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. 

Has the Great Recession killed the traditional Phillips Curve?

Before the New Classical revolution there was the Friedman/Phelps Phillips Curve (FPPC), which said that current inflation depended on some measure of the output/unemployment gap and the expected value of current inflation (with a unit coefficient). Expectations of inflation were modelled as some function of past inflation (e.g. adaptive expectations) - at its simplest just one lag in inflation. Therefore in practice inflation depended on lagged inflation and the output gap.

After the New Classical revolution came the New Keynesian Phillips Curve (NKPC), which had current inflation depending on some measure of the output/unemployment gap and the expected value of inflation in the next period. If this was combined with adaptive expectations, it would amount to much the same thing as the FPPC, but instead it was normally combined with rational expectations, where agents made their best guess at what inflation would be next period using all relevant information. This would include past inflation, but it would include other things as well, like prospects for output and any official inflation target.

Which better describes the data? The great attraction of the FPPC is that it can describe stagflation. We have a boom, which while it lasts steadily raises inflation. When the boom comes to an end, inflation stabilises, but at a much higher level than it began. So policy has to engineer a recession to get inflation back down again: a period in which above average unemployment is accompanied by above average inflation, which we call stagflation. If over this period we had had credible independent central banks setting inflation targets, the NKPC would not give us stagflation: when the boom came to an end, inflation would return to target. (For more explanation, see this post.) The trouble is we did not have inflation targeting during this period, so it is difficult to tell whether stagflation is evidence against the NKPC. (As an example of this ambiguity, see this survey of the empirical evidence by Nason and Smith. This enabled Robert Gordon to be quite supportive of the FPPC in 2009.)

The Great Recession could provide a much better test. In some countries output fell sharply in 2009, but has since seen a slow but steady recovery, such that the output gap today is less than it was in 2009. With the FPPC, inflation should have been steadily falling over this period, reaching its lowest level today. So if we plotted the output gap (x axis) and inflation (y axis) together, we should see a line pointing South East. With the NKPC, we can consider two polar cases. In the first, agents fully anticipate that the recovery will be slow, so we will get a sharp immediate fall in inflation, but subsequently inflation will rise towards the target. That will give us a line pointing North East. In the second, agents keep thinking inflation will return to target next year. That also gives us a line pointing North East, but it is flatter. [Postscript - I should have added that this last gives us what Krugman calls the Neo-paleo-Keynesian Phillips curve.]

Here is this plot for four countries, using OECD estimates for the output gap on the horizontal axis, consumer price inflation less 2% on the vertical axis, and OECD forecasts for 2014 and 2015. I’ve chosen these countries simply because in most of Europe we had a double dip recession, which is a more complicated experiment. If you do not like the idea of including forecasts, just ignore the last two points for each country.

The lines point North East, not South East. This gives more support to the rational expectations NKPC than the adaptive expectations FPPC. To take just one example, US inflation in 2013 is higher than it was in 2009, which is consistent with the NKPC. The traditional FPPC, on the other hand, would suggest that after a string of negative output gaps, US inflation should be a lot lower in 2013 than it was in 2009.

OK, now the caveats. Commodity prices will have an important influence on the CPI, and these are not part of either simple Phillips curve story. They may help explain the blip in inflation around 2011 in some countries, but they also helped depress inflation in 2009. Exchange rate changes will also matter. The simple Phillips curve also takes no account of non-linearity caused by a reluctance to cut nominal wages. And of course estimates of the output gap may be wrong.

In the case of Japan, we also had a recent increase in the inflation target. This may explain the forecast upward shift in inflation in 2014/5. If it does, that is clear evidence in favour of rational rather than adaptive expectations. 

All these caveats point to the need to do more empirical analysis. Nevertheless we can see why some more elaborate studies (like this for the US) can claim that recent inflation experience is consistent with the NKPC. It seems much more difficult to square this experience with the traditional adaptive expectations Phillips curve. As I suggested at the beginning, this is really a test of whether rational expectations is a better description of reality than adaptive expectations. But I know the conclusion I draw from the data will upset some people, so I look forward to a more sophisticated empirical analysis showing why I’m wrong.