Finance and Economics Discussion Series: 2008-37 Screen Reader version
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Estimating the common trend rate of inflation for consumer prices and consumer prices excluding food and energy prices
Michael T. Kiley
July 16, 2008
Figure 1: Estimates of trend for PCE inflation from IMA(1,1) models (percent, annual rate)
Year/Quarter | Model 1 (Bivariate) | Model 2 (PCE prices) | Model 3 (PCE prices excl. food and energy) |
1974Q4 | 9.645292 | 10.09051 | 9.48182 |
1975Q1 | 7.422274 | 7.940294 | 7.54904 |
1975Q2 | 6.01241 | 5.372467 | 6.333189 |
1975Q3 | 6.31306 | 7.116817 | 6.044604 |
1975Q4 | 6.498769 | 6.797667 | 6.438615 |
1976Q1 | 5.720014 | 4.789315 | 6.033527 |
1976Q2 | 4.411318 | 3.640049 | 4.768561 |
1976Q3 | 6.275214 | 5.633704 | 6.242828 |
1976Q4 | 6.264526 | 6.125148 | 6.271359 |
1977Q1 | 6.5879 | 6.871253 | 6.501197 |
1977Q2 | 5.910573 | 6.825331 | 5.804323 |
1977Q3 | 6.516162 | 6.1407 | 6.592761 |
1977Q4 | 5.838496 | 5.774795 | 5.891701 |
1978Q1 | 6.485117 | 6.538866 | 6.420559 |
1978Q2 | 6.877262 | 7.927914 | 6.640025 |
1978Q3 | 6.493713 | 7.096695 | 6.429487 |
1978Q4 | 7.045704 | 7.396218 | 6.966941 |
1979Q1 | 5.287004 | 7.383957 | 4.95076 |
1979Q2 | 8.693191 | 10.11627 | 8.170754 |
1979Q3 | 7.786806 | 9.763634 | 7.170701 |
1979Q4 | 8.389668 | 9.533531 | 8.006352 |
1980Q1 | 9.967452 | 11.32188 | 9.389673 |
1980Q2 | 8.967607 | 9.916128 | 8.739513 |
1980Q3 | 8.910764 | 9.34036 | 8.793279 |
1980Q4 | 9.655551 | 9.682053 | 9.615981 |
1981Q1 | 9.09904 | 10.08741 | 8.728645 |
1981Q2 | 7.366699 | 7.43719 | 7.527154 |
1981Q3 | 7.219671 | 6.713886 | 7.397878 |
1981Q4 | 6.935708 | 6.188673 | 7.171234 |
1982Q1 | 5.807248 | 5.262974 | 6.048142 |
1982Q2 | 5.177028 | 4.073129 | 5.49365 |
1982Q3 | 6.218989 | 5.760541 | 6.250993 |
1982Q4 | 5.559801 | 4.765169 | 5.777718 |
1983Q1 | 5.207656 | 3.732774 | 5.569043 |
1983Q2 | 3.322055 | 3.674366 | 3.353548 |
1983Q3 | 5.665701 | 4.879461 | 5.794319 |
1983Q4 | 3.443321 | 3.216926 | 3.762403 |
1984Q1 | 3.914349 | 3.98223 | 3.879312 |
1984Q2 | 4.330789 | 3.894594 | 4.499759 |
1984Q3 | 3.684449 | 3.291053 | 3.939499 |
1984Q4 | 2.923009 | 2.701868 | 3.142005 |
1985Q1 | 4.371113 | 3.867554 | 4.48447 |
1985Q2 | 3.356861 | 3.246681 | 3.500684 |
1985Q3 | 3.161251 | 2.74647 | 3.427228 |
1985Q4 | 3.203625 | 3.032247 | 3.309064 |
