Figure 1: One-Quarter-Ahead Federal Funds Rate Predictions for
Estimated Rules
Note: This figure displays the
one-quarter-ahead predictions of the level of the federal funds rate
from 1987:Q4 through 2025:Q3 for each specification in Section 2. The black line plots the
realized quarterly averages of the effective federal funds rate over the
same period. All rules are estimated over the full ‘Post-1987’ sample
using Tobit regressions. The prediction in quarter \(t\) is computed using the realized values
of \(\pi_t\), \(u_t\), and \(u^*_t\), the relevant lagged values of the
federal funds rate, \(\pi^* = 2\), and
the estimated parameters \(\hat{r}^*\),
\(\hat{\beta}_\pi\), \(\hat{\beta}_u\), \(\hat{\rho}\), and \(\hat{\gamma}\) from Table 1.
| Date | Actual_FFR | Non_Inertial | Inertial | Double_Inertial | AR1 | AR2 |
|---|---|---|---|---|---|---|
| 1987-10-01 00:00:00 | 6.92 | 4.794 | 6.81 | 6.897 | 6.806 | 6.916 |
| 1988-01-01 00:00:00 | 6.66 | 5.236 | 6.96 | 6.944 | 6.888 | 6.912 |
| 1988-04-01 00:00:00 | 7.16 | 5.752 | 6.805 | 6.528 | 6.623 | 6.393 |
| 1988-07-01 00:00:00 | 7.98 | 5.961 | 7.307 | 7.5 | 7.133 | 7.472 |
| 1988-10-01 00:00:00 | 8.47 | 6.352 | 8.142 | 8.518 | 7.971 | 8.536 |
| 1989-01-01 00:00:00 | 9.44 | 6.603 | 8.643 | 8.802 | 8.471 | 8.774 |
| 1989-04-01 00:00:00 | 9.73 | 6.305 | 9.5 | 10.002 | 9.462 | 10.11 |
| 1989-07-01 00:00:00 | 9.08 | 5.909 | 9.704 | 9.818 | 9.759 | 9.882 |
| 1989-10-01 00:00:00 | 8.61 | 5.378 | 9.006 | 8.563 | 9.095 | 8.515 |
| 1990-01-01 00:00:00 | 8.25 | 5.568 | 8.599 | 8.242 | 8.614 | 8.182 |
| 1990-04-01 00:00:00 | 8.24 | 5.73 | 8.289 | 7.982 | 8.247 | 7.906 |
| 1990-07-01 00:00:00 | 8.16 | 5.299 | 8.204 | 8.157 | 8.237 | 8.163 |
| 1990-10-01 00:00:00 | 7.74 | 4.556 | 8 | 7.973 | 8.155 | 8.03 |
| 1991-01-01 00:00:00 | 6.43 | 3.48 | 7.422 | 7.266 | 7.726 | 7.351 |
| 1991-04-01 00:00:00 | 5.86 | 2.817 | 6.084 | 5.4 | 6.388 | 5.362 |
| 1991-07-01 00:00:00 | 5.64 | 2.527 | 5.501 | 5.293 | 5.805 | 5.356 |
| 1991-10-01 00:00:00 | 4.82 | 2.129 | 5.227 | 5.267 | 5.581 | 5.403 |
| 1992-01-01 00:00:00 | 4.02 | 1.506 | 4.352 | 4.055 | 4.743 | 4.126 |
| 1992-04-01 00:00:00 | 3.77 | 1.096 | 3.534 | 3.268 | 3.926 | 3.341 |
| 1992-07-01 00:00:00 | 3.26 | 0.79 | 3.248 | 3.345 | 3.67 | 3.51 |
| 1992-10-01 00:00:00 | 3.04 | 1.037 | 2.814 | 2.716 | 3.15 | 2.802 |
| 1993-01-01 00:00:00 | 3.04 | 1.411 | 2.674 | 2.718 | 2.925 | 2.803 |
| 1993-04-01 00:00:00 | 3 | 1.428 | 2.676 | 2.857 | 2.925 | 2.971 |
| 1993-07-01 00:00:00 | 3.06 | 1.852 | 2.712 | 2.83 | 2.884 | 2.9 |
| 1993-10-01 00:00:00 | 2.99 | 1.945 | 2.786 | 2.956 | 2.945 | 3.037 |
| 1994-01-01 00:00:00 | 3.21 | 1.698 | 2.679 | 2.786 | 2.874 | 2.868 |
| 1994-04-01 00:00:00 | 3.94 | 2.235 | 2.978 | 3.222 | 3.098 | 3.309 |
| 1994-07-01 00:00:00 | 4.49 | 2.526 | 3.711 | 4.263 | 3.844 | 4.427 |
| 1994-10-01 00:00:00 | 5.17 | 3.136 | 4.331 | 4.728 | 4.406 | 4.84 |
| 1995-01-01 00:00:00 | 5.81 | 3.331 | 5 | 5.476 | 5.101 | 5.619 |
| 1995-04-01 00:00:00 | 6.02 | 2.904 | 5.526 | 6.026 | 5.754 | 6.229 |
| 1995-07-01 00:00:00 | 5.8 | 2.799 | 5.704 | 5.948 | 5.969 | 6.111 |
| 1995-10-01 00:00:00 | 5.72 | 2.926 | 5.52 | 5.48 | 5.744 | 5.563 |
| 1996-01-01 00:00:00 | 5.36 | 2.939 | 5.448 | 5.491 | 5.662 | 5.59 |
| 1996-04-01 00:00:00 | 5.24 | 2.803 | 5.089 | 4.96 | 5.295 | 5.016 |
