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From Trade-offs to Policy Ineffectiveness:
A History of the Phillips Curve
Thomas M. Humphrey
October 1986
Preface ......................................................................................................
3
The Early History of the Phillips Curve
The Evolution and Policy Implications of Phillips Curve Analysis ..................13
Early Versions of the Phillips Curve ....................................................
13
Introduction of Shift Variables ..............................................................
19
The Expectations-Augnaented Phillips Curve and the
Adaptive-Expectations Mechanism .........................................................
20
Statistical Tests of the Natural Rate Hypothesis
24
From Adaptive Expectations to Rational Expectations
26
Evaluation of Rational Expectations
28
Concluding Comments
30
Appendix
31
The famous Phillips curve trade-off relationship between inflation and unemployment, whose doctrinal history these essays chronicle, amply illustrates the
workings of two well-known "laws" in economics. It illustrates, first, statistician
Stephen M. Stigler’s Law of Eponymy, according to ~vhich no scientific discovery is
named for its original discoverer. For, as shown in the initial essay, Phillips was
far from the first to describe the relationship bearing his name. On the contrary,
in the two hundred years before him at least ten economists, including such celebrated names as David Hu,ne, He!iry Thornton, JohnStuart Mill, Irving Fisher,
and Jan Tinbergen, presented ver;ions of the curve.
The Phillips curve also exemplifies the workings of Goodheart’s Law, which,
as formulated by the British economist C.A.E. Goodheart, states that any observed
statistical regularity will collapse once the authorities try to exploit it for policy
purposes. Such a collapse was precisely the fate of the Phillips curve in the 1960s
and 1970s. For no sooner had Professor Phillips isolated what he thought was a
stable hundred-year empirical relationship between inflation and unemployment
than it started breaking down when policymakers sought to exploit it. The
resulting failure of the Phillips curv~ to hold still while the authorities attempted to
move the economy along it, trading off higher inflation for lower unemployment
until the best attainable combination had been reached, led to disenchantment with
and consequently reformulation of the Phillips curve idea. Circhmstances forced
economists to take account of inflationary expectations viewed as the chief factor
causing shifts in the curve.
Of these reformulated expectations-augmented Phillips curves, two in particular
have dominated recent thought. First came the Friedman-Phelps error-learning or
adaptive-expectations version (according to which trade-offs last only so long as
expectations are adjusting to actualities) followed closely by the Lucas-Sargent
market-clearing or new classical version (in which expectations adjust instantaneously). This latter version, embodying as it does the natural rate and rational
expectations hypotheses, teaches that the Phillips relationship is a purely adventitious
phenomenon genera.ted by unforeseeable random shocks and as such cannot be
exploited by systematic macroeconomic policies. The fact that John Stuart Mill
already had reached this same conclusion as early as 1833 suggests that there have
long been at least three competing views of the Phillips curve. One sees it as a
stable permanently exploitable trade-off; another as a temporary trade-off that
vanishes once expectations catch up with reality ; and the third as a purely statistical
relationship that cannot be exploited for policy purposes in either the short-run
or the long.
Thomas M. Humphrey
THE EARLY HISTORY OF THE
PHILLIPS CURVE
Although critics may dismiss it as a mere empirical
correlation masquerading as a tradeoff, the Phillips
curve relationship between inflation and unemployment has nevertheless been a key component of
macroeconomic models for the past 25 years., in
1960 Paul Samuelson and Robert Solow [16, p. 192]
named the relationship after A. W. Phillips, the New
Zealand economist who in 1958 gave it its best known
(but hardly its first) modern formulation (see Figure 1). Since then it has evolved through at least
five successive versions as analysts sought to expand
its explanatory power, its theoretical content, its
policy relevancy, and its ability to fit the facts.
Phillips’ [15, p. 290] initial zvaye-cha~ge version
w=f(U) related the rate of wage inflation w via the
function f( ) to the excess demand for labor as
Figure 1
PROFESSOR PHILLIPS" CURVE
~.. oin~ t8e6dl K ilnggld2 m
, ..
I
2
I
I
4
[
[
6
I
I I
8
.I I
10
12
Unemployment (%)
Phillips obtained his curve by fitting the equation
w = f(U) = --a + bU-c to the scatter of annual observations on wage inflation rates (w) and unemployment
rates (U) for the United Kingdom, 1861-1913. He
found also that observations for the years 1948-1957
lay close to his fitted curve, indicating its apparent
long-run empirical stability.
Source: Phillips [15, p. 285]
measured by U, the deviation of unemployment from
its equilibrium or labor-market clearing rate. Transformed thrgugh the assumed markup of prices over
wages into the price-change equation p=f (U), where
p is the rate of price inflation, it xvas widely interpreted as a stable enduring tradeoff or menu of
inflation-unemployment combinations from which the
authorities could choose. In its shi]t-adjusted form
p=f(U)+Z, it incorporated a vector of variables Z,
including past pri~e changes, trade union effects,
unemployment dispersion, demographic factors and
the like, to account for observed shifts in the inflationunemployment trad~off :or menu of policy choices.
In its e~’pecta.tio~s-a~g’me~.ted form p--p~=f(U),
where p~ is the expected rate of inflation, it asserted
(1) that the tradeoff is between unemployment and
unexpected inflation, (2) that the tradeoff vanishes
when expectations are realized, and (3) that unemployment returns to its natural equilibrium rate at
this point. Provided expectations adjust to actual
inflation with a lag, it also implied the accelerationist
notion that nnemployment can be pegged permanently
below its natural rate only if inflation is continually
accelerated so as to always stay a step ahead of expectations. That is, while denying a permanent tradeoff between unemployment and the rate of inflation,
it implied that there may be a permanent t,’adeoff
between nnemployment and the rate of acceleration of
inflation.
The preceding versions reflect a non-marketclearing view of the world, expressing as they do the
disequilibrium response of wages and prices to a
mismatching of demand and supply in the labor
market. By contrast, the alternative New Classical
or ~arket clearin~ version U=g(p--p~) assumes
that the labor market is always in equilibrium and
that deviations of unemployment from its natural
rate stem solely from inflation misperceptions and
vanish when those misperceptions end. When corn-
bined with the assumption of rational expectations
(according to which actual inflation differs from
expected inflation only by a random forecast error)
this version says that tradeoffs are solely the result
of unpredictable random shocks and cannot be exploited by systematic (predictable) policies.
The foregoing interpretations are well known. Not
so well known, however, is the origin and early history of the inflation-unemployment relationship. For
the most part, textbooks typically trace the idea to
Phillips’ famous 1958 Economica article without saying anything about what went before. The}, correctly
describe the five versions of the Pbillips curve outlined above. But they fail to note that ~tt ]east three
of those versions (including the version presented by
Phillips himself) had already been spelled out long
before Phillips. The result is to neglect at least ten
predecessors whose names deserve tO be associ’ated
with the Phillips curve. In an effort to redress this
oversight and to set the record straight, the paragraphs below document what Phillips’ Predecessors
had to say about the inflation-unemployment relationship.
John Law (1671-1729)
It is probably unrealistic to expect to find a
Phillips curve in the xvritings of John Law, the
famous eighteenth century banker and finance minister whose schemes to promote economic development
via the creation of a paper currency secured by land
ended with the collapse of the Mississippi Bubble in
1720. To be sure, he believed that money stimulates
real activity. But be also believed that it does so at
constant or even decreasing prices owing to the
availability of idle resources and scale economies in
production. As a result, {here is either no Phillips
curve inflation-unemployment relation in his analysis
or it works in the wroug direction--falling unemployment being associated with falling, not rising,
prices.
David Hume (1711-1776)
The prototypal Phillips curve analysis is to be
found in the writings of the eighteenth century Scottish philosopher-economist David Hume. As early
as 1752, he presented the essentials of a Phillips curve
relationship of the form U=g(dP/dt), where U is
the deviation of unemployment from its natural
(equilibrium) rate and dP/dt is the change in the
price level xvith respect to time. This relationship
derived straight from his assumption that unemploymeut disturbances stem from price perception errors
(the difference between actual and perceived prices)
and that such errors persist only when prices are
changing. Expressed symbolically, he assumed that
U = h(P--P~) and
P--P~ = k dP/dt
where P and P~ denote actual and perceived prices
and k is a coefficient relating price perception errors
to price level changes. Substitution of the latter
equation into the former yields Hume’s version of the
Pbillips curve U=g(dP/dt) mentioned above. That
version embodied his hypothesis that one must continually raise prices to peg unemployment at arbitrarily low levels since only by doing so can one
produce th~ price perception errors that sustain the
tradeoff. In short, Hume’s explanation stresses the
employment effects of unperceived monetary-induced
price changes..He [8, pp. 37-40] says:
though the high price of commodities be a necessary consequence of the encrease of gold and silver,
yet it follows not immediately upon that encrease;
but some time is required before the money circulates through the whole state and makes its effect
be felt on all ranks of people. At first, no alteration is perceived; by degrees the price rises, first
of one commodity, then of another; till the xvhole at
last reaches a just proportion with the new quantity of specie .... In my opinion, it is only in
this interval or intermediate situation, between the
acquisition of money and rise of prices, that the
encreasing quantity of gold and silver is favourable
to industry .... From the whole of this reasoning
we may conclude, that it is of no manner of consequence, xvith regard to the domestic happiness of a
state, whether money be in a greater or less quantity. The good policy of the magistrate consists
only in keeping it, if possible, still encreasing;
because, by that means, he keeps alive a spirit of
industry in the nation .... There is always an
interval before matters be adjusted to their new
situation; and this interval is as pernicious to industry, when gold and silver are diminishing, as it
is advantageous when these metals are encreasing.
Three points stand out in Hume’s analysis [10].
First, the tradeoff is between unemploymeut and unperceived changes in money and prices; it vanishes
once percdptions fully adjust to reality. Second,
price perceptions, though slow to adjust, eventually
catch up to one-time changes in the level of money
and prices. It follmvs that such changes can at best
generate temporary but not permanent tradeoffs.
Third, the only way the tradeoff can be sustained is
to generate a continual succession of changes in
money and prices. Hume here makes the distinctly
non-rational-expectations argument that such changes
will, because of the lag in the adjustment of price
perceptions, keep prices forever marching a step
ahead of perceptions, perpetually frustrating the
latter’s attempts to catch up. In this way, he claims,
the gap between actual and perceived prices will be
maintained thus permanently lowering unemployment. Hume notes that this process works symmetrically for price deflation--such deflation, if prolonged, produch~ix an enduring rise in unemployment.
It follo~vs at once that a permanent tradeoff
g(dP/dt) exists between unemployment and therate
of change of money and prices. One must therefore
agree with Charles R. Nelson’s [14, p. 2] recent
judgment that
Hume ~vas clearly of the opinion that the level of
activity ~vould be raised permanently by a steady
increase in the quantity of money, prices, and
wages. Hmne was therefore a believer in a stable,
long-run Phillips curve.
Henry Thornton (1760-1815)
Like Hume, Henry Thornton also described a
Phillips curve of the form U=g(dP/dt), Where the
variables are as defined above [10]. In his classic
An Enquiry into the Nature and E~fects o~ the Paper
Credit of Great Britain (1802) he [19, p. 237] says
that a monetary expansion stimulates employment
by raising prices:
. . . additional industry will be one effect of an
extraordinary emission of paper, a rise in the cost
[i.e., price] of articles will be another. Probably
no small part of that industry which is excited by
new paper is produced through the enhancement of
the cost of commodities.
This same tradeoff, he [19, p. 238] notes, also holds
in reverse as monetary and price deflation bring
painful rises in unemployment.
If we assume the augmented paper to be brought
back to its ordinary quantity, we must suppose
industry to languish for a time through the ill
success [of] mercantile transactions.
In his discussion of the Phillips curve, Thornton
~vas careful to distinguish between alternative levels
of money and prices and continuous changes of those
variables. Only the latter, he said, can affect real
activity and sustain the tradeoff. This is epitomized
in his [19, p. 256] remark that "it is the progressive
augmentation of bank paper, and not the magnitude
of its existing amount, which gives the relief." In
other words, money and prices stimulate activity only
when they are continually increasing. For, says
Thornton [19, p. 238], "While paper is encreasing,
and articles continue rising, mercantile speculations
appear more than ordinarily profitable." But "as
soon . . . as the circulating medium ceases to encrease, .the extra profit is at an end," and the stimulus
vanishesl Thus a one-time rise in the money stock
and level of prices cannot sustain the tradeoff. Instead, a continuous increase or "progressive augmentation" is required. The tradeoff is between output
and the rate of change of prices.
