Figure 1: Timing of futures and FOMC announcements
The figure is an illustration how the 3-month ahead federal funds futures contract expires in 3 months and can cover three FOMC meetings.
Figure 2: Construction of the Bu et al., 2021 shock series.
Panels (a)
and (b) show estimates \(\{\hat{\beta}_j\}_{j=1}^{30}\) from
equation (7), \(\Delta R^j_{s}=\theta_j+\beta_j\Delta
R^2_{s}+\xi^j_{s}\) for maturities \(j=1,...,30\) years are obtained by
regressing daily changes in zero-coupon Treasury yields from maturities
\(j=1,...,30\) on the daily change in
the constant maturity two-year Treasury. Estimates are obtained via OLS
with robust standard errors. Because response variables are zero-coupon
and the independent variable is constant maturity, the coefficient \(\hat{\beta}_2\) for the two-year will be
close to one, but not exactly. The effective lower bound of the federal
funds rate (ELB) is defined as defined as December 16, 2008 to December
16, 2015 and March 15, 2020 to March 16, 2022. Panels (c) and (d) show
the second step of the \(BRW\)
Fama-MacBeth regression in equation (8), \(\Delta
R^{j}_{s}=\alpha_j+\Delta i_s \hat{\beta}_j +v^j_{s}\) where
\(s=\)March 16, 2016 and August 9,
2011, respectively. The x-axis in panels (c) and (d) is \(\{\hat{\beta}_j\}_{j=1}^{30}\), the
coefficient estimates from the first-step in equation (7) for one- to 30-year
maturities plotted in panels (a) and (b). \(\hat{\beta}_j\) close to 1 are short-term
yields and \(\hat{\beta}_j\) close 0
are long-term yields. The y-axis in panels (c) and (d) is the daily
change in zero-coupon Treasury yields \(\{\Delta R^j_{s}\}_{j=1}^{30}\) for
maturities \(j=1,...,30\) years. The
estimated linear fit \(\Delta
\hat{i}_s\) is the monetary shock. The sample is from January
1995 to September 2024.
The figure has four panels. The top two panels display the responsiveness of Treasury yields to the change in the 2-year Treasury yield on days of FOMC announcements. The x-axis is maturities from 1 to 30 years and the y-axis is average responsiveness and ranges from -1 to 3. The top left panel shows the average responsiveness over the entire January 1995 to November 2023 sample. The series is near one for maturities 1 to 5. This is because the 2- year responds one to one for the 2-year and the neighboring maturities are tightly correlated. The series than slopes downward and is near zero for maturities 20 and above. 95 percent confidence bands surround the series and are above zero for maturities 1 to 15. The top right panel shows the average responsiveness over the period when the federal funds rate is at its effective lower bound (ELB, December 16, 2008 to December 16, 2015 and March 15, 2020 to March 16, 2022) and the non-ELB sample (January 1995 to November 2023, excluding the dates in the ELB sample). The non-ELB series has a responsiveness near y-value one for maturities 1 to 3. The responsiveness then slopes downward and reaches zero at maturity 20 and remains there. 95 percent confidence bands show that the responsiveness coefficients are above from maturities 1 to about 12. The ELB series is significantly higher than the non-ELB series for maturities 3 to about 15. The responsiveness is near one for maturities one to three and then peaks at y-value 2 near maturity 5 and falls towards 0 which it reaches around maturity 25. The bottom two panels show the second-stage of the Fama-MacBeth regression used to construct the Bu-Rogers-Wu (2022) monetary policy shock on two case study days. In each, the x-axis ranges from 0 to 1.1 and represents the average responsiveness of all Treasuries along the yield curve to the two-year Treasury. The y-axis ranges from -0.3 to 0.1 and represents the daily change in each Treasury on the given FOMC day. Both panels have red dots for each Treasury and an orange line showing the line of best fit amidst those dots. The dots in the bottom left panel start a little above 0 at 0 on the x-axis, and with a slight curve decrease to about -0.12 by an x-value of 1.1. The best fit line is negatively sloped, representing that the day shows a negative shock. The dots in the bottom right panel follow a horizontal fishhook shape, beginning with a value of approximately -0.1 at an x-value of 0, decreasing to -0.23 by an x-axis value of 0.8, then vertically curving such that at an x-value of 0 the y-value is approximately -0.1 and at an x-value of 0.8 we see a y-value of approximately -0.5. The line of best fit here is negative, indicating that the Fama-MacBeth regression derives a negative shock for this day.
Figure 3: Average responsiveness of the \(NS\) data to 2-Year Treasuries.
Estimates \(\hat{\beta}_j\) from
equation (7), but with the
updated \(NS\) instrument set \(\{MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5\}\)
regressed on the daily change in the constant maturity two-year
Treasury. Estimates are obtained via OLS with robust standard errors.
The effective lower bound of the federal funds rate (ELB) is defined as
defined as December 16, 2008 to December 16, 2015 and March 15, 2020 to
March 16, 2022. The sample is from January 1995 to September
2024.
The figure has two lines that display the responsiveness of the Nakamura-Steinsson (2018) instrument set to the change in the 2-year Treasury yield on days of FOMC announcements. The x-axis is the five instruments MP1, MP2, ED2, ED3, and ED4. The y-axis is average responsiveness and ranges from 0 to 3. The left line shows the average responsiveness over the entire January 1995 to November 2023 sample. The series is upward sloping starting near 0.5 for MP1 and ending near 1 for ED4. 95 percent confidence bands surround the series and are above zero for all maturities. This shows that maturities with horizons up to a year are on average responsive to changes in the 2-year Treasury yields. The right line shows the average responsiveness over the period when the federal funds rate is at its effective lower bound (ELB, December 16, 2008 to December 16, 2015 and March 15, 2020 to March 16, 2022) and the non-ELB sample (January 1995 to November 2023, excluding the dates in the ELB sample). The two series are similar with overlapping 95 percent confidence intervals, albeit with the non-ELB series higher for MP1 and MP2. The series are upward sloping and are near 1 for ED4, the longest maturity in our sample.
Figure 4: Time series of monetary shock series, January 1995 to
September 2024.