| 1996-07-01 00:00:00 | 5.31 | 3.081 | 5.025 | 5.019 | 5.172 | 5.079 |
| 1996-10-01 00:00:00 | 5.28 | 3.116 | 5.096 | 5.208 | 5.244 | 5.294 |
| 1997-01-01 00:00:00 | 5.28 | 3.253 | 5.092 | 5.128 | 5.213 | 5.188 |
| 1997-04-01 00:00:00 | 5.52 | 3.595 | 5.151 | 5.176 | 5.213 | 5.211 |
| 1997-07-01 00:00:00 | 5.53 | 3.53 | 5.365 | 5.549 | 5.458 | 5.634 |
| 1997-10-01 00:00:00 | 5.51 | 3.602 | 5.388 | 5.419 | 5.468 | 5.468 |
| 1998-01-01 00:00:00 | 5.52 | 3.653 | 5.379 | 5.385 | 5.448 | 5.426 |
| 1998-04-01 00:00:00 | 5.5 | 3.761 | 5.407 | 5.421 | 5.458 | 5.458 |
| 1998-07-01 00:00:00 | 5.53 | 3.692 | 5.376 | 5.378 | 5.438 | 5.416 |
| 1998-10-01 00:00:00 | 4.86 | 3.838 | 5.43 | 5.45 | 5.468 | 5.484 |
| 1999-01-01 00:00:00 | 4.73 | 3.943 | 4.821 | 4.381 | 4.784 | 4.28 |
| 1999-04-01 00:00:00 | 4.75 | 3.965 | 4.703 | 4.597 | 4.651 | 4.562 |
| 1999-07-01 00:00:00 | 5.09 | 4.123 | 4.749 | 4.723 | 4.672 | 4.696 |
| 1999-10-01 00:00:00 | 5.31 | 4.41 | 5.116 | 5.273 | 5.019 | 5.28 |
| 2000-01-01 00:00:00 | 5.68 | 4.808 | 5.39 | 5.444 | 5.244 | 5.409 |
| 2000-04-01 00:00:00 | 6.27 | 4.959 | 5.762 | 5.904 | 5.622 | 5.893 |
| 2000-07-01 00:00:00 | 6.52 | 4.891 | 6.302 | 6.6 | 6.224 | 6.651 |
| 2000-10-01 00:00:00 | 6.47 | 5.063 | 6.565 | 6.641 | 6.48 | 6.641 |
| 2001-01-01 00:00:00 | 5.59 | 4.683 | 6.452 | 6.374 | 6.429 | 6.363 |
| 2001-04-01 00:00:00 | 4.33 | 4.378 | 5.576 | 4.989 | 5.53 | 4.85 |
| 2001-07-01 00:00:00 | 3.5 | 3.515 | 4.249 | 3.473 | 4.243 | 3.3 |
| 2001-10-01 00:00:00 | 2.13 | 2.363 | 3.273 | 2.851 | 3.395 | 2.798 |
| 2002-01-01 00:00:00 | 1.73 | 1.719 | 1.882 | 1.147 | 1.995 | 1.017 |
| 2002-04-01 00:00:00 | 1.75 | 1.706 | 1.505 | 1.372 | 1.587 | 1.356 |
| 2002-07-01 00:00:00 | 1.74 | 2.113 | 1.593 | 1.69 | 1.607 | 1.696 |
| 2002-10-01 00:00:00 | 1.44 | 1.667 | 1.507 | 1.623 | 1.597 | 1.663 |
| 2003-01-01 00:00:00 | 1.25 | 1.663 | 1.225 | 1.154 | 1.29 | 1.142 |
| 2003-04-01 00:00:00 | 1.25 | 1.179 | 0.965 | 1 | 1.096 | 1.036 |
| 2003-07-01 00:00:00 | 1.02 | 1.106 | 0.952 | 1.112 | 1.096 | 1.181 |
| 2003-10-01 00:00:00 | 1 | 1.672 | 0.835 | 0.797 | 0.861 | 0.776 |
| 2004-01-01 00:00:00 | 1 | 2.051 | 0.881 | 0.942 | 0.841 | 0.916 |
| 2004-04-01 00:00:00 | 1.01 | 2.386 | 0.938 | 0.984 | 0.841 | 0.931 |
| 2004-07-01 00:00:00 | 1.43 | 2.616 | 0.987 | 1.019 | 0.851 | 0.949 |
| 2004-10-01 00:00:00 | 1.95 | 2.701 | 1.394 | 1.685 | 1.28 | 1.681 |
| 2005-01-01 00:00:00 | 2.47 | 3.007 | 1.933 | 2.271 | 1.811 | 2.277 |
| 2005-04-01 00:00:00 | 2.94 | 3.262 | 2.464 | 2.789 | 2.343 | 2.797 |
| 2005-07-01 00:00:00 | 3.46 | 3.452 | 2.936 | 3.223 | 2.823 | 3.229 |
| 2005-10-01 00:00:00 | 3.98 | 3.567 | 3.442 | 3.762 | 3.354 | 3.787 |
| 2006-01-01 00:00:00 | 4.46 | 3.934 | 3.992 | 4.289 | 3.885 | 4.307 |
| 2006-04-01 00:00:00 | 4.91 | 4.371 | 4.516 | 4.762 | 4.375 | 4.757 |
| 2006-07-01 00:00:00 | 5.25 | 4.509 | 4.96 | 5.185 | 4.835 | 5.184 |
| 2006-10-01 00:00:00 | 5.25 | 4.618 | 5.298 | 5.449 | 5.182 | 5.44 |
| 2007-01-01 00:00:00 | 5.26 | 4.558 | 5.287 | 5.232 | 5.182 | 5.181 |
| 2007-04-01 00:00:00 | 5.25 | 4.214 | 5.238 | 5.217 | 5.193 | 5.198 |
| 2007-07-01 00:00:00 | 5.07 | 3.849 | 5.166 | 5.163 | 5.182 | 5.173 |
| 2007-10-01 00:00:00 | 4.5 | 3.925 | 5.01 | 4.893 | 4.998 | 4.864 |
| 2008-01-01 00:00:00 | 3.18 | 3.458 | 4.396 | 4.064 | 4.416 | 3.996 |
| 2008-04-01 00:00:00 | 2.09 | 2.975 | 3.078 | 2.293 | 3.068 | 2.105 |