As for the tradeoff’s source, Thornton attributed it
chiefly to a tendency for money wages to consistently
’lag behind prices. He explicitly stated (1) that
inflation stimulates .activity, (2) that it does so by
reducing real wages and raising real profits, (3) that
this output-enhancing redistribution occurs because
money wages lag behind prices, and (4) that this.
wage lag persists as long as inflation is sustained.
Like Hume, he did not explain why the lag would
persist nor why wages would not eventually catch up
with prices once inflationary expectations had fully
adjusted to actual inflation. His analysis is largely
silent about inflation anticipations; he did not incorporate them into his Phillips curve.
Finally, he disagreed with Hume over the desirability of exploiting the Phillips curve for policy
purposes. I-Iume clearly believed that the policy
authorities in the closed world economy should exploit the curve, using monetary gold inflation to
stimulate employment. Hume [8, pp. 39-40] says as
much in his advice to the policymaker.
The good policy of the magistrate consists only in
keeping [money], if possible still enereasing; because, by that means, he keeps alive a spirit of
industry in the nation, and enereases the stock of
labor, in which consists all real power and riches.
In contrast, Thornton opposed the exploitation of
the Phillips curve for policy purposes. Such exploitation involved inflation, which he sa~v as an
unmitigated evil. All inflationary policy, he [19,
p. 239] said, is "attended with a proportionate hardship and injustice." True, output and employment
would rise. But such gains, he thought, would be
far too small to be worth the costs (uncertainty, in-
justice, social discontent) of higher inflation. In
short, the Phillips curve at the economy’s normal
level of operations was very steeply sloped, allowing
little increase in output per unit rise in inflation.
Thus while "paper possesses the faculty of enlarging
the quantity of commodities by giving life to some
new industry," the unfavorable tradeoff ensures that
"the increase of industry will by no means keep pace
with the augmentation of paper." Moreover, because
the economy normally operates close to its absolute
full capacity ceiling, stimulative policy will quickly
reach the point where
it is obvious that the antecedently i~ie persons to
whom we may suppose the [monetary infl6tion] to
give employ, are limited in number;-andthat,
therefore, if the encreased issue is indefinite, it
will set to work labourers, of whom a part ~vill be
drawn from other, and, perhaps, no less useful
occupations,
On these grounds he [19, p. 236] concluded that
there exist narrow "bounds to the benefit which is
to be derived from an augmentation of paper; and,
also, that a liberal, or, at most, a large increase of it,
will have all the advantageous effects of the most
extravagant emission."
The Attwood-Mill Debate
The Phillips curve concept continued to flourish in
the hands of more than one British classical writer
after Henry Thornton. That this is so is evident
from a glance at the celebrated interchange between
Thomas Attwood (1783-1856) and John Stuart Mill
(1806-1873) in the 1820s. Att~vood, an inflationist
proponent of inconvertible paper currency regimes
and full employment at any cost, believed in a stable
long-run tradeoff relationship of the form U=g(P)
where U and P denote unemployment and the price
level, both taken relative to their normal (base
period) values. Attwood used this relation, in which
the inflation variable enters as a price level rather
than its Hume-Thornton rate of change, to argue
(1) that high unemployment stems from low prices,
(2) that low unemployment emanates from high
prices, aud (3) that the government can and should
achieve a zero target rate of unemployment with
inflationary monetary expansion. For him nothing
short of absolute full employment would suffice. Said
he [3, p. 467], "so long as any number of industrious
honest workmen in the Kingdom are out of employ-
ment, supposing such deficiency of employment not
to be local but general, I should think it the duty,
and certainly the interest, of Govermnent, to continue
the depreciation of the currency until full employment is obtained and general prosperity. .... Restore
the depreciated state of the currency," he [2, p. 66]
declared, and "you restore everything that constitutes
the commercial prosperity of the nation."
Opposing him was John Stuart Mill who reasoned
in terms of the relationship U=g(P--P") where U
is the discrepancy between unemployment and its
natural steady-state level, P is the price level, and P~
is its expected or perceived level. Using this relationship, Mill argued (1) that tradeoffs are temporary,
(2) that they stem from unexpected price changes
and vanish once perceptions adjust to reality, and
(3) that, contrary to Attwood, one cannot peg real
activity at arbitrarily low levels simply by pegging a
nominal price (or inflation) variable since the txvo
variables are independent of each other in steadystate equilibrium [9].
To be sure, Mill admitted that a temporary inflationary stimulus is possible. It is true, he [13, p. 79]
said, that an unexpected inflation, if misperceived as a
rise in relative-prices, "may create a false opinion of
an increase of demand; which false opinion leads, as
the reality would do, to an increase of production."
But it is also true that the real expansion is "followed
. . by a fatal revulsion as soon as the delusion
ceases." In other words, once producers correctly
perceive price increases as nominal rather than real,
economic activity reverts to its steady-state level,
but only after undergoing a temporary recession to
correct for the excesses of the inflationary boom.
In Mill’s view, the steady-state Phillips curve is a
vertical line at the economy’s natural rate of unemployment. To assert otherwise (as Attwood did), he
thought, was to argue that people can be fooled perpetually into believing that nominal gains are real
and that commodities can be created from paper
money expansion. But according to Mill, one cannot
fool all the people all the time. Money illusion, he
contended, is not permanent. Attempts to peg real
activity are therefore bound to be futile. Inflation
cannot permanently stimulate activity. Mill’s reply
to Attwood dispels the notion that expectationsaugmented Phillips curves and the natural rate hypothesis are of recent origin.
Irving Fisher (1867-1947)
As noted above, Hume and Thornton helped lay
the theoretical foundations of the particular Phillips
curve relationship U=g(dP/dt). It was Irving
Fisher, however, who provided the first statistical
evidence of that relationship [7]. In his 1926
International Labour Reviezv article, "A Statistical
Relationship Between Unemployment and Price
Changes," he investigated the correlation between
unemployment U and lagged price changes (dP/dt)~,
where the subscript L denotes a linear distributed lag
(Fisher himself being the inventor of the lag distribution concept) on the price-change variable. ’Using
monthly U. S. data for the period 1915-1925, he
obtained correlation coefficients as high as 90 percent
between the two variables. Likewise, his time series
chart displayed a similar strong correspondence between lagged price changes and employment (see
Figure 2). From this evidence he concluded that
there was indeed a strong relationship between them.
He [7, p. 502] also concluded that the relationship
was causal as well as empirical, that causality runs
undirectionally from price changes to unemployment,
and that there are good theoretical reasons for this
being so. His theory of price-to-unemployment
Figure 2
IRVING FISHER’S 1926 CHART
SHOWING CO-MOVEMENTS BETWEEN LAGGED
PRICE CHANGES (~’) AND EMPLOYMENT (E)
15’
o
--15
ua
--30
.;-
~’ denotes a distributed lag or moving weighted
average of past price changes. Fisher interpreted
the sta[istica) correlation between the two series
as evidence of a causal relation running from
price changes to employment.
Source: Fisher [7, p. 502]
causality relies on fixed contracts, the inertia of
custom, and other inhibiting factors that prevent
costs from adjusting as fast as prices when prices
change. Owing to the lag of costs behind prices,
changes in the latter affect profits and thereby the
level of real activity and employment. Via this linkage, causality, he argued, runs from inflation to unelnployment as confirmed by his finding that the
former variable leads the latter.
Jan Tinbergen
Although, he presented no formal econometric
equations, Fisher was the first to offer empirical
corroboration o{ the Phillips curve’s market clearing
version U=g(dP/dt) according to which causality
runs from inflation to unemployment. By contrast,
Jan Tinbergen [4] in 1936 was the first to estimate
the alternative shift-augmented wage-change version
wT-f(U)-]-Z in which causality runs from unemployment or some equivalent measure of demand
pressure in the labor market to the wage inflation
rate and a vector of shift variables enters to affect
the wage-unemployment tradeoff. More precisely,
his equation was of the form AW=F(E,AP-~)
where AW is the change in money wages, E is
employment relative to its normal (i.e., trend) level,
and the lagged price-change variable Ap_~ represents
catch-up or cost-of-living wage adjustment factors
thought capable of shifting the curve. Thus in his
"An Economic Policy for 1936" he presents the
expression AW = 0.16 E -t- 0.27 Ap_~ in which the
numerical coefficients are estimated from the Netherlands data for the period 1923-1933.
About this equation three things must be said. It
was the first econometric Phillips curve equation ever
to appear in print. It also was the first to explain
the tradeoff in terms of the law of supply and demand
according to which the price of any good or service
(including labor) varies iu proportion to the excess
demand for it. In other xvords, for the first time the
Phillips curve was interpreted as a wage-reaction
function relating the disequilibrium response of
wages to demand pressure in the labor market, this
pressure being measured by employment relative to
trend. Finally, as mentioned above, Tinbergen’s
equation was the first to include a price change shift
variable to account for observed movements in the
wage-employment relationship. In these respects, it
9
foreshadowed 1960s-vintage wage equations that likexvise represented the Phillips curve as a demandpressure xvage-response function subject to shifts
owing to changes in the cost of living.
Tinbergen returned to the Phillips curve issue
once again in his Business C3~cles in the United
Kingdom 1870-1914, published in 1951 fully seven
years before Phillips’ contribution. There, using W
to denote wages and E to denote employment, he [21,
p. 50] writes the Phillips curve equation as
dW/dt = "v’V = f(E) = RE
and gives it the excess-demand wage-reaction interpretation. "The theory expressed" in .th~ equation,
he says, "may be given the well-knmvn formulation
that a high unemployment figure ’exerts a pressure
on’ the wage rate and that, on the other hand, a
small unemployment figure causes wages to go up."
He also notes that the equation’s empirical {it might
be improved if the demand-pressure variable were
entered nonlinearly and that this could be accomplished by replacing the employment variable E with
the inverse of the unemployment rate U-1. Finally,
he suggested adding variables representing cost-ofliving changes and the degree of unionization of
the labor force to the equation to improve its statistical fit. On all of these innovations he pioneered
the practice of fitting econometric Phillips curve
equations.
Klein and Goldberger
Lawrence Klein and Arthur Goldberger also estimated econometric inflation-unemployment equations
before Phillips. In their famous 1955 study An
Econometric Model of the United States, 1929-1952,
they [11, p. 19] presented a wage-change Phillips
curve equation of the form AW=F(U,AP-~). More
precisely, their equatiou was
AW = 4.11 -- 0.74 U + 0.52 AP-1 -1- 0.54 t
xvhere U is total unemployment, t is a time trend in
years (t=l in 1929), and the other variables are as
defined above.
Like Tinbergen, Klein and Goldberger expressed
the wage inflation variable in first difference rather
than percentage rate of change form. Besides including a time trend variable, they also entered the unemployment variable linearly rather than nonlinearly
10
into their equation. Except for these minor differences, their equation is virtually the same as the later
formulations of Phillips and R. G. Lipsey, who
clarified and extended Phillips’ work. And like those
latter writers, Klein and Goldberger interpreted their
equation as a wage-reaction function in which money
wages change in response to excess labor demand in
an effort to clear the market. According to them
[11, p. 181
the main reasoning behind this equation is that of
the law of supply and demand. Money wage rates
move in response to excess supply or excess demand
in the labor market. High unemployment represents high excess supply, and low unemployment
below customary frictional levels represents excess
demand.
Here is the essence of the Phillips-Lipsey interpretation, an interpretation that also runs in terms of
the law of supply and demand.
A. J. Brown and Paul Sultan
As documented above, the theoretical, empirical,
and econometric foundations of the Phillips curve
had been thoronghly established by the mid-1950s,
several years in advance of Phillips’ own contribution.
It remained, hmvever, for someone to present a
Phillips-type relationship on a statistical scatter diagram and then to draxv the familiar dowmvardsloping convex tradeoff curve that bears his name.
Credit for being the first to accomplish these tasks
goes not to Phillips himself but rather to two other
economists, A. J. Brown and Paul Sultan.
