Special Treasury Bonds Can Help Gauge Expected Inflation

April 01, 2004

Treasury inflation-indexed securities (TIIS) are good measures for expected inflation, but they aren't perfect because they don't take cumulative deflation into account. To better understand this, let's consider how we'd calculate expected inflation from a hypothetical 10-year zero-coupon TIIS and a similar 10-year conventional bond. (A zero-coupon bond pays a single principal payment, rather than a series of smaller payments [coupons] plus a principal payment.)

Suppose that the bond market considers that there are two possible outcomes for inflation over the next 10 years:

  1. there's a 90 percent chance that cumulative inflation will equal 2 percent;
  2. there's a 10 percent chance that cumulative inflation will equal -1 percent (deflation).

In such a situation, the market's true expectation of inflation will be 1.7 percent (0.9 x 0.02 + 0.1 x (-.01)). But because the principal payments on the TIIS are not reduced if there is deflation, the TIIS spread will equal 1.8 percent (0.9 x 0.02 + 0.1 x 0). In other words, when there is a possibility of cumulative deflation until maturity, the TIIS spread will tend to overstate expected inflation. And greater probabilities of deflation will increase this bias.

The probability of a cumulative fall in the U.S. Consumer Price Index over 10 years is probably very small, however; so, the bias is probably small. In fact, there has been no cumulative CPI deflation in any G-7 country during any 10-year period since 1960. The smallest such 10-year CPI increase is 1.6 percent, recorded in Japan from 1992 to 2002.

Because the probability of substantial cumulative deflation over 10 years is negligible, TIIS spreads are probably good measures of expected inflation. Even if the bias itself is large, if the probability of cumulative deflation over 10 years doesn't change much, changes in the TIIS spread will still measure changes in expected inflation.

Views expressed in Regional Economist are not necessarily those of the St. Louis Fed or Federal Reserve System.

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