The (??) Natural Rate of Unemployment

Milton Friedman defined the natural rate of unemployment, also known as the Non-Accelerating Inflation Rate of Unemployment (NAIRU), at least at the level of abstraction of this post:

"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 embedded in them the actual structural characteristics of the labor and commodity markets." -- Milton Friedman (1968), as quoted in James K. Galbraith (1998)

Two mathematical mistakes are embedded in the above definition.

First, what does Friedman mean by the "Walrasian system"? At the time of his statement, the Arrow-Debreu model of intertemporal equilibrium was becoming the canonical statement of general equilibrium theory. But the Arrow-Debreu model is a very short run model, in which the initial quantities of capital equipment are among the given endowments. Consequently, a solution to the model yields neither a rate of employment nor a rate of unemployment, independent of time. Rather, these rates are time-varying. So he cannot mean to refer to that model.

Now, Walras himself presented a model with given quantities of capital goods and a supposed steady state set of prices and quantities. But this model was just logically inconsistent. In consistent long-run economic models the set of capital goods are found by solving the model, not taken as givens. Thus, the logic of such models is not about allocating given resources among alternative ends. To refer to such a model as "the Walrasian system of general equilibrium" is dubious.

Second, Friedman's definition relies on an implicit mathematical theorem: that the equilibrium solution of whatever model he is talking about is unique. But no reason exists for such a theorem to hold in either the Arrow-Debreu model or a long run equilibrium model with many markets. I have myself created a model with multiple equilibria.

Here, then, is another example of right-leaning economists giving decades of policy advice based on theoretical claims with no support in economic theory. Unsurprisingly, the policy did not work empirically either, as can be seen by looking at results in the 1980s and 1990s. (These claims are not new. James Galbraith made my second point long ago.)

Have mainstream economists ever addressed this failure? Did they not mostly just continue their mistake with Dynamic Stochastic General Equilibrium (DSGE) models?

References

• Milton Friedman (1968) "The Role of Monetary Policy", American Economic Review Papers and Proceedings (May): pp. 1-17
• James K. Galbraith (1998) Created Unequal: The Crisis in American Pay, The Free Press.