38
between inflation and unemployment implied by each of the four specifications estimated in table
2.
The values of the coefficient of inflationary expectations implied by our parameter
estimates is plotted in figures 8a,b,c, and d for each of our four specifications. In all cases
coefficient values vary considerably over the sample. In all four specifications the coefficient on
inflation reaches a maximum value of one for at least a year at some point during the sample
period in the early to mid 80s. The four specifications differ in the exact timing of the increase in
the 70s, in how the 50s and 90s are treated, and in the date of the end of the period of a coefficient
of one on inflation.
These figures can be compared to the time path Brainard and Perry estimated for the
coefficient on inflation. Our estimates imply considerably more abrupt changes and more
persistence. They also imply more variation. However, it must be remembered that the method
Brainard and Perry used to estimate their values for the coefficient on inflation imposes
smoothness on the changes. When we smooth our estimates (not shown) they begin to resemble
the time path that Brainard and Perry found with one major difference. The Brainard Perry
estimates peak earlier and fall off more abruptly than our smoothed estimates.
We have varied the specifications presented above to anticipate possible objections to our
results. The specification with the CPI as the dependent variable shows that our results do not
depend on the experience of the 90s which may be atypical. Since non-linear estimation is
difficult when many parameters are being estimated, we have generally used very parsimonious
specifications for the lags on past price inflation when constructing inflationary expectations. One
might object that this parsimony forces the coefficient on inflation to do the work that a richer lag
19
We set a goal of 200 specifications, met that goal, and then estimated a few more to check
specific concerns that arose in the process of evaluating the 200 specifications. In randomly
39
structure would do. The specification where the GDP deflator is the dependent variable answers
this by matching the richest possible lag structure for price expectations (12 quarter unrestricted)
with the most parsimonious specification of the term in the coefficient of expectations. Likewise,
in most specifications, including lagged unemployment, and/or our term for nominal rigidity does
not change our fundamental results.
Our Durbin-Watson statistics for the two specifications using survey expectations show
considerable serial correlation. We have not attempted to correct for this problem because we lack
a credible instrument for price expectations which are endogenous with respect to the error in the
Phillips curve. We are unhappy with this drawback of the analysis, but estimates of our model we
have tried using simulated data suggest that the bias from ignoring the serial correlation in the
parameters we care about is minor.
Robustness of Results
As we have noted above, there are many aspects of the specification that are not dictated
by the theory. Our approach to this problem has been to estimate a wide array of different
specifications to determine whether our primary results are sensitive to changes in the
specification.
Because both the estimation of the model and the numerical analysis of the results
currently require human intervention, we have not been able to mechanize the process of
sensitivity testing. Thus we have not been able to do an exhaustive specification search. Instead
we estimated 218 different specifications. Many were run to test specific concerns. However,
most were chosen randomly.
19
Our survey of the results of these specifications yields the
choosing specifications we allowed all options with equal probability except that we found that
the 12 quarter unrestricted lag on inflation for the price expectations term was always
computationally burdensome so we did not include those specifications in those that were
randomly chosen.
40
following generalizations:
Figure 9 about here
1) Most important, nearly all the point estimates imply that significant gains in
employment are possible by increasing inflation from zero to a rate above 1.5 percent. This can be
seen in figure 9 which plots for each specification the optimal rate of inflation and the reduction in
unemployment that obtains from increasing inflation from zero to the optimal rate. There were
only 12 specifications where the estimated gain was less than 1 percentage point and only one
where it was negligible. This specification was a wage Phillips curve with a rich lag structure for
price expectations while the inflation term in the coefficient on expectations was constrained to be
an equally weighted sixteen quarter moving average of past inflation. Allowing a richer
specification for the impact of inflation on the use of expectations eliminates this result. Of the
other eleven specifications where the estimated impact is less than one percent, all are at least a
half a percentage point. Most of the specifications are wage equations, and none use the PCE
deflator as the dependent variable. Only one uses survey expectations. In no case are the
parameters of the inflation coefficient very precisely estimated so that values more typical of other
specifications cannot be ruled out.
2). It is not possible to robustly identify the relative importance of the effects of nominal
rigidity vs. the effects of near rationality. The majority of specifications that included our term for
20
In contrast, when the term for nominal rigidity was not included the coefficient on the square of
past inflation was nearly always 1.7 times its estimated standard error or more.
