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3.6 The Phillips Curve and Orthodox Keynesian Economics

The Phillips curve is concerned with the controversy over the relationship

between inflation and unemployment and is one of the most famous relationships

in macroeconomics (see Smithin, 2002). It should be noted that the first

statistical study investigating the relationship between unemployment and

inflation was carried out by Irving Fisher in 1926 (see Fisher, 1973). However,

the curve that bears A.W. Phillips’s name was derived from a statistical

investigation published in 1958 into the relationship between unemployment

(U) and the rate of change of money wages (W˙ ) in the UK over the period

1861–1957. As depicted in Figure 3.14, the estimated average relationship

was found to be non-linear and inverse. For example, at an unemployment

level of approximately 5.5 per cent, the rate of change of money wages was

zero per cent, while at an unemployment level of approximately 2.5 per cent

the rate of change of money wages was 2.0 per cent.

Remarkably, Phillips found that the data for the period 1948–57 fitted very

closely to the curve fitted for the earlier period, 1861–1913, given by equation

(3.6).

0.9 9.638(U)−1.394 (3.6)

To some, this finding suggested the possible existence of a stable long-run

negative relationship between wage inflation and unemployment.

Figure 3.14 The Phillips curve

Although the original Phillips paper (1958) was an empirical investigation

into the relationship between money wage inflation and unemployment, Phillips

opens his paper with an outline sketch of the underlying theoretical reasoning

that could be used to explain why we might expect to observe a negative

relationship between these two variables. He opens with these words:

When the demand for a commodity or service is high relative to the supply of it

we expect the price to rise, the rate of rise being greater the greater the excess

demand. Conversely, when the demand is low relative to the supply we expect the

price to fall, the rate of fall being greater the greater the deficiency of demand. It

seems plausible that this principle should operate as one of the factors determining

the rate of change of money wage rates.

Following Phillips’s pioneering work, there developed two strands to the

literature, one theoretical, the other empirical. On the empirical front, economists

were interested to establish whether a stable relationship between

inflation and unemployment prevailed in other market economies (for a discussion

of the empirical literature, see Santomero and Seater, 1978). As far as

the simultaneous achievement of low inflation and low unemployment was

concerned, the discovery of a possible stable trade-off between these two

objectives implied a policy dilemma, one which might be overcome if the

curve could be shifted to the left by appropriate economic policies. However,

the design of effective policies to achieve this objective would first necessitate

a coherent theoretical explanation of the economic forces which lay

behind the relationship.

The first major attempt to provide a robust theoretical underpinning to the

curve was provided by Lipsey (1960) through the combination of two postulated

relationships: (i) a positive linear relationship between the rate of increase

in money wages and the excess demand for labour (XL), and (ii) a negative

non-linear relationship between excess demand and unemployment. These

postulated relationships are given in equations (3.7) and (3.8).

W˙ (X ) [(D S )/S ] L L −L L (3.7)

XL (U) (3.8)

where DL is the demand for labour, SL is the supply of labour, is a positive

coefficient of wage flexibility, and is a variable negative parameter such

that when XL →0, U = U* and U* > 0; and when XL →, U →0. By

combining these two postulated relationships, Lipsey was able to provide an

economic rationale for Phillips’s observed non-linear inverse relationship

between the rate of change of money wages and unemployment shown in

Figure 3.14.

The relationship between wage change and excess demand for labour is

illustrated in Figure 3.15. Panel (a) shows that at any wage rate below We ,

wages will rise as a result of excess demand in the labour market. Panel (b)

shows that the rate of increase in money wage rates will be greater the larger

the excess demand for labour. For example, at a wage rate W1 in panel (a)

there is an excess demand for labour of aa. This excess demand is equal to 0a

in panel (b) and results in a rate of increase in money wage rates of W˙1. The

relationship between excess demand for labour and unemployment is illustrated

in Figure 3.16. Even when the labour market clears (that is to say, there

is neither excess demand nor excess supply) there will be some positive

amount of unemployment due to frictions in the labour market as people

change jobs and search for new employment, that is, 0e in Figure 3.16.

