ment was misspeci¬ed. Although money wages are set in negotiations, both

employers and employees are interested in real, not money, wages. Since

wage bargains are negotiated for discrete time periods, what affects the

anticipated real wage is the rate of in¬‚ation expected to exist throughout the

period of the contract. Friedman argued that the Phillips curve should be set

in terms of the rate of change of real wages. He therefore augmented the

basic Phillips curve with the anticipated or expected rate of in¬‚ation as an

additional variable determining the rate of change of money wages. The

expectations-augmented Phillips curve can be expressed mathematically by

the equation:

W = f (U ) + P e

™ ™ (4.2)

Equation (4.2) shows that the rate of money wage increase is equal to a

component determined by the state of excess demand (as proxied by the level

of unemployment) plus the expected rate of in¬‚ation.

Introducing the expected rate of in¬‚ation as an additional variable to ex-

cess demand which determines the rate of change of money wages implies

that, instead of one unique Phillips curve, there will be a family of Phillips

curves, each associated with a different expected rate of in¬‚ation. Two such

curves are illustrated in Figure 4.4. Suppose the economy is initially in

equilibrium at point A along the short-run Phillips curve (SRPC1) with unem-

ployment at UN, its natural level (see below) and with a zero rate of increase

of money wages. For simpli¬cation purposes in this, and subsequent, analysis

we assume a zero growth in productivity so that with a zero rate of money

wage increase the price level would also be constant and the expected rate of

in¬‚ation would be zero; that is, W = P = P e = 0 per cent. Now imagine the

™™™

authorities reduce unemployment from UN to U1 by expanding aggregate

demand through monetary expansion. Excess demand in goods and labour

markets would result in upward pressure on prices and money wages, with

commodity prices typically adjusting more rapidly than wages. Having re-

cently experienced a period of price stability ( P e = 0), workers would

™

misinterpret their money wage increases as real wage increases and supply

more labour; that is, they would suffer from temporary money illusion. Real

wages would, however, actually fall and, as ¬rms demanded more labour,

™

unemployment would fall, with money wages rising at a rate of W1 , that is,

The orthodox monetarist school 177

point B on the short-run Phillips curve (SRPC1). As workers started slowly to

adapt their in¬‚ation expectations in the light of the actual rate of in¬‚ation

experienced ( P = W1 ), they would realize that, although their money wages

™™

had risen, their real wages had fallen, and they would press for increased

money wages, shifting the short-run Phillips curve upwards from SRPC1 to

™

SRPC2. Money wages would rise at a rate of W1 plus the expected rate of

in¬‚ation. Firms would lay off workers as real wages rose and unemployment

would increase until, at point C, real wages were restored to their original level,

with unemployment at its natural level. This means that, once the actual rate of

in¬‚ation is completely anticipated ( P = P e ) in wage bargains (W1 = P e , that is

™1 ™ ™ ™

to say there is no money illusion), there will be no long-run trade-off between

unemployment and wage in¬‚ation. It follows that if there is no excess de-

mand (that is, the economy is operating at the natural rate of unemployment),

then the rate of increase of money wages will equal the expected rate of

in¬‚ation and only in the special case where the expected rate of in¬‚ation is

zero will wage in¬‚ation be zero, that is, at point A in Figure 4.4. By joining

points such as A and C together, a long-run vertical Phillips curve is obtained

at the natural rate of unemployment (UN). At UN the rate of increase in money

wages is exactly equal to the rate of increase in prices, so that the real wage is

constant. In consequence there will be no disturbance in the labour market.

At the natural rate the labour market is in a state of equilibrium and the actual

and expected rates of in¬‚ation are equal; that is, in¬‚ation is fully anticipated.

Figure 4.4 The expectations-augmented Phillips curve

178 Modern macroeconomics

Friedman™s analysis helped reconcile the classical proposition with respect to

the long-run neutrality of money (see Chapter 2, section 2.5), while still

allowing money to have real effects in the short run.

Following Friedman™s attack on the Phillips curve numerous empirical

studies of the expectations-augmented Phillips curve were undertaken using

the type of equation:

W = f (U ) + βP e

™ ™ (4.3)

Estimated values for β of unity imply no long-run trade-off. Conversely

estimates of β of less than unity, but greater than zero, imply a long-run

trade-off but one which is less favourable than in the short run. This can be

demonstrated algebraically in the following manner. Assuming a zero growth

in productivity so that W = P, equation (4.3) can be written as:

™™

P = f (U ) + βP e

™ ™ (4.4)

Rearranging equation (4.4) we obtain:

P ’ βP e = f (U )

™ ™ (4.5)

Starting from a position of equilibrium where unemployment equals U* (see

Figure 4.5) and the actual and expected rates of in¬‚ation are both equal to

zero (that is, P = P e ), equation (4.5) can be factorized and written as:

™™

P(1 ’ β) = f (U )

™ (4.6)

Finally, dividing both sides of equation (4.6) by 1 “ β, we obtain

™ f (U )

P= (4.7)

1’ β

Now imagine the authorities initially reduce unemployment below U* (see

Figure 4.5) by expanding aggregate demand through monetary expansion.

From equation (4.7) we can see that, as illustrated in Figure 4.5, (i) estimated

values for β of zero imply both a stable short- and long-run trade-off between

in¬‚ation and unemployment in line with the original Phillips curve; (ii)

estimates of β of unity imply no long-run trade-off; and (iii) estimates of β of

less than unity, but greater than zero, imply a long-run trade-off but one

which is less favourable than in the short run. Early evidence from a wide

range of studies that sought to test whether the coef¬cient (β) on the in¬‚ation

expectations term is equal to one proved far from clear-cut. In consequence,

The orthodox monetarist school 179

Figure 4.5 The trade-off between in¬‚ation and unemployment

during the early 1970s, the subject of the possible existence of a long-run

vertical Phillips curve became a controversial issue in the monetarist“

Keynesian debate. While there was a body of evidence that monetarists could

draw on to justify their belief that β equals unity, so that there would be no

trade-off between unemployment and in¬‚ation in the long run, there was

insuf¬cient evidence to convince all the sceptics. However, according to one

prominent American Keynesian economist, ˜by 1972 the “vertical-in-the-

long-run” view of the Phillips curve had won the day™ (Blinder, 1992a). The

reader is referred to Santomero and Seater (1978) for a very readable review

of the vast literature on the Phillips curve up to 1978. By the mid- to late

1970s, the majority of mainstream Keynesians (especially in the USA) had

come to accept that the long-run Phillips curve is vertical. There is, however,

still considerable controversy on the time it takes for the economy to return to

the long-run solution following a disturbance.

Before turning to discuss the policy implications of the expectations-aug-

mented Phillips curve, it is worth mentioning that in his Nobel Memorial

Lecture Friedman (1977) offered an explanation for the existence of a posi-

tively sloped Phillips curve for a period of several years, which is compatible