Near-Rational Wage and Price Setting and the Optimal Rates of Inflation and Unemployment

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We are grateful to a seminar participant at the Bank of Canada for suggesting this approach.

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By sorting our sample on the basis of long lags of the endogenous variable we considerably reduce concern about

sample selection on the basis of an endogenous variable.  

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contrast, our model allows the possibility that the coefficient on expected inflation will be lower

in extended periods of low inflation than in extended periods of high inflation.  Absent estimation

biases, we would expect the coefficient to approach 1.0 in a sufficiently inflationary environment. 

We first look at the empirical evidence using the conventional adaptive expectations framework. 

We then provide evidence using direct measures of inflationary expectations that address

Sargent’s [1971] criticism of the assumption that the coefficient on lagged inflation must equal

one in an accelerationist model.  Sargent argued that a coefficient of less than one on lagged

inflation may not reflect incomplete projection of inflation but rather forecasters' views that the

process generating inflation does not have a unit root.  By using direct measures of inflationary

expectations we can rule out the possibility that our results reflect differences in how people form

expectations rather than how they use them.

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In order to separately estimate wage and price Phillips curves for periods of low and high

inflation, we sorted the quarters since the Korean War according to the average CPI inflation rate

in the five-year period ending each quarter.  We first classified quarters with average inflation

rates below 3 percent as low inflation and quarters with average inflation rates above 4 percent as

high inflation.

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  By this sorting, the low inflation quarters run from 1954:1 through 1969:1 and

from 1995:3 through 1999:4, the end of our sample period.  The high inflation quarters run from

1970:2 through 1986:1 and from 1990:4 through 1993:2.  There are 77 quarters in the high

inflation sample and 77 quarters in the low inflation sample.  The mean CPI inflation rates in the

two samples are 2.0  percent and 6.3 percent.  This separation was used in half the wage and price

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inflation regressions.  In the other half we limited the low inflation sample to quarters with

inflation rates below 2.5  percent, which brought the sample size down to 62 quarters and reduced

the mean CPI inflation rate in the low inflation sample to 1.9 percent.

Estimates with Adaptive Expectations

 The quarterly Phillips curve equations we estimated were intended to span the

specifications that analysts have used in conventional estimation of NAIRU models except for the

fact that we did not constrain the coefficients on lagged inflation. To this end, we tried a large

number of data combinations and specifications on both wage and price Phillips curves, and ran

each separately for the low and high inflation samples just described.  In all cases the dependent

variable was an annualized inflation rate in either wages or prices, and the explanatory variables

were current or lagged values of unemployment, price inflation and, for the wage equations, trend

productivity growth.   For price inflation we used the CPI, the GDP deflator and the PCE deflator

and estimated price Phillips curves with each.  Twelve values of lagged inflation were used as

explanatory variables.  For wage inflation we used the best series available for any time period,

linking private ECI wages and salaries for 1980-1999 to the adjusted hourly earnings index for the

nonfarm economy for 1961-1980 and to adjusted hourly earnings in manufacturing for 1954-

1961.  Twelve lagged values of CPI inflation were used as explanatory variables.  For

unemployment we used the total rate, the 25-to-54 year old male rate, and Robert Shimer’s

demographically adjusted series.  We used  the current and three lagged values of unemployment

and, alternatively, the current and eleven lagged values.  For the wage Phillips curves, we used

two estimates of trend productivity growth, one being the series created by Robert Gordon and the

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All equations also used the customary dummy variables for the guidepost period in the 1960s and the price control period of

the 1970s, and used the difference between inflation with and without oil prices in 1979-1980 as an additional variable. 

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other a smoothed version of that series.  We ran regressions with the productivity coefficient both

freely estimated and constrained to be 1.0 (for the wage inflation equations), and with just the

current trend and with the current plus seven lagged values of the trend.

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Figures 3 and 4 about here

The key results are summarized in figure 3 for equations explaining wages and in figure 4

for equations explaining prices.  The figures present the results of 144 and 72 specifications

respectively.  Each point represents the sum of the coefficients on lagged inflation estimated for

the low and high inflation samples for one specification.  If the sum of coefficients were similar

for the two samples, the points would cluster along the forty-five degree line.  If they were similar

and near 1.0, the points would cluster near the upper right corner.  In fact, for both wages and

prices, and over the wide range of specifications and data we used, the points cluster near 1.0 on

the high inflation axis, but on the low-inflation axis, they range from around zero to around 0.5

for the wage equations. This is  consistent with the predictions of our model.  The range on the

price equations is broader and less conclusive.  The third of the observations at the highest end of

the range are from equations using the PCE deflator.  The mean values of the coefficients on the

high and low inflation axes respectively are 0.25 and 0.82 for the wage equations and 0.60 and

0.95 for the price equations.

Direct Measures of Inflationary Expectations

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