Phillips curve

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The Phillips curve is a historical inverse relation and tradeoff between the rate of unemployment and the rate of inflation in an economy. Stated simply, the lower the unemployment in an economy, the higher the rate of change in wages paid to labor in that economy.

The New Zealand-born economist A.W. Phillips, in his 1958 paper "The relationship between unemployment and the rate of change of money wages in the United Kingdom 1861-1957" published in the now quarterly journal Economica, observed an inverse relationship between money wage changes and unemployment in the British economy over the period examined. Similar patterns were found in other countries and in 1960 Paul Samuelson and Robert Solow took Phillips' work and made explicit the link between inflation and unemployment—when inflation was high, unemployment was low, and vice-versa.

It is little known that the American economist Irving Fisher pointed to this kind of Phillips curve relationship back in the 1920s. On the other hand, Phillips' original curve described the behavior of money wages. So some believe that the PC should be called the "Fisher curve."

In the years following his 1958 paper, many economists in the advanced industrial countries believed that Phillips' results showed that there was a permanently stable relationship between inflation and unemployment. One implication of this for government policy was that governments could control unemployment and inflation within a Keynesian policy. They could tolerate a reasonably high rate of inflation as this would lead to lower unemployment – there would be a trade-off between inflation and unemployment. For example, monetary policy and/or fiscal policy (i.e., deficit spending) could be used to stimulate the economy, raising gross domestic product and lowering the unemployment rate. Moving along the Phillips curve, this would lead to a higher inflation rate, the cost of enjoying lower unemployment rates.

To a large extent, a leftward movement along the PC describes the path of the U.S. economy during the 1960s, though this move was not a matter of deciding to achieve low unemployment as much as an unplanned side-effect of the Vietnam war. In other countries, the economic boom was more the result of conscious policies.

1 Stagflation
2 The Phillips curve, NAIRU and rational expectations
3 The Phillips curve today
- 3.1 Gordon's triangle model
4 Theoretical questions
5 Mathematics behind the Phillips curve
6 See also
7 External links

[edit] Stagflation

Into the 1970s, however, many countries experienced high levels of both inflation and unemployment also known as stagflation. Theories based on the Phillips curve suggested that this could not happen, and the curve came under concerted attack from a group of economists headed by Milton Friedman—arguing that the demonstrable failure of the relationship demanded a return to non-interventionist, free market policies. The idea that there was a simple, predictable, and persistent relationship between inflation and unemployment was abandoned by most if not all macroeconomists.

[edit] The Phillips curve, NAIRU and rational expectations

Short-Run Phillips Curve before and after Expansionary Policy, with Long-Run Phillips Curve (NAIRU)

New theories, such as rational expectations and the NAIRU (non-accelerating inflation rate of unemployment) arose to explain how stagflation could occur. The latter theory – also known as the theory of the "natural" rate of unemployment – distinguished between the short-term Phillips curve and the long-term one. The short-term PC looked like a normal PC but shifted in the long run as expectations changed. In the long run, only a single rate of unemployment (the NAIRU or "natural" rate) was consistent with a stable inflation rate. The long-run PC was thus vertical, so there was no trade-off between inflation and unemployment. Edmund Phelps won the Nobel Prize in Economics in 2006 for this.

In the diagram, the long-run Phillips curve is the vertical red line. The NAIRU theory says that when unemployment is at the rate defined by this line, inflation will be stable. However, in the short-run policymakers will face an inflation-unemployment rate tradeoff marked by the Initial Short-Run Phillips Curve. Policymakers can therefore reduce the unemployment rate temporarily, moving from point A to point B through expansionary policy. However, according to the NAIRU, exploiting this short-run tradeoff will raise inflation expectations, shifting the short-run curve rightward to the New Short-Run Phillips Curve and moving the point of equilibrium from B to C. Thus the reduction in unemployment below the "Natural Rate" will be temporary, and lead only to higher inflation in the long run.

Since the short-run curve shifts outward due to the attempt to reduce unemployment, the expansionary policy ultimately worsens the exploitable tradeoff between unemployment and inflation. That is, it results in more inflation at each short-run unemployment rate. The name "NAIRU" arises because with actual unemployment below it, inflation accelerates, while with unemployment above it, inflation decelerates. With the actual rate equal to it, inflation is stable, neither accelerating nor decelerating. One practical use of this model was to provide an explanation for Stagflation, which confounded the traditional Phillips curve.

The rational expectations theory said that expectations of inflation were equal to what actually happened, with some minor and temporary errors. This in turn suggested that the short-run period was so short that it was non-existent: any effort to reduce unemployment below the NAIRU, for example, would immediately cause inflationary expectations to rise and thus imply that the policy would fail. Unemployment would never deviate from the NAIRU except due to random and transitory mistakes in developing expectations about future inflation rates. In this perspective, any deviation of the actual unemployment rate from the NAIRU was an illusion.

However, in the 1990s in the U.S., it became increasingly clear that the NAIRU did not have a unique equilibrium and could change in unpredictable ways. In the late 1990s, the actual unemployment rate fell below 4 % of the labor force, much lower than almost all estimates of the NAIRU. But inflation stayed very moderate rather than accelerating. So, just as the Phillips curve had become a subject of debate, so did the NAIRU.

