Board of Governors of the Federal Reserve System

Figure 1. Convenience Yield

Chart: Line chart, by difference in percent yield of safe (Aaa) corporate bonds and the 10-year Treasury yield, quarterly from 1962 to 2024. There is one series “$$cy$$.” The series trends upwards over time starting from about 0.5 percent. It fluctuates between about 0 and 1 percent until it climbs to a peak of 2.5 percent in 2009. The series then falls on average after 2009 dropping from 2 percent to about 0.75 percent in the present day. Periods of recession (December 1969-November 1970, November 1973-March 1975, January 1980-July 1980, July 1981-November 1982, July 1990-March 1991, March 2001-November 2001, December 2007-June 2009, February 2020-April 2020) are denoted with grey bars.

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Figure 2. $$r^\ast$$

Chart: Line chart, by natural rate of interest in percentage points, quarterly from 1962 to 2024. There are two time series, our baseline estimates of $$r^\ast$$ in blue and the estimations of Holston, Laubach, and Williams (2017, 2023) $$r^\ast$$ from the Federal Reserve Bank of New York in red. The blue shaded region around the blue line denotes the 68% confidence band of $$r^\ast$$ from our estimates. The two series generally trend downward together, with the red line consistently above the blue. Our $$r^\ast$$ starts from about 3.5 percent and steadily declines to about 2.5 percent in 2008. It then drops to about 1 percent in 2009 and falls to about 0.75 percent this year. The red line starts at about 5.5 percent and similarly declines to about 2.5 percent in 2008, before dropping to about 1 percent in 2009 and fluctuating between 0 and 1 percent until present day. Periods of recession (December 1969-November 1970, November 1973-March 1975, January 1980-July 1980, July 1981-November 1982, July 1990-March 1991, March 2001-November 2001, December 2007-June 2009, February 2020-April 2020) are denoted with grey bars.

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Figure 3. $$r^\ast$$ and its components

Chart: Line chart, by percent yield, quarterly from 1962 to 2024. There are four lines: the blue line shows the estimates of $$r^\ast$$ (same as blue line in Figure 2); the black line shows $$g$$, trend output growth; the red line shows $$z$$, the residual term that captures the forces that move $$r^\ast$$ off the equilibrium path; the green line shows $$-\bar{cy}$$, the negative convenience yield once all transitory shocks have dissipated. $$r^\ast$$ is the same as the blue line in Figure 2. Trend output growth in black declines from 4 percent to 2 percent in present day with little disruption. The residual term $$z$$ fluctuates around 0 for the entire series, with some exception from 1980 to 2008 where it remains from about 0 to .20 percent. The negative convenience yield in green starts around –.40 percent and declines to a minimum of -2 percent from 2008 to 2016, rising to just below -1 percent in present day. Periods of recession (December 1969-November 1970, November 1973-March 1975, January 1980-July 1980, July 1981-November 1982, July 1990-March 1991, March 2001-November 2001, December 2007-June 2009, February 2020-April 2020) are denoted with grey bars.

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Figure 4. Comparison of the baseline model with HLW: the path of $$z$$

Chart: Line chart, by percentage points, quarterly from 1962 to 2024. There are two lines: the blue line shows our $$z$$, a residual term that captures the forces that move $$r^\ast$$ off the equilibrium path, and the red line shows the $$z$$ of Holston, Laubach, and Williams (2017, 2023). The blue shaded region denotes 68% confidence bands in our estimates of $$z$$. Our $$z$$ in blue is the same as the red line in Figure 3. The $$z$$ of Holston, Laubach, and Williams starts around 0 before dropping to around -.50 percent in 1983 and falling consistently over time to -2 percent in present day. Periods of recession (December 1969-November 1970, November 1973-March 1975, January 1980-July 1980, July 1981-November 1982, July 1990-March 1991, March 2001-November 2001, December 2007-June 2009, February 2020-April 2020) are denoted with grey bars.