Lipsey argued that, although unemployment would fall in response to positive

excess demand (for example, jobs become easier to find as vacancies

increase), unemployment would only asymptotically approach zero. In other

words, steadily increasing excess demand would be accompanied by increasingly

smaller reductions in unemployment.

In summary, Lipsey’s rationale suggests that, in its simplest form, the rate

of change of money wages depends on the degree of excess demand (or

supply) in the labour market as proxied by the level of unemployment. This

can be expressed by the equation:

Figure 3.15 The relationship between wage change and excess demand for

labour

Figure 3.16 The relationship between excess demand for labour and

unemployment

f (U) (3.9)

Referring back to Phillips’s opening statement in his 1958 paper, it is clear

that he viewed the high correlation between money wage inflation and unemployment

as strong evidence in favour of the ‘demand pull’ explanation of

inflation.

In Lipsey’s model, due to labour market frictions, equilibrium in the labour

market occurs when U = U* > 0 (see Lipsey, 1960, pp. 470–71). When U = U*,

the number of job vacancies (V) is equal to the number of unemployed who

are actively seeking work. Since SL equals the total number employed (E) and

unemployed (E + U), and DL equals the total number of vacancies (V) plus

the number employed (V + E), we can express the proportional excess

demand for labour as follows:

XL [(DL −SL )/SL ] [(V −U) /(E U)] (3.10)

Letting v = V/SL and u = U/SL, we can express the excess demand for labour

in terms of variables that can be measured, that is the vacancy rate (v) and the

unemployment rate (u).

XL v −u (3.11)

Over the business cycle the vacancy rate will be positively related to XL and

unemployment will be negatively related to XL, assuming the quit rate does

not exceed the hiring rate as XL increases.

Later, Hansen (1970) refined Lipsey’s analysis by assuming that vacancy

and unemployment rates are related in a hyperbolic form, that is, h = vu

where h = coefficient of friction in the labour market (with no friction in the

labour market h = 0 and either v or u = 0). The relationship between XL, u

and v when there are frictions present in the labour market is shown in Figure

3.17.

In panel (a) we can see that even when excess demand for labour is zero,

both the unemployment and vacancy rates are positive, reflecting friction in

the labour market. In a frictionless labour market the relationship between XL,

v and u will be a 45° line, as shown by AB. Panel (b) of Figure 3.17 shows all

the combinations of vu tracing out a hyperbolic curve. Anywhere along the

45° line indicates equilibrium in the labour market since with XL = 0, we also

have v = u. The existing degree of friction illustrated in Figure 3.17, panel

(b), is indicated by the position of the hyperbolic curve at F. With increasing

friction in the labour market this curve will shift out. In turn this will cause

the Phillips curve to shift to the right since the level of unemployment

consistent with XL = 0 increases as labour market friction increases. There is

strong evidence, for example, that such a shift occurred in the UK economy

in the late 1960s and early 1970s (Gujarati, 1972; see also Taylor, 1972).

Given Hansen’s refinements, the Phillips relationship can now be expressed

in the following form:

(h/u −u) w* h/u −u w* (3.12)

where w* is exogenously determined wage inflation (for example, brought

about by trade union power). In (3.12) we can see that the slope of the

Phillips curve is dependent on the coefficient of wage flexibility, , and the

position of the Phillips curve will be influenced by w* and also the degree of

friction in the labour market, h. The more inflexible the labour market the

higher the degree of friction, and the higher will wage inflation be for any

given level of unemployment (see Rothschild, 1971; Frisch, 1977; Lipsey,

1978).

During the 1960s the Phillips (1958) curve was quickly taken on board as

an integral part of the then-dominant orthodox Keynesian paradigm, not least

because it was interpreted by many orthodox Keynesians as implying a stable

long-run trade-off which provided the authorities a menu of possible inflation–

unemployment combinations for policy choice. Within academia the

Figure 3.17 The relationship between excess demand for labour, vacancy

and unemployment rates

45

XL > 0

XL < 0

XL

XL

A

B

u v

+

+ +

0

v

u

45

√h F

√h

XL = 0

(b)