The former, in his 1955 volume The Great Inflation 1939-1951, presented scatter diagrams similar to
Phillips’ (see Figure 3) that plotted annual wage
inflation rates against unemployment rates for the
United Kingdom for the periods 1880-1914 and 19201951, and for the United States for the period 19211948. From these charts Brown [5, pp. 91-101]
concluded (1) that the two variables are inversely
related, and (2) that the relationship between them
is nonlinear since wages change at faster rates at
!ow than at high rates of unemployment. He also
used his charts to estinaate the critical noninflationary
level of unemployment below which wage inflation
exceeds productivity growth so that prices rise. He
did not, however, fit a curve to his data. Thus,
although he presented a Phillips-type graph, he failed
to draw the eye-catching curve made famous by
Figure 3
Figure 4
A.J. BROWN’S SCATTER DIAGRAM
PAUL SULTAN’S ANTICIPATION
OF THE PHILLIPS CURVE
The Hypothetical Relationship of the
"Fullness" of Employment to Annual Price Changes
,7o
43.
2"
"80
United Kingdom
1881-1914
o7
99 1189
~Employment
M a x ! rn ~ m~b~l e :l .n.~f I a,_.t i o._.n_ _.
98 ¯ 90~066
82° 11
~_~ Hypothetical Relationship of
to Price Changes
¯ 88
1%
O05
93
0
2~
3~ 4 ~,.
% of Unemployment
Maximum of "Tolerable" Deflation
--1 -
Percentage Unemployed
Brown’s scatter diagram, presented 3 years before
Phillips’, shows an inverse nonlinear relation between wage inflation and unemployment.
Sultan’s hypothetical curve associates 4% unemployment with price stability, 2% unemployment
with an assumed maximum tolerable rate of
inflation of 2%, and 6% unemployment with a
maximum tolerable deflation rate of 2%.
Source: Sultan [17, p. 555]
Source: Brown [5, pp. 99-100]
Phillips. For this reason, one must reject A. P.
Thirhvall’s [~8] contention that the curve should
bear Brown’s name rather than Phillips’.
Priority for drawing the Phillips curve goes to
Paul Sultan, whose contribution predates phillips’
by one year. Thus, in his 1957 textbook Labor Economics, Sultan presents the curve in a diagram (see
Figure 4) described by him [17, p. 555] as follows:
the vertical scale measures the annual changes in
the price level expressed as a percentage, while the
horizontal scale measures the percentage of the
~vork force unemployed. The line relating unemployment to inflation . . . is strictly hypothetical,
but it suggests that the tighter the employment
situation the greater the hazard of inflation . : . .
Assuming that a fairly precise functional relationship exists between inflation and the level of employment, it is possible to determine the "safe"
degree of full employment. In our hypothetical
case, we are assuming that when uneraployment is
less than 2 percent of the work force, ~ve face the
dangers of inflation. And when unemployment is
:larger than 6 percent, we face .the problem of
serious deflal:ion.
Here is the first diagrammatic representation of the
price-chaqge Phillips curve as a stable tradeoff relationship :p=f(U) between- : inflation, and unemploy-
ment. On the basis of this diagram, three writers [1 ]
recently have suggested that the Phillips curve could
with equal justification be called the Sultan schedule.
Concluding Comments
Given the evidence presented in the preceding
paragraphs, the label "Phillips curve tradeoff" must
be judged both misleading and incomplete. For, as
documented above, Phillips xvas far from the first to
postulate an inflation-unemployment tradeoff or to
draw the curve bearing his name. Even the econometric wage-price equations employed in modern
Phillips curve analysis together with their excess
demand and alternative market clearing interpretations long predate Phillips. In short, Phillips and
his successors inherited (albeit unknowingly) these
concepts; they did not invent them. In this sense at
least, their xvork may be said to constitute the continuation rather than the origin of Phillips curve
analysis.
Still, it was Philiips’ formulation and not those of
his predecessors that captured the attention of the
economics profession. One must ask why this was so.
Certainly it cannot be explained by tl~e novelty of his
11
cnrve or its empirical derivation; these were hardly
innovations at the time he presented them. Nor can
it be attributed to any originality in his explanation
of his curve. His theory was simply the law of supply,
and demand according to which the price of any
commodity or service (including labor) changes at a
rate proportional to the excess demand for it. This
explanation of course had been advanced by Tinbergen years before Phillips¯ Rather his phenomenal
success probably stemmed from three factors. First
xvas his striking finding of the apparent near 100-year
empirical stability of his curve, a stability not suspected before. Second was the persuasive early expositions of his work provided by such.influential
economists as Lipsey [12], and Samuels0n and Solow
[16]. Especially inqportant was the Samuelson-Solow
interpretation of Phillips’ curve as a menu of policy
choices, a menu from which the authorities could
select the best (or least undesirable) inflationunemployment combination and then use their policy
instruments to attain it. By providing a ready-made
justification for discretionary intervention and activist fine tuning, this interpretation helped make the
Phillips curve immensely popular among Keynesian
policy advisors. Third was Phillips’ presentation of
his curve at just the right time to satisfy the Keynesians’ search for an explanation of how changes in
nominal income divide into price and quantity components. ~Vhatever the reason, his name alone was
attached to the tradeoff concept even though at least
ten predecessors over a period of roughly 250 years
also shared in its formulation.
Re~erences
Amid-Hozour, E.; D. T. Dick; and R. L. Lucier.
"Sultan Schedule and Phillips Curve; an Historical Note." Economica 38 (August 1971): 319-20.
Attwood, Thomas. The Remedy; or, Thoughts on
the Present Distresses. Second edition, with additions. London: 1816.
Evidence Before the Select Committee
on the Bank of England Charter, 1831-2, p. 467.
Bacon, Robert. "The Phillips Curve: Another
Forerunner." Economica 40 (August 1973) : 31415.
Brown, A.J. The Great Inflation, 1939-1951.
London: Oxford University Press, 1955.
12. Lipsey, R. G. "The Relation between Unemploymen~ and the Rate of Change of Money Wage Rates
in the United Kingdom, 1862-1957: A Further
Analysis." Economica 27 (February 1960): 1-32.
13. Mill, John Stuart. "The Currency Juggle." Tait’s
Edinbu.rg Magazine (1833). Reprinted in Vol. I
of his Dissertatio~s and Discussions. Boston : 1865.
14. Nelson, Charles R. "Adjustment Lags Yersus Information Lags: A Test of Alternative Explanations of the Phillips Curve Phenomenon." Journal
of Money, Credit and Banking 13 (February
1981) : 1-11.
15. Phillips, A. W. "The Relation between Unemploy-
ment and the Rate of Change of Money Wage
Rates in the United Kingdom, 1861-1957." Economica 25 (November 1958): 283-99.
Donner, Arthur and James F. McCollum. "The
Phillips Curve: An Historical Note." Economica
39 (August 1972) : 323-24.
Fisher, Irving. "A Statistical Relation between
Unemployment and Price Changes." Inte~mational
Labour Review 13 (June 1926) : 785-92. Reprinted
as "I Discovered the Phillips Curve." Jou,’nal of
Political Economy 81 (March/April 1973): 496502.
Hume, David. "Of Money" (1752). Reprinted in
his Writiugs on Economics. Edited by Eugene
Rotwein. Madison: University of Wisconsin Press,
1955.
Humphrey, Thomas M. "Two Views of Monetary
Policy: The Attwood-Mill Debate Revisited." Economic Review, Federal Reserve Bank of Richmond
63 (September/October 1977) : 14-22.
10.
"Of Hume, Thornton, the Quantity
Theory, and the Phillips Curve." Economic Review,
Federal Reserve Bank of Richmond 68 (November/
December 1982) : 13-18.
11. Klein, Lawrence R. and Arthur S. Goldberger. An
Econometric Model of the United States 1929-1952.
Amsterdam: North-Holland Publishing Company,
1955.
12
16. Samuelson, Paul A., and Robert M. Solow. "Analytical Aspects of Anti-inflation Policy." American
Ecouomic Review 50 (May 1960) : 177-94.
17. Sultan, Paul. Labor Economics. New York: Henry
Holt and Company, Inc., 1957.
18. Thirlxvall, A. P. "The Phillips Curve: An Historical Note." Economica 89 (August 1972) : 325.
19. Thornton, Henry. An Enquiry into the Natu~’e and
Effects of the Paper Credit of Great Britain
(1802). Edited with an introduction by F. A. yon
Hayek. New York: Rinehart and Company, Inc.,
1939.
20. Tinbergen, Jan. "An Economic Policy for 1936."
Repri.nted in his Selected Papers. Edited by L. H.
Klaassen, L. M. Koyck, and H. J. Witteveen. Amsterdam: North-Holland Publishing Company,
1959.
21.
Business Cycles in the United Kingdora, 1870-J91$. Amsterdam: North-Holland Publishing Company, 1951.
THE EVOLUTION AND POLICY IMPLICATIONS
OF PHILLIPS CURVE ANALYSIS
At the core of modern macroeconomics is some
version or another of the famous Phillips curve relationship bet~veen inflation and unemployment. The
Phillips curve, both in its original and more recently
reformulated expectations-augmented versions, has
two main uses. In theoretical models of inflation, it
provides the so-called "missing equation" that explains how changes in nominal income divide themselves into price and quantity components. On the
policy front, it specifies conditions contributing to
the effectiveness (or lack thereof) of expansionary
and disinflationary policies. For example, in its
expectations-augmented form, it predicts that the
power of expansionary measures to stimulate real
activity depends critically upon how price anticipations are formed. Similarly, it predicts that disinflationary policy will either work slowly (and painfully)
or swiftly (and painlessly) depending upon the speed
of adjustment of price expectations. In fact, few
macro policy questions are discussed without at least
some reference to an analytical framework that might
be described in terms of some version of the Phillips
curve.
As might be expected from such a widely used tool,
Phillips curve analysis has hardly stood still since its
beginnings in 1958. Rather it has evolved under the
pressure of events and the progress of economic
theorizing, incorporating at each stage such new
elements as the natural rate hypothesis, the adaptiveexpectations mechanism, and most recently, the rational expectations hypothesis. Each nmv element
expanded its explanatory power. Each radically
altered its policy implications. As a result, whereas
the Phillips curve was once seen as offering a stable
enduring trade-off for the policymakers to exploit,
it is now ~videly viewed as offering no trade-off at all.
In short, the original Phillips curve notion of the
potency of activist fine tuning has given way to the
revised Phillips curve notion of policy ineffectiveness.
The purpose of this article is to trace the sequence of
steps that led to this change. Accordingly, the paragraphs below sketch the evolution of Phillips curve
analysis, emphasizing in particular the theoretical
innovations incorporated into that analysis at each
stage and the policy implications of each innovation.
EARLY VERSIONS OF THE PHILLIPS CURVE
The idea of an inflation-unemployment trade-off is
hardly new. It was a key component of the monetary
doctrines of David Hume (1752) and Henry Thornton (1802). It was identified statistically by Irving
Fisher in 1926, although he viewed causation as
running from inflation to unemployment rather than
vice versa. It was stated in the form of an econometric equation by Jan Tinbergen in 1936 and again
by Lawrence Klein and Arthur Goldberger in 1955.
Finally, it was graphed on a scatterplot chart by A. J.
Brown in 1955 and presented in the form of a diagrammatic curve by Paul Sultan in 1957. Despite
these early efforts, hmvever, it was not until 1958
that modern Phillips curve analysis can be said to
have begun. That year saxv the publication of Professor A. "~¥. Phillips’ famous article in which he
fitted a statistical equation w=f(U) to annual data
on percentage rates of change of money wages (w)
and the unemployment rate (U) in the United Kingdom for the period !861-1913. The result, shown
in a chart like Figure 1 with wage inflation measured
vertically and unemployment horizontally, was a
smooth, downward-sloping convex curve that cut the
horizontal axis at a positive level of unemployment.
