Summary
Derives the Phillips Curve from the wage-setting and price-setting equations, linking inflation to unemployment. Anchored vs. de-anchored expectations explain different historical regimes (pre-70s, stagflation era, post-Volcker). The curve can be rewritten in terms of deviations from the natural rate.
Recall the wage-setting and price-setting equations:
Assume a linear functional form for :
Combine all of them to solve for :
Notice that this means rises as drops. What happens if we divide by last year’s prices?
Note that
So that:
Take logs on both sides and use the approximation for small to get the Phillips Curve:
Inflation decreases as unemployment increases because real wages decrease. The parameter captures the sensitivity of inflation to labor market slack.
Inflation Expectations and History
We used to assume (anchored expectations). This worked until the late 60s. However, expected inflation became de-anchored when we had oil shocks in the 70s. Suppose
We used to have , but during the 70s and 80s, it went close to 1, during which
This is a relation in the change in inflation versus the level of unemployment. This is sometimes referred to as the accelerationist Phillips Curve, because keeping unemployment below causes inflation to accelerate over time rather than just stay high.
Thankfully, by the 1990s, the Fed had largely brought down inflation back to normal levels through tight monetary policy, re-anchoring inflation expectations and restoring .
The Phillips Curve and the Natural Rate
Suppose (medium-run equilibrium). Replacing into the Phillips Curve, inflation drops out and we recover the natural rate of unemployment:
This is the same we derived from the labor market, now from a different angle. Replacing back into the Phillips Curve:
Inflation is above expectations when (the economy is running hot) and below expectations when (slack in the labor market). This form is what we carry into The IS-LM-PC Model.