1986Q1 | 3.694869 | 2.911451 | 4.039645 |
1986Q2 | 2.732722 | 0.925089 | 3.618993 |
1986Q3 | 3.392793 | 2.432488 | 3.75741 |
1986Q4 | 3.505978 | 2.740669 | 3.7863 |
1987Q1 | 3.665425 | 4.025162 | 3.505692 |
1987Q2 | 3.478512 | 3.585666 | 3.447243 |
1987Q3 | 3.855189 | 3.901563 | 3.792859 |
1987Q4 | 3.833563 | 3.548114 | 3.944242 |
1988Q1 | 3.929681 | 3.48235 | 4.124779 |
1988Q2 | 4.458064 | 4.082741 | 4.588795 |
1988Q3 | 4.463755 | 4.552938 | 4.425001 |
1988Q4 | 4.304527 | 4.101353 | 4.354557 |
1989Q1 | 4.483327 | 4.504102 | 4.471659 |
1989Q2 | 4.008542 | 4.902691 | 3.887276 |
1989Q3 | 3.48299 | 3.560142 | 3.499712 |
1989Q4 | 3.610695 | 3.399369 | 3.652068 |
1990Q1 | 4.251877 | 4.830521 | 4.162161 |
1990Q2 | 4.700539 | 4.502808 | 4.691318 |
1990Q3 | 4.417409 | 4.785865 | 4.338243 |
1990Q4 | 4.021136 | 4.991623 | 3.815911 |
1991Q1 | 4.109809 | 3.875726 | 4.166131 |
1991Q2 | 3.432752 | 2.907935 | 3.630536 |
1991Q3 | 3.481064 | 2.854327 | 3.687123 |
1991Q4 | 3.506048 | 3.043424 | 3.664714 |
1992Q1 | 3.608024 | 3.070249 | 3.768891 |
1992Q2 | 3.122642 | 2.772387 | 3.305877 |
1992Q3 | 2.937956 | 2.780755 | 3.044262 |
1992Q4 | 2.770791 | 2.633323 | 2.863393 |
1993Q1 | 2.512039 | 2.30538 | 2.628401 |
1993Q2 | 2.713209 | 2.45996 | 2.809303 |
1993Q3 | 2.1617 | 1.878656 | 2.318951 |
1993Q4 | 2.037505 | 1.995709 | 2.09833 |
1994Q1 | 1.972164 | 1.769625 | 2.057198 |
1994Q2 | 2.304281 | 1.991581 | 2.368406 |
1994Q3 | 2.799192 | 2.879823 | 2.752432 |
1994Q4 | 2.290732 | 2.259701 | 2.315479 |
1995Q1 | 2.152641 | 2.081053 | 2.189318 |
1995Q2 | 2.193782 | 2.149166 | 2.212804 |
1995Q3 | 2.07368 | 1.940716 | 2.10822 |
1995Q4 | 1.957839 | 1.85857 | 2.019629 |
1996Q1 | 2.000765 | 2.098808 | 1.967589 |
1996Q2 | 1.986889 | 2.254049 | 1.880044 |
1996Q3 | 1.851058 | 2.031239 | 1.799195 |
1996Q4 | 1.996884 | 2.237225 | 1.901993 |
1997Q1 | 1.854428 | 2.098209 | 1.773484 |
1997Q2 | 1.744094 | 1.666149 | 1.79715 |
1997Q3 | 1.473088 | 1.467225 | 1.526277 |
1997Q4 | 1.410609 | 1.415687 | 1.439658 |
1998Q1 | 1.259003 | 1.007776 | 1.399531 |
1998Q2 | 1.203358 | 0.878853 | 1.293267 |
1998Q3 | 1.285267 | 1.035216 | 1.347088 |
1998Q4 | 1.43215 | 1.197364 | 1.473623 |
1999Q1 | 1.335508 | 1.130329 | 1.381608 |
1999Q2 | 1.568226 | 1.656693 | 1.496157 |
1999Q3 | 1.561209 | 1.893902 | 1.465959 |
1999Q4 | 1.72868 | 2.087802 | 1.630909 |
2000Q1 | 2.144984 | 2.690107 | 1.987248 |