\(MP1\) is
the 30-minute change around an FOMC announcement in the current month’s
federal funds future if the FOMC announcement is in the first 23 days of
the month with an adjustment or the next month’s federal funds future if
the FOMC announcement is within the last seven days of the month. \(FF4\) is the change in the three-month
ahead federal funds futures within 30-minutes of an FOMC announcement.
\(NS\) is the first principal component
of the instrument set \(\{MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5\}\) which
is the 30-minute change in these futures around an FOMC announcement.
\(BRW\) is a Fama-MacBeth regression of
the daily change in one- to 30-year constant maturity Treasury yields.
\(NS\) data/\(BRW\) method is a Fama-MacBeth regression
of the \(NS\) data. \(BRW\) data/\(NS\) method is the first principal
component of the \(BRW\) data.
The series has six panels with each plotting one of the six monetary shock series studied in the paper. The x-axis ranges from January 1995 to November 2023. The y-axis ranges from -0.5 to 0.25 percentage point. All series fluctuate around zero. Panel a shows the MP 1 shock series. The series has several large spikes of about -0.37 percentage point around 2000. It is then close to zero and again has large negative spikes near 2009. From about 2010 to 2015 it is about zero. There is another large spike of -0.25 near 2020. Panel b shows the NS shock series. The series is similar to that of MP 1 in panel a, but with smaller negative spikes that never surpass -0.25 percentage point. From about about 2009 to 2015 the series is close to zero, but slightly positive. Panel c shows the FF 4 shock series. The series is similar to that of MP 1 and NS in panels b and c, respectively. The large negative spikes are closer in magnitude to those in panel b. Panel d shows the BRW shock series. The series has many positive and negative fluctu- ations around near. They are all within the range of -0.25 to 0.25 percentage point with no discernible pattern. Panel e shows a swapped shock series constructed from NS data and the BRW method. The shocks have very tiny fluctuations around zero that are unlikely to be outside the range -.10 to .10 percentage point. Panel f shows a swapped shock series constructed from BRW data and the NS method. The shocks have larger fluctuations around zero than those shown in panel e. The fluctuations range between about -.10 and .10 percentage point.
Figure 5: Distributions of monetary shock series, January 1995 to
September 2024
\(MP1\) is
the 30-minute change around an FOMC announcement in the current month’s
federal funds future if the FOMC announcement is in the first 23 days of
the month with an adjustment or the next month’s federal funds future if
the FOMC announcement is within the last seven days of the month. \(FF4\) is the change in the three-month
ahead federal funds futures within 30-minutes of an FOMC announcement.
\(NS\) is the first principal component
of the instrument set \(\{MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5\}\) which
is the 30-minute change in these futures around an FOMC announcement.
\(BRW\) a the Fama-MacBeth regression
of the daily change in one- to 30-year constant maturity Treasury
yields. \(NS\) data/\(BRW\) method is a Fama-MacBeth regression
of the \(NS\) data. \(BRW\) data/\(NS\) method is the first principal
component of the \(BRW\) data. The ELB
is defined as December 16, 2008 to December 16, 2015 and March 15, 2020
to March 16, 2022.
The series has six panels with each plotting the distributions of one of the six monetary shock series studied in the paper. Each panel has three distributions over three different samples: the full sample from January 1995 to November 2023, the ELB sample which is defined as December 16, 2008 to December 16, 2015 and March 15, 2020 to March 16, 2022, and the non-ELB sample which is the full sample excluding the ELB. The x-axis ranges from -0.5 to 0.5 percentage points. The y-axis is unlabeled. Panel a shows the MP 1 shock distribution. Over the full sample, the distribution is centered at zero and has a long left that extends to -.5 percentage point. The distribution in the non-ELB period is similar. The distribution in the ELB period is tightly centered at zero with a support ranging between about -0.10 to 0.05 percentage points. Panel b shows the NS shock distribution. It is similar across all three samples as the MP 1 distribution except for the left tails in the full and non-ELB samples extend only to -0.25 percentage points. In the ELB sample, the distribution is not centered at zero and has a slight right-ward shift. Panel c shows the FF 4 shock distribution. It is similar across all three samples as the MP 1 distribution except for the left tails in the full and non-ELB samples extend only to about -0.375 percentage points. Panel d shows the BRW shock distribution. The distribution does not look like those of the previous three panels. The distributions look the sample in all three samples and have a support ranging from -0.25 to 0.25 percentage point. There is a flat mass between about -0.12 and 0.12 percentage points. Panel e shows a swapped shock series constructed from NS data and the BRW method. Across all three samples, the distributions are tightly distribution around 0 with supports ranging from about -0.10 to 0.10 percentage points. Panel f shows a swapped shock series constructed from BRW data and the NS method. The distributions are centered right of zero with supports ranging from about -0.20 to 0.12 percentage point. There is a notable mass near about 0.05 percentage point for the ELB sample
Figure 6: Predictability coefficients with 95% confidence intervals.
Estimate of \(\hat{\beta}\)
in equation (9) \(\varepsilon^i_t=\alpha+\beta news^k_T
+e_T\) are obtained via OLS with robust standard errors that are
similar when bootstrapped. The sample is from January 1995 to September
2024 and excludes the second quarter of 2020. See Appendix Figure A.17 for results over additional subsamples and with different
controls. For the specification using the Blue Chip GDP revisions, we
follow Bauer and Swanson, 2023 and
exclude observations where the FOMC announcement is in the first three
business days of the month from 1995 to December 2000 and the first two
business days thereafter to ensure that the Blue Chip Survey was
completed prior to the FOMC announcement. Blue Chip GDP revisions are
the monthly revision of one-quarter ahead GDP growth forecasts. The
specification using non-farm payrolls assures that the FOMC meeting is
after the FOMC release which is typically the first Friday of every
month. Non-farm payrolls are the monthly change in the nonfarm payrolls
release. The ADS Index is the Aruoba et al., 2009 business conditions index.
The BKK index is the Brave et al., 2019 Big
Data index. \(MP1\) is the 30-minute
change around an FOMC announcement in the current month’s federal funds
future if the FOMC announcement is in the first 23 days of the month
with an adjustment or the next month’s federal funds future if the FOMC
announcement is within the last seven days of the month. \(FF4\) is the change in the three-month
ahead federal funds futures within 30-minutes of an FOMC announcement.