| 2008-07-01 00:00:00 | 1.94 | 1.86 | 1.865 | 1.301 | 1.954 | 1.19 |
| 2008-10-01 00:00:00 | 0.51 | 0 | 1.355 | 1.558 | 1.801 | 1.757 |
| 2009-01-01 00:00:00 | 0.18 | 0 | 0 | 0 | 0.34 | 0 |
| 2009-04-01 00:00:00 | 0.18 | 0 | 0 | 0 | 0.003 | 0 |
| 2009-07-01 00:00:00 | 0.16 | 0 | 0 | 0 | 0.003 | 0.111 |
| 2009-10-01 00:00:00 | 0.12 | 0 | 0 | 0 | 0 | 0.076 |
| 2010-01-01 00:00:00 | 0.13 | 0 | 0 | 0 | 0 | 0.021 |
| 2010-04-01 00:00:00 | 0.19 | 0 | 0 | 0 | 0 | 0.069 |
| 2010-07-01 00:00:00 | 0.19 | 0 | 0 | 0 | 0.014 | 0.167 |
| 2010-10-01 00:00:00 | 0.19 | 0 | 0 | 0 | 0.014 | 0.121 |
| 2011-01-01 00:00:00 | 0.16 | 0 | 0 | 0 | 0.014 | 0.121 |
| 2011-04-01 00:00:00 | 0.09 | 0 | 0 | 0 | 0 | 0.068 |
| 2011-07-01 00:00:00 | 0.08 | 0 | 0 | 0 | 0 | 0 |
| 2011-10-01 00:00:00 | 0.07 | 0 | 0 | 0 | 0 | 0.003 |
| 2012-01-01 00:00:00 | 0.1 | 0 | 0 | 0 | 0 | 0 |
| 2012-04-01 00:00:00 | 0.15 | 0 | 0 | 0 | 0 | 0.054 |
| 2012-07-01 00:00:00 | 0.14 | 0 | 0 | 0 | 0 | 0.119 |
| 2012-10-01 00:00:00 | 0.16 | 0 | 0 | 0 | 0 | 0.063 |
| 2013-01-01 00:00:00 | 0.14 | 0 | 0 | 0 | 0 | 0.106 |
| 2013-04-01 00:00:00 | 0.12 | 0 | 0 | 0 | 0 | 0.056 |
| 2013-07-01 00:00:00 | 0.08 | 0 | 0 | 0 | 0 | 0.036 |
| 2013-10-01 00:00:00 | 0.09 | 0 | 0 | 0 | 0 | 0 |
| 2014-01-01 00:00:00 | 0.07 | 0 | 0 | 0 | 0 | 0.029 |
| 2014-04-01 00:00:00 | 0.09 | 0.623 | 0 | 0 | 0 | 0 |
| 2014-07-01 00:00:00 | 0.09 | 0.735 | 0 | 0 | 0 | 0.036 |
| 2014-10-01 00:00:00 | 0.1 | 1.203 | 0 | 0.011 | 0 | 0.021 |
| 2015-01-01 00:00:00 | 0.11 | 1.357 | 0 | 0.039 | 0 | 0.039 |
| 2015-04-01 00:00:00 | 0.12 | 1.493 | 0 | 0.06 | 0 | 0.049 |
| 2015-07-01 00:00:00 | 0.14 | 1.897 | 0.034 | 0.103 | 0 | 0.059 |
| 2015-10-01 00:00:00 | 0.16 | 2.006 | 0.071 | 0.138 | 0 | 0.086 |
| 2016-01-01 00:00:00 | 0.36 | 2.364 | 0.151 | 0.189 | 0 | 0.106 |
| 2016-04-01 00:00:00 | 0.37 | 2.427 | 0.348 | 0.498 | 0.187 | 0.444 |
| 2016-07-01 00:00:00 | 0.4 | 2.499 | 0.37 | 0.396 | 0.197 | 0.309 |
| 2016-10-01 00:00:00 | 0.45 | 2.718 | 0.435 | 0.456 | 0.228 | 0.354 |
| 2017-01-01 00:00:00 | 0.7 | 3.056 | 0.54 | 0.545 | 0.279 | 0.419 |
| 2017-04-01 00:00:00 | 0.95 | 3.159 | 0.793 | 0.917 | 0.535 | 0.822 |
| 2017-07-01 00:00:00 | 1.15 | 3.175 | 1.03 | 1.156 | 0.79 | 1.072 |
| 2017-10-01 00:00:00 | 1.2 | 3.405 | 1.257 | 1.336 | 0.994 | 1.234 |
| 2018-01-01 00:00:00 | 1.45 | 3.865 | 1.382 | 1.33 | 1.045 | 1.169 |
| 2018-04-01 00:00:00 | 1.74 | 4.191 | 1.672 | 1.723 | 1.301 | 1.572 |
| 2018-07-01 00:00:00 | 1.92 | 4.351 | 1.97 | 2.039 | 1.597 | 1.892 |
| 2018-10-01 00:00:00 | 2.22 | 4.355 | 2.139 | 2.142 | 1.781 | 1.988 |
| 2019-01-01 00:00:00 | 2.4 | 3.965 | 2.354 | 2.47 | 2.087 | 2.38 |
| 2019-04-01 00:00:00 | 2.4 | 4.334 | 2.586 | 2.597 | 2.271 | 2.468 |
| 2019-07-01 00:00:00 | 2.19 | 4.37 | 2.592 | 2.488 | 2.271 | 2.331 |
| 2019-10-01 00:00:00 | 1.64 | 4.255 | 2.377 | 2.145 | 2.057 | 1.961 |
| 2020-01-01 00:00:00 | 1.26 | 3.968 | 1.812 | 1.383 | 1.495 | 1.152 |
| 2020-04-01 00:00:00 | 0.06 | 0 | 0 | 0 | 1.107 | 0.901 |
| 2020-07-01 00:00:00 | 0.09 | 0 | 0 | 0 | 0 | 0 |
| 2020-10-01 00:00:00 | 0.09 | 0 | 0 | 0 | 0 | 0.044 |
| 2021-01-01 00:00:00 | 0.08 | 0.301 | 0 | 0 | 0 | 0.021 |
| 2021-04-01 00:00:00 | 0.07 | 2.247 | 0.046 | 0.096 | 0 | 0.003 |
| 2021-07-01 00:00:00 | 0.09 | 3.938 | 0.328 | 0.232 | 0 | 0 |
| 2021-10-01 00:00:00 | 0.08 | 6.165 | 0.728 | 0.464 | 0 | 0.036 |
