The expectations-augmented Phillips curve

The prevailing Keynesian view of the Phillips curve was overturned by new ideas hatched during the 1960s and events in the 1970s (Mankiw, 1990). A central component of the new thinking involved Friedman’s critique of the

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trade-off interpretation of the Phillips curve. This was first provided by Fried-man (1966) in his debate with Solow (1966) over wage and price guideposts and had even been outlined much earlier in conversation with Richard Lipsey in 1960 (Leeson, 1997a). However, the argument was developed more fully in his famous 1967 Presidential Address. According to Friedman, the original Phillips curve which related the rate of change of money wages to unemploy-ment was misspecified. 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 inflation 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 inflation 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 inflation.

Introducing the expected rate of inflation 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 inflation. 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 simplification 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 inflation would be zero; that is, W˙ = =P˙ P˙^e=0per 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 firms demanded more labour, unemployment would fall, with money wages rising at a rate of W˙ ,₁ that is,

point B on the short-run Phillips curve (SRPC1). As workers started slowly to adapt their inflation expectations in the light of the actual rate of inflation experienced( ˙P=W˙ ),1 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 W^˙₁plus the expected rate of inflation. 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 inflation is completely anticipated ( ˙P₁=P˙ )^e in wage bargains ( ˙W₁=P˙ ,^e that is to say there is no money illusion), there will be no long-run trade-off between unemployment and wage inflation. 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 inflation and only in the special case where the expected rate of inflation is zero will wage inflation 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 inflation are equal; that is, inflation is fully anticipated.

Figure 4.4 The expectations-augmented Phillips curve

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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 inflation are both equal to zero (that is, P^˙=P˙ ),^e equation (4.5) can be factorized and written as:

˙( ) ( )

P1− =β f U (4.6)

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

˙ ( )

P f U

= 1−β (4.7)

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 inflation 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 coefficient (β) on the inflation expectations term is equal to one proved far from clear-cut. In consequence,

Figure 4.5 The trade-off between inflation 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 inflation in the long run, there was insufficient 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 with a vertical long-run Phillips curve at the natural rate of unemployment.

Friedman noted that inflation rates tend to become increasingly volatile at higher rates of inflation. Increased volatility of inflation results in greater

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uncertainty, and unemployment may rise as market efficiency is reduced and the price system becomes less efficient as a coordinating/communication mecha-nism (see Hayek, 1948). Increased uncertainty may also cause a fall in investment and result in an increase in unemployment. Friedman further argued that, as inflation rates increase and become increasingly volatile, governments tend to intervene more in the price-setting process by imposing wage and price con-trols, which reduces the efficiency of the price system and results in an increase in unemployment. The positive relationship between inflation and unemploy-ment then results from an unanticipated increase in the rate and volatility of inflation. While the period of transition could be quite long, extending over decades, once the economy had adjusted to high and volatile inflation, in Friedman’s view, it would return to the natural rate of unemployment.

4.3.2 The policy implications of the expectations-augmented Phillips