Inflation Expectations

I once heard an explanation of why economics is termed “the dismal science”. It’s because, you see, you can spend ten years of your life, full-time, working on a particular model of something … capturing inputs, backtesting sensitivity, creating theoretically acceptable models of transmission mechanisms … and finally, finally, have something that looks really good.

You walk down the street, show it to the first guy you meet, he says “What about taxes?”

You say “Oh …. bugger!” and go back to your office for another ten years. 

Inflation talk is all the rage now and the following paragraph by James Hamilton on Econbrowser caught my eye:

Greg Ip, Felix Salmon and Greg Mankiw are concerned that the 5-year TIPS-nominal spread has fallen relative to the 10 year, implying that the 5-year forward inflation rate (the so-called 5-year, 5-year break-even rate) has gone up. But I agree with the analysis by knzn and particularly Francisco Torralba that the facts are much less alarming than Ip’s graph might have seemed to suggest, and that the basic impression of stability of longer term expectations that one brings away from the graph I’ve plotted above is the correct one.

Well, let’s have a look at some fresh data:

Fed H.15 Data, Feb 20, 2008
Term Nominal TIPS Breakeven
5-Year 3.02% 0.77% 2.25%
10-Year 3.93% 1.55% 2.38%
5/5 Breakeven (Approx.: 2*2.38-2.25) 2.51%

So, as of February 20, the 5/5 Breakeven rate was (approximately) 2.51%, which is basically what it was on January 30, according to knzn. So far, so good: we’re getting a relatively constant number for the 5/5 BE. However, compare the data further with knzn’s calculations:

Time Series of 5/5 BE Rate Approx
Date 5-Year BE 10-Year BE 5/5 BE Effective
Fed Funds 
Jan 9 2.16% 2.25% 2.35%  4.26%  2.69%
Jan 30 2.12% 2.33% 2.54%  3.26%  2.30%
Feb 20 2.25% 2.38% 2.51%  3.00%  2.14%

I snuck two extra columns into the time-series because they’re important. The 2-Year Nominal is generally accepted as being the market expectation of the average Fed-Funds rate through the period. (I had a quick look for some research regarding just how good a predictor it is, but didn’t see anything. Somebody must have created the spreadsheet at some time! Come on, now! Let’s see a scatter plot of 2-Year Nominal Treasury Yields vs. two-years-following cumulative Fed Fund returns! Anybody?)

Anyway … it seems to me that if we’re to take the 5/5 BE rate as an estimate of inflation expectations, then we are assuming that the market is rational. And if the market is rational, then the two-year Treasury must also be a rational estimate of Fed Funds expectations. So right off the bat, we see that the estimate of 2.5% inflation from 2013-18 is dependent upon a pretty low Fed Funds rate over the next two years.

It should be noted that the argument developed here is very, very approximate. There is a liquidity premium that should be accounted for with investments of different terms (and isn’t); there are segmentation effects (only a few institutions can get the Fed Funds rate directly; anybody can buy a treasury); there are preferred habitat effects (some players will not switch between reals and nominals no matter how many fancy graphs you show them). All of the other caveats noted by Francisco Torralba apply as well.

OK, be patient, I’m getting to the point! As noted on Econbrowser Taylor has used coefficients of 0.5 for output and 1.5 for inflation to determine appropriate policy responses to deviations from ideal conditions.

OK, now here’s where my argument starts getting a little hairy! We will assume that the change in CPI is zero. Based on recent observations, we can be pretty sure inflation is not declining; the argument in Econbrowser that inspired this post is that expectations haven’t changed, either. The hairy part of this is that inflation expectations five years out are not the same thing as currently measured (trailing) inflation and they’re not the same thing as expectations for next year, either! It’s fairly difficult to refute an argument that inflation is expected to do … something … for the next year and then return to normal (due to wise actions by the omniscient Fed) in time for 5/5 BE to be unchanged too.

But I’m making an argument about the consistency of economic models here, so we’ll assume that the (simplified) theory presented here is accurate: there is an expectation that inflation will increase by 20bp over the next five years. The appropriate policy response, therefore (based solely on the inflation term) is to increase Fed Funds 30bp.

But Fed Funds have not been increased by 30bp … they’ve been dropped 125bp. The difference between these two figures, 155bp, must (if we are to assume perfection of our models AND perfection of Fed policy) be due to a Taylor response to the output term, which has a coefficient of 0.5. This only resolves if we have an output gap of 3%.

