Stagflation

In the 1970s, many countries experienced high levels of both inflation and unemployment also known as stagflation. Theories based on the Phillips curve suggested that this would not occur, and the curve came under attack from a group of economists headed by Milton Friedman.^[7] Friedman argued that the Phillips curve relationship was only a short-run phenomenon. This followed eight years after Samuelson and Solow [1960] wrote "All of our discussion has been phrased in short-run terms, dealing with what might happen in the next few years. It would be wrong, though, to think that our Figure 2 menu that related obtainable price and unemployment behavior will maintain its same shape in the longer run. What we do in a policy way during the next few years might cause it to shift in a definite way."^[12] As Samuelson and Solow had argued 8 years earlier, Friedman said that in the long run, workers and employers will take inflation into account, resulting in employment contracts that increase pay at rates near anticipated inflation. Unemployment would then begin to rise back to its previous level, but with higher inflation. This implies that over the longer-run there is no trade-off between inflation and unemployment. This is significant because it implies that central banks should not set unemployment targets below the natural rate.^[5]

More recent research suggests that there is a moderate trade-off between low-levels of inflation and unemployment. Work by George Akerlof, William Dickens, and George Perry,^[16] implies that if inflation is reduced from two to zero percent, unemployment will be permanently increased by 1.5 percent because workers have a higher tolerance for real wage cuts than nominal ones. For example, a worker will more likely accept a wage increase of two percent when inflation is three percent, than a wage cut of one percent when the inflation rate is zero.

Modern application

U.S. inflation and unemployment 1/2000 to 8/2014

Most economists no longer use the Phillips curve in its original form because it was too simplistic.^[17] A cursory analysis of US inflation and unemployment data from 1953 to 1992 shows no single curve 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 do not group easily, and a more formal analysis posits up to five groups/curves over the period.^[5]

However, modified forms of the Phillips curve that take inflationary expectations into account remain influential. The theory has several names, with some variation in its details, but all modern versions distinguish between short-run and long-run effects on unemployment. Modern Phillips curve models include both a short-run Phillips Curve and a long-run Phillips Curve. This is because in the short run, there is generally an inverse relationship between inflation and the unemployment rate; as illustrated in the downward sloping short-run Phillips curve. In the long run, that relationship breaks down and the economy eventually returns to the natural rate of unemployment regardless of the inflation rate.^[18]

The "short-run Phillips curve" is also called the "expectations-augmented Phillips curve", since it shifts up when inflationary expectations rise, Edmund Phelps and Milton Friedman argued. In the long run, this implies that monetary policy cannot affect unemployment, which adjusts back to its "natural rate", also called the "NAIRU". The popular textbook of Blanchard gives a textbook presentation of the expectations-augmented Phillips curve.^[19]

An equation like the expectations-augmented Phillips curve also appears in many recent New Keynesian dynamic stochastic general equilibrium models. As Keynes mentioned: "A Government has to remember, however, that even if a tax is not prohibited it may be unprofitable, and that a medium, rather than an extreme, imposition will yield the greatest gain".^[20] In these macroeconomic models with sticky prices, there is a positive relation between the rate of inflation and the level of demand, and therefore a negative relation between the rate of inflation and the rate of unemployment. This relationship is often called the "New Keynesian Phillips curve". Like the expectations-augmented Phillips curve, the New Keynesian Phillips curve implies that increased inflation can lower unemployment temporarily, but cannot lower it permanently. Two influential papers that incorporate a New Keynesian Phillips curve are Clarida, Galí, and Gertler (1999),^[21] and Blanchard and Galí (2007).^[22]

The traditional Phillips curve

The original Phillips curve literature was not based on the unaided application of economic theory. Instead, it was based on empirical generalizations. After that, economists tried to develop theories that fit the data.

New classical version

The Phillips curve equation can be derived from the (short-run) Lucas aggregate supply function. The Lucas approach is very different from that of the traditional view. Instead of starting with empirical data, he started with a classical economic model following very simple economic principles.

Start with the aggregate supply function:

${\displaystyle Y=Y_{n}+a(P-P_{e})\,}$

where Y is log value of the actual output, ${\displaystyle Y_{n}}$ is log value of the "natural" level of output, ${\displaystyle a}$ is a positive constant, ${\displaystyle P}$ is log value of the actual price level, and ${\displaystyle P_{e}}$ is log value of the expected price level. Lucas assumes that ${\displaystyle Y_{n}}$ has a unique value.

Note that this equation indicates that when expectations of future inflation (or, more correctly, the future price level) are totally accurate, the last term drops out, so that actual output equals the so-called "natural" level of real GDP. This means that in the Lucas aggregate supply curve, the only reason why actual real GDP should deviate from potential—and the actual unemployment rate should deviate from the "natural" rate—is because of incorrect expectations of what is going to happen with prices in the future. (The idea has been expressed first by Keynes, General Theory, Chapter 20 section III paragraph 4).

This differs from other views of the Phillips curve, in which the failure to attain the "natural" level of output can be due to the imperfection or incompleteness of markets, the stickiness of prices, and the like. In the non-Lucas view, incorrect expectations can contribute to aggregate demand failure, but they are not the only cause. To the "new Classical" followers of Lucas, markets are presumed to be perfect and always attain equilibrium (given inflationary expectations).

We re-arrange the equation into:

${\displaystyle P=P_{e}+{\frac {Y-Y_{n}}{a}}}$

Next we add unexpected exogenous shocks to the world supply ${\displaystyle v}$:

${\displaystyle P=P_{e}+{\frac {Y-Y_{n}}{a}}+v}$

Subtracting last year's price levels ${\displaystyle P_{-1}}$ will give us inflation rates, because

${\displaystyle P-P_{-1}\ \approx \pi }$

and

${\displaystyle P_{e}-P_{-1}\ \approx \pi _{e}}$

where ${\displaystyle \pi }$ and ${\displaystyle \pi _{e}}$ 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

${\displaystyle {\frac {Y-Y_{n}}{a}}=-b(U-U_{n})}$

where ${\displaystyle b}$ is a positive constant, ${\displaystyle U}$ is unemployment, and ${\displaystyle U_{n}}$ is the natural rate of unemployment or NAIRU, we arrive at the final form of the short-run Phillips curve:

${\displaystyle \pi =\pi _{e}-b(U-U_{n})+v.}$

This equation, plotting inflation rate ${\displaystyle \pi }$ against unemployment ${\displaystyle U}$ gives the downward-sloping curve in the diagram that characterizes the Phillips curve.

New Keynesian version

The New Keynesian Phillips curve was originally derived by Roberts in 1995,^[23] and since been used in most state-of-the-art New Keynesian DSGE models like the one of Clarida, Galí, and Gertler (2000).^[24][25]

${\displaystyle \pi _{t}=\beta E_{t}[\pi _{t+1}]+\kappa y_{t}}$

where

${\displaystyle \kappa ={\frac {\alpha [1-(1-\alpha )\beta ]\phi }{1-\alpha }}.}$

The current expectations of next period's inflation are incorporated as ${\displaystyle \beta E_{t}[\pi _{t+1}]}$.

Gordon's triangle model

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

1. demand pull or short-term Phillips curve inflation,
2. cost push or supply shocks, and
3. built-in inflation.

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 Phillips curve 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:

1. 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.)
2. 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.