Further, the concept of rational expectations had become subject to much doubt when it became clear that the main assumption of models based on it was that there exists a single (unique) equilibrium in the economy that is set ahead of time, determined independent of demand conditions. The experience of the 1990s suggests that this assumption cannot be sustained.

[edit] The Phillips curve today

Most economists no longer use the Phillips curve. However, among those that retain it, unlike the static Phillips curve that was popular in the 1960s, the new curve can undergo sudden changes, so that following a set policy can have markedly different results at different times—the "trade-off" can worsen (as in the 1970s) or get better (as in the 1990s).

This can be seen in a cursory analysis of US inflation and unemployment data 1953-92. There is no single curve that will fit the data, but there are three rough aggregations—1955-71, 1974-84, and 1985-92—each of which shows a general, downwards slope, but at three very different levels with the shifts occurring abruptly. The data for 1953-54 and 1972-73 does not group easily and a more formal analysis posits up to five groups/curves over the period.

[edit] Gordon's triangle model

Robert J. Gordon of Northwestern University has analysed the Phillips curve to produce what he calls the triangle model, in which the actual inflation rate is determined by the sum of

The last reflects inflationary expectations and the price/wage spiral. Supply shocks and changes in built-in inflation are the main factors shifting the short-run PC and changing the trade-off. In this theory, it is not only inflationary expectations that can cause stagflation. For example, the steep climb of oil prices during the 1970s could have this result.

Changes in built-in inflation follow the partial-adjustment logic behind most theories of the NAIRU:

Low unemployment encourages high inflation, as with the simple Phillips curve. But if unemployment stays low and inflation stays high for a long time, as in the late 1960s in the U.S., both inflationary expectations and the price/wage spiral accelerate. This shifts the short-run Phillips curve upward and rightward, so that more inflation is seen at any given unemployment rate. (This is with shift B in the diagram.)
High unemployment encourages low inflation, again as with a simple Phillips curve. But if unemployment stays high and inflation stays low for a long time, as in the early 1980s in the U.S., both inflationary expectations and the price/wage spiral slow. This shifts the short-run Phillips curve downward and leftward, so that less inflation is seen at each unemployment rate.

In between these two lies the NAIRU, where the Phillips curve does not have any inherent tendency to shift, so that the inflation rate is stable. However, there seems to be a range in the middle between "high" and "low" where built-in inflation stays stable. The ends of this "non-accelerating inflation range of unemployment rates" change over time.

[edit] Theoretical questions

The Phillips curve started as an empirical observation in search of a theoretical explanation. There are several major explanations of the short-term PC regularity.

To Milton Friedman there is a short-term correlation between inflation shocks and employment. When an inflationary surprise occurs, workers are fooled into accepting lower pay because they do not see the fall in real wages right away. Firms hire them because they see the inflation as allowing higher profits for given nominal wages. This is a movement along the Phillips curve as with change A. Eventually, workers discover that real wages have fallen, so they push for higher money wages. This causes the Phillips curve to shift upward and to the right, as with B.

Some economists reject this theory because it implies that workers suffer from money illusion. However, one of the characteristics of a modern industrial economy is that workers do not encounter their employers in an atomized and perfect market. They operate in a complex combination of imperfect markets, monopolies, monopsonies, labor unions, and other institutions. In many cases, they may lack the bargaining power to act on their expectations, no matter how rational they are, or their perceptions, no matter how free of money illusion they are. It is not that high inflation causes low unemployment (as in Milton Friedman's theory) as much as vice-versa. Low unemployment raises worker bargaining power, allowing them to successfully push for higher nominal wages. To protect profits, employers raise prices, so that low unemployment causes inflation.

Similarly, built-in inflation is not simply a matter of subjective "inflationary expectations" but also reflects the fact that high inflation can gather momentum and continue beyond the time when it was started, due to the objective price/wage spiral.

[edit] Mathematics behind the Phillips curve

The Phillips curve equation can be derived from the short-run aggregate supply equation. We start with the short-run aggregate supply function:

$Y = Y_n + a (P-P_e) \,$

where Y is the actual output, Y_n is the natural level of output, a is a positive constant, P is the actual price level, and P_e is the expected price level.

We re-arrange the equation into:

$P = P_e + \frac{Y-Y_n}{a} \,$

Next we add unexpected exogenous shocks to the world supply v:

$P = P_e + \frac{Y-Y_n}{a} + v \,$

Subtracting last year's price levels P_-1 will give us inflation rates, because

$P-P_{-1} = \Pi \,$

and

$P_e- P_{-1} = \Pi_e \,$

where Π and Π_e are the inflation and expected inflation respectively.

There is also a negative relationship between output and unemployment (as expressed by Okun's law). Therefore using

$\frac{Y-Y_n}{a} = -b(U-U(n)) \,$

where b is a positive constant, U is unemployment, and U_n is the natural rate of unemployment or NAIRU, we arrive at the final form of the short-run Phillips curve:

$\Pi = \Pi_e - b(U-U_n) + v \,$

This equation, plotting inflation rate Π against unemployment U gives the downward-sloping curve in the diagram that characterises the Phillips curve.