The situation gets worse if we consider the two-year note to be a good predictor of Fed Funds under the expectations hypothesis: the yield is now 2.14% (it’s been sub-2% recently) so let’s add a tiny term/liquidity/segmentation premium and say the market expects Fed Funds to be 2.00% for the forseeable future, which is a drop of about 2.5% from mid-January, which  resolves to an output gap of 5.6%.

Assume that potential real GDP growth is 3%.

We conclude that one of the following must be true:

  • Inflation expectations have in fact increased far beyond that shown by the simple model, or
  • The two-year note yield is not an reliable forecast of average Fed Funds, or
  • The Taylor rule has stopped working, or
  • Simple models are not capturing all the interelationships, or 
  • We’re going to have one hell of a recession … maybe a depression.

My bet is that both of the first two potential explanations are correct, with maybe a small contribution from natural scatter in Taylor Rule explanations. But I’ll bet a whole lot more on the idea that these models being discussed are just plain too damn simple.

And my point is … the markets are not just lacking in omniscience, they’re lacking in rationality. Don’t take the signals too seriously, or spend too much time obsessing over understanding what it’s trying to tell you.

Addendum: I will note, as I did on February 7 that the 5-year corrected market-derived inflation expectations measure is most certainly not flat:

The Cleveland Fed has updated its estimate of inflation expectations from TIPS … very interesting indeed. The breakeven rate is increasing slightly, but the analytical rate – which attempts to incorporate adjustments for the inflation-risk-premium and liquidity-premium – is skyrocketting. This epsiode [sic] will be very useful in determining the validity of these adjustments!

Presumably, a similarly derived correction to the 5/5 BE will have roughly the same size as the correction to the 5-BE. But I don’t know that for sure.

Also, note that segmentation plays a really strong role in some aspects of some markets. I’ll bet there are lots of players who would love to try on the arbitrage of long Fed-Funds / short 2-Year notes … but either can’t, or are scared of the rather special risks of shorting short Treasuries.

6 Responses to “Inflation Expectations”

  1. madequota says:

    This is another very in-depth analysis.

    One point you should always factor in is this: the Fed is by default, hawkish. Regional fed drones like Lacker, Poole, Fisher, and Yellen will always . . . always . . . interpret the economic situation in favour of raising rates. To them, inflation exists . . . even when the numbers say it doesn’t exist. Inflation must be fought . . . forever. It’s in their blood.

    Intelligent, well thought out situation analyses sometimes take second place.

    btw, what is an “Inflation Expection”?!


  2. jiHymas says:

    madequota – an Inflation Expectation is simply … er … the expectation of inflation. It will be reflected in, for instance, the wage hikes demanded by labour and the rate of interest demanded by investors.

    The long end of the yield curve is very sensitive to inflation expectations, while the short end trades off monetary policy. These are related, but not always similar, influences.

    For instance, a monetary policy far looser than the market likes would decrease short term rates (if fed funds are at 0.25% and expected to stay there, a one year T-Bill looks like a bargain at 1%) while increasing long term rates (if these fed funds at 0.25% are going to create inflation of 10%, who would buy a 30-year treasury yielding less than 15%?).

  3. madequota says:

    *smiling* actually, I know . . . I was just making a light hearted reference to the typo in your article’s heading: Inflation “Expections”!

    Happy budget day!


  4. jiHymas says:

    Eeep! Headline is fixed now.

    And a very happy budget day to you, madequota!

  5. […] In a recent post about Inflation Expectations, I opined that the only way I could see to make the market data on Fed Funds and Treasuries consistent was to assume that expectations (of both the market and the Fed) were for an output gap of 5.6% … which is a shockingly fierce recession and, given that the data indicate a period of two years plus, would be labelled a depression by many. So I don’t really have any quarrels with Professor Hamilton’s deduction that the Fed is “worried that a recession in the present instance would precipitate major financial instability”; with, I presume, the major financial instability feeding back into the real economy until we find ourselves all naked and homeless. […]

  6. […] As Accrued Interest points out, Treasury yields are being driven by fear, with investors piling into government guaranteed debt for the simple reason that they want to protect their capital. TIPS are simply maintaining a spread to nominals – an increasing spread, to be sure; inflation fears are part of the picture as I have previously discussed, but to ascribe the entire move to this is … boneheaded. Sorry folks, I just can’t think of any other word. […]

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