| 2022-01-01 00:00:00 | 0.12 | 7.229 | 0.9 | 0.53 | 0 | 0.003 |
| 2022-04-01 00:00:00 | 0.77 | 7.507 | 0.986 | 0.621 | 0 | 0.082 |
| 2022-07-01 00:00:00 | 2.19 | 7.735 | 1.634 | 1.644 | 0.606 | 1.197 |
| 2022-10-01 00:00:00 | 3.65 | 7.44 | 2.911 | 3.456 | 2.057 | 3.204 |
| 2023-01-01 00:00:00 | 4.52 | 7.292 | 4.253 | 4.862 | 3.548 | 4.694 |
| 2023-04-01 00:00:00 | 4.99 | 7.094 | 5.033 | 5.306 | 4.437 | 5.114 |
| 2023-07-01 00:00:00 | 5.26 | 6.316 | 5.341 | 5.435 | 4.917 | 5.279 |
| 2023-10-01 00:00:00 | 5.33 | 5.418 | 5.441 | 5.488 | 5.193 | 5.397 |
| 2024-01-01 00:00:00 | 5.33 | 5.256 | 5.48 | 5.415 | 5.264 | 5.314 |
| 2024-04-01 00:00:00 | 5.33 | 4.686 | 5.382 | 5.322 | 5.264 | 5.261 |
| 2024-07-01 00:00:00 | 5.26 | 4.351 | 5.324 | 5.293 | 5.264 | 5.261 |
| 2024-10-01 00:00:00 | 4.65 | 4.637 | 5.307 | 5.208 | 5.193 | 5.137 |
| 2025-01-01 00:00:00 | 4.33 | 4.469 | 4.709 | 4.272 | 4.569 | 4.116 |
| 2025-04-01 00:00:00 | 4.33 | 4.24 | 4.37 | 4.128 | 4.243 | 4.017 |
| 2025-07-01 00:00:00 | 4.29 | 4.191 | 4.361 | 4.324 | 4.243 | 4.261 |
Figure 2: One-Quarter-Ahead Federal Funds Rate Adjustment Predictions
for Estimated Rules
Note: This figure displays
the predicted adjustments to the federal funds rate from 1987:Q4 through
2025:Q3 for the single- and double-inertial specifications in Section 2. The black line plots the
realized changes to the quarterly averages of the effective federal
funds rate over the same period. The rules are estimated over the full
‘Post-1987’ sample using Tobit regressions. The prediction in quarter
\(t\) is computed using the realized
values of \(\pi_t\), \(u_t\), and \(u^*_t\), the relevant lagged values of the
federal funds rate, \(\pi^* = 2\), and
the estimated parameters \(\hat{r}^*\),
\(\hat{\beta}_\pi\), \(\hat{\beta}_u\), \(\hat{\rho}\), and \(\hat{\gamma}\) from Table 1.
Source:
FRED.
| Date | Actual_Change | Inertial_Change | Double_Inertial_Change |
|---|---|---|---|
| 1987-10-01 00:00:00 | 0.08 | -0.03 | 0.057 |
| 1988-01-01 00:00:00 | -0.26 | 0.04 | 0.024 |
| 1988-04-01 00:00:00 | 0.5 | 0.145 | -0.132 |
| 1988-07-01 00:00:00 | 0.82 | 0.147 | 0.34 |
| 1988-10-01 00:00:00 | 0.49 | 0.162 | 0.538 |
| 1989-01-01 00:00:00 | 0.97 | 0.173 | 0.332 |
| 1989-04-01 00:00:00 | 0.29 | 0.06 | 0.562 |
| 1989-07-01 00:00:00 | -0.65 | -0.026 | 0.088 |
| 1989-10-01 00:00:00 | -0.47 | -0.074 | -0.517 |
| 1990-01-01 00:00:00 | -0.36 | -0.011 | -0.368 |
| 1990-04-01 00:00:00 | -0.01 | 0.039 | -0.268 |
| 1990-07-01 00:00:00 | -0.08 | -0.036 | -0.083 |
| 1990-10-01 00:00:00 | -0.42 | -0.16 | -0.187 |
| 1991-01-01 00:00:00 | -1.31 | -0.318 | -0.474 |
| 1991-04-01 00:00:00 | -0.57 | -0.346 | -1.03 |
| 1991-07-01 00:00:00 | -0.22 | -0.359 | -0.567 |
| 1991-10-01 00:00:00 | -0.82 | -0.413 | -0.373 |
| 1992-01-01 00:00:00 | -0.8 | -0.468 | -0.765 |
| 1992-04-01 00:00:00 | -0.25 | -0.486 | -0.752 |
| 1992-07-01 00:00:00 | -0.51 | -0.522 | -0.425 |
| 1992-10-01 00:00:00 | -0.22 | -0.446 | -0.544 |
| 1993-01-01 00:00:00 | 0 | -0.366 | -0.322 |
| 1993-04-01 00:00:00 | -0.04 | -0.364 | -0.183 |
| 1993-07-01 00:00:00 | 0.06 | -0.288 | -0.17 |
| 1993-10-01 00:00:00 | -0.07 | -0.274 | -0.104 |
| 1994-01-01 00:00:00 | 0.22 | -0.311 | -0.204 |
| 1994-04-01 00:00:00 | 0.73 | -0.232 | 0.012 |
| 1994-07-01 00:00:00 | 0.55 | -0.229 | 0.323 |
| 1994-10-01 00:00:00 | 0.68 | -0.159 | 0.238 |
