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I will assume that unemployment is a function of actual inflation minus expected inflation. I will also assume that people are smart enough that no policy will cause them to make forecast errors of the same sign period after period after period.
Friedman's conclusion follows if there is the additional assumption that expected inflation is a constant plus a linear function of lagged inflation. In this case, unless the coefficients sum to one and the constant is zero, it is possible to cause a constant non zero forecast error. It can't be that people are dumb enough to stick with a constant plus a linear function with coefficients that sum to anything but one if that rule is exploited to make surprise inflation always always positive.
However, I know of no one who ever wrote that such a simple model of expectations is the truth. Rather some people including Cagan, Friedman, Tobin, and Solow asserted that something like that is a useful approximation at some times in some places. Many authors expressed belief in a more complicated story in which inflation expecttions are anchored if inflation is low and variable but not anchored if inflation is high and/or steady.
I think such expectations can be modelled either as a result of boundedly rational learning with hypothesis testing or ration Bayesian updating. I will try to do so (famous last words of this post which sensible readers will read).
The monetary authority will, in fact, stick to a simple rule (but agents do *not* know that the rule never changes). It can target inflation and is tempted to trick firms into supplying more than they would under perfect foresight by setting actual inflation higher than expected inflation. I will assume that perfect inflation forecasting causes unemployment to be 5%. This is the non accelerating inflation rate of unemployment. Unemployment is linear in the inflation expectations error so the long term average unemployment is equal to the long term average expectations error.
The simple rule may be stochastic with targets based on coins flipped and dice rolled etc in secret. The monetary authority wants low unemployment and low inflation.
The question is can the long term average unemployment rate be lower than 5%
First bounded rationality with hypothesis testing. The bounded rationality is forecasting with a simple rule which might included parameters estimated by OLS on old data of. In the very simplest rule expected inflation is 2% no matter what. The hypothesis testing part is it is assumed that forecasting rules are ordered from a firwt rule to a second etc. When agents use rule n they also test the null that rule n gives optimal forecasts against the alternative that rule n+1 gives better forecasts. The switch to rule n+1 if the null is rejected a the 5% level (as always this can be any level and as always I choose 5% because everyone does). I will assume that rules are also ordered so if rule n gives persistent underestimates of future inflation, rule n+1 gives higher forecasts.
Forecasting rule 1 is forecast inflation equals 2%. Rule 2 is forecast inflation is equal to a constant estimated by OLS. Rule 3 is forecast inflation is equal to an estimated constant plus an estimated coefficient times lagged inflation. Rule 4 is a regression on two lags of inflation. the series of rules goes on to infinity always adding more and more parameters to be estimated, and includes the actual inflation rule (the monetary policy rule for this silly model).
Friedmans story about accelerating inflation at 3% unemployment works in this model. Rule 2 is flexible enough for his example. If inflation is higher than forecast inflation by a constant, the estimated constant term in the regression grows without bound.
A key necessary assumption is that agents never accumulate more than a finite amount of data about the Monetary authority. A sensible way of putting this is that learning about the Fed Open Market Committee restarts each time a new Fed chairman is appointed. To make things not too easy for myself, I assume that once agents pass from rule 1 to rule 2 they stick with it using all data to estimate parameters. The data used to test the current rule against the next one are only those accumulated with the current chairman. I will assume Chairmen are replaced at known fixed intervals of say 100 periods of time.
Fed open market committe members know all this. They can set inflation so the 2% forecast rule is never rejected against the estimated constant. The optimal strategy will be mixed, that is they will randomize inflation so it isn't too easy to learn what the best estimated constant is. I will assume they set inflation equal to a constant plus a mean zero white noise disturbance term (to be clear the expected value of the random term conditional on lagged information is always zero)
Clearly FOMCs can achieve set inflation to be 2.000001% plus a mean 0 variance 1 constant term without getting caught before the chairman's term expires. This means that the long run average unemployment rate can be less than the NAIRU. This means that there is a long run tradeoff between average unemployment and average inflation.
update: we have a winner so the offer immediately below has expired.
if anyone has read this far, please tell me in comments and I will praise you to the sky in a new post]
Friedman's argument can be true, unemployment can depend only on expectation errors and there can be a long run inflation unemployment tradeoff. There is a big difference between trying to achieve constant unemployment lower than the NAIRU and trying to achieve average unemployment lower than the NAIRU. Friedman also implicitly assumed that the monetary authority never changes and is known to never change.
Basically his implicit assumption is either the Fed can set unemployment to any constant or there is a natural rate. This doesn't follow for many many reasons. I just described one.
OK I talked about Bayesian learning. This post is already way too long. The idea about Bayesian is we start with a prior with a huge mass at inflation is 2% plus a mean zero disturbance term. Then there are positive prior probabilities on a huge variety of other models. However all of the other models have time varying coefficients which follow random walks. This means that the forecast conditional on belief in model N depends on parameters estimated with exponentially weighted lagged data. This means that given the 2.0000001% plus noise rule, the ratio of the likelihood for those models to the likelihood with the 2% plus noise model doesn't growth without bound. This means that the posterior keeps a huge mass on 2% and there is a long run tradeoff between long run average unemployment and long run average inflation.