2000Q2 | 1.753131 | 2.36026 | 1.662421 |
2000Q3 | 1.407059 | 2.153986 | 1.329564 |
2000Q4 | 1.45827 | 1.968279 | 1.397968 |
2001Q1 | 2.150893 | 2.485558 | 1.987874 |
2001Q2 | 2.183344 | 2.497564 | 2.010985 |
2001Q3 | 1.744384 | 1.781942 | 1.762977 |
2001Q4 | 1.953098 | 1.235523 | 2.080756 |
2002Q1 | 1.642948 | 1.088882 | 1.763341 |
2002Q2 | 1.78496 | 1.770215 | 1.789193 |
2002Q3 | 1.817925 | 1.763615 | 1.812044 |
2002Q4 | 1.591991 | 1.71883 | 1.582852 |
2003Q1 | 1.527585 | 2.210631 | 1.402912 |
2003Q2 | 1.380385 | 1.652238 | 1.353484 |
2003Q3 | 1.56523 | 1.886463 | 1.506959 |
2003Q4 | 1.571379 | 1.746658 | 1.543319 |
2004Q1 | 1.988748 | 2.36571 | 1.872906 |
2004Q2 | 2.336364 | 2.987663 | 2.198529 |
2004Q3 | 2.047529 | 2.558962 | 1.998417 |
2004Q4 | 2.224616 | 2.727805 | 2.039639 |
2005Q1 | 2.265006 | 2.510843 | 2.228393 |
2005Q2 | 2.244683 | 2.75899 | 2.163824 |
2005Q3 | 2.137926 | 3.223583 | 1.96802 |
2005Q4 | 2.205903 | 3.064052 | 2.108895 |
2006Q1 | 2.117677 | 2.669056 | 2.073295 |
2006Q2 | 2.415613 | 3.085816 | 2.361799 |
2006Q3 | 2.365867 | 2.928747 | 2.322852 |
2006Q4 | 2.179386 | 2.207992 | 2.179361 |
2007Q1 | 2.237042 | 2.409129 | 2.237343 |
2007Q2 | 2.035857 | 2.638129 | 2.006232 |
2007Q3 | 2.024587 | 2.511332 | 2.002965 |
2007Q4 | 2.155329 | 2.693351 | 2.126832 |
Figure 2: RMSE for overall PCE prices (rolling 16-quarter estimates) (percentage points, annual rate)
Year/quarter | Atkeson/Ohanian | Model 1 (Bivariate) | Model 2 (PCE prices) |
1974Q4 | 2.916713 | 3.107676 | 2.471289 |
1975Q1 | 3.065968 | 3.123675 | 2.522397 |
1975Q2 | 3.129595 | 3.109294 | 2.506519 |
1975Q3 | 3.168816 | 3.119036 | 2.544876 |
1975Q4 | 3.194197 | 3.129373 | 2.578711 |
1976Q1 | 3.194027 | 3.127315 | 2.586447 |
1976Q2 | 3.179712 | 3.124712 | 2.632908 |
1976Q3 | 3.13127 | 3.053519 | 2.573636 |
1976Q4 | 3.019079 | 2.861724 | 2.408606 |
1977Q1 | 2.737271 | 2.525058 | 2.181651 |
1977Q2 | 2.478593 | 2.344091 | 2.090512 |
1977Q3 | 2.202432 | 2.011543 | 1.943815 |
1977Q4 | 1.999562 | 1.580369 | 1.849556 |
1978Q1 | 2.004118 | 1.525332 | 1.842455 |
1978Q2 | 2.013184 | 1.509236 | 1.71345 |
1978Q3 | 1.942764 | 1.375137 | 1.580278 |
1978Q4 | 1.722063 | 1.286931 | 1.411661 |
1979Q1 | 1.608053 | 1.77349 | 1.517309 |
1979Q2 | 1.538933 | 1.804088 | 1.51694 |
1979Q3 | 1.456527 | 1.863517 | 1.436833 |
1979Q4 | 1.410653 | 1.874073 | 1.373713 |
