06 The Phillips Curve

TOC

Inflation, Expected inflation and unemployment The Phillips curve and its mutations Inflation Expectations Phillips curve and natural rate of unemployment

Motivation:

Find the relationship between inflation and unemployment

Inflation, Expected inflation and unemployment

The wage determination equation:

The price determination equation:

Assume a specific form for

express the wage determination as:

replace in the price detemination equation to get:

That is the relation between the price level, the expected price level and the unemployment rate.

The equation holds for any period t:

Dividing both sides by

Note that and

Since we have defined expected inflation as:

Note that our definition of expected inflation implies that we know the price level of the previous period.

Replace both sides, we get

Dividing both sides by , we get

By approxiamting the left-hand-side, we get

( Approximation: )

Reorganising and assuming both sides are equal then

An increase in leads to an increase in

Given , an increase in , or an increase in , leads to an increase in

Given , a decrease in leads to an increase in

The Phillips curve and its mutations

Original Phillips curve

Assume that inflation varies from year to year around some value , it make sense for wage setters to expect and

This is the original Phillips curve. Since the expected inflation is constant, we should expect a negative relationship between unemployment and inflation.

However, the original relation vanished in the 1970s because wage setters changed the way they formed inflation expectations. And expectations that had been anchored (i.e. roughly constant) became de-anchored

Inflation Expectations

Define inflation expectations formally:

The higher the value of , the more people and companies will revise their expectations about what inflation will be in in the face of any change in the previous year’s inflation

Before the 70s, as inflation was not persistnet, people and companies ignored past inflation, thus is close to zero

After the 70s, as inflation increased and was persistent, they started to use information form previous years. By mid-70s, evidence suggests that was close to one

Replace inflation to the expression of inflation:

if , we get the original Phillips curve. If we get:

the inflation rate depends not only on the unemployment rate but also on last year’s inflation rate

Accelerationist Phillips curve

Assume , the relation becomes

which is called the accelerationist Phillips curve

The unemployment leads to a lower increase (decrease) of the inflation rate with respect to its previous year.

Lower unemployment leads to a lower decrease (increase) of the inflation rate with respect to its previous year.

Re-anchoring of expectations

In the 90s, the Phillips curve relation changed again because of a change in monetary policy. Many central banks increasingly emphasised their commitment to maintaining low and stable inflation. Many indicated that they would maintain inflation close to a given target, typically around 2%. If people and companies believe in the power of CBs to achieve this policy, even if inflation is different from the target in a given year, they may expect inflation to be constant around the target. And thus expectations that had been de-anchored became re-anchored again.

Note:

The Phillips curve relation is a relation between inflation, expected inflation and unemployment.

Relation between inflation and unemployment depends very much on how people form expectations

Phillips curve and natural rate of unemployment

Original Phillips curve: no such a thing as the natural rate of , it just reflect the a trade-off between inflation and unemployment: low inflation rate high unemployment

Recall that the natural rate of unemployment is the unemployment rate such that

Equivalently, the natural rate of unemployment is the unemployment rate such that

then , where we drop the time index because we assume that are constant

thus

The higher the mark-up () or the higher the factors that affect wage setting (z), the higher is the

The higher the sensitivity of inflation to the unemployment rate (), the lower is the

Since

thus

so we can express the relationship as:

If is equal to , then will be equal to

If is below , then will be higher than

If is above , then will be lower than

We can use this expression to roughly estimate the natural rate of unemployment.

For example, if we take the PC estimation from the period 1970-1995 in which , so is obtained when