21
When we generated standard data with a standard Phillips Curve model and attempted to
estimate our model on it this is what happened.
22
Instead we had one of three other problems: 1) the program was trying to drive the sigma to
zero, 2) the program was driving the constant term in the coefficient of expectations to negative
infinity and the coefficient on the square of past inflation to infinity in order to eliminate
coefficient values between 1 and the lower floor, or 3) in some very rich specifications the first
41
the effects of nominal rigidity give results like those for the PCE in table 2. These do suggest a
role for both nominal rigidity and near rationality. However, in many specifications that include
both effects, the effect of past inflation on the coefficient of expectations is not measured
precisely being about the same size as its estimated standard error.
20
In other cases, the
optimization routine was trying to drive estimates of the standard deviation of desired wage
changes to zero. In six specifications not represented in figure 9 we obtained converged estimates
for the parameters, but the estimated values for sigma were sufficiently large that there was no
single rate of inflation at which the unemployment rate was minimized. It simply fell to the
natural rate asymptotically as in the models estimated for our 1996 paper.
3) We encountered few problems with applying non-linear estimation. We did look for and
find a few cases where there were multiple local minimums, but these reflected minor differences
in the lag structures that were not substantive. Of the 218 specifications we estimated we were
unable to obtain converged values for about 30. This might be a serious concern because under the
hypothesis of fully rational behavior the model's parameters are not identified and it might be that
the non-linear estimation program is trying to drive the constant term in the coefficient on
inflationary expectations to infinity in order to drive the coefficient on expectations to 1.
21
However, this is not what was happening in any of the cases of convergence problems that we
encountered.
22
derivatives of a group of unrelated parameters became so close to co-linear that it was impossible
to invert the approximation to the Hessian used in the maximization routine.
42
Overall, the results from estimating our model support the theory we have laid out. They
suggest that the macroeconomic policy should aim for an optimal rate of inflation that is in the
range of 1.5 to 4 percent. Either higher or lower rates seem likely to result in lower output and
employment.
Conclusion
This paper provides an alternative to natural rate models of unemployment. Natural rate
models provide a wonderful economics “just-so” story based on the idea that firms and workers
take full account of expected inflation in setting current wages and prices. This behavior produces
a unique long run unemployment rate that is consistent with any steady rate of inflation and a
short run Phillips curve in which unemployment above or below the natural rate causes inflation
to decelerate or accelerate.
Our model of the macro economy rests on behavioral underpinnings that are supported by
a range of related evidence including the psychological literature on decision making and
perception, direct survey evidence on how people react to inflation, and the advice of
compensation professionals. We propose that when inflation is low it is not especially salient, and
wage and price setting will respond less than proportionally to expected inflation. At sufficiently
high rates of inflation, by contrast, anticipating inflation becomes important and wage and price
setting responds fully to expected inflation. This behavioral difference between our model and the
natural rate model has significant implications both for estimating the relation between inflation
and real activity in the macro economy and for informing the conduct of macroeconomic policy.
43
Our model is supported by the evidence. Estimates of coefficients on expected inflation,
whether as conventionally measured by lagged inflation or as measured by direct surveys of
expectations, are greater when inflation is high than when it is low. Estimates of our model
provide further support. Rather than a natural rate of unemployment that is invariant to the rate of
inflation, our model traces out a range of equilibrium unemployment rates associated with
different ongoing inflation rates. The optimal unemployment rate is the minimum of this range.
The natural unemployment rate is a special case: it is the equilibrium unemployment rate at high
inflation rates (and ignoring downward wage rigidity, at zero inflation). It is noticeably above the
optimal unemployment rate.
The optimal rate of inflation is low, perhaps not far from current
values, but not zero. Operating with an inflation rate either higher or lower than the optimal leads
to a higher rate of unemployment in the long run.
The distinctive feature of our model is especially important for estimation. In recent years,
as low inflation rates have come to be the norm, NAIRUs estimated from the empirical
counterpart of the natural rate model have proven to be misleading guides to policy makers and
economic analysts. In the mid-1990s, these models typically projected 6 percent as the lowest
sustainable unemployment rate, yet real output has grown at a 4-percent annual rate since then and
the unemployment rate has fallen to 3.9 percent. The NAIRUs estimated for the early 1960s, the
previous period of moderate inflation, also appear unrealistic. When adapted for estimation, the
model we have developed should provide more useful estimates of the attainable levels of
employment and output to serve as guides for stabilization policy and as anchors to longer run
projections.