| 1995-01-01 00:00:00 | 0.64 | -0.17 | 0.306 |
| 1995-04-01 00:00:00 | 0.21 | -0.284 | 0.216 |
| 1995-07-01 00:00:00 | -0.22 | -0.316 | -0.072 |
| 1995-10-01 00:00:00 | -0.08 | -0.28 | -0.32 |
| 1996-01-01 00:00:00 | -0.36 | -0.272 | -0.229 |
| 1996-04-01 00:00:00 | -0.12 | -0.271 | -0.4 |
| 1996-07-01 00:00:00 | 0.07 | -0.215 | -0.221 |
| 1996-10-01 00:00:00 | -0.03 | -0.214 | -0.102 |
| 1997-01-01 00:00:00 | 0 | -0.188 | -0.152 |
| 1997-04-01 00:00:00 | 0.24 | -0.129 | -0.104 |
| 1997-07-01 00:00:00 | 0.01 | -0.155 | 0.029 |
| 1997-10-01 00:00:00 | -0.02 | -0.142 | -0.111 |
| 1998-01-01 00:00:00 | 0.01 | -0.131 | -0.125 |
| 1998-04-01 00:00:00 | -0.02 | -0.113 | -0.099 |
| 1998-07-01 00:00:00 | 0.03 | -0.124 | -0.122 |
| 1998-10-01 00:00:00 | -0.67 | -0.1 | -0.08 |
| 1999-01-01 00:00:00 | -0.13 | -0.039 | -0.479 |
| 1999-04-01 00:00:00 | 0.02 | -0.027 | -0.133 |
| 1999-07-01 00:00:00 | 0.34 | -0.001 | -0.027 |
| 1999-10-01 00:00:00 | 0.22 | 0.026 | 0.183 |
| 2000-01-01 00:00:00 | 0.37 | 0.08 | 0.134 |
| 2000-04-01 00:00:00 | 0.59 | 0.082 | 0.224 |
| 2000-07-01 00:00:00 | 0.25 | 0.032 | 0.33 |
| 2000-10-01 00:00:00 | -0.05 | 0.045 | 0.121 |
| 2001-01-01 00:00:00 | -0.88 | -0.018 | -0.096 |
| 2001-04-01 00:00:00 | -1.26 | -0.014 | -0.601 |
| 2001-07-01 00:00:00 | -0.83 | -0.081 | -0.857 |
| 2001-10-01 00:00:00 | -1.37 | -0.227 | -0.649 |
| 2002-01-01 00:00:00 | -0.4 | -0.248 | -0.983 |
| 2002-04-01 00:00:00 | 0.02 | -0.225 | -0.358 |
| 2002-07-01 00:00:00 | -0.01 | -0.157 | -0.06 |
| 2002-10-01 00:00:00 | -0.3 | -0.233 | -0.117 |
| 2003-01-01 00:00:00 | -0.19 | -0.215 | -0.286 |
| 2003-04-01 00:00:00 | 0 | -0.285 | -0.25 |
| 2003-07-01 00:00:00 | -0.23 | -0.298 | -0.138 |
| 2003-10-01 00:00:00 | -0.02 | -0.185 | -0.223 |
| 2004-01-01 00:00:00 | 0 | -0.119 | -0.058 |
| 2004-04-01 00:00:00 | 0.01 | -0.062 | -0.016 |
| 2004-07-01 00:00:00 | 0.42 | -0.023 | 0.009 |
| 2004-10-01 00:00:00 | 0.52 | -0.036 | 0.255 |
| 2005-01-01 00:00:00 | 0.52 | -0.017 | 0.321 |
| 2005-04-01 00:00:00 | 0.47 | -0.006 | 0.319 |
| 2005-07-01 00:00:00 | 0.52 | -0.004 | 0.283 |
| 2005-10-01 00:00:00 | 0.52 | -0.018 | 0.302 |
| 2006-01-01 00:00:00 | 0.48 | 0.012 | 0.309 |
| 2006-04-01 00:00:00 | 0.45 | 0.056 | 0.302 |
| 2006-07-01 00:00:00 | 0.34 | 0.05 | 0.275 |
| 2006-10-01 00:00:00 | 0 | 0.048 | 0.199 |
| 2007-01-01 00:00:00 | 0.01 | 0.037 | -0.018 |
| 2007-04-01 00:00:00 | -0.01 | -0.022 | -0.043 |
| 2007-07-01 00:00:00 | -0.18 | -0.084 | -0.087 |
| 2007-10-01 00:00:00 | -0.57 | -0.06 | -0.177 |
| 2008-01-01 00:00:00 | -1.32 | -0.104 | -0.436 |
| 2008-04-01 00:00:00 | -1.09 | -0.102 | -0.887 |
| 2008-07-01 00:00:00 | -0.15 | -0.225 | -0.789 |
| 2008-10-01 00:00:00 | -1.43 | -0.585 | -0.382 |
| 2009-01-01 00:00:00 | -0.33 | -0.51 | -0.51 |
| 2009-04-01 00:00:00 | 0 | -0.18 | -0.18 |
| 2009-07-01 00:00:00 | -0.02 | -0.18 | -0.18 |
| 2009-10-01 00:00:00 | -0.04 | -0.16 | -0.16 |
| 2010-01-01 00:00:00 | 0.01 | -0.12 | -0.12 |
| 2010-04-01 00:00:00 | 0.06 | -0.13 | -0.13 |
| 2010-07-01 00:00:00 | 0 | -0.19 | -0.19 |
| 2010-10-01 00:00:00 | 0 | -0.19 | -0.19 |
| 2011-01-01 00:00:00 | -0.03 | -0.19 | -0.19 |
| 2011-04-01 00:00:00 | -0.07 | -0.16 | -0.16 |
| 2011-07-01 00:00:00 | -0.01 | -0.09 | -0.09 |
| 2011-10-01 00:00:00 | -0.01 | -0.08 | -0.08 |
| 2012-01-01 00:00:00 | 0.03 | -0.07 | -0.07 |
