## More on the adaptive inflation expectations hypothesis

This post will be long, fairly wonky, and confused. I am typing, because I just have to stop playing with FRED and write something. My claim is that expected inflation over the next 5 (and 10 and 20) years is very similar to actual inflation over the past year. I think the data generally fit the crudest most mechanical adaptive expectations hypothesis.

This would be interesting for two reasons.

First, the adaptive expectations hypothesis has been treated with utter contempt for roughly 4 decades. It is considered an example of the sort of thing which economists must utterly reject. The effort to replace it has lead to a lot of mildly interesting math and highly implausible assumptions.

Second, there is a huge and very vigorous discussion of forward guidance by the Fed Open Market (FOMC) Committee. It has been argued that even when the Federal Funds rate is essentially zero, the FOMC can stimulate the economy by causing higher expected inflation. It is generally agreed that the FOMC has been convinced by this argument. I think this implies that there should be anonalous increases in expected inflation on the dates when the FOMC began to try to cause higher expected inflation — roughly the announcements of QE 1-4, operation twist and of forward guidance of how long it will keep the Federal Funds rate extremely low. An excellent fit of expected inflation using only lagged inflation creates serious difficulty for those who think the FOMC always could and finally has promoted higher expected inflation.

I think I will put the actual post after the jump.

I will show time series and scatter graphs of two time series one of which should be lagged inflation and one of which should correspong roughly to expected inflation. Here’s a graph before the reader gets too bored.

My variables for lagged inflation are the percent increase in the consumer price index (CPI) (blue) and CPI excluding food an energy (green). My variable for expected inflation is the 5 year constant maturity TIPS breakeven (in red explained below). Notably all three variables fluctuate, but the breakeven is usually between the two measures of past inflation or very near the closer of the two. The exception is during the total freakout late 2008 and early 2009.

I should stress that this is not all information available to market participants. The price indices are reported monthly. The price index for a month is reported during the next month. I will look at asset prices the month of the prices and not after the prices are reported. I think this is a minor problem, since the prices of ordinary goods and services are sticky and I am using changes over a full year. I did it because it is quick and easy.

My variable for expected inflation is the 5 year constant maturity TIPS breakeven. I have taken the monthly average of the daily series so the frequency is the same as the freequency of measured past inflation. It is the difference beteen the return on regular nominal treasuries which pay dollars in 5 years compared to the Fed staff’s estimate of the real 5 year return on Treasury inflation protected securities (TIPS) which pay a multiple of the CPI (that is are bonds indexed to the CPI). Both series are constructed by fitting a yield curve to the market prices of bonds. This is especially problematic for the TIPS real interest rate series, because there are rather few different TIPS. The 5 year constant maturity series involves some fairly heroic interpolation.

Fed staff (among others) stress that the TIPS breakeven is not equal to market particpants expected inflation. The reason is that regular nominal Treasuries are more liquid and their price includes a liquidity premium. The expected return on TIPS is generally higher, so the breakeven is general lower than expected inflation. During the period of total panic and desperate quest for ready cash or equivalent, the liquidity premium appears to have become huge. TIPS became very cheap compared to regular tresuries and the breakeven became negative. I don’t deal with this, but just consider the months of blind terror to be exceptional. I assume they were September 2008 through May 2009.

OK another graph. Here I use a weighted average of the two series for lagged inflation. The green line is

core CPI inflation times 0.75 plus CPI inflation times 0.25. The weight was chosen by eyeballing and trying to make the green line look like the red line.

I think the series are dramatically similar (except for the panic period late 2008 through early 2009).

To check more (I apologise for the graphs — I am having computer trouble and made them in excel) I look at the scatter. In the first scatter I have the 5 year constant maturity breakeven on the y axis and the weighted average past year inflation on the x axis. I have connected the dots to show that the ones with very low breakevens all occured at roughly the same time.

except for the 8 funny months (September 2008 through April 2009) that is an amazing scatter. I stress that it shouldn’t be that way — there is little useful information in the month to month fluctuations in inflation in the past 12 months. Also there is almost no room for the effects of QE and other forward guidance.

I can’t resist two more graphs. One shows the same variables for the period May 2009 through January 2013. The scatter is very compact. The slope is slightly under one. There does seem to be less impact of lagged inflation over 2% on expected inflation.