Not only does our model fit the facts better than NAIRU models, it is also more cogent
44
theoretically. NAIRU models serve well as what Irving Fisher would call “the first
approximation.” They are derived from the assumption that all people behave according to what
economists call economic rationality, or else their deviations from that behavior perfectly cancel
out. This paper relies, as a first approximation, on exactly such economic thinking. But Irving
Fisher also urged economists to make “the Second [and even the Third] Approximation.” With
aggregate Phillips Curves such further approximations involve departures from perfectly rational
decision-making. The evidence available on the subject suggests that the lay public in setting
wages and prices do not have the same model of the economy as economists. Given the
complication of their decisions and, for the most part, their lack of training as economists, it
would, indeed, be surprising if they did. It is thus highly unlikely that the welter of
interdependent intuitively-based decisions of a real economy will produce a coefficient of
inflationary expectations on wage and price inflation that is always exactly one. This paper has
offered a theory for such a departure as price and wage setters under-adjust for inflation when it is
not very salient and when the cost of such behavior is low. This theory yields an optimal level of
inflation and unemployment. It also fits the facts.
45
References
Akerlof, George A., William T. Dickens, and George L. Perry. 1996. “The Macroeconomics of
Low Inflation,” BPEA 1:1996, 1-76.
Akerlof, George A., and Janet L. Yellen. 1985. "A Near Rational Model of the Business Cycle
with Wage and Price Inertia," Quarterly Journal of Economics, 100 (Supplement), 823-38.
Ball, Laurence, N. Gregory Mankiw, and David Romer. 1988. “The New Keynesian Economics
and the Output-Inflation Tradeoff,” BPEA, 1988:1, 1-82.
Blanchard, Olivier J. 1999. Macroeconomics: Second Edition. Upper Saddle River, NJ: Prentice
Hall.
Blinder, Alan S., and others. 1998. Asking About Prices: A New Approach to Understanding
Price Stickiness. New York: Russell Sage Foundation.
Brainard, William C., and George L. Perry. 2000. “Making Policy in a Changing World.” In
Economic Events, Ideas, and Policies: The 1960s and After, edited by William Brainard
and George Perry. Brookings (forthcoming).
Davis, Steven J., John C. Haltiwanger, and Scott Schuh. 1996. Job Creation and Job Destruction.
Cambridge, Mass.: MIT Press.
Eckstein, Otto and Roger Brinner. 1972. “The Inflation Process in the United States,” Joint
Economic Committee of the Congress of the United States. Washington: Government
Printing Office.
Fair, Ray C. 2000 “Testing the NAIRU Model for the United States,” The Review of Economics
and Statistics, 82 (1,February), 64-71.
46
Feldstein, Martin. 1997. “The Costs and Benefits of Going from Low Inflation to Price
Stability,” in Reducing Inflation: Motivation and Strategy, edited by Christina D. Romer
and David H. Romer. Chicago: University of Chicago Press.
Friedman, Milton. 1968. “The Role of Monetary Policy,” The American Economic Review, 58
(March), 1-17.
Gleitman, Henry. 1996. Basic Psychology. New York: Norton.
Gray, Jo Anna. 1978. “On Indexation and Contract Length,” Journal of Political Economy, 86
(February), 1-18.
Gordon, Robert J. 1997. “The Time-Varying NAIRU and Its Implications for Economic Policy,”
Journal of Economic Perspectives, 11 (Winter), 11-32.
_____________. 1998. “Foundations of the Goldilocks Economy: Supply Shocks and the Time-
varying NAIRU.” BPEA 2:1998, 297-346.
Greenspan, Alan. 1989. Statement before the Committee on Banking, Finance and Urban Affairs
of the U.S. House of Representatives, January 24. Federal Reserve Bulletin (March).
Hendricks, Wallace E. and Lawrence M. Kahn. 1985. Wage Indexation in the United States: Cola
or Uncola
®
? Cambridge, MA: Ballinger .