1980Q1 | 1.421203 | 1.875505 | 1.416476 |
1980Q2 | 1.428481 | 1.798937 | 1.24245 |
1980Q3 | 1.451366 | 1.804831 | 1.251104 |
1980Q4 | 1.565648 | 1.894665 | 1.379121 |
1981Q1 | 1.80183 | 2.040676 | 1.702567 |
1981Q2 | 2.010515 | 2.093321 | 1.779162 |
1981Q3 | 2.144561 | 2.147272 | 1.805957 |
1981Q4 | 2.219362 | 2.176931 | 1.794619 |
1982Q1 | 2.234372 | 2.187779 | 1.789649 |
1982Q2 | 2.21577 | 2.173607 | 1.791462 |
1982Q3 | 2.179323 | 2.155539 | 1.783202 |
1982Q4 | 2.140106 | 2.128517 | 1.73649 |
1983Q1 | 2.016785 | 1.731021 | 1.565493 |
1983Q2 | 1.957058 | 1.70297 | 1.567671 |
1983Q3 | 1.943361 | 1.703275 | 1.606044 |
1983Q4 | 1.93612 | 1.651533 | 1.601528 |
1984Q1 | 1.932018 | 1.654285 | 1.553648 |
1984Q2 | 1.919477 | 1.677343 | 1.543268 |
1984Q3 | 1.874005 | 1.676406 | 1.521111 |
1984Q4 | 1.747764 | 1.576038 | 1.41132 |
1985Q1 | 1.50126 | 1.428203 | 1.016611 |
1985Q2 | 1.233832 | 1.36825 | 0.912549 |
1985Q3 | 0.99792 | 1.296376 | 0.845529 |
1985Q4 | 0.824707 | 1.214433 | 0.804605 |
1986Q1 | 0.727828 | 1.197573 | 0.7834 |
1986Q2 | 0.756589 | 1.196578 | 0.999996 |
1986Q3 | 0.788607 | 1.087648 | 0.974053 |
1986Q4 | 0.838222 | 0.992766 | 0.979758 |
1987Q1 | 0.860249 | 0.942199 | 0.984545 |
1987Q2 | 0.858601 | 0.930607 | 0.982869 |
1987Q3 | 0.841982 | 0.751668 | 0.917508 |
1987Q4 | 0.840925 | 0.755127 | 0.927302 |
1988Q1 | 0.858202 | 0.75628 | 0.947782 |
1988Q2 | 0.859757 | 0.704973 | 0.942836 |
1988Q3 | 0.854975 | 0.695999 | 0.94893 |
1988Q4 | 0.855286 | 0.697348 | 0.939829 |
1989Q1 | 0.846573 | 0.595819 | 0.910802 |
1989Q2 | 0.822924 | 0.521339 | 0.901562 |
1989Q3 | 0.810026 | 0.552883 | 0.932526 |
1989Q4 | 0.820285 | 0.617019 | 1.002442 |
1990Q1 | 0.818443 | 0.558656 | 1.00732 |
1990Q2 | 0.758978 | 0.572568 | 0.804811 |
1990Q3 | 0.75015 | 0.633089 | 0.828218 |
1990Q4 | 0.851151 | 0.697709 | 0.954094 |
1991Q1 | 0.902837 | 0.767681 | 0.983216 |
1991Q2 | 0.926891 | 0.773886 | 0.981419 |
1991Q3 | 0.929184 | 0.786544 | 0.981207 |
1991Q4 | 0.926602 | 0.806522 | 0.973657 |
1992Q1 | 0.905392 | 0.844819 | 0.955231 |
1992Q2 | 0.888858 | 0.858605 | 0.947982 |
1992Q3 | 0.909185 | 0.876704 | 0.954474 |
1992Q4 | 0.924988 | 0.891267 | 0.965445 |
1993Q1 | 0.934382 | 0.90159 | 0.967959 |
1993Q2 | 0.936119 | 0.929528 | 0.955061 |
1993Q3 | 0.92835 | 0.887144 | 0.925882 |
1993Q4 | 0.885547 | 0.81052 | 0.828917 |
1994Q1 | 0.891944 | 0.81574 | 0.833137 |
