President Joseph R. Biden Jr.’s audacious proposal for $1.9 trillion in additional stimulus this year has generated concern among some, including former Treasury Secretary Lawrence H. Summers, that the package may overheat the US economy and cause inflation. Yet the bond market, often a place where such concerns are registered, does not seem worried. Current changes in bond yields suggest only a tiny rise in future inflation. Could the markets be telling us something?
In fact, bond market complacence should not be taken as strong evidence against the risk of overheating. The postwar history of US and foreign bond markets shows that bond yields are not good predictors of inflation. Yields largely reflect the behavior of inflation over many years in the past, not the future. It is far from clear whether inflation will rise significantly, but if it does, bond markets are not likely to have predicted it.
In the standard textbook model, bond investors care about future inflation over the life of a bond because inflation reduces the real value of their future investment returns. The 10-year yield should thus be a good indicator of concerns about inflation over the next 10 years. Higher expected inflation ought to result in a higher bond yield.
The table below presents evidence that bond yields have failed to predict inflation over nearly 70 years in the United States. Yields are also poor predictors of inflation in three other advanced economies. Monthly yields are regressed on the current 12-month consumer price index (CPI) inflation rate plus an average inflation rate over some period in the future or the more distant past. The 10-year backward inflation average is the average rate of inflation over the 10 years before the yield is observed, and the 10-year forward inflation average is the average rate of inflation over the following 10 years. The 10-year forward inflation average is what 10-year bond investors should be most concerned about.
The first line of the table shows that a 10-year average of past inflation is the best predictor for US yields, with an R2 of 0.82. A one percentage point increase in past inflation raises the yield 1.11 percentage point. The current inflation rate has only a small effect of 0.18 percentage point. The next few lines show that shorter backward averages of inflation lead to a worse fit (smaller R2), but the coefficient on past average inflation remains close to 1, while the one on current inflation is small. It appears that bond markets agree with Winston Churchill’s dictum, “The further back I look, the further forward I can see.”
The following lines show that forward averages of inflation have coefficients near 0 and do not improve the fit at all compared to a regression on current inflation only. Thus, bond yields are not good predictors of inflation over any future horizon. This calls into question the value of Churchill’s dictum, for predicting inflation at least.
Roughly similar results are obtained for the United Kingdom, Japan, and France. In each country, the 10-year backward average of inflation is the best predictor of 10-year bond yields. In the United Kingdom and France, yields respond slightly to average inflation 1 to 2 years ahead, but the improvement in the R2 is tiny. Only in Japan do bond yields have any predictive power over long-run future inflation, but the coefficients, though statistically significant, are far below 1 and the increase in R2 is small. Even in Japan, 10-year backward inflation is a far more significant predictor of yields than any measure of forward inflation.
These results are supported by a casual examination of bond yields and inflation in each of these countries, shown in the figure below. The shaded regions denote periods in which inflation broke out significantly above or below its 5-year moving average. Yield movements in the months immediately prior to these episodes are small and as often in the wrong direction (opposite to the coming inflation shift) as the right one. For the most part, yields move concurrently with inflation, with occasional evidence of a lagged response.
In the United States, yields were flat before the first inflationary episode. They then rose steadily during the episode, reaching a peak concurrently with the peak in inflation. Yields rose a bit shortly before each of the next two inflationary episodes, but inflation also started to rise shortly before it crossed its 5-year moving average, marking the start of the episode. Yields continued to rise during each episode, reaching a peak a few months after the peak in inflation. Bond yields reached their all-time peak just two months before the start of the sole disinflationary episode, beginning to fall at exactly the same time as inflation.
The largest episodes of inflation and disinflation tended to occur in the 1970s and 1980s. Since then, movements of inflation have been smaller and briefer. There has been a trend of declining yields relative to inflation, the widely noted falling real interest rate. Fluctuations around this trend generally seem to be concurrent with fluctuations in inflation, neither leading nor lagging inflation to any noticeable degree.
Overall, there is no evidence to suggest that bond markets are good predictors of inflation.
|Regressions of 10-year bond yields on consumer price inflation|
January 1952–December 2020
January 1963–December 2020
|Measure of average inflation||Average inflation||Current inflation||R2||Average inflation||Current inflation||R2|
October 1966–December 2020
January 1957–December 2020
|Average inflation||Current inflation||R2||Average inflation||Current inflation||R2|
|n.a. = not applicable|
|Note: This table presents results from monthly regressions of the 10-year government bond yield on the current 12-month inflation rate (which is also the 1-year backward average) and an average inflation rate over the indicated period in the past or future. Yield is monthly average for the United States and United Kingdom and end of month for Japan and France. For the United Kingdom, redemption yields are used from January 1963 to January 1970 and zero coupon yields afterwards. 0.35 percentage points are subtracted from redemption yields, which is the average difference between redemption and zero coupon yields in the months in which they overlap. Inflation averages are compound annual growth rates of consumer prices over periods ranging from 12 to 120 months. Data ranges displayed refer to availability of bond yield and consumer price index. Regressions have different sample periods depending on lags or leads needed to calculate the respective inflation averages.|
|Sources: Authors’ calculations based on data from Bank of England (including the Millennium of Macroeconomic Data for the UK dataset); government bond yields for France, Japan, and the United States from Macrobond; and Bank for International Settlements and US Bureau of Labor Statistics via Macrobond.|
1. Since the announcement of the proposed package on January 14, 10-year yields have risen 0.19 percentage points and 5-year yields are up 0.08 points. An alternative gauge of inflation expectations may be derived from the difference between conventional and inflation-indexed yields, also known as inflation compensation. (Inflation-indexed securities pay a fixed yield in addition to the value of any inflation between their issuance and maturity. They were introduced in 1997.) 10-year inflation compensation has risen 0.15 percentage points and 5-year inflation compensation is up 0.32 percentage points. The larger rise in 5-year compensation reflects a surprise decline in the 5-year inflation-indexed yield that may reflect a sharp rise in Federal Reserve purchases of these securities, which typically trade in less liquid markets and are subject to larger price fluctuations than conventional Treasury securities. Data are from Bloomberg.
2. The current 12-month inflation rate is effectively a 1-year backward average of inflation.
3. James Geary, Geary’s Guide to the World’s Great Aphorists, New York: Bloomsbury, 2007, p. 6.
4. In regressions of future inflation on current inflation and current yield, the coefficient on current yield is close to 0, and the R2 is essentially unchanged when yield is dropped from the regression.
5. These coefficients are statistically significant in the United Kingdom but not in France, based on Newey-West standard errors allowing for 12th-order autocorrelated residuals.
6. Three episodes just missed the 10 percent cutoff: the rise of inflation around 1990 in the United Kingdom and the bursts of inflation just before 1970 and around 1980 in France. In none of these episodes did yields display any noticeable anticipatory increase.
7. The 12-month inflation rate is itself a backward-looking measure. A sudden rise in monthly inflation might be expected to push up yields immediately yet not show up in the 12-month inflation rate for several months, so the absence of even a few months of anticipatory bond market response is noteworthy.