The Phillips Curve• Empirical relationship between inflation and unemployment.• Derivation of Phillips Curve.• The natural rate.• Determining expectations: the accelerationist Phillips curve.Phillips Curve• Aggregate supply:P(t) = (1+ µµµµ )P(t)e(1- αααα u(t)+z)• Divide by Pt-1:P(t) /P(t-1) = (1+µµµµ) P(t)e/ P(t-1) (1- αααα u(t)+z)• Approximate as:ππππ(t) = ππππe(t) + (µµµµ+z) - αααα u(t)The Phillips Curve and The Natural Rate of Unemploymentππππ (t) = ππππ (t) => u = (µµµµ+z)ααααππππ(t) = ππππ (t) - αααα (u(t) - u )enneExpectations• Reasonable way to compute expected inflation: some function of past inflation.• Suppose ππππe(t) = a ππππ(t-1)•Ifa = 0, we haveππππ(t) = - αααα (u(t)-un)In this case, inflation and unemployment are inversely related.•Ifa = 1, we haveππππ(t)- ππππ(t-1) = - αααα (u(t)-un)In this case, the change in inflation and unemployment are inversely related.Expectations over time• Prior to 1970, inflation was on average zero and a=0 was a reasonable approximation.• 1970-2000: inflation rose steadily throughout 70’s. Expected inflation is now better approximated using last period’s inflation (a=1).Expectations-augmented Phillips Curve• We can write the expectations-augmented Phillips curve as: ππππ(t)- ππππ(t-1) = - αααα (u(t)-un)• Implications:– If u(t)>un, inflation is decreasing.– If u(t)< un, inflation is increasing.NAIRU• When u(t)=unwe have ππππ(t)=ππππ(t-1)• The natural rate of unemployment is the rate of unemployment at which the inflation rate is not changing and the price level is not accelerating.• We call this unemployment rate the NAIRU (Non-accelerating-inflation-rate of unemployment).Changes in the natural rate:•Since un = (µ+z)/α , changes in labor market conditions over time may lead to changes in the natural rate.• Cross-country differences in labor market policies also imply cross-country differences in the natural rate of unemployment.• Europe and U.S. both have relatively stable inflation but Europe has higher unemployment –this implies Europe has a higher natural rate of unemployment.Wage indexation• Suppose a fraction b of wage contracts are indexed to current inflation. In this case the Phillips curve is:ππππ(t) = bππππ(t) +(1-b)ππππ (t) - αααα (u(t)-un)• Again suppose ππππ (t) = ππππ(t-1)• Solving we obtain:ππππ(t)- ππππ(t-1) = - (αααα/(1-b)) (u(t)-un)• Wage indexation increases the slope of the Phillips curve: a 1 percentage point increase in unemployment above the natural rate implies a (αααα/(1-b)) percentage point reduction in the rate of inflation.Summary:• If unemployment is above (below) the natural rate the expectations-augmented Phillips curve implies that inflation is increasing (decreasing).• When unemployment equals the natural rate of unemployment (NAIRU), inflation is stable.• Cross-country variation in labor market policies and conditions implies cross-country variation in the natural rate of
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