I disagree 0.1% with Wren-Lewis (I object to his use of the word "need") and about 0.01% with Kling who suggests a claim about what was necessary without quite making it.
Now I cut and paste an over long comment with which I polluted Kling's comment thread. I do not recommend reading the same old same old. I seriously considered posting this to my hard drive (but not my trash can -- I'm a word horder).
Thanks for the link. I think that you and Wren-Lewis agree 100%.
The 0.1% is that I think Friedman's story (in which backward looking expectations were pretty explicit) is sufficient to explain stagflation in the USA in the 1970 but not necessary. I think the pre-Friedman and contra Friedman Keynesians could fit the facts too.
[this "comment" has become much too long for a comments thread. The rest is over here]
My now old tired argument is that a model in which expected inflation is a constant plus 0.5 times lagged inflation fits the 1970s US data fine, but implies a long term inflation unemployment tradeoff and does not imply acceleration.
The model is obviously not the truth and not just because all models are false by definition. We can be sure it isn't a true claim about expectations by introspection, that is a thought experiment. No one can believe that after a thousand years of exactly 10% inflation year after year, expected future inflation will be 5%. I know of no evidence that anyone ever believed any such thing (although I'm sure someone somewhere did, because tinfoil hats).
It was obvious to prominent Keynesians (I am thinking of Solow and Tobin) that the one lag autoregressive expectations model wasn't the truth. It is also obvious that in around 1970 and 1971, they thought something like it was an approximation useful to US policy makers. This view seems to me to be supported by US aggregate data through 1980 (and through 2014). I think that Friedman's position is that Keynesians should not be allowed to use friedman's methodology of positive economics and their claim that an equation was useful there and then must be interpreted as a claim that it is a universal truth. If that was his view, he was much more generoust to Solow Samuelson and Tobin than well to get personal I ever was in the 20th century (and at least the first 10 years of the 21st). I believed that they believed in a Phillips curve with no expectations term at all. I was clearly totally wrong.
As I note from time to time to time to time, it was standard to include price inflation in estimates of the Phillips relation from say Phillips's second paper on the topic on. There was a debate which can be translated into contemporary econospeak as "in around 1970, Solow believed that US inflation expectations (unlike Latin American inflation expectations) were anchored."
This doesn't mean that he predicted that they would remain anchored. Like Keynes, he clearly and definitely said that the relationship between inflation and real variables was not stable and that they decoupled given high inflation.
Solow's position was very explicitly that inflation expectations are sometimes anchored and sometimes not. So high or steady inflation is eventually reflected one for one in expectations, but low and variable inflation isn't (so the average forecast error can increase in the average inflation rate). I think that this is very devinitely the view currently expressed by, among others, Ben Bernanke, Janet Yellen and Narayana Kocherlakota. I also think it is consistent with the evidence. In any case, it is the current view of many top status economists, who remember the 1970s as we do, and is the standard view among monetary policy makers.
For example, I just noticed this
In this Economic Letter, we focus on two simple extensions that are potentially important to the current inflation outlook.note especially "Cogley, Timothy, Giorgio E. Primiceri, and Thomas J. Sargent. 2010. “Inflation-Gap Persistence in the U.S.” American Economic Journal: Macroeconomics 2(1), pp. 43–69 (which I haven't read).
The first extension incorporates anchored inflation expectations with the constraint that long-run inflation eventually returns to the Fed’s inflation target of 2% (see Williams 2006, Stock and Watson 2010, and Cogley, Primiceri, and Sargent 2010).
The semi new point I would like to make here is that Solow's position is entirely consistent with the argument Friedmans AEA presidential address. Friedman discussed only the case of a FOMC which set a very low unemployment target (3% IIRC). If one accepts his assertion that this would lead to accelerating inflation (as I do) nothing much follows. It doesn't follow that the Fed can't stabilize. It doesn't follow that the Fed can't cause long term average unemployment to be lower or higher (within limits).
It is an example which makes it clear that belief in an expectations unaugmented Phillips curve is unreasonable. Almost nobody ever believed in an expectations unaugmented Phillips curve. Samuelson and Solow definitely did not. Hicks made an argument almost identical to Friedman's in 1967. http://www.economics.ox.ac.uk/materials/working_papers/paper399.pdf
I think the key event was the spread of the strange belief that Samuelson, Solow et al believed in an expectations unaugmented Phillips curve. It was believed by, well for example, Robert Waldmann that looking at the data they saw a pattern and just decided to assume it was a structural relationship. I think that this strange delusion (about what Samuelson and Solow thought) was extremely influential exactly because they were famously brilliant economists. Also they and especially Samuelson were top figures in the formalization of economic theory, so a perceived error by Samuelson due to insufficient respect for theory was shocking. The take home lesson was that you better not trust data without formal theory -- that looking at data and thinking in English could lead very smart people to think very stupid things.
I don't know exactly when or how the strange delusion about old Keynsians began. It is certainly expressed in Friedman's Nobel lecture (in which he doesn't name his straw Keynesians).
Tnis all means I agree with Krugman about the role of Friedman Phelps and stagflation in causing the rational expectations revolution. However I also think that incorrect beliefs about what people who disagreed with Friedman said were crucial too.