The curve itself was given a straightforward interpretation: it sho~ved the response of wages to the
excess demand for labor as proxied by the inverse of
the unemployment rate. Low unemployment spelled
high excess demand and thus upward pressure on
wages. The greater this excess labor demand the
13
Figure 1
EARLY PHILLIPS CURVE
w Wage Inflation Rate (%)
Phillips Curve Trade-off
Relationship Between
Inflation and Unemployment
Frictional (and Structural)
Unemployment Rate at
Which Overall Excess
Demand for Labor is
Zero and Wages are
therefore Stable
U
Unemployment
Rate
U
At unemployment rate Uf the labor market
is in equilibrium and wages are stable. At
lower unemployment rates excess demand
exists to bid up wages. At higher unemployment rates excess supply exists to bid down
wages. The curve’s convex shape shows that
increasing excess demand for labor runs into
diminishing marginal returns in reducing unemployment. Thus successive uniform de
creases in unemployment (horizontal gray
arrows) require progressively larger increases
in excess demand and hence wage inflation
rates (vertical black arrows) as we go from
point a to b to c to d along the curve.
faster the rise in wages. Similarly, high unemployment spelled negative excess demand (i.e., excess
labor supply) that put deflationary pressure on
wages. Since the rate of change of ~vages varied
directly with excess demand, which in turn varied
inversely with nnemployment, wage inflation would
rise with decreasing unemployment and fall with
increasing unemployment as indicated by the negative
slope of the curve¯ Moreover, owing to unavoidable
frictions in the operation of the labor market, it
followed that some frictional unemployment would
14
exist even when the market xvas in equilibrium, that
is, when excess labor demand was zero and wages
were stable. Accordingly, this frictional unemployment was indicated by the point at which the Phillips
curve crosses the horizontal axis. According to
Phillips, this is also the point to which the economy
returns if the authorities ceased to maintain disequilibrium in the labor market by pegging the excess
demand for labor. Finally, since increases in excess
demand would likely run into diminishing marginal
returns in reducing unemployment, it followed that
the curve must be convex--this convexity showing
that successive uniform decrements in unemployment
would require progressively larger increments in
excess demand (and thus wage inflation rates) to
achieve them.
Popularity of the Phillips Paradigm
Once equipped with the foregoing theoretical foundations, the Phillips curve gained swift acceptance
among economists and policymakers alike. It is
important to understand why this was so. At least
three factors probably contributed to the attractiveness of the Phillips curve. One was the remarkable
temporal stability of the relationship, a stability revealed by Phillips’ own finding that the same curve
estimated for the pre-World War I period 1861-1913
fitted the United Kingdom data for the post-World
War II period 1948-1957 equally well or even better.
Such apparent stability in a two-variable relationship
over such a long period of time is uncommon in
empirical economics and served to excite interest in
the curve.
A second factor contributing to the success of the
Phillips curve was its ability to accommodate a wide
variety of inflation theories. The Phillips curve
itself explained inflation as resulting from excess
demand that bids up wages and prices. It was entirely neutral, however, about the causes of that
phenomenon. Now excess demand can of course be
generated either by shifts in demand or shifts in
supply regardless of the causes of those shifts.
Thus a demand-pull theorist could argue that excessdemand-induced inflation stems from excessively
expansionary aggregate demand policies while a costpush theorist could claim that it emanates from tradeunion monopoly power and real shocks operating on
labor supply. The Phillips curve could accommodate
both views. Economists of rival schools could accept
the Phillips curve as offering insights into the nature
of the inflationary process even while disagreeing on
the causes of and appropriate remedies for inflation.
Finally, the Phillips curve appealed to policymakers because it provided a convincing rationale for
their apparent failure to achieve full employment
with price stability--twin goals that were thought to
be mutually compatible before Phillips’ analysis.
When criticized for failing to achieve both goals
simultaneously, the authorities could point to the
Phillips curve as showing that such an outcome was
impossible and that the best one could hope for was
either arbitrarily low unemployment or price stability
but not both. Note also that the curve, by offering a
menu of alternative inflation-unemployment combinations from which the authorities could choose,
provided a ready-made justification for discretionary
intervention and activist fine tuning. Policymakers
had but to select the best (or least undesirable)
combination on the menu and then use their policy
instruments to achieve it. For this reason too the
curve must have appealed to some policy authorities,
not to mention the economic advisors who supplied
the cost-benefit analysis underlying their choices.
From Wage-Change Relation to
Price-Change Relation
As noted above, the initial Phillips curve depicted a
relation between unemployment and wage inflation.
Policymakers, however, usually specify inflation targets in terms of rates of change of prices rather than
wages. Accordingly, to make the Phillips curve more
useful to policymakers, it was therefore necessary to
transform it from a wage-change relationship to a
price-change relationship. This transformation was
achieved by assuming that prices are set by applying a constant mark-up to unit labor cost and so move
in step with wages--or, more precisely, move at a
rate equal to the differential between the percentage
rates of growth of wages and productivity (the latter
assumed zero here).1 The result of this transformation ~vas the price-change Phillips relation
i Let prices P be the product of a fixed markup K (including normal profit margin and provision for depreciation) applied to unit labor costs C,
(1) P = KC.
Unit labor costs by definition are the ratio of hourly
wages W to labor productivity or output per labor hour
Q,
(2) C = W/Q.
Substituting (2) into (1), taking logarithms of both sides
of the resulting expression, and then differentiating with
respect to time yields
(3) p : w - q
where the louver case letters denote the percentage rates
of change of the price, wage, and productivity variables.
Assuming productivity growth q is zero and the rate of
wage change ~v is an inverse function of the unemployment rate yields equation (1) of the text.
(1) p = ax(U)
where p is the rate of price inflation, x(U) is overall
excess demand in labor and hence product markets-this excess demand being an inverse function of the
unemployment rate--and a is a price-reaction coefficient expressing the response of inflation to excess
demand. From this equation the authorities could
determine how much unemployment would be associated with any given target rate of inflation. They
could also use it to measure the effect of policies
undertaken to obtain a more favorable Phillips curve,
i.e., policies aimed at lowering the price-response
coefficient and the amount of unemployment associated with any given level of excess demand.
Trade-Offs and Attainable Combinations
The foregoing equation specifies the position (or
distance from origin) and slope of the Phillips curve
--two features stressed in policy discussions of the
early 1960s. As seen by the policymakers of that era,
the curve’s position fixes the inner boundary, or
frontier, of feasible (attainable) combinations of
inflation and unemployment rates (see Figure 2).
Determined by the structure of labor and product
markets, the position of the curve defines the set of
all coordinates of inflation and unemployment rates
the authorities could achieve via implementation of
monetary and fiscal policies. Using these macroeconomic demand-management policies the authorities
could put the economy anywhere on the curve. They
could not, however, operate to the left of it. The
Phillips curve was viewed as a constraint preventing
them from achieving still lower levels of both inflation
and unemployment. Given the structure of labor and
product markets, it would be impossible for monetary and fiscal policy alone to reach inflationunemployment combinations in the region to the left
of the curve.
The slope of the curve was interpreted as showing
the relevant policy trade-offs (rates of exchange
between policy goals) available to the authorities. As
explained in early Phillips curve analysis, these
trade-offs arise because of the existence of irreconcilable conflicts among policy objectives. When the
goals of full employment and price stability are not
simultaneously achievable, then attempts to move the
economy closer to one will necessarily move it further
away from the other. The rate at which one objective
must be given up to obtain a little bit more of the
other is measured by the slope of the Phillips curve.
For example, when the Phillips curve is steeply
sloped, it means that a small reduction in unemploy15
Figure 2
TRADE-OFF$ AND
ATTAINABLE COMBINATIONS
Price Inflation Rate (%)
rates of unemployment in exchange for permanently
higher rates of inflation or vice versa. Put diffeiently, the curve was interpreted as offering a menu
of alternative inflation-unemployment combinations
from which the authorities could choose. Given the
menu, the authorities’ task was to select the particular
inflation-unemployment mix resulting in the smallest
social cost (see Figure 3). To do this, they would
have to assign relative weights to the twin evils of
Phillips Curve
~
~
p = ax(U):
~.~.~ Frontier
Shows Attainable
~
Inflation-Unemployment
Combinations
Slope
~,-.~------ Indicates
Region of ~
Figure 3
THE BEST SELECTION ON
THE MENU OF CHOICES
Trade-off
Unatt.a ina.ble\~X~
Combinations
p Price Inflation Rate
Phillips Curve Constraint
The position or location of the Phillips
curve defines the frontier or set of
attainable inflation-unemployment combinations. Using monetary and fiscal policies,
the authorities can attain all combinations
lying upon the frontier itself but none in
the shaded region below it. In this way the
curve acts as a constraint on demandmanagement policy choices. The slope
of the curve shows the trade-offs or rates
of exchange between the two evils of
inflation and unemployment.
ment would be purchased at the cost of a large increase in the rate of inflation. Conversely, in relatively flat portions of the curve, considerably lower
unemployment could be obtained fairly cheaply, that
is at the cost of only slight increases in inflation.
Knowledge of these trade-offs would enable the
authorities to determine the price-stability sacrifice
necessary to buy any given reduction in the unemployment rate.
The Best Selection on the Phillips Frontier
The preceding has described the early view of the
Phillips curve as a stable, enduring trade-off permitring the authorities to obtain permanently lower
16
Optimum Feasible
Inflation-Unemployment
Combination
Social
Disutility
Contours
The bowed-out curves are social disutility
contours. Each contour shows all thecombinations of inflation and unemployment
resulting in a given level of social cost or
harm. The closer to the origin, the lower
the social cost. The slopes of these contours
reflect the relative weights that society (or
the policy authority) assigns to the evils of
inflation and unemployment. The best
combination of inflation and unemployment that the policymakers can reach, given
the Phillips curve constraint, is the mix
appearing on the lowest attainable social
disutility contour.
Here the additional
social benefit from a unit reduction in
unemployment will just be worth the
extra inflation cost of doing so.
inflation and unemployment in accordance with their
views of the comparative harm caused by each. Then,
using monetary and fiscal policy, they would move
along the Phillips curve, trading off unemployment
for inflation (or vice versa) until they reached the
point at which the additional benefit from a further
reduction in unemployment was just ~vorth the extra
inflation cost of doing so. Here xvould be the optimum, or least undesirable, mix of inflation and unemployment. At this point the economy would be on its
loxvest attainable social disutility contour (the bowedout curves radiating outward from the origin of
Figure 3) allowed by the Phillips curve constraint.
Here the unemployment-inflation combination chosen
would be the one that minimized social harm. It was
of course understood that if this outcome involved a
positive rate of inflation, continuous excess money
growth ~vould be required to maintain it. For without
such monetary stimulus, excess demand would disappear and the economy would return to the point
at which the Phillips curve crosses the horizontal
axis.
Different Preferences, Different Outcomes
It was also recognized that policymakers might
differ in their assessment of the comparative social
cost of inflation vs. unemployment and thus assign
different policy weights to each. Policymakers who
believed that unemployment was more undesirable
than rising prices would assign a much higher relative
weight to the former than would policymakers who
judged inflation to be the worse evil. Hence, those
with a marked aversion to unemployment would
prefer a point higher up on the Phillips curve than
would those more anxious to avoid inflation, as shown
in Figure 4. Whereas one political administration
might opt for a high pressure economy on the
grounds that the social benefits of low unemployment
exceeded the harm done by the inflation necessary to
achieve it, another administration might deliberately
aim for a low pressure economy because it believed
that some economic slack was a relatively painless
means of eradicating harmful inflation. Both groups
would of course prefer combinations to the southwest
of the Phillips constraint, down closer to the figure’s
origin (the ideal point of zero inflation and zero unemployment). As pointed out before, however, this
would be impossible given the structure of the economy, which determines the position or location of the
Phillips frontier. In short, the policymakers would
be constrained to combinations lying on this boundary, unless they were prepared to alter the economy’s
structure.
F igu re 4
DIFFERENT PREFERENCES,
DIFFERENT POLICY CHOICES
p Price Inflation Rate
Phillips Curve Constraint
I nflation-U nemployment
Choice of an
Unemployment-Averse
Administration
Social Disutility Contours:
Unemployment Weighted
More Heavily
Inflation Weighted
More Heavily
Choice of an
I nflation-Averse
Administration
Different political administrations may
differ in their evaluations of the social
harmfulness of inflation relative to that of
unemployment. Thus in their policy deliberations they will attach different relative
weights to the two evils of inflation and unemployment. These weights will be reflected in the slopes of the social disutility
contours (as those contours are interpreted
by the policymakers). The relatively flat
contours reflect the views of those attaching
higher relative weight to the evils of inflation; the steep contours to those assigning
higher weight to unemployment. An unemployment-averse administration will choose
a point on the Phillips curve involving more
inflation and less unemployment than the
combination selected by an inflation-averse
administration.
