# Varieties of Phillips Curves

As one might have guessed from my previous post, I am skeptical of the use of the Phillips curve for generating predictions. One reason that I am skeptical is because I’m not entirely sure about the direction of causality between output and inflation. (The original Phillips curve was concerned with the relationship between unemployment and wage inflation. The present discussion of Phillips curves follows the contemporary literature in referencing the relationship between output and inflation.) Once again, the source of disagreement can be found in the differences between the New Keynesian and Monetarist literature.

The New Keynesian Phillips Curve

As discussed previously the New Keynesian Phillips curve is derived based on the assumption that prices are sticky. Specifically, one of two assumptions is made. First, it is assumed that only a subset of firms are capable of adjusting their prices in any given period (literally, assuming the can opener). The second alternative assumption is that it is costly to adjust prices. Based on these types of assumptions, the NK Phillips curve is given by:

$\pi_t = \beta E_t \pi_{t + 1} + by_t$

where $\pi$ is the rate of inflation, $\beta$ is the discount factor, $E$ is the expectations operator, $y$ is the output gap, and $b$ is a parameter.

The NK Phillips curve essentially implies that inflation is determined by “excess capacity.” When output is below potential, this exerts negative influence on the inflation rate. (This is why you often even commentators on financial news networks say that they don’t anticipate inflation given the excess capacity in the economy.) However, when output is above potential there is upward pressure on inflation. Regardless, the causation in the NK Phillips curve runs from output to inflation.

The Monetarist Phillips Curve

Long before A.W. Phillips plotted his curve, Irving Fisher had discovered the statistical relationship between employment and inflation (International Labour Review, 1926). Fisher identified the statistical relationship and made the following claim regarding causation:

“But as the economic analysis already cited certainly indicates a causal relationship between inflation and employment or deflation and unemployment, it seems reasonable to conclude that what the charts show is largely, if not mostly, a genuine and straightforward causal relationship; that the ups and downs of employment are the effects, in large measure, of the rises and falls of prices, due in turn to the inflation and deflation of money and credit.”

In other words, Fisher saw the direction of causation as going in the opposite direction as New Keynesians; inflation was causing fluctuations in employment.

This Fisherian view of the Phillips curve was embraced by Milton Friedman and fellow Old Monetarists under the accelerationist hypothesis. In Friedman’s 1967 address to the American Economic Association, he details a relationship between the unemployment and inflation with causation running from the latter to the former. Friedman hypothesized that the only way that a central bank would be able to achieve an unemployment target below the “natural rate of unemployment” was through accelerated increases in the rate of inflation. Again, this is in contrast to the NK Phillips curve.

New Monetarists have much the same view as Old Monetarists, however, the conclusions depend on the level of information and monetary policy. For example, suppose that there are two type of individuals, buyers and sellers. Assume that money growth is stochastic. For simplicity assume that money growth is either “high” or “low”. There are two periods of analysis. Increases in the money supply take place in the second period. Now suppose that buyers know in the first period if money growth will be high or low. Sellers do not have this knowledge. In addition, define the value of money as:

$\phi_t = {{\phi_{t - 1}}\over{\mu_t}}$

where $\mu$ is the rate of money growth and $\phi_t$ is the value of money. It follows that when money growth is high the value of money is lower than when money growth is low. Thus, since buyers know about the state of money growth prior to the sellers, they will seek to spend more of their money balances when money growth is high than when it is low. Put differently, increases in money growth causes higher rates of inflation and a higher level of production. This is the basic Fisherian view of the Phillips curve.

The central bank could remove the uncertainty surrounding money growth by simply announcing and committing to a money growth target. However, since buyers no longer have the informational advantage, the positive correlation between inflation and output disappears. In fact, the higher rate of money growth implies that the cost associated with holding money rises thereby causing buyers to economize on money balances and reducing consumption. (This is the insight of the Friedman rule and the discussion of the optimal quantity of money.) Thus, when money growth is known with certainty, there is a negative relationship between inflation and output.

So Why Do We Care?

The reason that we care about the varieties of Phillips curves is because they provide vastly different implications. The New Keynesian Phillips curve implies that inflation is, in part, caused by the relationship between output and potential. So long as output is below potential, this exerts negative pressure on inflation.

The Monetarist view is in direct contrast to NK Phillips curve. Rather than output exerting a causal influence on inflation, the causation is reversed. However, even this conclusion has been shown in recent years to be dependent upon the structure of information available to different economic agents about monetary policy. If all agents are perfectly informed as to policy, the relationship between inflation and output is negative.

These views provide non-trivial differences in prescriptions for policy.

### 5 responses to “Varieties of Phillips Curves”

1. A quick brown

2. Alda Dorsay

Thx for information.

3. Inflation is neither the cause or result of unemployment. Rather both are simultaneous consequence of increased aggregate demand.