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On the P curve discussion. To try to clarify semantics, and what I think the discussion is about.
I take ``belief in the Phillips curve’’ to mean ``belief that there is a positive relation, however complex and shifting, between inflation and activity.”
It does not mean that one believes in the NK version (I do not), nor that the natural rate of unemployment is constant (I do not), or that it is independent of the interest rate (I believe the dependence is marginal), or that there is no hysteresis (I believe there is some).
I then think of the Phillips curve as the logical implication of three propositions:
First that there is a wage relation, determining nominal wages as a function of actual and expected prices, and all the factors that may affect wage setting. I think of one of the main factors as the unemployment rate, but it is not the only one.
Second that there is a price relation, determining nominal prices as a function of actual and expected nominal costs, and all the factors that affect product market competition. Macroeconomists used to think of markups as stable. Recent evidence suggests otherwise.
Third, that there are nominal rigidities, in wage determination and/or in price determination. These imply that the wage and price relations, rather than determining real wages and unemployment, determine price inflation, wage inflation, and unemployment.
These relations are the wage and price Phillips curves. They are relations between endogenous variables, and thus there may indeed be a need to use instrumental variable techniques to uncover the causal relations.
All three relations are complex and have changed over time. Things are not however as bad as asserted by Farmer, Cochrane, and others. Look at the relation between wage inflation and unemployment for the euro zone or for Germany, from Kalantzis.
Yet, identifying the relevant factors in each one is difficult. Achieving identification is equally difficult (this is why I find cross-region evidence---as opposed to the time series evidence---more convincing). And, yes, policy makers must take the uncertainty into account.
But this does not mean that one can ignore them and replace them by a belief equation.
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