Pessimistic Phillips Curve and the
"Cruel Dilemma"
In the early 1960s, there was much discussion of
the so-called "cruel-dilemma" problem imposed by an
unfavorable Phillips curve. The cruel dilemma refers
17
to certain pessimistic situations where none of the
available combinations on the menu of policy choices
is acceptable to the majority of a country’s voters
(see Figure 5). For example, suppose there is some
maximum rate of inflation, A, that voters are just
willing to tolerate without removing the party in
power. Likewise, suppose there is some maximum
tolerable rate of unemployment, B. As shown in
Figure 5, these limits define the zone of acceptable or
politically feasible combinations of inflation and
unemployment. A Phillips curve that occupies a
position anywhere within this zone will satisfy society’s demands for reasonable price stability and high
employment. But if both limits are exceeded and the
curve lies outside the region of satisfactory outcomes,
the system’s performance will fall short of what was
expected of it, and the resulting discontent may
severely aggravate political and social tensions.
If, as some analysts alleged, the Phillips curve
tended to be located so far to the right in the chart
that no portion of it fell within the zone of acceptable
combinations, then the policymakers would indeed be
confronted with a painful dilemma. At best they
could hold only one of the variables, inflation or
unemployment, down to acceptable levels. But they
could not hold both simultaneously within the limits
of toleration. Faced with such a pessimistic Phillips
curve, policymakers armed only with traditional
demand-management policies would find it impossible
to achieve combinations of inflation and unemployment acceptable to society.
Policies to Shift the Phillips Curve
It was this concern and frustration over the seeming inability of monetary and fiscal policy to resolve
the unemployment-inflation dilemma that induced
some economists in the early 1960s to urge the adoption of incomes (wage-price) and structural (labormarket) policies. Monetary and fiscal policies alone
were thought to be insufficient to resolve the cruel
dilemma since the most these policies could do was to
enable the economy to occupy alternative positions on
the pessimistic Phillips curve. That is, monetary
and fiscal policies could move the economy along the
given curve, but they could not move the curve itself
into the zone of tolerable outcomes. What was
needed, it was argued, were new policies that would
twist or shift the Phillips frontier toward the origin
of the diagram.
Of these measures, incomes policies would be
directed at the price-response coefficient linking inflation to excess demand. Either by decreeing this
18
Figure 5
PESSIMISTIC PHILLIPS CURVE
AND THE "CRUEL DILEMMA"
p Prfce Inflation Rate
~
J
~=
I~,
/\
~b
~lk
I\
Pessimistic or Unfavorable
Phillips Curve; Lies
Outside the Zone of
Tolerable Outcomes
Phillips Curve
Shifted Down by
Incomes and/or
Structural Policies
:;~.: 3"’ ~. ~:.~.~’: ~
A = Maximum Tolerable Rate of Inflation
B = Maximum Tolerable Rate of Unemployment
Given the unfavorable Phillips curve, policymakers are confronted with a cruel choice.
They can achieve acceptable rates of inflation (point a) or unemployment (point b)
but not both. The rationale for incomes
(wage-price) and structural (labor market)
policies was to shift the Phillips curve down
into the zone of tolerable outcomes.
coefficient to be zero (as with wage-price freezes),
or by replacing it with an officially mandated rate of
price increase, or simply by persuading sellers to
moderate their wage and price demands, such policies
would lower the rate of inflation associated with any
given level of unemployment and thus twist down the
Phillips curve. The idea was that wage-price controls
would hold inflation down while excess demand was
being used to boost employment.
Should incomes policies prove unworkable or prohibitively expensive in terms of their resourcemisallocation and restriction-of-freedom costs, then
the authorities could rely solely on microeconomic
structural policies to improve the trade-off. By en-
hancing the efficiency and performance of labor and
product markets, these latter policies could lower the
Phillips curve by reducing the amount of unemployment associated ~vith any given level of excess demand. Thus the rationale for such measures as jobtraining and retraining programs, job-information
and iob-counseling services, relocation subsidies, antidiscrimination laws and the like was to shift the
Phillips frontier down so that the economy could
obtain better inflation-unemployment combinations.
II.
INTRODUCTION OF SHIFT VARIABLES
Up until the mid-1960s the Phillips curve received
xvidespread and largely uncritical acceptance. Few
questioned the usefulness, let alone the existence, of
this construct. In policy discussions as well as economic textbooks, the Phillips curve was treated as a
stable, enduring relationship or menu of policy
choices. Being stable (and barring the application of
incomes and structural policies), the menu never
changed.
Empirical studies of the 1900-1958 U. S. data soon
revealed, hoxvever, that the menu for this country
was hardly as stable as its original British counterpart and that the Phillips curve had a tendency to
shift over time. Accordingly, the trade-off equation
xvas augmented with additional variables to account
for such movements. The inclusion of these shift
variables marked the second stage of Phillips curve
analysis and meant that the trade-off equation could
be written as
(2) p = ax(U)q-z
where z is a vector of variables--productivity, profits, trade union effects, unemployment dispersion and
the like--thought capable of shifting the inflationunemployment trade-off.
In retrospect, this vector or list was deficient both
for what it included and what it left out. Excluded
at this stage were variables representing inflation
expectations--later shown to be a chief cause of the
shifting short-run Phillips curve. Of the variables
included, subsequent analysis would reveal that at
least three--productivity, profits, and measures of
union monopoly power--were rednndant because
they constituted underlying determinants of the
demand for and supply of labor and as such were
already captured by the excess demand variable, U.
This criticism, however, did not apply to the unemployment dispersion variable, changes in which were
independent of excess demand and were indeed capable of causing shifts in the aggregate Phillips curve.
To explain how the dispersion of unemployment
across separate micro labor markets could affect the
aggregate trade-off, analysts in the early 1960s used
diagrams similar to Figure 6. That figure depicts a
representative micromarket Phillips curve, the exact
replica of which is presumed to exist in each local
labor market and aggregation over which yields the
macro Phillips curve. According to the figure, if a
given national unemployment rate U* were equally
distributed across local labor markets such that the
same rate prevailed in each, then wages everywhere
would inflate at the single rate indicated by the point
w* on the curve. But if the same aggregate unemployment were unequally distributed across local
markets, then wages in the different markets would
inflate at different rates. Because of the curve’s
convexity (which renders wage inflation more responsive to leftward than to rightward deviations
from average unemployment along the curve) the
average of these wage inflation rates would exceed
the rate of the no-dispersion case. In short, the
diagram suggested that, for any given aggregate
unemployment rate, the rate of aggregate wage inflation varies directly with the dispersion of unemployment across micromarkets, thus displacing the macro
Phillips curve to the right.
From this analysis, economists in the early 1960s
concluded that the greater the dispersion, the greater
the outward shift of the aggregate Phillips curve. To
prevent such shifts, the authorities were advised to
apply structural policies to minimize the dispersion of
unemployment across industries, regions, and occupations. Also, they were advised to minimize unemployment’s dispersion over time since, with a convex
Phillips curve, the average inflation rate would be
higher the more unemployment is allowed to fluctuate
around its average (mean) rate.
A Serious Misspecification
The preceding has shown how shift variables were
first incorporated into the Phillips curve in the earlyto mid-1960s. Notably absent at this stage were
variables representing price expectations. To be
sure, the past rate of price change was sometimes
used as a shift variable to represent catch-up or costof-living adjustment factors in wage and price demands. Rarely, however, was it interpreted as a
proxy for anticipated inflation. Not until the late
1960s were expectational variables fully incorporated
into Phillips curve equations. By then, of course,
19
Figure 6
EFFECTS OF UNEMPLOYMENT
DISPERSION
w Wage Inflation Rate
Local Phillips Curve:
The Same for
Micromarkets A and B
wA
Line Showing Weighted
Average of Local Wage
Inflation Rates wA and wB
Macro Wage
Inflation Rate:
Dispersion Case
No-Dispersion Case
inflationary expectations had become too prominent
to ignore and many analysts were perceiving them as
tbe dominant cause of observed shifts in the Phillips
curve.
Coinciding with this perception was the belated
recognition that the original Phillips curve involved a
misspecification that could only be corrected by the
incorporation of a price expectations variable in the
trade-off. The original Phillips curve was expressed
in terms of nominal wage changes, w=f(U). Since
neoclassical economic theory teaches that real rather
than nominal wages adjust to clear labor markets,
however, it follows that the Phillips curve should
have been stated in terms of real wage changes.
Better still (since wage bargains are made with an
eye to the future), it should have been stated in terms
of expected real wage changes, i.e., the differential
between the rates of change of nominal wages and
expected future prices, w--pe--f(U). In short, the
original Phillips curve required a price expectations
term to render it correct. Recognition of this fact
led to the development of the expectations-augmented
Phillips curve described below.
III.
UB
tf aggregate unemployment at rate U* were
evenly distributed across individual labor
markets such that the same rate prevailed
everywhere, then wages would inflate at the
rate w* both locally and nationally. But if
aggregate unemployment U* is unequally
distributed such that rate UA exists in
market A and UB in market B, then wages
will inflate at rate wA in the former market
and wB in the latter. The average of ti~ese
local inflation rates at aggregate unemployment rate U* is wo which is higher than
inflation rate w* of the no-dispersion case.
Conclusion: The greater the dispersion of
unemployment, the higher the aggregate
inflation rate associated with any given
level of aggregate unemployment. Unemployment dispersion shifts the aggregate
Phillips curve rightward.
20
THE EXPECTATIONS-AUGMENTED PHILLIPS CURVE
AND THE ADAPTIVE-EXPECTATIONS MECHANISM
The original Phillips curve equation gave way to
the expectations-augmented version in the early
1970s. Three innovations ushered in this change.
The first was the respecification of the excess demand variable. Originally defined as an inverse
function of the unemployment rate, x(U), excess
demand was redefined as the discrepancy or gap
between the natural and actual rates of unemployment, UN--U. The natural (or full employment)
rate of unemployment itself was defined as the rate
that prevails in steady-state equilibrium when expectations are fully realized and incorporated into all
wages and prices and inflation is neither accelerating
nor decelerating. It is natural in the sense (1) that
it represents normal full-employment equilibrium in
the labor and hence commodity markets, (2) that it
is independent of the steady-state inflation rate, and
(3) that it is determined by real structural forces
(market frictions and imperfections, job information
and labor mobility costs, tax laws, unemployment
subsidies, and the like) and as such is not susceptible
to manipulation by aggregate demand policies.
The second innovation was the introduction of
price anticipations into Phillips curve analysis resulting in the expectations-augmented equation
(3) p = a(U~-U)+po
where excess demand is now written as the gap
between the natural and actual unemployment rates
and pe is the price expectations variable representing
the anticipated rate of inflation. This expectations
variable entered the equation with a coefficient of
unity, reflecting the assumption that price expectations are completely incorporated in actual price
changes. The unit expectations coefficient implies
the absence of money illusion, i.e., it implies that
people are concerned with the expected real purchasing power of the prices they pay and receive . (or,
alternatively, that they wish to maintain their prices
relative to the prices they expect others to be charging) and so take anticipated inflation into account.
As will be shown later, the unit expectations coefficient also implies the complete absence of a trade-off
between inflation and unemployment in 10ng-run
equilibrium when expectations are fully realized.
Note also that the expectations variable is the sole
shift variable in the equation. All other shift variables have been omitted, reflecting the view, prevalent
in the early 1970s, that changing price expectations
were the predominant cause of observed shifts in
the Phillips curve.
Expectatlons-Generating Mechanism
The third innovation was the incorporation of an
expectations-generating mechanism into Phillips
curve analysis to explain how the price expectations
variable itself was determined. Generally a simple
adaptive-expectations or error-learning mechanism
was used. According to this mechanism, expectations are adjusted (adapted) by some fraction of the
forecast error that occurs when inflation turns out
to be different than expected. In symbols,
where the dot over the price expectations variable
indicates the rate of change (time derivative) of that
variable, p--p" is the expectations or forecast error
(i.e., the difference between actual and expected price
inflation), and b is the adjustment fraction. Assuming, for example, an adjustment fraction of ~, equation 4 says that if the actual and expected rates of
inflation are 10 percent and 4 percent, respectively-i.e., the expectational error is 6 percent--then the
expected rate of inflation will be revised upward by
an amount equal to half the error, or 3 percentage
points. Such revision will continue until the expectational error is eliminated.