Holland, A. Steven. 1995. “Inflation and Wage Indexation in the Postwar United States,” Review
of Economics and Statistics 77 (February), 172-176.
Kahneman, Daniel and Amos Tversky. 1979. “Prospect Theory: An Analysis of Decision under
Risk,” Econometrica 47 (March), 263-92.
King, Robert G. And Mark W. Watson, 1994 :The Post-War U.S. Phillips Curve: A Revisionist
47
Econometric History,” Carnegie-Rocherster Conference Series on Public Policy, 41, 157-
219.
Kunreuther, Howard. 1978. Disaster Insurance Protection Public Policy Lessons. New York:
Wiley.
Kusko, Andrea, James M. Poterba, and David W. Wilcox, “Employee Decisions With Respect to
401(k) Plans: Evidence from Individual Level Data.” NBER Working Paper 4635.
Cambridge, MA: National Bureau of Economic Research, February, 1994.
Krueger, Anne O. 1991. “Report of the Commission on Graduate Education in Economics,”
Journal of Economic Literature, 29 (September), 1035-53.
Leonard, Jonathan S. 1987. “In the Wrong Place at the Wrong Time: The Extent of Frictional
Unemployment,” in Unemployment and the Structure of Labor Markets, edited by Kevin
J. Lang and Jonathan S. Leonard. New York: Basil Blackwell.
Levine, David I. 1993. “Fairness, Markets, and Ability to Pay: Evidence from Compensation
Executives,” American Economic Review, 83 (December), 1241-59.
Lucas, Robert E., Jr. 1973. “Expectations and the Neutrality of Money,” Journal of Economic
Theory, 4 (April), 103-24.
Mankiw, N. Gregory. 1985. "Small Menu Costs and Large Business Cycles: A Macroeconomic
Model of Monopoly," Quarterly Journal of Economics 100 (May) 529-37.
Milkovich, George T. and Jerry M. Newman. 1984. Compensation. Plano, TX: Business
Publications.
Modigliani, Franco and Lucas Papademos. 1975. “Targets for Monetary Policy in the Coming
Year.” BPEA 1:1975, 141-65.
48
Nisbett, Richard and Lee Ross. 1980. Human Inference: Strategies and Shortcomings of Social
Judgment. Englewood Cliffs, NJ: Prentice-Hall.
Papke, Leslie E. 1995. "Participation in and Contributions to 401(k) Pension Plans: Evidence
from Plan Data," Journal of Human Resources (Spring), 30, 311-45.
Phelps. Edmund S. 1968. “Money Wage Dynamics and Labor-Market Equilibrium,” The Journal
of Political Economy, 76 (July, Part 2), 678-711.
Rock, Milton L., and Lance A. Berger. 1991. The Compensation Handbook: A State of the Art
Guide to Compensation Strategy and Design, Third Edition. New York: McGraw-Hill.
Sargent, Thomas J. 1971. “A Note on the ‘Accelerationist’ Controversy,” Journal of Money
Credit and Banking, 3 (August), 721-5.
______________ 1973. “Rational Expectations, the Real Rate of Interest, and the Natural Rate of
Unemployment,” BPEA, 2:1973, 429-72.
Shafir, Eldar, Peter Diamond and Amos Tversky. 1997. “Money Illusion,” Quarterly Journal of
Economics, 112 (May), 341-74.
Shiller, Robert J. 1997. “Why Do People Dislike Inflation?”, in Reducing Inflation: Motivation
and Strategy, edited by Christina D. Romer and David H. Romer. Chicago: University of
Chicago Press.
Shimer, Robert J. 1998. “Why Is the U.S. Unemployment Rate So Much Lower?”In NBER
Macroeconomics Annual, edited by Ben S. Bernanke and Julio Rotemberg. Cambridge,
Mass: National Bureau of Economic Research.
Staiger, Douglas, James Stock and Mark W. Watson. 1997. “The NAIRU, Unemployment and
Monetary Policy,” Journal of Economic Perspectives, 11 (Winter), 33-49.
49
Stock, James H. and Mark W. Watson. 1998. “Median Unbiased Estimation of Coefficient
Variance in a Time-varying Parameter Model.” Journal of the American Statistical
Association 93 (March): 349-58.
Dostları ilə paylaş: |