it is not zero, but it is still much less than one. 

Estimates of Phillips curves with direct measures of expectations—the inflation expectations

from the University of Michigan Survey of Consumers and from the Livingston Survey of the

expectations of professional forecasters—yield similar results.  In periods of high inflation the

coefficients in both wage and price equations are both close to one.  But, in times of low

inflation the coefficient in wage equations is much less than one, averaging about .3 over many

different model specifications; for price equations it averages .6.  These findings question the

universality of Phillips Curves with coefficients of one on proxies for expected inflation.

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Resolution with Economic Theory.  The preceding findings suggest respective ways in

which the assumptions or the predictions of natural rate theory are poor descriptions of economic

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