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Figure 5. $$r^\ast$$ in confidence bands

Chart: Line chart, by percentage points, quarterly from 1962 to 2024. There are two lines: the blue line indicates the width of the 68% confidence bands for our model while the red line indicates the width of the 68% confidence bands for Holston, Laubach, and Williams (2017, 2023). Both trend net downward from about 1.7 percent to .50 percent in 2008. The red line shoots up to just over 2 percent in 2009 before falling back down to .75 percent and finishing to around 1.2 percent in present day. Our confidence band in blue only mildly jumps up to around .70 percent in 2009, wavering around there until present day. Periods of recession (December 1969-November 1970, November 1973-March 1975, January 1980-July 1980, July 1981-November 1982, July 1990-March 1991, March 2001-November 2001, December 2007-June 2009, February 2020-April 2020) are denoted with grey bars.

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Figure 6. The stance of Policy ($$r-r^\ast$$)

Left chart: Line chart, by percentage points, quarterly from 1962 to 2024. The blue line represents the difference in the ex-ante real policy rate $$r$$, measured by subtracting the model’s estimate of inflation over the next three months (annualized) from the policy rate, and $$r^\ast$$. We estimate a negative real policy rate gap during much of the 1960s and 1970s hovering around 0 to -3 percent. From 1979 to 1991, the gap is mostly positive, fluctuating between around 1 and 3 percent and spiking to near 7 percent in 1981-82. The series wavers between about 2 and -2 percent until 2020. Behavior from 2019 to present day is detailed in discussion of the right graph. Periods of recession (December 1969-November 1970, November 1973-March 1975, January 1980-July 1980, July 1981-November 1982, July 1990-March 1991, March 2001-November 2001, December 2007-June 2009, February 2020-April 2020) are denoted with grey bars. Monetary policy tightening cycles (February 1994-March 1995, July 1999-July 2000, June 2004-August 2006, December 2015-July 2018, and March 2022-present) are given by black dashed bars.

Right chart: Line chart, by percentage points, quarterly from 2019 to 2024. The blue line represents the difference in the ex-ante real policy rate $$r$$, measured by subtracting the model’s estimate of inflation over the next three months (annualized) from the policy rate, and $$r^\ast$$. In 2019, the line started around 0 percent before falling to around 5 percent in the middle of 2021. It then shot up to near 2 percent before falling back to just over 1 percent in present day. The Covid pandemic recession of February 2020-April 2020 is in grey bars, while the current monetary policy tightening cycle beginning in March 2022 is in black dashed bars.

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Figure 7. Estimates of $$r^\ast$$ based on Different series of US Corporate Yields

Chart: Line chart, by percentage points, quarterly from 1962 to 2024. There are two lines: the red line denotes the benchmark model estimates of $$r^\ast$$, while the blue line shows the posterior median estimate of $$r^\ast$$ from using the Baa spread to calculate convenience yield rather than the Aaa spread. The blue and grey shaded areas represent 68% and 95% confidence bands, respectively, around estimates of the benchmark model of $$r^\ast$$. Both lines follow the same rough trajectory, starting from 3.5 percent and dropping to around 2 percent in 1975. After climbing back up to around 3.5 percent in 1985, both lines fall to 2 percent before dropping between 0 and 1 percent after 2009. Periods of recession (December 1969-November 1970, November 1973-March 1975, January 1980-July 1980, July 1981-November 1982, July 1990-March 1991, March 2001-November 2001, December 2007-June 2009, February 2020-April 2020) are denoted with grey bars.

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Figure 8. US Corporate Yields

Chart: Line chart, in percent yield, quarterly from 1919 to 2024. There are two lines: the red line is the yield of Aaa corporate bonds, and the blue line is the yield of Baa corporate bonds. The blue and red lines start near 7 and 6 percent, respectively, and both drop to around 3.5 percent in 1946. The two lines then move roughly together gradually up to a high of around 17 and 16 percent, respectively in 1982. The two lines respectively fall from there to around 3.5 and 3 percent in 2021, before finishing around 6.5 percent and 5.5 percent in present day. Periods of recession (August 1918-March 1919, January 1920-July 1921, May 1923-June 1924, October 1926-November 1927, August 1929-March 1933, May 1937-June1938, February 1945-October 1945, November 1948-October 1949, July 1953-May 1954, August 1957-April 1958, April 1960-February 1961, December 1969-November 1970, November 1973-March 1975, January 1980-July 1980, July 1981-November 1982, July 1990-March 1991, March 2001-November 2001, December 2007-June 2009, February 2020-April 2020) are denoted with grey bars.