Analysts also demonstrated that equation 4 is
equivalent to the proposition that expected inflation
is a geometrically declining weighted average of all
past rates of inflation with the weights summing to
one. This unit sum of weights ensures that any constant rate of inflation eventually will be fully anticipated, as can be seen by writing the error-learning
mechanism as
(5) pe ~ Nvip-i
where :~ indicates the operation of summing the past
rates of inflation, the subscript i denotes past time
periods, and vi denotes the weights attached to past
rates of inflation. With a stable inflation rate p
unchanging over time and a unit sum of weights, the
equation’s right-hand side becomes simply p, indicating that when expectations are formulated adaptively via the error-learning scheme, any constant
rate of inflation ~vill indeed eventually be fully anticipated. Both versions of the adaptive-expectations
mechanism (i.e., equations 4 and 5) were combined
with the expectations-augmented Phillips equation to
explain the mutual interaction of actual inflation,
expected inflation, and excess demand.
The Natural Rate Hypothesis
These three innovations--the redefined excess demand variable, the expectations-augmented Phillips
curve, and the error-learning mechanism---formed the
basis of the celebrated natural rate and accelerationist
hypotheses that radically altered economists’ and
policymakers’ views of the Phillips curve in the late
1960s and early 1970s. According to the natural
rate hypothesis, there exists no permanent trade-off
between unemployment and inflation since real economic variables tend to be independent of nominal
ones in steady-state equilibrium. To be sure, tradeoffs may exist in the short run. For example, surprise inflation, if unperceived by wage earners, may,
by raising product prices relative to nominal wages
and thus lowering real wages, stimulate employment
temporarily. But such trade-offs are inherently
transitory phenomena that stem from unexpected
inflation and that vanish once expectations (and the
wages and prices ~mbodying them) fully adjust to
inflationary experience. In the long run, when inflationary surprises disappear and expectations are
realized such that wages reestablish their preexisting levels relative to product prices, unemployment
21
returns to its natural (equilibrium) rate. This rate
is compatible with all fully anticipated steady-state
rates of inflation, implying that the long-run Phillips
curve is a vertical line at the natural rate of unemployment.
Equation 3 embodies these conclusions. That equation, when rearranged to read p--p"=a(Ux--U),
states that the trade-off is between unexpected inflation (the difference between actual and expected
inflation, p--p~) and unemployment. That is, only
surprise price increases could induce deviations of
unemployment from its natural rate. The equation
also says that the trade-off disappears when inflation
is fully anticipated (i.e., when p--p" equals zero), a
result guaranteed for any steady rate of inflation by
the error-learning mechanism’s unit stun of weights.
Moreover, according to the equation, the right-hand
side nmst also be zero at this point, which implies
that unemployment is at its natural rate. The natural
rate of unemployment is therefore compatible with
any constant rate of inflation provided it is fully
anticipated (which it eventually must be by virtue of
the error-learning xveights adding to one). In short,
equation 3 asserts that inflation-unemployment tradeoffs cannot exist when inflation is fully anticipated.
And equation 5 ensures that this latter condition
must obtain for all steady inflation rates such that the
long-run Phillips curve is a vertical line at the natural
rate o~ unemployment.~
The message of the natural rate hypothesis was
clear. A higher stable rate of inflation could not
buy a permanent drop in joblessness. Movements to
the left along a short-run Phillips curve only provoke
expectational wage/price adjustments that shift the
curve to the right and restore unemployment to its
natural rate (see Figure 7). In sum, Phillips curve
trade-offs are inherently transitory phenomena. Attempts to exploit them ~vill only succeed in raising
the permanent rate of inflation without accomplishing a lasting reduction in the ~inemployment rate.
~ Actually, the long-run Phillips curve may become positively sloped in its upper ranges as higher inflation leads
to
greater inflatiou variability
(volatilii~y,
unpredictability)
that raises
the_natural ii./
rate of unemployment. Higher and
/
hencd more variable ’and erratic inflation can raise the. equilibrium level of
unemployment by generating increased
U
uncertainty that inhibits busihegg activity and by introdueing noise imo mar.ket price’ signals,
thusreducing the efficiency of the price system as a
coordinating gad allocating m~chanism.
.~
22
Figure 7
THE NATURAL RATE
HYPOTHESIS AND ADJUSTMENT
TO STEADY-STATE EOUILIBRIUM
Price Inflation Rate
Short-run
Phillips Curves
L
| Long-ru Vertical
Phillips Curve
I
4%,
So
S1
2%’.
01
Natural Rate
of Unemployment
The vertical line L through the natural rate
of unemployment UN is the long-run steady
state Phillips curve along which all rates of
inflation are fully anticipated. The downward-sloping lines are short-run Phillips
curves each corresponding to a different
given expected rate of inflation. Attempts
to lower unemployment from the natural
rate UN t~ U1 by raising inflation to 3 percent along the short-run trad~off curve SO
will only induce shifts in the short-run curve
to S1, S2, 83 as expectations adjust to the
higher rate of inflation. The economy
travels the path ABCDE to the n’ew steady
state equilibrium, point E, where unemployment is at its preexisting natural rate but
inflation is higher than it was originally.
The Acceleratlonlst Hypothesis
The expectations:augmented Phillips curve, wtieti
combined with the error-learning process, also
yielded the celebrated accelerdtionist hypothesis that
dominated many policy discussions in the inflationary
1970s. This hypothesis, a corollary of the natural
rate concept, states that since there exists no long-run
trade-off between unemployment and inflation, attempts to peg the former variable below its natural
(equilibrium) level must produce ever-increasing
inflation. Fueled by progressively faster monetary
expansion, such price acceleration would keep actual
inflation always running ahead of expected inflation,
thereby perpetuating the inflationary surprises that
prevent unemployment from returning to its equilibrium level (see Figure 8).
Accelerationists reached these conclusions .via the
following route. They noted that equation 3 posi_ts
that unemployment can differ from its natural level
only so long as actual inflation deviates from expected inflation. But that same equation together
with equation 4 implies that, by the very nature of
the error-learning mechanism, such deviations cannot
persist unless inflation is continually accelerated so
that it always stays ahead of expected inflation.8 If
inflation is not accelerated, but instead stays constant, then the gap between actual and expected
inflation will eventually be closed. Therefore acceleration is required to keep the gap open if unemployment is to be maintained below its natural equilibrium
level. In other ~vords, the long-run trade-off implied
by the accelerationist hypothesis is between unemployment and the rate of acceleration of the inflation
rate, in contrast to the conventional trade-off between
unemployment and the inflation rate itself as implied
by the original Phillips curve#
Policy Implications of the Natural Rate
and Accelerationlst Hypotheses
At least two policy implications stemmed from the
natural rate and accelerationist propositions. First,
a Taking the time derivative of equation 3, then assuming
that the deviation of U from U~ is pegged at a constant
level by the authorities such that its rate of change is
zero, and then substituting equation 4 into the resulting
expression yields
~ = b(p--pe)
~vhich says that the inflation rate must accelerate to stay
ahead of expected inflation.
4 The proof is simple. Merely substitute equation 3 into
the expression presented in the preceding footnote to
obtain
~ = ba(Ux--U)
which says that the trade-off is between the rate of
acceleration of inflation p and unemployment U relative
to its natural rate.
Figure 8
THE ACCELERATIONIST
HYPOTHESIS
p Price Inflation Rate
Long-run Vertical
Phillips Curve
P3
P2’
S2
Short-run
Phillips
Curves
0
UN
Natural Rate
of Unemployment
Since the adjustment of expected to actual
inflation works to restore unemployment to
its natural equilibrium level UN at any
steady rate of inflation, the authorities must
continually raise (accelerate) the inflation
rate if they wish to peg unemployment at
some arbitrarily low level such asU1. Such
acceleration, by generating a continuous
succession of inflation surprises, perpetually
frustrates the full adjustment of expectations that would return unemployment to
its natural rate. Thus attempts to peg
unemployment at U1 will provoke explosive, ever-accelerating inflation.
The
economy will travel the path ABCD with
the rate of inflation rising from zero to Pl
toP2tO P3 etc.
the authorities could either peg unemployment or
stabilize the rate o~ inflation but not both. If they
pegged unemployment, they would lose control of
the rate of inflation because the latter accelerates
when unemployment is held below its natural level.
Alternatively, if they stabilized the inflation rate,
23
the), would lose control of unemployment since the
latter returns to its natural level at any steady
STATISTICAL TESTS OF THE
rate of inflation. Thus, contrary to the original
NATURAL RATE HYPOTHESIS
Phillips hypothesis, they could not peg unemployment
at a given constant rate of inflation. They could,
The preceding has examined the third stage of
however, choose the steady-state inflation rate at
Phillips curve analysis in which the natural rate hypothesis was formed. The fourth stage involved
which unemployment returns to its natural level.
statistical testing of that hypothesis. These tests,
A second policy implication stemming from the
conducted in the early- to mid-1970s, led to criticisms
natural rate hypothesis was that the authorities could
of
the adaptive-expectations or error-learning model
choose from among alternative transitional adjustof
inflationary expectations and thus helped prepare
ment paths to the desired steady-state rate of inflathe way for the introduction of the alternative
tion. Suppose the authorities wished to move from a
rational expectations idea into Phillips curve analysis.
high inherited inflation rate to a zero or other low
The tests themselves were mainly concerned with
target inflation rate. To do so, they must lower
estimating the numerical value of the coefficient on
inflationary expectations, a major determinant of the
the price-expectations variable in the expectationsinflation rate. But equations 3 and 4 state that the
augmented Phillips curve equation. If the coefficient
only way to lower expectations is to create slack
is one, as in equation 3, then the natural rate hypothecapacity or excess supply in the economy. Such
sis is valid and no long-run inflation-unemployment
slack raises unemployment above its natural level and
trade-off exists for the policymakers to exploit. But
thereby causes the actual rate of inflation to fall
if the coefficient is less than one, the natural rate
below the expected rate so as to induce a downward
revision of the latter.5 The equations also indicate hypothesis is refuted and a long-run trade-off
exists. Analysts emphasized this fact by writing the
that how fast inflation comes down depends on the
6
anaount of slack created. Much slack means fast expectations-augmented equation as
adjustment and a relatively rapid attainment of the
(6) p = a(U~--U)q-¢p~
inflation target. Conversely, little slack means sluggish adjustment and a relatively slow attainment of
where 6 is the coefficient (with a value of between
zero and one) attached to the price expectations varithe inflation target. Thus the policy choice is between
able.
In long-run equilibrium, of course, expected
adjustment paths offering high excess unemployment
inflation equals actual inflation, i.e., p~p. Setting
for a short time or lower excess unemployment for a
expected inflation equal to actual inflation as required
long time (see Figure 9)d
for long-run equilibrium and solving for the actual
rate of inflation yields
5 The proof is stralghtforward. Simply substitute equation 3 iuto equation 4 to obtain
i~e = ba(U~--U).
This express!on says that expectations will ’be adjusted
downward (pc will be negative) only if unemployment
exceeds its natural rate.
Note that the equatiou developed in footnote 4 states
that disinflation will occur at a faster pace the larger the
unelnploymeut gap.
7 Controls advocates proposed a third policy choice: use
wage-price controls to hold actual below expected iuflation so as to force a swift reductiou oi the latter. Overlooked was the fact that controls would have little impact
on expectatious unless the public was convinced that the
trend of prices when controls were in force was a reliable
indicator of the future price trend after controls were
lifted. Convincing the public would be difficult if controls
had failed to stop inflation in the past. Aside from this,
it is hard to see why controls should have a stronger
impact on expectations than a preannounced, de~nonstrated policy of disinflationary money growth.
24
a
¯ .(7) p = 1--
Beside~ showing that the long-run Phillips curve is
steeper than its short-run counterpart (since the slope
parameter of the former, a/(1--qS), exceeds that of
the latter, a), equation 7 shows that a long-run tradeoff exists only if the expectations coefficient is less
than one. If the coefficient is one, however, the slope
term is infinite, which means that there is no relation
between inflation and unemployment so that the
trade-off vanishes (see Figure 10).
Many of the empirical tests estimated the coefficient to be less than unity and concluded that the
natural rate hypothesis was invalid. But this conclusion ~vas sharply challenged by economists who
contended that the tests contained statistical bias that
Figure g
ALTERNATIVE DISINFLATION PATHS
p Price Inflation Rate
p Price Inflation Rate
SA
sA L
Long-run Vertical
Phillips Curve
PA
PA
Initial Short-run
Phillips Curve for
Expected Inflation PA..
