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Friday, 18 July 2014

Further thoughts on Phillips curves

In a post from a few days ago I looked at some recent evidence on Phillips curves, treating the Great Recession as a test case. I cast the discussion as a debate between rational and adaptive expectations. Neither is likely to be 100% right of course, but I suggested the evidence implied rational expectations were more right than adaptive. In this post I want to relate this to some other people’s work and discussion. (See also this post from Mark Thoma.)

The first issue is why look at just half a dozen years, in only a few countries. As I noted in the original post, when looking at CPI inflation there are many short term factors that may mislead. Another reason for excluding European countries which I did not mention is the impact of austerity driven higher VAT rates (and other similar taxes or administered prices), nicely documented by Klitgaard and Peck. Surely all this ‘noise’ is an excellent reason to look over a much longer time horizon?

One answer is given in this recent JEL paper by Mavroeidis, Plagborg-Møller and Stock. As Plagborg-Moller notes in an email to Mark Thoma: “Our meta-analysis finds that essentially any desired parameter estimates can be generated by some reasonable-sounding specification. That is, estimation of the NKPC is subject to enormous specification uncertainty. This is consistent with the range of estimates reported in the literature….traditional aggregate time series analysis is just not very informative about the nature of inflation dynamics.” This had been my reading based on work I’d seen.

This is often going to be the case with time series econometrics, particularly when key variables appear in the form of expectations. Faced with this, what economists often look for is some decisive and hopefully large event, where all the issues involving specification uncertainty can be sidelined or become second order. The Great Recession, for countries that did not suffer a second recession, might be just such an event. In earlier, milder recessions it was also much less clear what the monetary authority’s inflation target was (if it had one at all), and how credible it was.

How does what I did relate to recent discussions by Paul Krugman? Paul observes that recent observations look like a Phillips curve without any expected inflation term at all. He mentions various possible explanations for this, but of those the most obvious to me is that expectations have become anchored because of inflation targeting. This was one of the cases I considered in my earlier post: that agents always believed inflation would return to target next year. So in that sense Paul and I are talking about the same evidence.

Before discussing interpretation further, let me bring in a paper by Ball and Mazumder. This appears to come to completely the opposite conclusion to mine. They say “we show that the Great Recession provides fresh evidence against the New Keynesian Phillips curve with rational expectations”. I do not want to discuss the specific section of their paper where they draw that conclusion, because it involves just the kind of specification uncertainties that Mavroeidis et al discuss. Instead I will simply note that the Ball and Mazumder study had data up to 2010. We now have data up to 2013. In its most basic form, the contest between the two Phillips curves is whether underlying inflation is now higher or lower than in 2009 (see maths below). It is higher. So to rescue the adaptive expectations view, you have to argue that underlying inflation is actually lower now than in 2009. Maybe it is possible to do that, but I have not seen that done.

However it would be a big mistake to think that the Ball and Mazumder paper finds support for the adaptive expectations Friedman/Phelps Phillips curve. They too find clear evidence that expectations have become more and more anchored. So in this sense the evidence is all pointing in the same way.

So I suspect the main differences here come from interpretation. I’m happy to interpret anchoring as agents acting rationally as inflation targets have become established and credible, although I also agree that it is not the only possible interpretation (see Thomas Palley and this paper in particular). My interpretation suggests that the New Keynesian Phillips curve is a more sensible place to start from than the adaptive expectations Friedman/Phelps version. As this is the view implicitly taken by most mainstream academic macroeconomics, but using a methodology that does not ensure congruence with the data, I think it is useful to point out when the mainstream does have empirical support.

Some maths

Suppose the Phillips curve has the following form:

p(t) = E[p(t+1)] + a.y(t) + u(t)

where ‘p’ is inflation, E[..] is the expectations operator, ‘a’ is a positive parameter on the output gap ‘y’, and ‘u’ is an error term. We have two references cases:

Static expectations: E[p(t+1)] = p(t-1)

Rational expectations: E[p(t+1)] = p(t+1) + e(t+1)

where ‘e’ is the error on expectations of future inflation and is random. Some simple maths shows that under static expectations, negative output gaps are associated with falling inflation, while under rational expectations they are associated with rising inflation. If we agree that between 2009 and today we have had a series of negative output gaps, we just need to ask whether underlying inflation is now higher or lower than in 2009. 


  1. In my opinion, a somewhat mixed approach is probably best. Adaptive expectations are a rule-of.thumb for people who don't pay attention to the economy, who don't care, who don't have the patience or capability to read economic data. Rational expectations require a certain background knowledge. Financial institutions like banks, insurance companies and big international companies certainly have the necessary information and through them, rational expectations are transmitted to consumers. This setup might explain the above average volatility of investment as well as the nominal wage downward rigidity during crises.

    OF HISTORICAL EXPERIENCE by Robert J. Shiller February 1998 as one way out of what seems to be less of a problem (see Krugman blog July 23, 2013
    'The Death of High Inflation').

  3. I think that in your discussion of the evidence, the rational expectations hypothesis benefits very much from being the residual claimant. Basically, you note recent deviations from a simple model of autoregressive expectations. Given the choice between only two models, you may be right that, for the past 5 or 6 years the autoregressive model has fit US data very poorly.

    However, there are many possible stories about expectations. I would like to look at elicited expectations and, in particular,the median response in the U Michigan Ipsos/ Reuters survey of US consumers.

    First I note that the simple autoregressive model fits the data extraordinarily well. I may be ignorant, but I think that the performance of the simple autoregressive model is incomprarably superior to that of any DSGE model. Second I note this is a pre-Friedman paleo Keynesian model.

    Finally I admit that it fails at roughly sometime around January 20th 2009. However, the new pattern of expectations sure doesn't look like the REH. The survey median is not onlcy consistently higher than my guess based on lagged inflation (0.75% + 0.7*(lagged CPI inflation) but also consistently higher than the inflation the consumers were attempting to forecast. This looks to me like a gross rejection of the hypothesis that survey elicited forecasts are conditional means.

    The forecasts also do not correspond to a credible official inflation target. They are consstently higher than the official inflation target. To me the graph does not suggest that the rational expectations assumption is working OK. It seems to me to show complete detachment from reality.

    More thoughts on the graph here


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