Now the graph which amazes me the most. This shows data from before the fall of the house of Lehman. This was during the great moderation. the Fed aimed roughly to target inflation at about 2% and keep unemployment pretty low. More importantly, it was generally believed that the Fed could achieve its aims. Yet the breakeven fluctuated with lagged inflation. The slope is again slightly under one (zero would correspond more closely to prevailing theory).

What if it is not expectations, but simply a reflection of current interest rate conditions, and FED actions? If you look at TIPS yields since they came out, the yield has followed the short rate trend down for the most part.

Right now the FED is flooding the system with reserves, which drives the short rate to ZERO. To keep rates at their target (25bps), they are paying interest on the reserves. If not, then reserve holders would try to get rid of the reserves they don’t need (banks would not hold reserves unless required to) – driving short rates to zero. TIPS to me, simply reflect this current condition, and maybe are not looking forward that far.

The very nature of TIPS is the inflation protection, which people are paying a premium for right now. So let’s say I want to collect some risk free interest. I could buy treasuries, or TIPS. But, interest rates are so low right now that any inflation, IF it reared its head, would quickly destroy my regular treasury holding. So why not collect a little less interest, maybe even negative, to park my money, and if the CPI trends to 6%, then I am protected.

Let me expand on this idea of expected inflation. Do bond investors really factor inflation a decade out in their purchase decisions? If that is the case why were 30 year treasury yields around 8% in 1990? Doesn’t that mean bond investors back then expected much higher inflation than we have experienced since 1990?

I think it does. There is, in fact, come useful information about future inflation rates in the long term yield curve (not that you couldn’t guess as well what inflation would be without looking at them but that a computer couldn’t guess as well).

But also the market clearing subjectively expected real interest rate varies. A 9% 30 year rate corresponds to expected inflation higher than 4%.

Higher yields on longer bonds definitely does not imply the average investor expects inflation to increase. There is a risk premium — the short term return on long term bonds is risky and it a lot of money is controlled by risk averse people with short time horizons.

Robert: I’m 58. I can (just) remember what it was like back in the olden days, when we used to use adaptive expectations.

The general formula was, IIRC:

Xe(t)-Xe(t-1)=B[X(t-1)-Xe(t-1)]

where 0

And I can distinctly remember thinking: “Hang on. Should X be interpreted as the price level, or as the rate of inflation? And why couldn’t B be greater than one, or less than zero?”

And I can remember puzzling over those questions, and not having any answers, and not seeing any way to go about answering them.

Thanks God for rational expectations, which gave me an answer to those questions. Because it told me to think about the data generating X, to see what assumptions about X and B would make sense, and not lead to people making obvious repeated mistakes.

The olden days, in that respect, really were the bad old days.

I expand on all that in this old post: http://worthwhile.typepad.com/worthwhile_canadian_initi/2010/07/rational-vs-adaptive-expectations-a-false-dichotomy.html

What you are doing here is much closer to rational expectations than what “adaptive expectations” used to mean in the olden days.

The equation solves out to expected x_t is a weighted average of lagged x with the weights declining exponentially in the lag.

My equation is expected inflation from t to t+5 is 0.8 or 0.9 times inflation in t-1. This is a cruder equation than adaptive expectations (but easier to do with FRED).

It has nothing to do with rational expectations (for one thing in my discussion I am imposing the coefficient of 1 not 0.8 to 0.9). If fits the data.

I think a rationally expectation of a variable which changes almost not at all (the 20 year breakeven) can’t have so much variance and apparent mean reversion.

I am defending adaptive expections as you knew them. I use yearly inflation not an exponential average of lagged monthly inflation for convenience.

Adaptive Inflation Expectations Hypothesis Minimizes Effectiveness of Fed Communication at ZLB

[…]Returning to Robert’s claim, I suspect the recent strong correlation between the previous year’s actual inflation and inflation expectations for the next 5 or 20 years is partially due to the lengthy period of low inflation that came prior. In other words, if inflation were to start trending higher or lower over an elongated period, I predict inflation expectations would lag actual inflation while moving in the same direction. The adaptive inflation expectations hypothesis will therefore still hold, only more years of recent data will need to be incorporated into expectations formation.[…]

[…] post too long. I have tried to avoid being rude (really) and see an earlier post for more recent data supporting the adaptive expectations […]