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Phelps (1967) and Friedman (1968) defined the natural rate of unemployment.

Friedman did it in words:
"At any moment of time, there is some level of unemployment which has the property that it is consistent with equilibrium in the structure of real wage rates. At that level of unemployment, real wage rates are tending on the average to rise at a 'normal' secular rate, i.e., at a rate that can be infinitely maintained so long as capital formation, technological improvements, ect., remain on their long--run trends. A lower level of unemployment is an indication that there is excess demand for labor that will produce upward pressure on real wages. A higher level of unemployment is an indication that there is excess supply of labor that will produce downward pressure on real wage rates. The 'natural rate of unemployment', in other words, is the level that would be ground out by the Walrasian system of general equilibrium equations, provided there is imbedded in them the acutal structural characteristics of the labor and commodity markets, including market imperfection, stochastic variability in demands and supplies, the cost of gathering information about job vacancies and labor availabilities,
the cost of mobility, and so on."
Friedman tried to link the natural rate to the Walrasian system. Thinking about this more technically this could mean that the natural rate of unemployment is caused by imperfect competition in the labor market.

Phelps did it in terms of the augmented Phillips curve:

Δpt = f(ut)+ pet - pt-1

where pt is the price level at time t, ut is the unemployment rate at time t, and pet is the expected price level in period t formed at time t-1.

After some time (and a long thought which is described in Phelps (1995)) Phelps arrived at the following Phillips curve:

Δwt = f(ut)+wet - wt-1

where wt is the money wage.

Here, the story goes as follows: The unemployment rate might move to so low a level that, to moderate the associated quit rate, every firm wants to offer its employees a better real wage as an inducement not to quit with such readiness; but as alle firms pass along the implied money wage increase, the price level increases in proportion, an increase that is unexpected; to keep the unemployment rate down, there must be a succession of such wage increases and hence continually unexpected inflation-- greater than whatever rate was expected.

In other words, the quit rate of employees is a decreasing function (an idea which leads to the new Keynesian "efficient-wage hypothesis" by Yellen (1984)) of firm's relative wage. For simplicity, only the relative wage and the unemployment rate determine the quit rate. The striking idea is now that un (the equilibrium steady state unemployment rate) is such that f(un)=0 and un > 0.

Now look at the natural rate of unemployment without considering monetary policy. Looking at Friedman's statement, the natural rate is an equilibrium of imperfect competition.

In this sense the natural rate of unemployment requires this: A steady-state (Nash) equilibrium. The steady-state assumption was already mentioned by Phelps. Why do we need this assumption? Basically one needs a fixed number of workers (employed or unemployed) and vacancies (unfilled or filled). There are other labor market inflow specifications which are more complicated. Closely related to this labor market inflow specification is the following labor market paradoxon, which is not understood or recognized by many (including all politicians): Rising number of employment and the one hand and rising unemployment rate on the other hand.

For example, this fact has been observed in Austria since 2000.

This paradoxon can be simply explained if we look at the inflow into the labor market. Besides unemployed and employed workers there is third group namley people who are "out of the labor force" meaning that they currently have no job and moreover do not receive unemployment benefits (hence are not regarded as unemployed). If such people enter the labor market (filling a vacancy) employment rise but on the other hand some workers are laid off which influences the unemployment rate.

The natural rate is a (Nash) equilibrium, since imperfect competition, assuming that agents behave somehow strategically, requires a non-cooperative solution concept. But in such models we are usually confronted with the problem of multiplicity of equilibria. Well, this is mainly a problem for interpreting the natural rate(s). Here, I don't want to mention stability of refinement issues, which partly determine the convergence behavior since behind any equilibrium concept there is an implicit dynamic process.

related items:
Today's Nobel Prize in Economics, Mahalanobis

References:
Phelps, Edmund S. 1967. "Phillips Curves, Expectations of Inflation and Optimal Unemployment Over Time," Economica, Vol. 34, No. 135, (August), pp. 254-281
Friedman, Milton, 1968, "The Role of Monetary Policy", AER, Vol. 58, No. 1, (March), pp. 1-17
Yellen, Janet L., 1984, "Efficiency Wage Models of Unemployment", AER, Vol. 74, No. 2 (May), pp. 200-205.
Phelps, Edmund S. 1995, "The origins and further development of the natural rate of unemployment", Cambridge University Press, Chapter 2, pp. 15-31

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