| 2012-04-01 00:00:00 | 0.05 | -0.1 | -0.1 |
| 2012-07-01 00:00:00 | -0.01 | -0.15 | -0.15 |
| 2012-10-01 00:00:00 | 0.02 | -0.14 | -0.14 |
| 2013-01-01 00:00:00 | -0.02 | -0.16 | -0.16 |
| 2013-04-01 00:00:00 | -0.02 | -0.14 | -0.14 |
| 2013-07-01 00:00:00 | -0.04 | -0.12 | -0.12 |
| 2013-10-01 00:00:00 | 0.01 | -0.08 | -0.08 |
| 2014-01-01 00:00:00 | -0.02 | -0.09 | -0.09 |
| 2014-04-01 00:00:00 | 0.02 | -0.07 | -0.07 |
| 2014-07-01 00:00:00 | 0 | -0.09 | -0.09 |
| 2014-10-01 00:00:00 | 0.01 | -0.09 | -0.079 |
| 2015-01-01 00:00:00 | 0.01 | -0.1 | -0.061 |
| 2015-04-01 00:00:00 | 0.01 | -0.11 | -0.05 |
| 2015-07-01 00:00:00 | 0.02 | -0.086 | -0.017 |
| 2015-10-01 00:00:00 | 0.02 | -0.069 | -0.002 |
| 2016-01-01 00:00:00 | 0.2 | -0.009 | 0.029 |
| 2016-04-01 00:00:00 | 0.01 | -0.012 | 0.138 |
| 2016-07-01 00:00:00 | 0.03 | -0 | 0.026 |
| 2016-10-01 00:00:00 | 0.05 | 0.035 | 0.056 |
| 2017-01-01 00:00:00 | 0.25 | 0.09 | 0.095 |
| 2017-04-01 00:00:00 | 0.25 | 0.093 | 0.217 |
| 2017-07-01 00:00:00 | 0.2 | 0.08 | 0.206 |
| 2017-10-01 00:00:00 | 0.05 | 0.107 | 0.186 |
| 2018-01-01 00:00:00 | 0.25 | 0.182 | 0.13 |
| 2018-04-01 00:00:00 | 0.29 | 0.222 | 0.273 |
| 2018-07-01 00:00:00 | 0.18 | 0.23 | 0.299 |
| 2018-10-01 00:00:00 | 0.3 | 0.219 | 0.222 |
| 2019-01-01 00:00:00 | 0.18 | 0.134 | 0.25 |
| 2019-04-01 00:00:00 | 0 | 0.186 | 0.197 |
| 2019-07-01 00:00:00 | -0.21 | 0.192 | 0.088 |
| 2019-10-01 00:00:00 | -0.55 | 0.187 | -0.045 |
| 2020-01-01 00:00:00 | -0.38 | 0.172 | -0.257 |
| 2020-04-01 00:00:00 | -1.2 | -1.26 | -1.26 |
| 2020-07-01 00:00:00 | 0.03 | -0.06 | -0.06 |
| 2020-10-01 00:00:00 | 0 | -0.09 | -0.09 |
| 2021-01-01 00:00:00 | -0.01 | -0.09 | -0.09 |
| 2021-04-01 00:00:00 | -0.01 | -0.034 | 0.016 |
| 2021-07-01 00:00:00 | 0.02 | 0.258 | 0.162 |
| 2021-10-01 00:00:00 | -0.01 | 0.638 | 0.374 |
| 2022-01-01 00:00:00 | 0.04 | 0.82 | 0.45 |
| 2022-04-01 00:00:00 | 0.65 | 0.866 | 0.501 |
| 2022-07-01 00:00:00 | 1.42 | 0.864 | 0.874 |
| 2022-10-01 00:00:00 | 1.46 | 0.721 | 1.266 |
| 2023-01-01 00:00:00 | 0.87 | 0.603 | 1.212 |
| 2023-04-01 00:00:00 | 0.47 | 0.513 | 0.786 |
| 2023-07-01 00:00:00 | 0.27 | 0.351 | 0.445 |
| 2023-10-01 00:00:00 | 0.07 | 0.181 | 0.228 |
| 2024-01-01 00:00:00 | 0 | 0.15 | 0.085 |
| 2024-04-01 00:00:00 | 0 | 0.052 | -0.008 |
| 2024-07-01 00:00:00 | -0.07 | -0.006 | -0.037 |
| 2024-10-01 00:00:00 | -0.61 | 0.047 | -0.052 |
| 2025-01-01 00:00:00 | -0.32 | 0.059 | -0.378 |
| 2025-04-01 00:00:00 | 0 | 0.04 | -0.202 |
| 2025-07-01 00:00:00 | -0.04 | 0.031 | -0.006 |
Figure 3: Year-ahead Federal Funds Rate Predictions for Estimated
Rules
Note: This figure displays the year-ahead predictions
for the level of the federal funds rate from 1987:Q4 through 2025:Q3 for
the AR(2) and double-inertial specifications in Section 2. The black line plots the
realized quarterly averages of the effective federal funds rate over the
same period. The rules are estimated over the full ‘Post-1987’ sample
using Tobit regressions. Year-ahead predictions are constructed
recursively, with predicted federal funds rate values replacing realized
lagged rates in subsequent forecast steps. The predictions are
conditional on realized values of \(\pi\), \(u\), and \(u^*\) over the forecast horizon, use \(\pi^* = 2\), and use the estimated
parameters from Table 1. See Section 4.2
for details.
Source: FRED.
