Consumer price index (CPI) inflation hit a multi-decade high of 5 percent in May 2021 (12-month change), sparking considerable speculation as to how long inflation will remain high. Readings from the bond market suggest inflation will drop all the way to the Federal Reserve’s 2 percent target in 2022, whereas economic forecasters see continued above-target inflation of around 2.5 percent. The bond market has been somewhat better than economists at predicting inflation over a one-to-two-year horizon, suggesting a return to 2 percent inflation next year. However, neither bond markets nor economists have a great track record at forecasting inflation, so more persistent inflation cannot be ruled out.
Previous posts (here and here) showed that long-term bond yields and long-term inflation compensation derived from bond yields are not good predictors of future inflation. Another post showed that economic forecasters are better at predicting inflation than consumers, but that neither group is especially accurate. This post compares the predictive accuracy of bond markets and economists over both short-term and long-term horizons. It finds that although short-term inflation compensation from bond yields has slightly better predictive accuracy than economists’ projections, economists are actually better at long-term forecasting.
Figure 1 displays the ten-year bond yield, ten-year inflation compensation (data start in 1999), ten-year ahead inflation expectations of economic forecasters, and CPI inflation averaged ten years into the future to line up inflation outcomes with their predicted values. The inflation averages end in 2011 because there are not ten years of future data after that point. The graph is split into two panels to magnify changes in the data after 2000, when inflation and inflation forecasts were relatively stable over time. Bond yields, inflation compensation, and economists’ forecasts all miss most of the fluctuations in future long-term inflation.
Figure 2 displays the one-year bond yield, two-year inflation compensation, one-year ahead inflation expectations of economic forecasters, and average CPI inflation over the following year. Bond yields, inflation compensation, and economists’ forecasts all miss most of the fluctuations in future short-term inflation, but inflation compensation may capture a bit more of the swings than the other measures.
Table 1 displays regressions of inflation calculated over different horizons on lagged inflation compensation and economists’ forecasts. Each regression also includes lagged four-quarter inflation. In each column, the lags are equal in length to the length of the period over which inflation is averaged. Thus, a five-year average of inflation is regressed on variables that are lagged by five years. The regressions also include a lagged dummy variable to control for unusual market conditions during the Global Financial Crisis. The dummy is set to 1 in 2008Q4 and 2009Q1 and 0 in other periods. The figures show large outliers in inflation compensation in these quarters. Including a control for these outliers allows for a larger and more statistically significant estimate of the predictive power of inflation compensation for future inflation.
Columns 1 and 2 show that two-year inflation compensation has positive and strongly significant coefficients, whereas economists’ one-year forecasts have negative and insignificant coefficients. The overall predictive power is rather low, however, as indicated by adjusted R2 statistics far below 1. Columns 3 and 4 show that the coefficients on five-year and ten-year inflation compensation have the wrong sign, with the ten-year coefficient being statistically significant. The coefficients on economists’ long-term forecasts have the correct sign and are strongly significant. The adjusted R2 of 0.35 indicates moderate predictive power.
One drawback of inflation compensation is that it is available only since 1999, a period in which inflation has been relatively stable. Table 2 presents information on a cruder measure of bond market inflation expectations, the bond yield, going back to 1981. As in table 1, table 2 displays regressions of inflation calculated over different horizons on lagged bond yields, lagged economists’ forecasts, and lagged four-quarter inflation. The regressions do not include a dummy variable, as bond yields do not have outliers comparable to those of inflation compensation.
Column 1 shows that neither the one-year yield nor economists’ one-year forecast has a significant coefficient. Column 2 again shows no significant coefficient on the two-year yield and one-year forecast, but the coefficient on the forecast is considerably larger than that on the yield and is nearly significant at the 10 percent level. Despite the lack of statistical significance, the overall predictive power is moderate, as indicated by an adjusted R2 statistic of 0.43. Column 3 again finds no significant coefficients on the five-year yield and long-term economists’ forecast, but both coefficients are positive and the coefficient on economists’ forecasts is large and nearly significant at the 10 percent level. The adjusted R2 of 0.66 indicates moderate predictive power. Column 4 displays similar coefficients as column 3, but now the coefficient on economists’ forecasts is statistically significant. Predictive power is quite high, with an adjusted R2 of 0.86.
