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

9

Feldstein (1997) has estimated very large deadweight losses from the tax distortions of going from zero to two

percent inflation.  His calculations  omitted the tax sheltering of pension plans, 401k’s, IRA’s and other tax-saving

devices.  The deadweight losses will be almost zero for savers who fail to exhaust their possibilities for tax deferred

savings. Kusko, Poterba, and Wilcox (1994) found only 1 percent of 401k  participants in a medium-sized

manufacturing plant were constrained, and,  similarly, Papke (1995) found that less than 1 percent of contributions to

401(k) plans were in excess of $5,000 in 1987.   Feldstein’s calculations were based on a model with no uncertainty-

induced precautionary savings.  Independent of any considerations of tax sheltering, inclusion of such precautionary

saving will likely reduce by almost 90%  the estimates of the tax-distortion welfare loss.  

23

will be the optimum. Since the firms are monopolistic competitors, producing more output

increases the welfare of the owners of the firms.  Also, with the labor market characterized by the

payment of efficiency wages, unemployed workers are happy to supply more labor if it is

demanded. Their welfare will be improved if they obtain work at the going wage, so workers, as

well as owners of firms, will have increased welfare as employment increases. Our concept of the

optimal rate of inflation ignores both the transactions (e.g. the so-called “shoe-leather”) costs of

higher inflation as well as the tax-distortion effects, both of which we consider to be small.

9

   It

also ignores other considerations, such as  inflation's redistributive effects,  loss of confidence in

the currency,  effects on exchange rates, and the improved allocation of resources that results from

small amounts of inflation in the presence of nominal wage and price rigidities. We continue to

refer to the rate of inflation that minimizes the unemployment rate as the optimal rate below

despite the uncertainty about what rate would be optimal in the broader context that included

these considerations. 

Empirical Evidence for Near-Rational Wage and Price Setting

In this section we discuss three related types of evidence for the importance of the type of

behavior we describe.  We begin with a recounting of the findings of Brainard and Perry's recent

analysis of a Phillips Curve model with time-varying parameters. We then do a simple exercise in

---

10

For typical applications see James H. Stock and Mark W. Watson (1998) and Robert J. Gordon (1998).

11

 See Brainard and Perry (2000).

24

which we estimate Phillips Curves on a split sample to see how the estimated coefficient of

inflation differs between periods of high and low inflation. Finally, we estimate the model

described in the previous section and present estimates of the optimal rate of inflation and the

gains from being at the optimal rate as opposed to higher or lower rates of inflation.

Time Varying Parameters  

In the Brainard and Perry paper that we described at the outset, the authors were

addressing how uncertainty affects policy making.  Their empirical work demonstrating one key

source of uncertainty reveals precisely the departures from conventional NAIRU models that our

model predicts.  Previous work examining how NAIRU had varied over time assumed the NAIRU

framework and allowed time variation only in the intercept of the equation.

10

  Brainard and Perry

applied a general Kalman filter estimation that permits all the key Phillips curve parameters to

vary—lagged inflation and unemployment as well as the intercept.—and lets the data to choose

the allocation of time variation among them.

11

  Figure 2, which summarizes their results with CPI

inflation as the dependent variable, shows substantial time variation in the coefficient of the

lagged inflation term and virtual stability in the intercept and the inverse unemployment rate,

which they measure by the unemployment rate of 25-to-54 year old men to account for

demographic changes over time.  The coefficient on lagged inflation is low during periods of low

inflation and approaches 1.0 only in the inflationary middle years of the period.

Figure 2 about here

---

25

The virtual stability over time in the unemployment coefficient and intercept in the

Brainard-Perry time-varying estimates is also worth noting.  Rather than attributing the episodes

of sustained low unemployment to declines in a NAIRU that is invariant to inflation, these results

attribute them instead to a change in price and wage setting behavior that accompanied periods of

low inflation.  The juxtaposition of coefficients on lagged inflation that change with the inflation

regime with constant coefficients elsewhere is predicted by the model we have described above. 

Brainard and Perry compared their Kalman filter estimates with recursive least squares

estimates, which are also shown in figure 2.  These comparisons suggest why conventional

estimation has seemed to support the NAIRU model since it was first introduced in the

inflationary mid-1970s by Modigliani and Papademos (1975).  Before that time, lagged inflation

in Phillips curves was consistently estimated to have a coefficient well below 1.0.  But the large

increase in inflation in the mid-1970s corresponded to the period of  large variance in inflation

and fixed coefficient estimation has been dominated by that episode ever since. If the coefficients

in fact have varried over time, any procedure that assumes that they are fixed will yield

misleading results. This includes the recursive estimates which treat them as fixed in each interval

over which they are estiamted.

Periods of Low and High Inflation

The postwar U.S. economy has experienced extended episodes of both low and moderately

high inflation that permit direct comparison of the NAIRU model with our model.  Conventional

NAIRU models use a modified Phillips curve in which lagged inflation is taken as a measure of

adaptive inflationary expectations and the coefficients on lagged inflation sum to 1.0.  By

---