| Date | Actual_FFR | Double_Inertial_YearAhead | AR2_YearAhead |
|---|---|---|---|
| 1987-10-01 00:00:00 | 6.92 | 5.538 | 5.851 |
| 1988-01-01 00:00:00 | 6.66 | 5.703 | 5.568 |
| 1988-04-01 00:00:00 | 7.16 | 6.901 | 7.017 |
| 1988-07-01 00:00:00 | 7.98 | 6.988 | 6.697 |
| 1988-10-01 00:00:00 | 8.47 | 7.136 | 6.543 |
| 1989-01-01 00:00:00 | 9.44 | 6.731 | 5.561 |
| 1989-04-01 00:00:00 | 9.73 | 8.136 | 7.676 |
| 1989-07-01 00:00:00 | 9.08 | 9.146 | 9.175 |
| 1989-10-01 00:00:00 | 8.61 | 8.978 | 8.964 |
| 1990-01-01 00:00:00 | 8.25 | 10.087 | 10.953 |
| 1990-04-01 00:00:00 | 8.24 | 9.338 | 9.798 |
| 1990-07-01 00:00:00 | 8.16 | 7.641 | 7.152 |
| 1990-10-01 00:00:00 | 7.74 | 7.469 | 7.064 |
| 1991-01-01 00:00:00 | 6.43 | 7.119 | 6.938 |
| 1991-04-01 00:00:00 | 5.86 | 7.152 | 7.672 |
| 1991-07-01 00:00:00 | 5.64 | 6.592 | 7.443 |
| 1991-10-01 00:00:00 | 4.82 | 5.506 | 6.301 |
| 1992-01-01 00:00:00 | 4.02 | 3.202 | 3.101 |
| 1992-04-01 00:00:00 | 3.77 | 3.475 | 4.103 |
| 1992-07-01 00:00:00 | 3.26 | 3.499 | 4.627 |
| 1992-10-01 00:00:00 | 3.04 | 1.977 | 2.533 |
| 1993-01-01 00:00:00 | 3.04 | 1.373 | 1.775 |
| 1993-04-01 00:00:00 | 3 | 1.908 | 2.694 |
| 1993-07-01 00:00:00 | 3.06 | 1.36 | 1.632 |
| 1993-10-01 00:00:00 | 2.99 | 1.689 | 2.028 |
| 1994-01-01 00:00:00 | 3.21 | 2.019 | 2.495 |
| 1994-04-01 00:00:00 | 3.94 | 2.033 | 2.37 |
| 1994-07-01 00:00:00 | 4.49 | 2.266 | 2.643 |
| 1994-10-01 00:00:00 | 5.17 | 2.186 | 2.296 |
| 1995-01-01 00:00:00 | 5.81 | 2.935 | 3.132 |
| 1995-04-01 00:00:00 | 6.02 | 4.222 | 4.945 |
| 1995-07-01 00:00:00 | 5.8 | 4.459 | 5.113 |
| 1995-10-01 00:00:00 | 5.72 | 5.066 | 6.069 |
| 1996-01-01 00:00:00 | 5.36 | 5.402 | 6.624 |
| 1996-04-01 00:00:00 | 5.24 | 5.01 | 5.92 |
| 1996-07-01 00:00:00 | 5.31 | 4.348 | 4.787 |
| 1996-10-01 00:00:00 | 5.28 | 4.482 | 5.004 |
| 1997-01-01 00:00:00 | 5.28 | 3.915 | 4.049 |
| 1997-04-01 00:00:00 | 5.52 | 4.226 | 4.439 |
| 1997-07-01 00:00:00 | 5.53 | 4.578 | 4.913 |
| 1997-10-01 00:00:00 | 5.51 | 4.505 | 4.67 |
| 1998-01-01 00:00:00 | 5.52 | 4.598 | 4.734 |
| 1998-04-01 00:00:00 | 5.5 | 5.074 | 5.484 |
| 1998-07-01 00:00:00 | 5.53 | 4.82 | 5.005 |
| 1998-10-01 00:00:00 | 4.86 | 4.795 | 4.922 |
| 1999-01-01 00:00:00 | 4.73 | 4.874 | 4.995 |
| 1999-04-01 00:00:00 | 4.75 | 4.851 | 4.912 |
| 1999-07-01 00:00:00 | 5.09 | 4.992 | 5.048 |
| 1999-10-01 00:00:00 | 5.31 | 3.716 | 2.891 |
| 2000-01-01 00:00:00 | 5.68 | 4.395 | 3.908 |
| 2000-04-01 00:00:00 | 6.27 | 4.737 | 4.247 |
| 2000-07-01 00:00:00 | 6.52 | 5.506 | 5.267 |
| 2000-10-01 00:00:00 | 6.47 | 5.616 | 5.232 |
| 2001-01-01 00:00:00 | 5.59 | 6.073 | 5.92 |
| 2001-04-01 00:00:00 | 4.33 | 6.709 | 6.977 |
| 2001-07-01 00:00:00 | 3.5 | 6.323 | 6.505 |
| 2001-10-01 00:00:00 | 2.13 | 5.591 | 5.818 |
| 2002-01-01 00:00:00 | 1.73 | 3.536 | 3.175 |
| 2002-04-01 00:00:00 | 1.75 | 1.747 | 1.108 |
| 2002-07-01 00:00:00 | 1.74 | 1.422 | 1.192 |
| 2002-10-01 00:00:00 | 1.44 | 0 | 0 |
| 2003-01-01 00:00:00 | 1.25 | 0.602 | 0.336 |
| 2003-04-01 00:00:00 | 1.25 | 1.091 | 1.248 |
| 2003-07-01 00:00:00 | 1.02 | 0.897 | 1.174 |
| 2003-10-01 00:00:00 | 1 | 0.283 | 0.258 |
| 2004-01-01 00:00:00 | 1 | 0.298 | 0.302 |
| 2004-04-01 00:00:00 | 1.01 | 0.693 | 0.706 |
| 2004-07-01 00:00:00 | 1.43 | 0.469 | 0 |
| 2004-10-01 00:00:00 | 1.95 | 0.873 | 0.413 |
| 2005-01-01 00:00:00 | 2.47 | 1.031 | 0.456 |
| 2005-04-01 00:00:00 | 2.94 | 1.166 | 0.487 |
| 2005-07-01 00:00:00 | 3.46 | 2.087 | 1.778 |