(a)

textbook interpretation of the Phillips curve came to be presented as a proposition

that permanently low levels of unemployment could be realistically

achieved by tolerating permanently high levels of inflation. As James Galbraith

(1997) points out, in 1968 mainstream American Keynesians were ‘committed

to Samuelson and Solow’s (1960) version of the Phillips curve’. According

to Robert Leeson (1994a, 1997a, 1999), this is not how Bill Phillips himself

ever viewed the relationship he had discovered. In Leeson’s view, Phillips’s

1958 paper was an attempt to locate the level of unemployment consistent

with price stability. Richard Lipsey has confirmed that Phillips had ‘no tolerance

for accepting inflation as the price of reducing unemployment’ (Leeson,

1997a). However, up to at least the late 1960s the prevailing Keynesian

economic orthodoxy used the Phillips curve to predict the rate of inflation

which would result from different target levels of unemployment being attained

by activist aggregate demand policies, with particular emphasis on

fiscal instruments. As DeLong (1998) points out, once those target rates of

unemployment kept falling, the inflationary outcome of this approach to

macroeconomic policy was inevitable and duly arrived with a vengeance with

the ‘Great Peacetime Inflation’ of the 1970s.

One of the main reasons why the Phillips curve was quickly adopted by

orthodox Keynesians was that it seemed to provide an explanation of inflation

which was missing in the then-prevailing macroeconomic model. The

reader will recall from the discussion contained in section 3.3 that within the

IS–LM model the price level is assumed to be fixed at less than full employment,

with the result that up to full employment, changes in aggregate demand

affect the level of real income and employment. Up to full employment

money wages are assumed to be fixed and unresponsive to changes in aggregate

demand. Only when full employment is reached will changes in aggregate

demand affect the price level. The Phillips curve allowed the orthodox

Keynesian theory of output and employment determination to be linked to a

theory of wage and price inflation. Following Lipsey (1978), this is illustrated

in Figure 3.18. The top panel of Figure 3.18 depicts the standard IS–LM

model, while the bottom panel shows the Phillips curve with the modified

axes of price inflation (P˙ ) and output/income (Y). Panel (b) is derived by

assuming (i) that the level of output depends on the level of employment and

that the level of unemployment is inversely related to the level of employment,

and (ii) a hypothesis that prices are set by a mark-up to unit costs of

production, the main component of which is wages. Put in its simplest form,

the mark-up pricing hypothesis suggests that price inflation depends on money

wage inflation minus productivity growth. In this context it is interesting to

note that the estimated Phillips curve (Figure 3.14) showed that an unemployment

level of approximately 2.5 per cent was compatible with stable

prices because at this level of unemployment the rate of change of money

Figure 3.18 The link between the Keynesian model and wage and price

inflation

wages was approximately equal to the then average growth of productivity of

2 per cent. Suppose the economy is initially operating at a full employment

level of income (YFE), that is, the intersection of IS0 and LM0 in panel (a) of

Figure 3.18. Reference to panel (b) reveals that the full employment level of

income is compatible with stable prices; that is, ˙P = 0. Following a onceand-

for-all expansionary real impulse, the IS curve shifts outwards to the

right, from IS0 to IS1, and real income rises above its full employment level of

YFE to Y1. Reference to panel (b) reveals that as income rises above its full

employment level, price inflation increases to P˙1. As prices increase, the real

value of the money supply is reduced, causing the LM curve to shift to the

left, from LM0 to LM1, and the economy returns to full employment, that is,

the intersection of IS1 and LM1 in panel (a). At full employment stable prices

prevail, that is, ˙P = 0 in panel (b).

Following the influential contribution from Samuelson and Solow (1960),

the Phillips curve was interpreted by many orthodox Keynesians as implying

a stable long-run trade-off which offered the authorities a menu of possible

inflation–unemployment combinations for policy choice (see Leeson, 1994b,

1997a, 1997b, 1997c). Following the Samuelson–Solow paper the trade-off

has generally been expressed in terms of price inflation rather than wage

inflation. However, by the late 1960s/early 1970s, both inflation and unemployment

had begun to increase, as is evident from Tables 1.4 and 1.5. As we

will discuss in the next chapter, the notion of a stable relationship between

inflation and unemployment was challenged independently by Milton Friedman

(1968a) and Edmund Phelps (1967), who both denied the existence of a

permanent (long-run) trade-off between inflation and unemployment.