\(NS\) is the first principal component
of the instrument set \(\{MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5\}\) which
is the 30-minute change in these futures around an FOMC announcement.
\(BRW\) is a Fama-MacBeth regression of
the daily change in one- to 30-year constant maturity Treasury yields.
\(NS\) data/\(BRW\) method is a Fama-MacBeth regression
of the \(NS\) data. \(BRW\) data/\(NS\) method is the first principal
component of the \(BRW\)
data.
The purpose of this figure is to suggest the predictability of several shocks shocks by using bivariate regressions of each shock on a source a macroeconomic news released shortly before the shock. The figure is a coefficient plot. The y-axis ranges from -0.03 to 0.08. The x-axis represents shocks, with labels of “MP1,” “FF4,” “NS,” “BRW,” “NS data, BRW method,” and ”BRW data, NS method.” above each of these labels is four lines with 95% confidence intervals, each representing the coefficient of a bivariate regression associated with a particular source of regular macroeconomic news. These news sources are Blue Chip GDP REvisions, Nonfarm Payrolls, the ADS Index, and the BKK Index. For “MP1”, the point for the coefficient estimate associated with Blue Chip GDP Revi- sions is approximately 0.045, with a confidence interval stretching from approximately 0.08 to 0.01. This is the only significant coefficient–all other lines show insignificance. But this shows that this shock is predictable. For “FF4”, the point for the coefficient estimate associated with Blue Chip GDP Revi- sions is approximately 0.037, with a confidence interval stretching from approximately 0.065 to 0.01. The point for the coefficient estimate associated with Nonfarm Payrolls is approxi- mately 0.04, with a confidence interval stretching from approximately 0.078 to 0.005. These are the only significant coefficients–all other lines show insignificance. But this shows that this shock is predictable. For “NS”, the point for the coefficient estimate associated with Blue Chip GDP Revisions is approximately 0.03, with a confidence interval stretching from approximately 0.05 to 0.01. The point for the coefficient estimate associated with Nonfarm Payrolls is approximately 0.037, with a confidence interval stretching from approximately 0.061 to 0.01. These are the only significant coefficients–all other lines show insignificance. But this shows that this shock is predictable. For “BRW,” all lines’ confidence intervals encompass zero ,indicating that no coefficients are significant and that the shock is not predictable. For “NS data, BRW method”, the point for the coefficient estimate associated with Non- farm Payrolls is approximately 0.01, with a confidence interval stretching from approximately 0.021 to 0.001. This is the only significant coefficient–all other lines show insignificance. But this shows that this shock is predictable. For “BRW data, NS method,” all lines’ confidence intervals encompass zero ,indicating that no coefficients are significant and that the shock is not predictable.
Figure 7: Forecast revision coefficients and 95% confidence intervals
\(\hat{\beta}\) in eq. (10) \(\text{Blue Chip GDP Revisions}_T=\alpha+\beta
\varepsilon_T^i+e_T\) is estimated via OLS. Robust standard
errors are similar when bootstrapped. The full sample is from January
1995 to September 2024 and the \(NS\)
sample is from January 1995 to August 2015. Following Bauer and Swanson, 2023, we exclude
observations where the FOMC announcement is in the first three business
days of the month from 1995 to December 2000 and the first two business
days thereafter to ensure that the Blue Chip Survey was completed prior
to the FOMC announcement. See Appendix Figure B.18 for results over additional subsamples and with different
controls. \(MP1\) is the 30-minute
change around an FOMC announcement in the current month’s federal funds
future if the FOMC announcement is in the first 23 days of the month
with an adjustment or the next month’s federal funds future if the FOMC
announcement is within the last seven days of the month. \(FF4\) is the change in the three-month
ahead federal funds futures within 30-minutes of an FOMC announcement.
\(NS\) is the first principal component
of the instrument set \(\{MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5\}\) which
is the 30-minute change in these futures around an FOMC announcement.
\(BRW\) is a Fama-MacBeth regression of
the daily change in one- to 30-year constant maturity Treasury yields.
\(NS\) data/\(BRW\) method is a Fama-MacBeth regression
of the \(NS\) data. \(BRW\) data/\(NS\) method is the first principal
component of the \(BRW\)
data.
for the first panel ranges from -20 to 20 while the y-axis for the second panel ranges from -3 to 2. In the first panel, above each shock there is a coefficient point estimate with a 95% confidence interval for both over the ELB sample and the non-ELB sample. For MP1, the coefficient estimate for the non-ELB sample is approximately 0.5 and the confidence interval is not visible, and it is just barely not significant; for the ELB sample, the coefficient estimate is approximately 3 with a confidence interval from -19 to 13. For FF4, the coefficient estimate for the non-ELB sample is approximately 0.5 and the confidence interval is not visible, and it is significant; for the ELB sample, the coefficient estimate is approximately 0 with a confidence interval from -8 to 8. For NS, the coefficient estimate for the non-ELB sample is approximately 1 and the confidence interval ranges from 1.1 to 0.9; for the ELB sample, the coefficient estimate is approximately 2 with a confidence interval from -2 to 7. For BRW, the coefficient estimate for the non-ELB sample is approximately 0 and the confidence interval ranges from -0.1 to 0.1; for the ELB sample, the coefficient estimate is approximately - 0.5 with a confidence interval from -0.5 to -1.1. For NS data with the BRW method, the coefficient estimate for the non-ELB sample is approximately 0 and the confidence interval ranges from -0.1 to 0.1; for the ELB sample, the coefficient estimate is approximately 8 with a confidence interval from 20 to -5. For BRW data with the NS method, the coefficient estimate for the non-ELB sample is approximately 0.2 and the confidence interval ranges from -0.3 to 0.1; for the ELB sample, the coefficient estimate is approximately 2 with a confidence interval from 0 to 4. In the second panel, coefficient estimates and 95% confidence intervals are plotted over the sample specifications of “Full Sample,” “Full Sample controlling for the financial crisis,” “Full Sample controlling for the financial crisis and COVID,” “NS Sample,” ”ELB episodes,” and ”Non-ELB Episodes,” whose specifications can be found in the description for Figure A.16. For MP1, all plotted coefficients with their confidence intervals are similar to as shown in Figure 7, except coefficient significance is shown for “Full sample with COVID controls,” “Full sample controlling for the financial crisis and COVID,” “NS Sample,” and “non-ELB Sample.” For FF4, all coefficients across all samples are significant and positive, with coefficient estimates ranging from 0.7 to 0.9. For NS, all coefficients across all samples are significant and positive, with all approximately equal to 1. For BRW, all coefficients across all samples are not significant, with coefficient estimates close to 0. For NS data with BRW methodology, all coefficients across all samples are not significant, with coefficient estimates ranging from -0.1 to 0.8. For BRW data with NS methodology, all coefficients across all samples are not significant, with coefficient estimates ranging from -1 to 1.