| 2005-10-01 00:00:00 | 3.98 | 2.711 | 2.51 |
| 2006-01-01 00:00:00 | 4.46 | 3.202 | 3.03 |
| 2006-04-01 00:00:00 | 4.91 | 3.615 | 3.394 |
| 2006-07-01 00:00:00 | 5.25 | 4.2 | 4.02 |
| 2006-10-01 00:00:00 | 5.25 | 4.731 | 4.539 |
| 2007-01-01 00:00:00 | 5.26 | 5.133 | 4.934 |
| 2007-04-01 00:00:00 | 5.25 | 5.419 | 5.32 |
| 2007-07-01 00:00:00 | 5.07 | 5.452 | 5.426 |
| 2007-10-01 00:00:00 | 4.5 | 4.923 | 4.704 |
| 2008-01-01 00:00:00 | 3.18 | 4.794 | 4.735 |
| 2008-04-01 00:00:00 | 2.09 | 4.611 | 4.683 |
| 2008-07-01 00:00:00 | 1.94 | 4.053 | 4.142 |
| 2008-10-01 00:00:00 | 0.51 | 2.671 | 2.744 |
| 2009-01-01 00:00:00 | 0.18 | 0.012 | 0 |
| 2009-04-01 00:00:00 | 0.18 | 0 | 0 |
| 2009-07-01 00:00:00 | 0.16 | 0 | 1.077 |
| 2009-10-01 00:00:00 | 0.12 | 0 | 0 |
| 2010-01-01 00:00:00 | 0.13 | 0 | 0 |
| 2010-04-01 00:00:00 | 0.19 | 0 | 0 |
| 2010-07-01 00:00:00 | 0.19 | 0 | 0 |
| 2010-10-01 00:00:00 | 0.19 | 0 | 0 |
| 2011-01-01 00:00:00 | 0.16 | 0 | 0 |
| 2011-04-01 00:00:00 | 0.09 | 0 | 0 |
| 2011-07-01 00:00:00 | 0.08 | 0 | 0 |
| 2011-10-01 00:00:00 | 0.07 | 0 | 0 |
| 2012-01-01 00:00:00 | 0.1 | 0 | 0 |
| 2012-04-01 00:00:00 | 0.15 | 0 | 0 |
| 2012-07-01 00:00:00 | 0.14 | 0 | 0 |
| 2012-10-01 00:00:00 | 0.16 | 0 | 0 |
| 2013-01-01 00:00:00 | 0.14 | 0 | 0 |
| 2013-04-01 00:00:00 | 0.12 | 0 | 0 |
| 2013-07-01 00:00:00 | 0.08 | 0 | 0 |
| 2013-10-01 00:00:00 | 0.09 | 0 | 0 |
| 2014-01-01 00:00:00 | 0.07 | 0 | 0 |
| 2014-04-01 00:00:00 | 0.09 | 0 | 0 |
| 2014-07-01 00:00:00 | 0.09 | 0 | 0 |
| 2014-10-01 00:00:00 | 0.1 | 0 | 0 |
| 2015-01-01 00:00:00 | 0.11 | 0 | 0 |
| 2015-04-01 00:00:00 | 0.12 | 0 | 0 |
| 2015-07-01 00:00:00 | 0.14 | 0 | 0 |
| 2015-10-01 00:00:00 | 0.16 | 0 | 0 |
| 2016-01-01 00:00:00 | 0.36 | 0.018 | 0 |
| 2016-04-01 00:00:00 | 0.37 | 0.113 | 0 |
| 2016-07-01 00:00:00 | 0.4 | 0.234 | 0 |
| 2016-10-01 00:00:00 | 0.45 | 0.352 | 0 |
| 2017-01-01 00:00:00 | 0.7 | 0.801 | 0.241 |
| 2017-04-01 00:00:00 | 0.95 | 0.676 | 0 |
| 2017-07-01 00:00:00 | 1.15 | 0.826 | 0 |
| 2017-10-01 00:00:00 | 1.2 | 0.978 | 0.012 |
| 2018-01-01 00:00:00 | 1.45 | 1.491 | 0.687 |
| 2018-04-01 00:00:00 | 1.74 | 1.801 | 0.937 |
| 2018-07-01 00:00:00 | 1.92 | 2.056 | 1.031 |
| 2018-10-01 00:00:00 | 2.22 | 2.061 | 0.762 |
| 2019-01-01 00:00:00 | 2.4 | 2.536 | 1.437 |
| 2019-04-01 00:00:00 | 2.4 | 2.796 | 1.812 |
| 2019-07-01 00:00:00 | 2.19 | 2.777 | 1.758 |
| 2019-10-01 00:00:00 | 1.64 | 3.124 | 2.313 |
| 2020-01-01 00:00:00 | 1.26 | 3.13 | 2.238 |
| 2020-04-01 00:00:00 | 0.06 | 1.544 | 1.855 |
| 2020-07-01 00:00:00 | 0.09 | 0 | 1.199 |
| 2020-10-01 00:00:00 | 0.09 | 0 | 0 |
| 2021-01-01 00:00:00 | 0.08 | 0 | 0 |
| 2021-04-01 00:00:00 | 0.07 | 0.026 | 0 |
| 2021-07-01 00:00:00 | 0.09 | 0.212 | 0 |
| 2021-10-01 00:00:00 | 0.08 | 0.637 | 0 |
| 2022-01-01 00:00:00 | 0.12 | 1.455 | 0 |
| 2022-04-01 00:00:00 | 0.77 | 2.269 | 0 |
| 2022-07-01 00:00:00 | 2.19 | 2.934 | 0 |
| 2022-10-01 00:00:00 | 3.65 | 3.122 | 0 |
| 2023-01-01 00:00:00 | 4.52 | 3.238 | 0 |
| 2023-04-01 00:00:00 | 4.99 | 4.405 | 1.607 |
| 2023-07-01 00:00:00 | 5.26 | 6.194 | 4.662 |
| 2023-10-01 00:00:00 | 5.33 | 7.033 | 6.206 |
| 2024-01-01 00:00:00 | 5.33 | 6.619 | 5.823 |
| 2024-04-01 00:00:00 | 5.33 | 6.099 | 5.443 |
| 2024-07-01 00:00:00 | 5.26 | 5.753 | 5.288 |
| 2024-10-01 00:00:00 | 4.65 | 5.413 | 4.933 |
| 2025-01-01 00:00:00 | 4.33 | 5.2 | 4.784 |
| 2025-04-01 00:00:00 | 4.33 | 5.147 | 4.784 |
| 2025-07-01 00:00:00 | 4.29 | 4.996 | 4.566 |