{"id":1838,"date":"2008-02-22T21:29:47","date_gmt":"2008-02-23T01:29:47","guid":{"rendered":"http:\/\/www.prefblog.com\/?p=1838"},"modified":"2008-02-22T21:29:47","modified_gmt":"2008-02-23T01:29:47","slug":"inflation-expections","status":"publish","type":"post","link":"https:\/\/prefblog.com\/?p=1838","title":{"rendered":"Inflation Expectations"},"content":{"rendered":"

I\u00a0once heard an\u00a0explanation of why economics is termed “the dismal science”.\u00a0It’s because, you see, you can spend\u00a0ten years of your life, full-time, working on a particular model of something … capturing inputs,\u00a0backtesting sensitivity, creating theoretically acceptable models of transmission mechanisms … and finally, finally, have something that looks really good.<\/p>\n

You walk down the street, show it to the first guy you meet, he says\u00a0“What about taxes?”<\/p>\n

You say “Oh …. bugger!” and go back to your office for another ten years.\u00a0<\/p>\n

Inflation talk is all the rage now and the following paragraph by James Hamilton<\/a> on Econbrowser<\/em> caught my eye:<\/p>\n

Greg Ip<\/a>, Felix Salmon<\/a> and Greg Mankiw<\/a> 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<\/a> and particularly Francisco Torralba<\/a> 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.<\/p><\/blockquote>\n

Well, let’s have a look at some fresh data<\/a>:<\/p>\n

\n\n\n\n\n\n\n
Fed H.15 Data, Feb 20, 2008<\/td>\n<\/tr>\n
Term<\/td>\nNominal<\/td>\nTIPS<\/td>\nBreakeven
\nRate<\/td>\n<\/tr>\n
5-Year<\/td>\n3.02%<\/td>\n0.77%<\/td>\n2.25%<\/td>\n<\/tr>\n
10-Year<\/td>\n3.93%<\/td>\n1.55%<\/td>\n2.38%<\/td>\n<\/tr>\n
5\/5 Breakeven (Approx.: 2*2.38-2.25)<\/td>\n2.51%<\/td>\n<\/tr>\n<\/table>\n<\/div>\n

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<\/a>. 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:<\/p>\n

\n\n\n\n\n\n\n
Time Series of 5\/5 BE Rate Approx<\/td>\n<\/tr>\n
Date<\/td>\n5-Year BE<\/td>\n10-Year BE<\/td>\n5\/5 BE<\/td>\nEffective
\nFed Funds\u00a0<\/td>\n		2-Year
\nNominal\u00a0<\/td>\n<\/tr>\n
Jan 9<\/td>\n2.16%<\/td>\n2.25%<\/td>\n2.35%<\/td>\n\u00a04.26%<\/td>\n\u00a02.69%<\/td>\n<\/tr>\n
Jan 30<\/td>\n2.12%<\/td>\n2.33%<\/td>\n2.54%<\/td>\n\u00a03.26%<\/td>\n\u00a02.30%<\/td>\n<\/tr>\n
Feb 20<\/td>\n2.25%<\/td>\n2.38%<\/td>\n2.51%<\/td>\n\u00a03.00%<\/td>\n\u00a02.14%<\/td>\n<\/tr>\n<\/table>\n<\/div>\n

I snuck two extra columns into the time-series because they’re important. The 2-Year Nominal is generally accepted<\/a> as being the market expectation<\/a> 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?)<\/p>\n

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.<\/p>\n

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\u00a0get 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<\/a> apply as well.<\/p>\n

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

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<\/em> 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.<\/p>\n

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.<\/p>\n

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<\/a> of 3%.<\/p>\n

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\u00a0 resolves to an output gap of 5.6%.<\/p>\n

Assume that potential real GDP growth is 3%<\/a>.<\/p>\n

We conclude that one of the following must be true:<\/p>\n