Monday, March 19, 2012

Weird Econometrics (TIPS)

The TIPS spread is the interest rate spread between a regular treasury and the corresponding inflation protected treasury.  It functions as a measure of expected inflation, and I was curious about its specific mechanisms. Especially since the theory forms the basis of a cornerstone of the NGDP targeting utopia, it seemed important to look into the effectiveness of TIPS at estimating inflation.

I downloaded the monthly TIPS spread data, as well as the monthly percent change CPI data from FRED.  From the monthly percent change CPI, I calculated the average annual inflation from each month to the month 5 years in the future.  The data is plotted on the xy-scatter below.

The x-axis is the 5-year TIPS spread for a given month, and the y-axis is the actual average inflation over the course of the next five years.  The FRED data on the TIPS spread only starts in January 2003, and since I wanted inflation over the next five years after each month, the CPI data could only give five year future average inflation up to March 2007.  Excel calculates the trendline to be y=-0.8105x + 4.4188, with the 95% confidence interval on the slope as (-1.03553, -0.5854) and a 95% confidence interval on the intercept as (3.894, 4.944).  Thus, a one percent increase in the TIPS spread in a month predicts a -0.81 percentage point drop in the actual average inflation over the future five year period.  This is a very peculiar given the TIPS spread is used as such a common tool to describe inflation expectations, especially by a certain market monetarist who uses them to tell his stories.

At first glance, this seems to reject rational expectations.  Rational expectations predicts a regression equation with a slope of approximately 1 and a small intercept, as future inflation should always be fully predicted in the TIPS spread.  Yet, in the data, one sees a negative slope, with an intercept that's actually relatively large.

However, the expectations hypothesis can still be salvaged from the Sumnerian perspective of having to take the policy regime into account.  One could interpret the negative relationship as expectations in an inflation targeting regime: when expected inflation is low, future actual inflation is higher; when expected inflation is high, future actual inflation is lower, all because the Fed takes the forecast into account and adjusts accordingly.

With this analysis, we could approximate the inflation target.  Wherever the Fed target is, it should lie on the line y=x, where the expectation is the actual inflation.  At that point, the Fed is "satisfied" with what inflation is forecasted to be, and therefore sees no reason to change it with policy.   For the mean parameter values for the regression, this intersection is at about 2.44% inflation.  With the various values in the confidence interval, the target can also range from 1.91% to 3.11%.  These values seem reasonable for the Federal Reserve's legacy of flexible inflation targeting.

Even after this analysis, a wrinkle persists; why do markets consistently predict lower inflation rates that in actuality?  Based on this graph, there seems to be an arbitrage opportunity.  As soon as the TIPS spread goes above the critical value of 2.44, actual inflation will likely be lower.   As soon as the TIPS spread goes below 2.44, actual inflation will likely be higher.  Perhaps this anomaly will be washed out with more data.  The time period analyzed was less than 5 years, which may not have been enough for the market to learn, especially given that the 5-Year bonds bought at the beginning of the period had not matured yet by the end.

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