Figure 8: Impulse response functions of local projections to a 1
percentage point monetary shock, x-axis is days and y-axis is percentage
points. Estimates of \(\hat{\beta}_{(h)}\) in equation (11) \(\pi_{t+h}=\alpha_{(h)}+{\beta_{(h)}}
\varepsilon_t^{i}+\Gamma_{(h)}z_t+e_t^{(h)}, \quad e_t^{(h)} \sim
\mathcal{N}(0,\sigma_{(h)})\) are obtained via the Canova and Ferroni, 2022 toolbox with
robust heteroskedasticity and autocorrelation consistent (HAC) standard
errors reported at 90 percent error bands. The daily inflation series
\(\pi_t\) is the 30-day percentage
change of the Billion Prices Project daily price index which is publicly
available from July 2008 to August 2015 via Cavallo and Rigobon, 2016. All monetary shock series shown
are calculated over the January 1995 to August 2015 sub-sample instead
of the full 1995 to 2024 sample. \(MP1\) is the 30-minute change around an
FOMC announcement in the current month’s federal funds future if the
FOMC announcement is in the first 23 days of the month with an
adjustment or the next month’s federal funds future if the FOMC
announcement is within the last seven days of the month. \(FF4\) is the change in the three-month
ahead federal funds futures within 30-minutes of an FOMC announcement.
\(NS\) is the first principal component
of the instrument set \(\{MP1,MP2,ED2,ED3,ED4\}\) which is the
30-minute change in these futures around an FOMC announcement. \(BRW\) is a Fama-MacBeth regression of the
daily change in one- to 30-year constant maturity Treasury yields. \(NS\) data/\(BRW\) method is a Fama-MacBeth regression
of the \(NS\) data. \(BRW\) data/\(NS\) method is the first principal
component of the \(BRW\)
data.
The figure has six panels, one for each of the six monetary shock series studied. Each panel plots an impulse response of daily inflation with 90 percent error bands to a one standard deviation monetary shock. The x-axis ranges from 0 to 60 days and the y-axis ranges from -2 to 1.5. Panel a is the daily impulse response for the NS shock series. The panel suggests that the positive inflation response is temporary and short lived and the response is conventionally- signed after 30 days. At impact and for ten periods, inflation responds positively before turning negative. The local projection series starts near zero, rises to 0.05 at day 5 and then drops slightly below zero at day 10. The series remains above zero until day 25 where it then decays towards -0.1 at day 35 and remains there until the end of the period shown. There are 90 percent confidence intervals surrounding this series. The upper confidence interval ranges from 0.3 to -0.05 and is mostly positive except when it drops below zero for days 33 onward. The lower confidence interval from 0.02 to -0.4 and is mostly negative. Panel b is the daily impulse response for the BRW shock series. The panel suggests that there is no adverse response of inflation. The series is zero at impact and fluctuates between y-values -0.05 and 0.5 until day 55 when it declines towards -0.15 by day 60. There are 90 percent confidence intervals surrounding this series. The upper confidence interval ranges from 0.005 to 0.25 and is always positive. The lower confidence interval ranges from -0.005 to -0.25. Panel c is the daily impulse response for the MP1 shock series. It is like the NS shock series in panel a, except for days 50 to 60 where it rises slightly above zero but not so that it is significantly above zero. Panel d is the daily impulse response for the FF4 shock series. It is like the NS shock series in panel a. Panel e is the daily impulse response for the swapped shock series with the BRW method- ology and the NS data. It rises from zero to a peak near 1 around day 30 and then drops to -1 by day 50 and remains at that value thereafter. The error bands are above zero until about day 30 and below zero around day 50 suggesting positive and significant initial values and negative and significant later values. Panel f is the daily impulse response for the swapped shock series with the NS method- ology and the BRW data. It is similar the MP 1 and FF 4 shock series, but not statistically significant from zero.
Figure 9: Impulse responses to a 25 basis point monetary shock, x-axis
is months and y-axis is percentage points. Impulse responses are
estimates from equation (12) \(Y_T=\alpha+ B(L)
Y_{T-1}+s_1Y_T^{2Y}+\tilde{u}_T\) obtained via the Canova and Ferroni, 2022 Bayesian VAR
toolbox with 68 percent error bands, 20,000 draws, and 8 lags. The
sample of monetary shock series is from January 1995 to December 2019
while the sample of economic data is from January 1973 to February 2020.
\(MP1\) is the 30-minute change around
an FOMC announcement in the current month’s federal funds future if the
FOMC announcement is in the first 23 days of the month with an
adjustment or the next month’s federal funds future if the FOMC
announcement is within the last seven days of the month. \(FF4\) is the change in the three-month
ahead federal funds futures within 30-minutes of an FOMC announcement.
\(NS\) is the first principal component
of the instrument set \(\{MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5\}\) which
is the 30-minute change in these futures around an FOMC announcement.
\(BRW\) is a Fama-MacBeth regression of
the daily change in one- to 30-year constant maturity Treasury yields.
IP is the industrial production index, CPI is the consumer price index,
excess bond premium is from Gilchrist and Zakrajšek, 2012, and the two-year Treasury is the end of the
month daily change in the zero-coupon yield. All sources of series are
detailed in Appendix D.