UN
UN
High Excess
Unemployment
ACB = Fast disinflation path involving high
excess unemployment for a short
time.
~ Low Excess
Unemployment
ADEB = Gradualist disinflation path involving low excess unemployment for
a long time.
To move from high-inflation point A to zero-inflation point B the authorities must first travel
along short-run Phillips curve SA, lowering actual relative to expected inflation and thereby
inducing the downward revision of expectations that shifts the short-run curve leftward until
point B is reached. Since the speed of adjustment of expectations depends upon the size of
the unemployment gap, it follows that point B will be reached faster via the high excess unemployment path ACB than via the low excess unemployment path ADEB. The choice is between
high excess unemployment for a short time or low excess unemployment for a long time.
tended to work against the natural rate hypothesis.
These critics pointed out that the tests typically used
adaptive-expectations schemes as empirical proxies
for the unobservable price expectations variable.
They further showed that if these proxies were inappropriate measures of inflationary expectations
then estimates of the expectations coefficient could
well be biased downward. If so, then estimated coefficients of less than one constituted no disproof of the
natural rate hypothesis. Rather they constituted evidence of inadequate measures of expectations.
Shortcomings of the Adaptlve-Expectations
Assumption
In connection with the foregoing, the critics argued
that the adaptive-expectations scheme is a grossly
inaccurate represeqtation of how people formulate
price expectations. They pointed out that it postulates naive expectational behavior, holding as it does
that people form anticipations solely from a weighted
average of past price experience with weights that
are fixed and independent of economic conditions and
25
Figure 10
THE EXPECTATIONS
COEFFICIENT AND THE
LONG-RUN STEADY-STATE
PHILLIPS CURVE
p Price Inflation Rate
Long-run
Steady-State
Phillips Curve:
t
Short-run
Phillips
Curves
uN
u
Statistical tests of the natural rate hypothesis sought to determine the magnitude
of the expectations coefficient ~ in the
long-run steady-state Phillips curve equation
tional errors. That people would fail to exploit information that would improve expectational accuracy
seems implausible, however. In short, the critics
contended that adaptive expectations are not wholly
rational if other information besides past price
changes can improve inflation predictions.
Many economists have since pointed out that it is
hard to accept the notion that individuals would continually form price anticipations from any scheme
that is inconsistent with the way inflation is actually
generated in the economy. Being different from the
true inflation-generating mechanism, such schemes
will produce expectations that are systematically
wrong. If so, rational forecasters will cease to use
them. For example, suppose inflation were actually
accelerating or decelerating. According to equation 5,
the adaptive-expectations model would systematically
underestimate the inflation rate in the former case
and overestimate it in the latter. Using a unit
weighted average of past inflation rates to forecast a
steadily rising or falling rate would yield a succession of one-way errors. The discrepancy between
actual and expected inflation would persist in a perfectly predictable way such that forecasters would
be provided free the information needed to correct
their mistakes. Perceiving these persistent expectational mistakes, rational individuals would quickly
abandon the error-learning model for more accurate
expectations-generating schemes. Once again, the
adaptive-expectations mechanism is implausible because of its incompatibility with rational behavior.
a
p= ~ (UN-U)"
A coefficient of one means that no permanent trade-off exists and the steady-state
Phillips curve is a vertical line through the
natural rate of unemployment. Conversely,
a coefficient of less than one signifies the
existence of a long-run Phillips curve trade
off with negative slope for the policymakers
to exploit. Note that the long-run curves
are steeper than the short-run ones, indicating that permanent trade-oils are less
favorable than temporary ones.
policy actions. It implies that people look only at
past price changes and ignore all other pertinent
information--e.g., money growth rate changes, exchange rate movements, announced policy intentions
and the like--that could be used to reduce expecta-
26
FROM ADAPTIVE EXPECTATIONS TO
RATIONAL EXPECTATIONS
The shortcomings of the adaptive-expectations
approach to the modeling of expectations led to the
incorporation of the alternative rational expectations
approach into Phillips curve analysis. According to
the rational expectations hypothesis, individuals will
tend to exploit all available pertinent information
about the inflationary process when making their
price forecasts. If true, this means that forecasting
errors ultimately could arise only from random
(unforeseen) shocks occurring to the economy. At
first, of course, price forecasting errors might also
arise because individuals initially possess limited or
incomplete information about, say, an unprecedented
new policy regime, economic structure, or inflationgenerating mechanism. But it is unlikely that this
condition would persist. For if the public were
truly rational, it would quickly learn from these inflationary surprises or prediction errors (data on which
it acquires costlessly as a side condition of buying
goods) and incorporate the free new information
into its forecasting procedures, i.e., the source of
forecasting mistakes would be swiftly perceived and
systematically eradicated. As kno~vledge of policy
and the inflationary process improved, forecasting
models would be continually revised to produce more
accurate predictions. Soon all systematic (predictable) elements influencing the rate of inflation ~vould
become known and fully understood, and individuals’
price expectations would constitute the most accurate (unbiased) forecast consistent with that knowledge.a "~,Vhen this happened the economy would converge to its rational expectations equilibrium and
people’s price expectations would be the same as
those implied by the actual inflation-generating mechanism. As incorporated in natural rate Phillips curve
models, the rational expectations hypothesis implies
that thereafter, except for-unavoidable surprises due
to purely random shocks, price expectations would
always be correct and the economy would always be
at its long-run steady-state equilibrium.
Policy Implications of Rational Expectations
The strict (flexible price, instantaneous market
clearing) rational expectations approach has radical
policy implications. When incorporated into natural
rate Phillips curve equations, it implies that systematic policies--i.e., those based on feedback control
rules defining the authorities’ response to changes in
the economy---cannot influence real variables such as
output and unemployment even in the short run,
since people would have already anticipated what the
policies are going to be and acted upon those anticipations. To have an impact on output and employment, the authorities must be able to create a divergence between actual and expected inflation. This
follows from the proposition that inflation influences
real variables only when it is unanticipated. To lower
unemployment in the Phillips curve equation
a(UN--U), the authorities must be able to alter the
actual rate of inflation without simultaneously causing
an identical change in the expected future rate. This
may be impossible if the public can predict policy
actions.
8 Put differently, rationality implies that current expectationa! errors are uncorrelated with past errors and with
all other known information, such correlations already
having been perceived and exploited in the process df
improving price forecasts.
Policy actions, to the extent they are systematic,
are predictable. Systematic policies are simply feedback rules or response functions relating policy variables to past values of other economic variables.
These policy response functions can be estimated and
incorporated into forecasters’ price predictions. In
other words, rational individuals can use past observations on the behavior of the authorities to discover
the policy rule. Once they know the rule, they can
use current observations on the variables to which
the policymakers respond to predict future policy
moves. Then, on the basis of these predictions, they
can correc} for the effect of anticipated policies beforehand by making appropriate adjustments to nominal wages and prices. Consequently, when stabilization actions do occur, they will have no impact on
real variables like unemployment since they will have
been discounted and neutralized in advance. In short,
rules-based policies, being in the information set used
by rational forecasters, will be perfectly anticipated
and for that reason will have no impact on unemployment. The only conceivable way that policy can have
even a short-run influence on real variables is for it
to be unexpected, i.e., the policymakers must either
act in an unpredictable random fashion or secretly
change the policy rule. Apart from such tactics,
which are incompatible with most notions of the
proper conduct of public policy, there is no way the
authorities can influence real variables, i.e., cause
them to deviate from their natural equilibrium levels.
The authorities can, however, influence a nominal
variable, namely the inflation rate, and should concentrate their efforts on doing so if some particular
rate (e.g., zero) is desired.
As for disinflation strategy, the rational expectations approach generally calls for a preannounced
sharp swift reduction in money growth--provided of
course that the government’s commitment to ending
inflation is sufficiently credible to be believed. Having chosen a zero target rate of inflation and having
convinced the public of their determination to achieve
it, the policy authorities should be able to do so
without creating a costly transitional rise in unemployment. For, given that rational expectations
adjust infinitely fagter than adaptive expectations to a
credible preannounced disinflationary policy (and
also that wages and prices adjust to clear markets
continuously) the transition to price stability should
be relatively quick and painless (see Figure 11).
27
Figure 1 1
COSTLESS DISINFLATION
UNDER RATIONAL
EXPECTATIONS AND
POLICY CREDIBILITY
p Price Inflation Rate
Steady-State
Phillips Curve
Initial
Inflation
Rate
Costless
Disinflation Path
Zero Target
Inflation Rate
B
Assuming expectational rationality, wage/
price flexibility, and full policy credibility, a
preannou nced permanent reduction in
money growth to a level consistent with
~table prices theoretically lowers expected
and thus actual inflation to zero with no
accompanying transitory rise in unemployment. The economy moves immediately from
point A to point B on the vertical steady-state
Phillips curve. Here is the basic prediction of
the rational expectations--natural rate
model: that fully anticipated policy cha~ges
(including credible preannounced ones)
affect only inflation but not output and
employment.
No Exploitable Trade-Offs
To summarize, the rationality hypothesis, in conjunction with the natural rate hypothesis, denies the
existence of exploitable Phillips curve trade-offs in
the short run as well as the loug. In so doing, it
differs from the adaptive-expectations version of
28
natural rate Phillips curve models. Under adaptiveexpectations, short-run trade-offs exist because such
expectations, being baclnvard looking and slow to
respond, do not adjust instantaneously to eliminate forecast errors arising from policy-engineered
changes in the inflation rate. With expectations
adapting to actual inflation with a lag, monetary
policy can generate unexpected inflation and consequently influence real variables in the short run. This
cannot happen under rational expectations where
both actual and expected inflation adjust identically
and instantaneously to anticipated policy changes.
In short, under rational expectations, systematic
policy cannot induce the expectational errors that
generate short-run Phillips curves? Phillips curves
may exist, to be sure. But they are purely adventitious phenomena that are entirely the result of unpredictable random shocks and cannot be exploited by
policies based upon rules.
In sum, no role remains for systematic countercyclical stabilization policy in Phillips curve models
embodying rational expectations and the natural rate
hypothesis. The only thing such policy can influence in these models is the rate of inflation which
adjusts immediately to expected changes in money
growth. Since the models teach that the full effect
of rules-based policies is on the inflation rate, it
follows that the authorities--provided they believe
that the models are at all an accurate representation
of the way the world works--should concentrate
their efforts on controlling that nominal inflation
variable since they cannot systematically influence
real variables. These propositions are demonstrated
with the aid of the expository model presented in the
Appendix on page 21.
VI.
EVALUATION OF RATIONAL EXPECTATIONS
The preceding has shown how the rational expectations assumption combines with the natural rate
hypothesis to yield the policy-ineffectiveness conclusion that no Phillips curves exist for policy to exploit
9 Note that the rational expectations hypothesis also rules
out the accelerationist notion of a stable trade-off between
unemployment and the rate of acceleration of the inflation
rate. If expectations are formed consistently with the
way inflation is actually generated, the authorities will
not be able to fool people by accelerating inflation or by
accelerating the rate of acceleration, etc. Indeed, no
systematic policy xvill work if expectations are formed
consistently xvith the xvay inflation is actually generated
in the economy.
even in the short run. Given the importance of the
rational expectations component in modern Phillips
curve analysis, an evaluation of that component is
now in order.
One advantage of the rational expectations hypothesis is that it treats expectations formation as a
part of optimizing behavior. By so doing, it brings
the theory of price anticipations into accord with the
rest of economic analysis. The latter assumes that
people behave as rational optimizers in the production
and purchase of goods, in the choice of jobs, and in
the making of investment decisions. For consistency,
it should assume the same regarding expectational
behavior.
.
In this sense, the rational expectations theory is
superior to rival explanations, all of which implytha~.
expectations may be consistently wrong. It is the
only theory that denies that people make systematic
expectation errors. Note that it does not claim that
people possess perfect foresight or that their expectations are always accurate. What it does claim is
that they perceive and eliminate regularities in their
forecasting mistakes. In this way they discover the
actual inflation generating process and use it in forming price expectations. And with the public’s rational
expectations of inflation being the same as the mean
value of the inflation generating process, those expectations cannot be wrong on average. Any errors will
be random, not systematic. The same cannot be said
for other expectations schemes, however. Not being
identical to the expected value of the true inflation
generating process, those schemes will produce biased
expectations that are systematically wrong.