The apparently strong predictive power of economists’ forecasts in table 2 is mainly derived from the years before 2000, when both inflation and forecasts of inflation were trending downward. As shown in table 1, which focuses on the years since 1999, predictive power of economists’ forecasts is at best moderate and limited to longer horizons.
|Table 1 Regressions of inflation on lagged inflation compensation and professional forecaster survey expectations|
|1-year inflation||2-year inflation||5-year inflation||10-year inflation|
|Lagged 1-year inflation||-0.29||-0.17||-0.09||-0.01|
|Lagged 2-year inflation compensation||1.07**||0.69*|
|Lagged 5-year inflation compensation||-0.25|
|Lagged 10-year inflation compensation||-0.57**|
|Lagged 1-year-ahead inflation forecasts||-0.34||-0.45|
|Lagged 10-year-ahead inflation forecasts||3.11**||1.87**|
|Lagged dummy variable||3.54**||2.01*||-0.98||-1.05**|
|Note: Variables are lagged four quarters when regressing one-year inflation, eight quarters when regressing two-year inflation, twenty quarters when regressing five-year inflation, and forty quarters when regressing ten-year inflation. The first column uses quarterly observations from 2000Q1 to 2021Q1, the second column from 2001Q1 to 2021Q1, the third column from 2004Q1 to 2021Q1, and the fourth column from 2009Q1 to 2021Q1. Newey-West standard errors in parentheses. The ** and * symbols denote significance at 1 and 5 percent levels, respectively.|
|Sources: Authors’ calculations using data from Federal Reserve Bank of Philadelphia Survey of Professional Forecasters; and Federal Reserve Board and US Bureau of Labor Statistics via Macrobond.|
|Table 2 Regressions of inflation on lagged bond yields and professional forecaster survey expectations|
|1-year inflation||2-year inflation||5-year inflation||10-year inflation|
|Lagged 1-year inflation||-0.12||-0.17||-0.13**||-0.09**|
|Lagged 1-year bond yield||0.17|
|Lagged 2-year bond yield||0.09|
|Lagged 5-year bond yield||0.12|
|Lagged 10-year bond yield||0.11|
|Lagged 1-year-ahead inflation forecasts||0.29||0.50|
|Lagged 10-year-ahead inflation forecasts||0.29||0.28*|
|Note: Variables are lagged four quarters when regressing one-year inflation, eight quarters when regressing two-year inflation, twenty quarters when regressing five-year inflation, and forty quarters when regressing ten-year inflation. The first column uses quarterly observations from 1982Q3 to 2021Q1, the second column from 1983Q3 to 2021Q1, the third column from 1986Q1 to 2021Q1, and the fourth column from 1991Q1 to 2021Q1. Ten-year expectations for 1981Q1-1991Q3 are from the Hoey survey. Newey-West standard errors in parentheses. The ** and * symbols denote significance at 1 and 5 percent levels, respectively.|
|Sources: Authors’ calculations using data from Federal Reserve Bank of Philadelphia Survey of Professional Forecasters; Federal Reserve Board; and US Bureau of Labor Statistics and US Department of Treasury via Macrobond.|
1. Two-year inflation compensation as of June 18 (latest available and after release of May inflation data) was 2.8 percent. (Source: Federal Reserve Board.) Because the adjustment of bond principal value to inflation is lagged about three months, this compensation reading covers inflation over the period from March 2021 to March 2023. Assuming inflation compensation of 3.5 percent for 2021 (based on June 2021 Consensus Forecasts) implies compensation of 2.1 percent for 2022. Also based on Consensus Forecasts, the median economist’s forecast of 2022 CPI inflation as of June 14 was 2.6 percent. The Federal Reserve’s inflation target is based on the personal consumption expenditures (PCE) measure of inflation, which tends to run slightly lower than CPI inflation.
2. The Federal Reserve does not report one-year compensation because liquidity premiums and lags in the adjustment of principal and coupon payments for inflation introduce a volatile error in one-year compensation.
3. Principal results are not affected by the addition of a longer backward average of inflation.
The data underlying this analysis are available here [zip].