The figure shows impulse response functions for four variables and four different shock series for a total of 16 panels. The x-axis ranges from 0 to 50 months and the y-axis ranges from -4 to 0 on the industrial production row, -1 to 0.2 on the CPI row, -0.2 to 0.5 on the excess bond premium row, -0.3 to 0.5 on the 2-year Treasury Row. There are 68 percent error bands round each impulse response function. The figure shows that the impulse response functions across the shocks, the columns of the figure, are similar. The first row plots the impulse responses to industrial production. All series are similar in shape and sign. For the first two columns, the FF4 and MP1 shock series are similar with initial responses around -2 that decline to -3.75 by month 10 and rise steadily back to a little more than 2 by month 50. These responses are statistically significant. Columns 3 and 4, the NS and BRW series, respectively, are similar but with initial responses of 0.5 and near 0, respectively. The former declines to about -1.5 and the latter to about -2. Thereafter, the impulse responses climb to about 0.5. These impulse responses are statistically significant. The second row plots the impulse responses to the CPI. Columns 1,2, and 4, the shock series of MP 1, FF 4, and BRW , respectively, are all similar. The CPI is near zero on impact in the first two and near -0.25 in column four. All three decline to about -1 over the period shown. Column 3, the NS shock series, is smaller in magnitude. The CPI falls from 0 on impact to about -0.5 by period 50. These impulse responses are statistically significant. The third row plots the impulse responses to the excess bond premium. The series all have an initial impact coefficient near 0.2 to 0.4 and then steadily decline to 0 by about period 20. These impulse responses are statistically significant to about period 20. The fourth row plots the impulse responses to the 2-year Treasury. The impact response is 0.25 by construction on all of the series. The series then drops to 0 by about period 10. In the case of the NS shock series show in the third column, the response remains near zero. In the case of the other series, the response drops to about -0.2 and then rises towards zero by about period 40. Only the NS and BRW shock series in columns 3 and 4, respectively, are statistically significant from period 0 to about 5.
Figure 10: Impulse response to a 25 basis point monetary shock, x-axis
is months and y-axis is percentage points. Impulse responses are
estimates from equation (12) \(Y_T=\alpha+ B(L)
Y_{T-1}+s_1Y_T^{2Y}+\tilde{u}_T\) obtained via the Canova and Ferroni, 2022 Bayesian VAR
toolbox with 68 percent error bands, 20,000 draws, and 8 lags. The
sample of monetary shock series is from January 1995 to December 2019
while the sample of economic data is from January 1973 to February 2020.
\(NS\) data/\(BRW\) method is a Fama-MacBeth regression
of the \(NS\) data, the instrument set
\(\{MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5\}\)
which is the 30-minute change in these futures around an FOMC
announcement. \(BRW\) data/\(NS\) method is the first principal
component of the \(BRW\) data, the
daily change in one- to 30-year constant maturity Treasury yields. IP is
the industrial production index, CPI is the consumer price index, excess
bond premium is from Gilchrist and Zakrajšek, 2012,
and the two-year Treasury is the end of the month daily change in the
zero-coupon yield. All sources of series are detailed in Appendix D.
The figure shows impulse response functions for four variables and 2 different shock series for a total of 8 panels. The shocks are the swapped shocks, meaning “BRW Methodology, NS Data” and ”NS Methodology, BRW Data.” The x-axis ranges from 0 to 50 months and the y-axis ranges from 0 to 4 on the industrial production row, -0.5 to 1 on the CPI row, -0.3 to 0.2 on the excess bond premium row, -0.2 to 0.5 on the 2-year Treasury Row. There are 68 percent error bands round each impulse response function. The first row plots the impulse responses to industrial production. The “BRW Methodol- ogy, NS Data” shows an initial impact of about 1.3 that rises to 1.5 by quarter 4 before falling down to 0 by quarter 30. The “NS Methodology, BRW Data” shows an initial response of 1.9 that rises to 3.8 by the quarter 15 before falling to 0.5 by quarter 50. The second row plots the impulse responses to the CPI. The “BRW Methodology, NS Data” shows an initial impact of about 0.2 that rises to approximately 0.5 by quarter 4 and stays approximately there. The “NS Methodology, BRW Data” shows an initial response of -0.25 that rises to 0.4 by the quarter 50. The third row plots the impulse responses to the excess bond premium. The “BRW Methodology, NS Data” shows an initial impact of about 0 that rises to approximately 0.08 by quarter 13 before steadily falling to 0 by quarter 40. The “NS Methodology, BRW Data” shows an initial response of -0.25 that rises to 0.1 by the quarter 30 before falling to near 0 by quarter 50. The fourth row plots the impulse responses to the 2-year treasury. The “BRW Method- ology, NS Data” shows an initial impact of about 0.3 that rises to just under 0.4 in quarter 3 before falling to just above 0 by quarter 50. The “NS Methodology, BRW Data” shows an initial response of 0.25 that rises to 0.4 by the quarter 3 before falling to approximately 0 by quarter 50.
Figure A.11: Total daily number of trades of federal funds futures
contracts. Source: CME Group Inc.
This figure plots the daily trading volume of federal funds futures contracts. The x-axis ranges from 2004 to 2023. The y-axis ranges from 0 to $1.5 million. The figure shows that volumes were about $0.25 million from 2004 to 2009 where they then dropped to just about 0 and remained there until 2014. From 2014 onward, the volume fluctuates but peaks near $1.2 million in 2019. The figure shows the volume tends to drop in periods when the federal funds rate is at the effective lower bound (December 16, 2008 to December 16, 2015 and March 15, 2020 to March 16, 2022).
Figure A.12: Time windows around FOMC announcements for federal funds
rate futures.
