Thanks for the link. That's a very interesting paper. But it doesn't describe the model the Cleveland Fed was using prior to the 2008 crisis. Rather, it is a new model that some staff members are advocating. In particular they want to use the inflation expectations inherent in inflation swaps instead of TIPs to measure expected inflation (and real yields).
I must say that I hadn't heard of inflation swaps (essentially forward contracts on inflation) until now. But then I lead a very sheltered life.
Anyway, their main claim is that expected inflation calculated from inflation swaps is a better measure than that calculated from TIPs data. They support their claim in part by comparisons to surveys of expected inflation held by real humans.
A major problem with TIPs data is that it includes all sorts of things, such as liquidity premia. From page 18 of their paper:
Use of data on TIPS yields is problematic not only for the recent financial crisis. Studies by Sack and Elsasser (2004), Shen (2006), and D’Amico, Kim, and Wei (2008) reveal that the TIPS breakeven inflation rate consistently fell below survey measures of inflation expectations and that TIPS yields contain a liquidity premium that, in the time period prior to 2004, was unreasonably large and difficult to account for in any rational pricing framework. Shen (2006) finds evidence of a drop in the liquidity premium on TIPS around 2004 that he attributes to the U.S. Treasury’s greater issuance of TIPS around that time, as well as to the beginning of exchange traded funds that purchased TIPS. This accumulated evidence on the distortions to TIPS yields led us to employ inflation swap rates and survey inflation forecasts as a more reliable reflection of real yields and expected inflation.
They have this very interesting conclusion:
Comparing our model prices of inflation-indexed bonds to those of Treasury Inflation Protected Securities (TIPS) suggests that TIPS were
significantly underpriced prior to 2004 and again during the 2008-2009 financial crisis.
I had reached the same conclusion as regards Canadian RRBs, by intuition rather than by learned models. It's the main reason why I loaded up on RRBs at the end of 2008.
I gave up here
Consider a discrete time environment with multiple periods, each of length ∆t measured in years. Let Mt be the nominal pricing kernel with dynamics Mt+∆t Mt = e−it∆t−12P4j=1 φ2jh2j,t∆t−P4j=1 φjhj,t√∆tj,t+∆t
That's the equation of a generalized Weiner process, with four factors driving volatility instead of the usual single factor. The math is pretty heavy (although not for this type of literature). But it hardly gets used in the empirical part -- you can just skip over it.
George