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# The long-run Phillips curve

The augmented Phillips curve has an important consequence: the long-run Phillips curve must be vertical.

Fig. 15.2: The long-term Phillips curve.

To realize this, start by drawing a Phillips curve for 1 = 3%. The only point on this curve that may apply in the long run is %W = 3% (point A). For example, %W = 2% and it" = 3% is not consistent with equilibrium in the long run as there is no level of inflation which is consistent with these values. i = 3% is not possible as real wages would go to zero. i = 2% is not possible since it would be unreasonable to continue to expect 3% inflation if inflation each year was 2%.

According to the neo-classical synthesis, we may temporarily be anywhere on the lower Phillips curve when I = 3%, but the economy must eventually return to point A (as long Ie = 3%)

Now draw a Phillips curve for if = 6%. Again, on this curve there is only one point is consistent with equilibrium in the long run and that is the point where %W = 6% (point B). This point must be exactly above A as the new curve must be exactly three units above the first curve.

If we draw all possible Phillips curves, we see that all points consistent with long run equilibrium must lie on a vertical curve and this curve is called the long-run Phillips curve. In the long run, the economy must return to this curve. This means that in the long run, there is no relation between inflation and unemployment. In the long term, the economy returns to the natural unemployment rate as in the classical model.

# Summary of the Phillips curves

In the neo-classical synthesis, the augmented Phillips curve is called the short-run Phillips curve. It is assumed to be stable as long as expectations of future inflation do not change. To summarize, we have three Phillips curves:

The traditional Phillips curve. nW = f(U) and the same downward sloping relationship applies to both the short and the long run.

The short-run Phillips curve (SPC). nw = f(U) + n and the curve is valid only in the short run (SPC = Short-run Phillips Curve).

The long-run Phillips curve (LPC). nw = nM, U = UN and there is no relationship between nw and U (UN is the natural rate of unemployment).

# The classical model and the long-term Phillips curve

In the classical model, L and the real wage are determined from equilibrium conditions in the labor market. L and W/P, therefore, are only affected by the marginal product of labor (which determines the demand for labor) and by the utility function of the employees (which determines the supply of labor). All unemployment is voluntary and L, U or W/P are all affected by exogenous variables only.

In the classical model, inflation is determined solely by the growth in the money supply %M. From the quantity theory of money, M-V = PY and if the growth rate of M is nM, then P must increase by the same rate as V and Y are constant. From the quantity theory we can conclude that n = nM must hold. The relationship M-V = P-Y is therefore sometimes called the quantity theory in levels while n = nM is called the quantity theory in rates.

In the classical model, inflation is balanced and nW = n (real wage is constant). Since n = nM, we have n = nM = nW. As U is not affected by any endogenous variables, there is no relationship between nW och U in the classical model and the vertical LPC applies even in the short run. The position on the LPC determined by nM.

Unlike the neo-classical synthesis, where the economy temporarily may depart from LPC, the economy must always be on the LPC in the classical model.

# Developments around 1960

The augmented Phillips curve and the long-run Phillips curve where developed during the late 1960s by Milton Friedman and Edmund Phelps. Friedman argued that a stable Phillips curve could exist in the short run as long individuals did not expect changes in the economy. Eventually, expectations would change and the traditional Phillips curve would shift and we would return to a point on the long-run Phillips curve.

If the Phillips curve depends on n, we can no longer expect observations of unemployment and wage inflation to nicely line up on a downward sloping curve. Instead, different observations will belong to different Phillips curves that move over time and we should expect to see all possible combinations of U och i .

Most Keynesian chose to hold on to the traditional Phillips curve. If you buy the augmented Phillips curve, you must buy the long-run Phillips curve and the economy must automatically return to the natural level of unemployment. This would violate one of the main results in the Keynesian analysis namely that the economy may be stuck in a long-run equilibrium with a high level of involuntary unemployment. With the long-run Phillips curve, it would again be impossible to determine the rate of inflation within the Keynesian model as all levels of inflation would be consistent with equilibrium (as for the Keynesian model without the Phillips curve). Since the traditional Phillips curve had a strong empirical support at this time, there was no reason to give it up.

Milton Friedman argued that this stable relationship was a pure coincidence. He predicted that observations in line with Figure X would be common in the future. A period of "stagflation", a situation with high unemployment and high inflation, in the early 70s was a great victory for the augmented Phillips curve and a serious setback for the Keynesian model. According to the Keynesian model, the government should pursue an expansionary policy if unemployment was high and a tight policy if inflation was high. The Keynesian model had no answer on what policy to pursue if both were high.

In the late 1970s it was clear that the augmented Phillips curve was superior to the traditional Phillips curve which from now on was assumed to be valid only in the short run. The neo-classical synthesis became the most popular model in macroeconomics and the synthesis is still the dominating model in macroeconomics taught in introductory and intermediate courses. The synthesis is also often the starting point for more advanced models in macro economics.

It should be noted that the development in the 1970s was a setback for the Keynesian model which incorporated the Phillips curve. The Keynesian model without the Phillips curve was less affected by the debate. With constant wages it does determine all of the macroeconomic variables but without the Phillips curve, it cannot explain inflation (see chapter 14). For this reason, many macro economists believe that the Keynesian model can be used in the short run or in recession when prices and wages do not change very much.

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