This figure plots the time between trades around FOMC meetings that changes in federal funds rate futures are taken over. Each row is for a different federal funds rate future, including MP 1, MP 2, and FF 4. The first column is histograms and the second column is a timeseries plot. The x-axis of each histograms represents minutes between trades before and after the FOMC meeting. For MP 1 and FF 4, the x-axis ranges from 30 to 900, while the x-axis for MP 2 ranges from 30 to 1110. The y-axis ranges from 0 to 0.06. All histograms are concentrated near 30 with long right tails out to the end of the graph, with the right tail of MP 1 being fatter than the tails of the other two. The x-axis of each of the time series plots represents the date, ranging from January 1995 to January 2025. The y-axis represents minutes between trades before and after the FOMC meeting, ranging from 0 to 900 for MP 1 and FF 4 while ranging from 0 to 1500 for MP 2. The time series plots have a horizontal red line at 30 minutes, representing the minimum time over which these trades can be compared. From 2005 to 2009, and again from 2015 to 2020 all instruments are approximately against this 30 minute line. From 1995 to 2005, 2009 to 2015, and 2020 to 2022, all instruments show a large degree of variation, with y-values of 400 being common. MP 1 shows more volatility than FF 4 and MP 2 during these times. Finally there is a pronounced spike in December 2015 for all instruments, with a value of approximately 1200 for FF 4 and MP 2 and 900 for MP 1.
Figure A.13: Time windows around FOMC announcements for eurodollar
futures. SOFR futures replace eurodollar futures starting in January
2022.
This figure plots the time between trades around FOMC meetings that changes in eurodollar futures are taken over. Each row is for a different quarterly eurodollar future, including ED2, ED3, and ED4. The first column is histograms and the second column is a timeseries plot. The x-axis of each histograms represents minutes between trades before and after the FOMC meeting. For all instruments, the x-axis ranges from 30 to 100. The y-axis ranges from 0 to 0.2. All histograms are concentrated near 30 with long right tails out to the end of the graph. The x-axis of each of the time series plots represents the date, ranging from January 1995 to January 2025. The y-axis represents minutes between trades before and after the FOMC meeting, ranging from 0 to 100 for all instruments. The time series plots have a horizontal red line at 30 minutes, representing the minimum time over which these trades can be compared. From 1995 to 2005 and from 2020 to 2022, there is considerably volatility in the timeseries plots, with trades regularly covering 60 minutes for comparison. This volatility also appears to a lesser degree from 2009 to 2020 for ED2. At all other times, instruments are close to 30 minutes with minor deviations.
Figure A.14: Real-time versions of Nakamura and Steinsson, 2018 and Bu et al., 2021 series. Monetary shock series are
calculated from January 1995 to September 2024. Real-time estimates
calculate the shocks from the first 30 FOMC announcements and then
update the estimates recursively. From the 31st estimate onward, each
shock observation only contains information that was available at the
time of the FOMC announcement. \(NS\)
is the first principal component of the instrument set \(\{MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5\}\) which
is the 30-minute change in these futures around an FOMC announcement.
\(BRW\) is a Fama-MacBeth regression of
the daily change in one- to 30-year constant maturity Treasury
yields.
This figure shows two scatterplots, comparing the NS and BRW shocks, respectively, to their counterparts calculated in real-time. The x-axis represents dates, ranging from 1995 to 2025. The y-axis represents values of the shocks, ranging from -0.3 to 0.3. In each graph, there are dots for the shock calculated traditionally and dots for the shock calculated in real-time, with a light grey vertical line connecting them to show the difference. In both graphs, there is a text box showing the correlation between the shocks and their real-time versions is each 0.99. In the scatterplot for the NS shocks and its real-time counterpart, the dots are almost exactly aligned, with the largest deviations from each other occurring in the early 2000s and 2009. The dots are centered around 0 and are more scattered before 2009, and from 2009 to 2015 are tightly grouped just up from 0, and thereafter show some variation again with a positive bias. In the scatterplot for the BRW shocks and its real-time counterpart, the dots are almost exactly aligned, with the largest deviations from each other occurring in the early 2000s and 2009. The dots are centered around 0 and fairly homoskedastic throughout.
Figure A.15: Nakamura and Steinsson, 2018 series with and without
long-term rates. Monetary shock series are calculated from January 1995
to September 2024. \(NS\) is the first
principal component of the instrument set \(\{MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5\}\) which
is the 30-minute change in these futures around an FOMC announcement.
\(NS\) with long-term rates augments
the original instrument set with one-, five-, ten-, and 30-year Treasury
yields.
The figure shows two time series plots, the original NS shock series and a version constructed from intraday changes in long-term rates in the principal component analysis. The x-axis is from 1995 to 2025 and the y-axis is from -0.3 to 0.3. The two series fluctuate around 0 and are tightly correlated with a correlation coefficient of 0.93. There are larger negative shocks occuring prior to 2010 and after most of the shocks are close to 0.
Figure A.16: Monetary shock series under different scaling assumptions.
Monetary shock series are calculated from January 1995 to September
2024. \(NS\) is the first principal
component of the instrument set \(\{MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5\}\) which
is the 30-minute change in these futures around an FOMC announcement.
\(BRW\) is a Fama-MacBeth regression of
the daily change in one- to 30-year constant maturity Treasury
yields.
This figure shows two time series plots, comparing the NS and BRW shocks, respectively, to their counterparts calculated using a different scaling (1-year constant maturity Treasury for the BRW shock, and 2-year zero-coupon yield for the NS shock). The x-axis represents dates, ranging from 1995 to 2025. The y-axis represents values of the shocks, ranging from -0.25 to 0.2. The NS shocks have a correlation of 1.00 and the same sign 100% of the time, while the BRW shocks have a 0.998 correlation and the same sign 98% of the time. Both shocks and their differently scaled counterparts are visually indistinguishable from their time series plots in Figure 4.
Figure A.17: Predictability regressions. Estimate of \(\hat{\beta}\) in eq. (9) \(\varepsilon^i_T=\alpha+\beta news^k_T
+e_T\) are OLS. Panel (a) is the full sample from January 1995 to
September 2024. Panel (b) is the full sample ex-crisis which excludes
the first three months of 2009. Panel (c) is the full sample ex crisis
and Covid which excludes the first three months of 2009 and the second
quarter of 2020. Panel (d) is the NS sample from January 1995 to August
2015. Panel (e) is the ELB sample defined as December 16, 2008 to
December 16, 2015 and March 15, 2020 to March 16, 2022. Panel (f) is the
non-ELB sample defined as all dates except those in panel (e). For the
specification using the Blue Chip GDP revisions, we follow Bauer and Swanson, 2023 and exclude
observations where the FOMC announcement is in the first three business
days of the month from 1995 to December 2000 and the first two business
days thereafter to ensure that the Blue Chip Survey was completed prior
to the FOMC announcement. Blue Chip GDP revisions are the monthly
revision of one-quarter ahead GDP growth forecasts. The specification
using non-farm payrolls assures that the FOMC meeting is after the FOMC
release which is often the first Friday of every month. Non-farm
payrolls are the monthly change in the nonfarm payrolls release. The ADS
Index is the Aruoba et al., 2009 business conditions index.
