One way for central banks to gauge long-term inflation expectations is to look at the \(n\)-year-forward, \(m\)-year-ahead expected inflation rate. For instance, the two-year-forward, three-year-ahead expected inflation is the expected change of prices two years from now, over the following three years. As of December 2014, that would be the inflation rate expected in Dec. 2016, over the 2017-2019 period.

Central banks like these forward measures because they eliminate--or at least diminish--the influence of short-term inflation inflation expectations.

One data source for the construction of such forward measures are surveys of forecasters. The ECB Survey of Professional Forecasters asks participants for their inflation outlook over the next year, the next two years, and the next five years. Using those overlapping horizons one can infer the forward expected inflation rate from this equation:

$$(1+\pi _{0,5}^{e})^{5}=(1+\pi _{0,2}^{e})^{2} (1+\pi _{2,3}^{e})^{3}, $$
where \({\pi}_{n,m}^{e}\) is the annual rate of inflation expected \(n\) years from now, over the next \(m\) years. The forward inflation rate we're interested in is the second term on the right-hand side.

Likewise,

$$(1+\pi _{0,2}^{e})^{2}=(1+\pi _{0,1}^{e}) (1+\pi _{1,1}^{e}), $$
So
$$(1+\pi _{0,5}^{e})^{5}=(1+\pi _{0,1}^{e}) (1+\pi _{1,1}^{e}) (1+\pi _{2,3}^{e})^{3} $$
If you estimate the forward expected inflation rates this way and plot the time series, this is what you get:

I am surprised to see that, despite much talk of deflation and falling inflation expectations, the inflation expectations that matter most (the long-run, forward rate, in green) is firmly glued slightly above 2%. The intermediate forward rate (i.e. one-year-forward, one-year-ahead) has declined moderately over the past year from 2% to 1.7%. The only inflation expectation that has dropped dramatically is the short-term rate (inflation expected over the next year), which is now close to 1%, down from 1.5% a year ago, and 1.9% two years ago.

This undermines the case for quantitative easing in Europe. Granted, the ECB might be looking at other measures of inflation expectations (i.e. inflation compensation from nominal and inflation-linked bonds, inflation swap rates, consumer surveys of inflation expectations, etc.) And the ECB might also be worried, besides inflation expectations, about credit growth, output growth, etc.

P.S. By the way, the formulas above were written thanks to the Mathjax tool for Blogger. With Mathjax added to your blog, you can type formulas as you would with LaTex. And if you are not fluent in LaTex, this website is helpful. You just type in your formulas, with the help of some buttons, and it produces the LaTex code for you.

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