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Figure 9. Estimates of the Convenience Yield trend

Chart: Line chart, in percentage points, quarterly from 1962 to 2024. There are two lines: the red line is the convenience yield taken as the difference between Aaa corporate bond yields and US Treasury bond yields, and the blue line is the convenience yield taken as the difference between Baa corporate bond yields and US Treasury bond yields. The two lines move roughly together starting from about .40 percent to 1.6 percent for blue and 1.1 percent for red in 1975. They then fall to around .30 percent for red in 1984 and .10 percent for blue in 1985 before both gradually rise again. The yields peak at about 2.7 percent for blue and almost 2 percent for red in 2008, then gradually trend down to around 1.5 and 1.2 percent for blue and red, respectively, in present day. Periods of recession (December 1969-November 1970, November 1973-March 1975, January 1980-July 1980, July 1981-November 1982, July 1990-March 1991, March 2001-November 2001, December 2007-June 2009, February 2020-April 2020) are denoted with grey bars.

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Figure 10. Output Gaps

Chart: Line chart, in percentage points, quarterly from 1962 to 2024. There are three lines: the blue line denotes our estimated output gap, the red line denotes the output gap of Holston, Laubach and Williams (2017, 2023), and the green line denotes the output gap of the Congressional Budget Office (CBO). The blue shaded region denotes 68% confidence bands around our estimates. Each line starts at an output gap between around -1 and -3 percent and oscillates cyclically around 0 percent. The lines follow the same path until 2008 when the HLW red line rises to between about 1 and 7 percent and the CBO green line falls to nearly -5 percent, increases to 0 by 2020, then falls off again to nearly -10 percent following the pandemic. Our blue line oscillates around 0 percent during this time but rises to nearly 2 percent by present day. Periods of recession (December 1969-November 1970, November 1973-March 1975, January 1980-July 1980, July 1981-November 1982, July 1990-March 1991, March 2001-November 2001, December 2007-June 2009, February 2020-April 2020) are denoted with grey bars.

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Figure 11. Trend Growth ($$g$$)

Chart: Line chart, in percentage points, quarterly from 1962 to 2024. There are two lines: the blue line is our estimated $$g$$ and the red line is the g from Holston, Laubach, and Williams (2017, 2023). 68% confidence bands are denoted by the shaded blue region around our estimates. Both estimates trend downwards steadily, with the red line starting around 1.25 percent and the blue just under 1 percent and both finishing around .55 percent points. Our blue line is generally estimated higher than the red line of HLW, particularly since the early 1970s recession. Periods of recession (December 1969-November 1970, November 1973-March 1975, January 1980-July 1980, July 1981-November 1982, July 1990-March 1991, March 2001-November 2001, December 2007-June 2009, February 2020-April 2020) are denoted with grey bars.

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Figure 12. The Real Policy and Private Sector Rate Gaps

Chart: Line chart, in percentage points, quarterly from 1962 to 2024. There are two lines: the blue line is the difference between the ex-ante real policy rate and $$r^\ast$$, with 68% confidence bands shaded in blue; the red line is the difference between the ex-ante one-period real private sector rate and the natural real rate faced by the private sector, with 68% confidence bands shaded in red. The two series move nearly in tandem with one another since their inception. The series’ start around -2.5 percent, trends up to nearly 2 percent by 1973, drops to -4 percent in 1978 before skyrocketing to 7 percent in 1981. The series drops to 2 percent by 1983 and remains cyclical between 2 percent and -2 percent until 2020. Finally, the series drops to nearly -5 percent before jumping back up to around 2 percent in 2023, finishing out around 1 percent in present day. Periods of recession (December 1969-November 1970, November 1973-March 1975, January 1980-July 1980, July 1981-November 1982, July 1990-March 1991, March 2001-November 2001, December 2007-June 2009, February 2020-April 2020) are denoted with grey bars.

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