The BKK index is the Brave et al., 2019 Big
Data index. \(MP1\) is the 30-minute
change around an FOMC announcement in the current month’s federal funds
future if the FOMC announcement is in the first 23 days of the month
with an adjustment or the next month’s federal funds future if the FOMC
announcement is within the last seven days of the month. \(FF4\) is the change in the three-month
ahead federal funds futures within 30-minutes of an FOMC announcement.
\(NS\) is the first principal component
of the instrument set \(\{MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5\}\) which
is the 30-minute change in these futures around an FOMC announcement.
\(BRW\) is a Fama-MacBeth regression of
the daily change in one- to 30-year constant maturity Treasury yields.
\(NS\) data/\(BRW\) method is a Fama-MacBeth regression
of the \(NS\) data. \(BRW\) data/\(NS\) method is the first principal
component of the \(BRW\) data.
This figure shows the predictability coefficient plots of Figure 6, including the same specifi- cations for the x- and y-axes, but over different samples with a panel for each specifications. There are 6 panels, one for “Full Sample,” another for “Full Sample excluding the financial crisis,” another for “Full Sample excluding the financial crisis and COVID,” another for the “NS Sample,” another for ”ELB episodes,” and a final one for ”Non-ELB Episodes.” The panel for “Full Sample” is identical to Figure 6 and serves as a point of reference. The panel for “Full Sample excluding the financial crisis” excludes the first 3 months of 2009. All predictor variables for MP 1 do not show significance at the 95% level except for nonfarm payrolls, which is positivly associated. All predictor variables for FF 4 do not show significance at the 95% level. All predictor variables for NS do not show significance at the 95% level. All predictor variables for BRW do not show significance at the 95% level except for nonfarm payrolls, which is positively associated. All predictor variables for NS data with BRW methodology do not show significance at the 95% level except for the BKK index, which is negatively associated. All predictor variables for BRW data with NS methodology do not show significance at the 95% level except for nonfarm payrolls, which is negatively associated. The panel for “Full Sample excluding the financial crisis and COVID” excludes the first 3 months of 2009 and the second quarter of 2020. All predictor variables for MP 1 do not show significance at the 95% level except for Blue Chip GDP revisions, which is positively associated. All predictor variables for FF 4 do not show significance at the 95% level except for Blue Chip GDP Revisions, which is positively associated, and nonfarm payrolls, which is positively associated. All predictor variables for NS do not show significance at the 95% level except for Blue Chip GDP Revisions, which is positively associated, and nonfarm payrolls, which is positively associated. All predictor variables for BRW do not show significance at the 95% level. All predictor variables for NS data with BRW methodology do not show significance at the 95% level. All predictor variables for BRW data with NS methodology do not show significance at the 95% level. The panel for “NS Sample” covers January 1995 to August 2015. All predictor variables for MP 1 do not show significance at the 95% level except for Blue Chip GDP revisions, which is positively associated. All predictor variables for FF 4 do not show significance at the 95% level except for Blue Chip GDP Revisions, which is positively associated. All predictor variables for NS do not show significance at the 95% level except for Blue Chip GDP Revisions, which is positively associated, and nonfarm payrolls, which is positively associated. All predictor variables for BRW do not show significance at the 95% level. All predictor variables for NS data with BRW methodology do not show significance at the 95% level. All predictor variables for BRW data with NS methodology do not show significance at the 95% level. The panel for “ELB episodes” covers December 16, 2008 to December 16, 2015 and March 15, 2020 to March 16, 2022. All predictor variables for MP 1 do not show significance at the 95% level except for nonfarm payrolls, which is positively associated. All predictor variables for FF 4 do not show significance at the 95% level except for nonfarm payrolls, which is positively associated. All predictor variables for NS do not show significance at the 95% level. All predictor variables for BRW do not show significance at the 95% level except for nonfarm payrolls, which is positively associated, and the ADS index, which is positively associated. All predictor variables for NS data with BRW methodology do not show significance at the 95% level except for nonfarm payrolls, which is negatively associated. All predictor variables for BRW data with NS methodology do not show significance at the 95% level. The panel for “Non-ELB episodes” covers January 1995 to November 2023 xcluding De- cember 16, 2008 to December 16, 2015 and March 15, 2020 to March 16, 2022. All predictor variables for MP 1 do not show significance at the 95% level except for Blue Chip GDP revisions, which is positively associated, and the BKK index, which is positively associated. All predictor variables for FF 4 do not show significance at the 95% level except for Blue Chip GDP revisions, which is positively associated. All predictor variables for NS do not show significance at the 95% level except for Blue Chip GDP revisions, which is positively associated, and nonfarm payrolls, which is positively associated, and the BKK index, which is positively associated. All predictor variables for BRW do not show significance at the 95% level. All predictor variables for NS data with BRW methodology do not show significance at the 95% level. All predictor variables for BRW data with NS methodology do not show significance at the 95% level.
Figure B.18: Forecast revision coefficients and 95% confidence intervals.