Biased expectations schemes are difficult to justify
theoretically. Systematic mistakes are harder to
explain than is rational behavior. True, nobody
really knows how expectations are actually formed.
But a theory that says that forecasters do not continually make the same mistakes seems intuitively
more plausible than theories that imply the opposite.
Considering the profits to be made from improved
forecasts, it seems inconceivable that systematic expectational errors would persist. Somebody would
surely notice the errors, correct them, and profit by
the corrections. Together, the profit motive and
competition would reduce forecasting errors to randomness.
Criticisms of the Rational Expectations
Approach
Despite its logic, the rational expectations hypothesis still has many critics. Some still maintain that
expectations are basically nonrational, i.e., that most
people are too naive or uninformed to formulate unbiased price expectations. Overlooked is the counterargument that relatively uninformed people often
delegate the responsibility for formulating rational
forecasts to informed specialists and that professional
forecasters, either through their ability to sell superior forecasts or to act in behalf of those without
same, will ensure that the economy will behave as if
all people were rational. One can also note that the
rational expectations hypothesis is merely an implication of the uncontroversial assumption of profit
(and utility) maximization and that, in any case,
economic analysis can hardly proceed without the
rationality assumption. Other critics insist, however,
that expectational rationality cannot hold during the
transition to new policy regimes or other structural
changes in the economy since it requires a long time
to understand such changes and learn to adjust to
them. Against this is the counterargument that such
changes and their effects are often foreseeable from
the economic and political events that precede them
and that people can quicldy learn to predict regime
changes just as they learn to predict the workings of a
given regime. This is especially so when regime
changes have occurred in the past. Having experienced such changes, forecasters will be sensitive to
their likely future occurrence.
Most of the criticism, however, is directed not at
the rationality assumption per se but rather at
another key assumption underlying its policyineffectiveness result, namely the assumption of no
policymaker information or maneuverability advantage over the private sector. This assumption states
that private forecasters possess exactly the same
information and the ability to act upon it as do the
authorities. Critics hold that this assumption is implausible and that if it is violated then the policy
ineffectiveness result ceases to hold. In this case, an
exploitable short-run Phillips curve reemerges, allowing some limited scope for systematic monetary policies to reduce unemployment.
For example, suppose the authorities possess more
and better information than the public. Having this
information advantage, they can predict and hence
respond to events seen as purely random by the
public. These policy responses will, since they are
unforeseen by the public, affect actual but not expected inflation an~t thereby change unemployment
relative to its natural rate in the (inverted) Phillips
curve equation UN--U: (l/a) (p--p~).
Alternatively, suppose that both the authorities
and the public possess identical information but that
29
the latter group is constrained by long-term contractual obligations from exploiting that information.
For example, suppose workers and employers make
labor contracts that fix nominal wages for a longer
period of time than the authorities require to change
the money stock. With nominal wages fixed and
prices responding to money, the authorities are in a
position to lower real wages and thereby stimulate
employment with an inflationary monetary policy.
In these ways, contractual and informational constraints are alleged to create outpnt- and employmentstimulating opportunities for systematic stabilization
policies. Indeed, critics have tried to demonstrate as
nmch by incorporating such constraints into rational
expectations Phillips curve models similar to the one
outlined in the Appendix of this article.
Proponents of the rational expectations approach,
however, doubt that such constraints can restore the
potency of activist policies and generate exploitable
Phillips curves. They contend that policymaker
information advantages cannot long exist when government statistics are published immediately upon
collection, when people have wide access to data
through the news media and private data services,
and when even secret policy changes can be predicted from preceding observable (and obvious)
economic and political pressures. Likewise, they
note that fixed contracts permit monetary policy to
have real effects only if those effects are so inconsequential as to provide no incentive to renegotiate
existing contracts or to change the optimal type of
contract that is negotiated. And even then, they note,
such monetary changes become ineffective ~vhen the
contracts expire. More precisely, they question the
whole idea of fixed contracts that underlies the sticky
wage case for policy activism. They point out that
contract duration is not invariant to the type of policy
being pursued but rather varies with it and thus
provides a weak basis for activist fine-tuning.
Finally, they insist that such policies, even if effective, are inappropriate. In their view, the proper role
for policy is not to exploit informational and contractual constraints to systematically influence real
activity but rather to neutralize the constraints or to
minimize the costs of adhering to them. Thus if
people form biased price forecasts, then the policymakers should publish unbiased forecasts. And if the
policy authorities have informational advantages over
private individuals, they should make that information pnblic rather than attempting to exploit the advantage. That is, if information is costly to collect
and process, then the central authority should gather
30
it and make it freely available. Finally, if contractual
wages and prices are sticky and costly to adjust, then
the authorities should minimize these price adjustment costs by following policies that stabilize the
general price level.
In short, advocates of the rational expectations
approach argue that feasibility alone constitutes insufficient justification for activist policies. Policies
should also be socially beneficial. Activist policies
hardly satisfy this latter criterion since their effectiveness is based on deceiving people into making expectational errors. The proper role for policy is not to
influence real activity via deception but rather to
reduce information deficiencies, to eliminate erratic
variations of the variables under the policymakers’
control, and perhaps also to minimize the costs of
adjusting prices.
VII.
CONCLUDING COMMENTS
The preceding paragraphs have traced the evolution of Phillips curve analysis. The chief conclusions
can be stated succinctly. The Phillips curve concept
has changed radically over the past 25 years as the
notion of a stable enduring trade-off has given way
to the policy-ineffectiveness view that no such tradeoff exists for the policymakers to exploit. Instrumental to this change ~vere the natural rate and
rational expectations hypotheses, respectively. The
former says that trade-offs arise solely from expectational errors xvhile the latter holds that systematic
macroeconomic stabilization policies, by virtue of
their very predictability, cannot possibly generate
sucla errors. Taken together, the two hypotheses
imply that systematic demand management policies
are incapable of influencing real activity, contrary to
the predictions of the original Phillips curve analysis.
On the positive side, the two hypotheses do imply
that the government can contribute to economic stability by following policies to mini,nize the expectational errors that cause output and employment to
deviate from their normal full-capacity levels. For
example, the authorities could stabilize the price level
so as to eliminate the surprise inflation that generates
confusion between absolute and relative prices and
that leads to perception errors. Similarly, they could
direct their efforts at minimizing random and erratic
variations in the monetary variables under their control. In so doing, not only would they lessen the
number of forecasting mistakes that induce deviations
from output’s natural rate, they would reduce policy
uncertainty as xvell.
Besides the above, the natural rate-rational expectations school also notes that microeconomic structural policies can be used to achieve what macro
demand policies cannot, namely a permanent reduction in the unemploylnent rate. For, by improving
the efficiency and performance of labor and product
markets, such micro policies can lower the natural
rate of unemployment and shift the vertical Phillips
curve to the left. A similar argument was advanced
in the earl), 1960s by those who advocated structural
policies to shift the Phillips curve. It is on this
point, therefore, that one should look for agreement
between those who still affirm and those who deny
the existence of exploitable inflation-unemployment
trade-offs.
APPENDIX
A SIMPLE ILLUSTRATIVE MODEL
The policy ineffectiveness proposition discussed in
Section V of the text can be clarified with the aid of a
simple illustrative model. The model consists of four
components, namely an (inverted) expectationsaugmented Phillips curve
(1) UN--U = (l/a) (p_pe),
a monetarist inflation-generating mechanism
(2) p ---= m-t-~,
a policy reaction function or feedback control rule
(3) m
and a definition of rational inflation expectations
(4) pO= E[p[I].
Here U and U~ are the actual and natural rates of
unemployment, p and p~ the actual and expected rates
of inflation, m the rate of nominal monetary growth
per unit of real money demand (the latter assumed
to be a fixed constant except for transitory disturbauces), ~ and /z are random error terms with mean
values of zero, E is the expectations operator, I denotes all information available when expectations are
formed, and the subscripts T and --1 denote target
and previous period values of the attached variables.
Of these four equations, the first expresses a tradeoff between unemployment (relative to its natural
level) and surprise (unexpected) inflation.~ Equation 2 expresses the rate of inflation p as the sum of
1 There exists a current dispute over the proper interpretation of the Phillips curve equation 1. The rational
expectatious literature interprets it as an aggregate
suppl.y function stating that firms produce the normal
capacity level of output when actual and expected inflation are equal but produce in excess of that level (thus
pushing U below U~) when fooled by unexpected inflation. This view holds that firms mistake unanticipated
general price increases for rises in the particular (relative) prices of their own products. Surprised by inflation,
the growth rate of (demand adjusted) money m
and a random shock variable ~ having a mean (expected) value of zero. In essence, this equation says
that inflation is generated by excess money growth
and transitory disturbances unrelated to money
growth. Equation 3 says that the policy authorities
set the current rate of monetary growth in an effort
to correct last period’s deviations of the unemployment and inflation rates from their predetermined
target levels, UT and p~. Also, since money growth
cannot be controlled perfectly by the feedback rule,
the slippage is denoted by the random variable /x
with a mean of zero that causes money growth to
deviate unpredictably from the path intended by the
authorities. Note that the disturbance term /.* can
also represent deliberate monetary surprises engineered by the policy authorities. Finally, the last
equation defines anticipated inflation p~ as the mathematical expectation of the actual inflation rate conditional on all information available when the expectation is formed. Included in the set of available
information are the inflation-generating mechanism,
the policy reaction function, and the values of all
past and predetermined variables in the model.
To derive the policy ineffectiveness result, first
calculate mathematical expectations of equations 2
and 3. Remembering that the expected values of the
random terms in those equations are zero, this step
yields the expressions
they treat the price increase as special to themselves and
so expand output. An alternative interpretation vie~vs
the equation as a price-setting relation according to which
businessmen, desiring to maintain their constant-marketshare relative prices, raise their prices at the rate at ~vhich
they expect other businessmen to be raising theirs and
then adjust that rate upward if demand pressure appears.
Either interpretation yields the same result: expectational errors cause output and unemployment to deviate
from their natural levels. The deviations disappear when
the errors vanish.
31
(5)
pe = meand
(6)
me ~ c(U-1--U@--d(p-l--pT)
which state that, under rational expectations and
systematic feedback policy rules, the anticipated
future rate of inflation equals the expected rate of
monetary growth which in turn is given by the deterministic (known) component of the monetary policy
rule. The last step is to substitute equations 2, 3, 5,
and 6 into equation 1 to obtain the reduced form
expression
(7) U~--U = (l/a) (~-(-/z)
which states that deviations of unemployment from
its natural rate result solely from inflation surprises
caused by random shocks.
To see the policy ineffectiveness result, note that
only the unsystematic or unexpected random component of monetary policy, nl--nle~-/x, enters the
the reduced form equation.2 The systematic com_o Note that both the monetary-surprise equation m-me=u
and the price-surprise equation p_pe=~ embody the
famous orthogonality property according to which forecast errors m-me and p-pc are independent of (orthogonal to) all information available when the forecast is
made. In particular, the forecast errors are independent
of the past and predetermined values of all variables and
of the systematic components of the policy rule and
inflation-generating mechanism. This is as it should be.
For if the errors were not independent of the foregoing
variables, then information is not being fully exploited
and expectations are not rational.
32
ponent is absent. This means that systematic (rulesbased) monetary policies cannot affect the unemploynlent rate. Only unexpected money growth matters.
No Phillips curve trade-offs exist for systematic
policy to exploit.~
To summarize, the strict (flexible price, continuous
market clearing) rational expectations-natural rate
model depicted here implies that expectational errors
are the only source of departure from steady-state
equilibrium, that such errors are random, short-lived,
and immune to systematic policy manipulation, and
therefore that rules-based policies can have no impact
on real variables like unemployment since those
policies will be fully foreseen and allowed for in
wage/price adjustments. Thus, except for unpredictable random shocks, steady-state equilibrium prevails and systematic monetary changes produce no
surprises, no disappointed expectations, no transitory
impacts on real economic variables. In short, Phillips
curves are totally adventitious phenomena generated
by unforeseeable random shocks and as such cannot
be exploited by systematic policy even in the short
FUll.
a Of course random policy could affect output. That is,
the authorities could influence real activity by manipulating the disturbance term ~ in the policy reaction function in a haphazard unpredictable way. Randomness,
however, is not a proper basis for public policy.
,,i
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Post Ot~fice Box 27622, Richmond,Virginia 23261
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