# Inflation Expectations

Whereas our forecast of the price level relies on Federal Open Market Committee (FOMC) member projections, one can also assess the likely magnitude of future price increases by looking at bond markets. Bond traders must form expectations of inflation when deciding what they are willing to pay or accept for a bond. If bond traders overestimate inflation, bond buyers will tend to gain at the expense of bond sellers. If bond traders underestimate inflation, bond sellers will tend to gain at the expense of bond buyers. Since neither buyers nor sellers want to lose on a transaction, they have a strong incentive to estimate inflation accurately. What do their trades imply about the expected rate of inflation?

Using the Fisher equation and interest rates on traditional Treasuries and Treasury inflation-protected securities (TIPS), we can estimate the expected annual inflation implied by bond prices. The Fisher equation states that i = r + E(π), where i is the nominal interest rate, r is the real (or, inflation-adjusted) interest rate, and E(π) is expected inflation. Rearranging, we get the formula E(π) = i - r.

Traditional Treasuries promise to pay a specified dollar amount at some point in the future. TIPS, in contrast, adjust the future payment based on the changes in the consumer price index (CPI). These assets have the same issuer, meaning there is no difference in issuer risk, and can be considered for a given maturity date, meaning there is no difference in duration risk. There is a small difference in inflation risk, but otherwise these assets are identical.

Given the similarities between these two assets outlined above, we use the interest rate on traditional Treasuries as a measure of the nominal interest rate and the interest rate on TIPS as a measure of the real interest rate. Hence, expected inflation can be estimated by subtracting the TIPS rate from the traditional Treasuries rate. The Federal Reserve refers to this implied market expectation of inflation as the breakeven inflation rate. Others call it the TIPS spread.

Recall that TIPS are adjusted for inflation using the CPI. Hence, the TIPS spread measures the implied market expectation of CPI inflation. Our preferred measure of inflation––and the measure used throughout this report––is the personal consumption expenditures price index (PCEPI). Since CPI inflation usually exceeds PCEPI inflation, the TIPS spread likely overstates expected PCEPI inflation.

In order to estimate expected PCEPI inflation, we adjust the TIPS spread by the average difference between CPI and the PCEPI inflation. More formally, E(π_PCEPI) = TIPS spread - (π_CPI - π_PCEPI).

From January 2010 to January 2020, CPI inflation averaged 1.8 percent. PCEPI inflation averaged 1.6 percent. The average difference between CPI and PCEPI inflation was 0.2 percentage points. Thus, our estimate of expected PCEPI inflation subtracts 20 basis points from the TIPS spread.

As noted above, there is a small difference in the inflation risk associated with traditional Treasuries and TIPS. If inflation differs from what was expected when the asset was purchased, someone holding traditional Treasuries will gain or lose while someone holding TIPS will see the final payment they receive adjusted for inflation. Hence, traditional Treasuries are associated with additional risk.

Since the interest rate on traditional Treasuries reflects the additional inflation risk of traditional Treasuries, expected inflation is likely lower than our estimates suggest. The risk that actual inflation will deviate significantly from what is expected is widely thought to be very low. Hence, the upward bias in our estimates is probably very small. As such, we acknowledge but make no effort to correct for this bias.

We present the expected average annual PCEPI inflation rates over the five- and ten-year horizons above.