Estimates of \(\hat{\beta}\) in eq. (10) \(\text{Blue Chip GDP revisions}_T=\beta
\varepsilon_T^i+e_T\) are obtained via OLS. The robust standard
errors are similar when bootstrapped. The full sample is from January
1995 to September 2024. Crisis controls are indicator variables for the
first three months of 2009 and Covid controls are for the second quarter
of 2020. The \(NS\) sample is from
January 1995 to August 2015. The ELB is defined as December 16, 2008 to
December 16, 2015 and March 15, 2020 to March 16, 2022. Following Bauer and Swanson, 2023, we exclude
observations where the FOMC announcement is in the first three business
days of the month from 1995 to December 2000 and the first two business
days thereafter to ensure that the Blue Chip Survey was completed prior
to the FOMC announcement. \(MP1\) is
the 30-minute change around an FOMC announcement in the current month’s
federal funds future if the FOMC announcement is in the first 23 days of
the month with an adjustment or the next month’s federal funds future if
the FOMC announcement is within the last seven days of the month. \(FF4\) is the change in the three-month
ahead federal funds futures within 30-minutes of an FOMC announcement.
\(NS\) is the first principal component
of the instrument set \(\{MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5\}\) which
is the 30-minute change in these futures around an FOMC announcement.
\(BRW\) is a Fama-MacBeth regression of
the daily change in one- to 30-year constant maturity Treasury yields.
\(NS\) data/\(BRW\) method is a Fama-MacBeth regression
of the \(NS\) data. \(BRW\) data/\(NS\) method is the first principal
component of the \(BRW\) data.
The figure has two panels. Each panel is a coefficient plot similar to Figure 7. The x-axis is the same as described for Figure 7. The y-axis for the first panel ranges from -20 to 20 while the y-axis for the second panel ranges from -3 to 2. In the first panel, above each shock there is a coefficient point estimate with a 95% confidence interval for both over the ELB sample and the non-ELB sample. For MP1, the coefficient estimate for the non-ELB sample is approximately 0.5 and the confidence interval is not visible, and it is just barely not significant; for the ELB sample, the coefficient estimate is approximately 3 with a confidence interval from -19 to 13. For FF4, the coefficient estimate for the non-ELB sample is approximately 0.5 and the confidence interval is not visible, and it is significant; for the ELB sample, the coefficient estimate is approximately 0 with a confidence interval from -8 to 8. For NS, the coefficient estimate for the non-ELB sample is approximately 1 and the confidence interval ranges from 1.1 to 0.9; for the ELB sample, the coefficient estimate is approximately 2 with a confidence interval from -2 to 7. For BRW, the coefficient estimate for the non-ELB sample is approximately 0 and the confidence interval ranges from -0.1 to 0.1; for the ELB sample, the coefficient estimate is approximately - 0.5 with a confidence interval from -0.5 to -1.1. For NS data with the BRW method, the coefficient estimate for the non-ELB sample is approximately 0 and the confidence interval ranges from -0.1 to 0.1; for the ELB sample, the coefficient estimate is approximately 8 with a confidence interval from 20 to -5. For BRW data with the NS method, the coefficient estimate for the non-ELB sample is approximately 0.2 and the confidence interval ranges from -0.3 to 0.1; for the ELB sample, the coefficient estimate is approximately 2 with a confidence interval from 0 to 4. In the second panel, coefficient estimates and 95% confidence intervals are plotted over the sample specifications of “Full Sample,” “Full Sample controlling for the financial crisis,” “Full Sample controlling for the financial crisis and COVID,” “NS Sample,” ”ELB episodes,” and ”Non-ELB Episodes,” whose specifications can be found in the description for Figure A.16. For MP1, all plotted coefficients with their confidence intervals are similar to as shown in Figure 7, except coefficient significance is shown for “Full sample with COVID controls,” “Full sample controlling for the financial crisis and COVID,” “NS Sample,” and “non-ELB Sample.” For FF4, all coefficients across all samples are significant and positive, with coefficient estimates ranging from 0.7 to 0.9. For NS, all coefficients across all samples are significant and positive, with all approximately equal to 1. For BRW, all coefficients across all samples are not significant, with coefficient estimates close to 0. For NS data with BRW methodology, all coefficients across all samples are not significant, with coefficient estimates ranging from -0.1 to 0.8. For BRW data with NS methodology, all coefficients across all samples are not significant, with coefficient estimates ranging from -1 to 1.
Figure C.19: Impulse responses to a 25 basis point \(NS\) shock series, x-axis is months and
y-axis is percentage points. Panel (a) is figure (3) in Bauer and Swanson, 2022. Estimates in
panels (b) and (c) are from equation (12) \(Y_T=\alpha+ B(L)
Y_{T-1}+s_1Y_T^{2Y}+\tilde{u}_T\) obtained via the Canova and Ferroni, 2022 Bayesian VAR
toolbox with 68 percent error bands and 20,000 draws. IP is the
industrial production index, CPI is the consumer price index, excess
bond premium is from Gilchrist and Zakrajšek, 2012,
and the 2-year Treasury is the end of the month daily change in the
zero-coupon yield. All sources of series are detailed in Appendix D.
The figure shows impulse response functions for four variables and 3 different shock series for a total of 12 panels. The x-axis ranges from 0 to 50 months and the y-axis ranges from -2 to 0 on the industrial production row, -1 to 0 on the CPI row, 0 to 0.4 on the excess bond premium row, -0.3 to 0.3 on the 2-year Treasury Row. There are 68 percent error bands round each impulse response function. The figure shows that the impulse response functions across the shocks, the columns of the figure, are similar. The second column is pulled directly from Bauer and Swanson (2022). The second column is replicating their results. The third column is replicating the other two columns but using 8 lags in our specification rather than the 12 used in Bauer and Swanson (2022). Columns 1 and 2 are identical, except for column 2 having narrower error bands. The initial response of inflation is approximately -0.1 and falls to approximately -0.4 by quarter 10 before rising to -0.2 by quarter 50. The initial response of CPI is approximately -0.1 and falls to -0.3 by quarter 50. The initial response of the excess bond premium is approximately 0.07 and falls to 0 by quarter 12. The initial response of the 2-year Treasury is 0.25 and falls to near 0 by quarter 50. Columns 3 is similar to the other two columns but has slight differences. The initial response of inflation is approximately -0.07 and falls to approximately -0.9 by quarter 10 before rising to 0.2 by quarter 50. The initial response of CPI is approximately -0.2 and falls to -0.45 by quarter 50. The initial response of the excess bond premium is approximately 0.17 and falls to 0 by quarter 20. The initial response of the 2-year Treasury is 0.25 and falls to near 0 by quarter 10.