Chapter 9 Mccallum Inflation and Unemployment
Chapter 9 McCallum Inflation and Unemployment
Introduction/Review
Recently, we have considered models in which output is fixed; we have instead focused attention on the dynamics of inflation.
Macroeconomics is concerned with business cycles, however, so we will return to that topic.
So far, we have just the Keynesian model to use when analyzing business cycle fluctuations.
Key assumptions of that model were (1) a fixed nominal wage and (2) non-market-clearing in the labor market.
When the price level rises, the real wage falls, firms demand and employ more labor and produce more output.
More on the Keynesian Model
The Keynesian model’s assumption of a fixed nominal wage is clearly not adequate (as our inflation models should make abundantly clear).
A simple fix-up might be proposed: Make the nominal wage pre-determined rather than exogenous. One could add an equation to explain the evolution of W over time, even if its value is fixed within a period.
The (Early) Phillips Curve
Phillips observed that the rate of change in wages was related to the unemployment rate over long periods in the U.K.
Phillips argued that unemployment could be taken as an indicator of the demand-supply disequilibrium status in the labor market, and argued that one would expect wages to rise when unemployment was low and to fall when unemployment was high.
Algebraically, this thought (and the empirical relationship) could be summarized:
,
where is the log of the nominal wage.
Note: this equation would provide a simple way to explain the changing level of the nominal wage from period to period in the Keynesian model.
If prices reflect a “markup” over wages, we should observe a similar relation between price inflation and unemployment.
See Fig. 9.4 in McCallum.
The Expectations Augmented Phillips Curve
The original Phillips curve had a conceptual flaw noted by Friedman and Phelps.
Actually, the change in thereal wage should be related to the unemployment rate:
But, one period ahead (when wages are set), has not been observed, so it needs to be replaced with an expectation.
Illustrate this with a diagram.
Explain what happens with monetary stimulus in this model (short run and long run).
Phillips Curves and the Keynesian Model, Again
Note that the Keynesian AS curve will shift with expected inflation.
When expectations are correct and the labor market is in complete demand-supply equilibrium, AS and AD will intersect at the same output level that was determined in the classical model. One can argue that the long run of the Keynesian model is compatible with the classical model.
Under this interpretation our old Keynesian model would also be consistent with the expectations augmented Phillips curve.
Lucas and Monetary Misperceptions
The expectations-augmented Phillips curve arguments were compatible with the assumption of adaptive expectations. Friedman specifically argued that adjustment to the long run could take years—this means business cycles could be prolonged.
If expectations are rational and markets clear, it is more difficult to develop models in which business cycles are important.
One important (conceptually, if not empirically) is Lucas’s model of monetary misperceptions, which does rely on the rational expectations assumption.
Lucas Model Assumptions
Lucas imagines that individuals observe prices of goods they produce quickly, but learn about the overall level of prices more slowly. In any period, individuals observe their own price, the “local” price, but only have an expectation about the general price level.
He also assumes that individuals will want to work and produce more when the relative price of their good (the good they produce) is high.
Example: After hurricanes, roofers will work more because the prices are firm in the roof repair market.
One twist in the Lucas model is that knowledge about my own price gives me some information about what is likely to be happening to the aggregate price level (depending on the historic sources of variability in the “local” and aggregate price levels).
Let z index one of many “local” markets. In equations:
Further,
(This is derived from more primitive assumptions in the Lucas paper).
So, output in market z is:
Averaging over all markets:
This is the Lucas aggregate supply curve. In some ways it is similar to the augmented Phillips curve model, although the underpinnings differ.
Chapter 9 Problem 3 has a more complete Lucas model.