Long-Run Phillips Curve
What is Long-Run Phillips Curve?
The long-run Phillips curve is vertical at the natural rate of unemployment, showing no permanent trade-off between inflation and unemployment.
In the long run, expectations adjust, so trying to push unemployment below the natural rate only raises inflation. It corresponds to long-run aggregate supply at potential output. Only supply-side changes can shift it.
Long-Run Phillips Curve: a worked example
An economy has a natural rate of unemployment of 5 percent and sits there with inflation at 2 percent, a point on both the long run Phillips curve and the short run curve drawn for 2 percent expected inflation. Expansionary policy pushes actual unemployment down to 3 percent, and inflation rises to 6 percent as the economy slides up the short run curve. Workers then bargain for raises that match the 6 percent they now expect, firm costs rise, and the short run curve shifts up. Unemployment returns to 5 percent while inflation stays at 6 percent. Compare the starting and ending points. Unemployment is 5 percent both times, and inflation is 4 percentage points higher, 6 minus 2. Both points sit on the same vertical long run Phillips curve at 5 percent unemployment.
The mistake students make with long-run phillips curve
Reading the vertical line as full employment in the everyday sense. A point on the long run Phillips curve still leaves 5 percent of the labor force out of work in this example, because the natural rate includes frictional unemployment from people between jobs and structural unemployment from mismatched skills. What disappears at the natural rate is cyclical unemployment, the part tied to the business cycle. Students who treat the long run curve as a zero unemployment line then cannot explain why a government would ever fund retraining or job matching programs.
Long-Run Phillips Curve questions
Why is the long-run Phillips curve vertical?
The long run Phillips curve is vertical because expectations eventually catch up to whatever inflation rate policy delivers. Once workers and firms build 6 percent inflation into wage contracts and price lists, the real wage returns to where it started and hiring returns to normal, leaving unemployment back at the natural rate. Any inflation rate is therefore compatible with the same unemployment rate in the long run, which draws as a vertical line at the natural rate.
What shifts the long-run Phillips curve?
Only a change in the natural rate of unemployment shifts it. Better job matching services, retraining that cuts structural unemployment, or a demographic shift toward workers who change jobs less often can pull the natural rate down and move the curve left. Anything that raises frictional or structural unemployment moves it right. Expected inflation is the one thing that does not shift it. A jump in expected inflation moves the short run curve up instead, leaving the long run curve exactly where it was.
How does the long-run Phillips curve relate to long-run aggregate supply?
The long run Phillips curve is the labor market view of long run aggregate supply. Both are vertical, one at the natural rate of unemployment and one at potential output, and both say the economy settles at the same real position whatever the price level does. A labor market improvement that lowers the natural rate shifts the long run Phillips curve left and long run aggregate supply right at once. Capital deepening can raise potential output without touching the natural rate, so the two do not always move together.
Formula / Example
This is the live Phillips Curve sandbox. Drag the curves, or open the full version.
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