1994Q2 | 0.901714 | 0.786608 | 0.821447 |
1994Q3 | 0.846932 | 0.768019 | 0.771385 |
1994Q4 | 0.636337 | 0.712539 | 0.551881 |
1995Q1 | 0.516425 | 0.637116 | 0.48579 |
1995Q2 | 0.466617 | 0.624075 | 0.485944 |
1995Q3 | 0.458231 | 0.607025 | 0.486945 |
1995Q4 | 0.47142 | 0.582896 | 0.494688 |
1996Q1 | 0.464816 | 0.511656 | 0.472403 |
1996Q2 | 0.462886 | 0.491136 | 0.486394 |
1996Q3 | 0.438753 | 0.453003 | 0.472219 |
1996Q4 | 0.48337 | 0.453778 | 0.511277 |
1997Q1 | 0.562714 | 0.493522 | 0.587944 |
1997Q2 | 0.578105 | 0.492373 | 0.600701 |
1997Q3 | 0.599498 | 0.50999 | 0.605359 |
1997Q4 | 0.60126 | 0.519921 | 0.61292 |
1998Q1 | 0.594103 | 0.512261 | 0.595917 |
1998Q2 | 0.607726 | 0.521733 | 0.615912 |
1998Q3 | 0.639532 | 0.489996 | 0.598746 |
1998Q4 | 0.689457 | 0.502986 | 0.628052 |
1999Q1 | 0.785371 | 0.601551 | 0.735467 |
1999Q2 | 0.813709 | 0.644143 | 0.764601 |
1999Q3 | 0.825639 | 0.677965 | 0.77457 |
1999Q4 | 0.819721 | 0.68473 | 0.766994 |
2000Q1 | 0.827151 | 0.683733 | 0.776687 |
2000Q2 | 0.82218 | 0.696183 | 0.764643 |
2000Q3 | 0.818411 | 0.709978 | 0.756963 |
2000Q4 | 0.784425 | 0.687978 | 0.717965 |
2001Q1 | 0.762099 | 0.689803 | 0.73027 |
2001Q2 | 0.784837 | 0.696803 | 0.771952 |
2001Q3 | 0.777756 | 0.685055 | 0.762432 |
2001Q4 | 0.774174 | 0.676611 | 0.765124 |
2002Q1 | 0.823498 | 0.695239 | 0.822126 |
2002Q2 | 0.814107 | 0.688013 | 0.801922 |
2002Q3 | 0.788277 | 0.675246 | 0.778357 |
2002Q4 | 0.738969 | 0.661299 | 0.749804 |
2003Q1 | 0.635256 | 0.583262 | 0.647071 |
2003Q2 | 0.64393 | 0.636708 | 0.67188 |
2003Q3 | 0.65394 | 0.659856 | 0.687194 |
2003Q4 | 0.713827 | 0.743356 | 0.758221 |
2004Q1 | 0.72806 | 0.765457 | 0.753401 |
2004Q2 | 0.728108 | 0.753999 | 0.759361 |
2004Q3 | 0.733129 | 0.789556 | 0.773957 |
2004Q4 | 0.721048 | 0.817822 | 0.777651 |
2005Q1 | 0.675325 | 0.800135 | 0.712827 |
2005Q2 | 0.630962 | 0.799917 | 0.645806 |
2005Q3 | 0.623744 | 0.815307 | 0.650213 |
2005Q4 | 0.695204 | 0.817904 | 0.700851 |
2006Q1 | 0.656626 | 0.802782 | 0.638824 |
2006Q2 | 0.680555 | 0.803245 | 0.66791 |
2006Q3 | 0.694917 | 0.805305 | 0.697138 |
2006Q4 | 0.780183 | 0.85059 | 0.748655 |
2007Q1 | 0.817353 | 0.886248 | 0.781304 |
Figure 3: RMSE for PCE prices excluding food and energy prices (rolling 16-quarter estimates) (percentage points, annual rate)
Year/quarter | Atkeson/Ohanian | Model 1 (Bivariate) | Model 3 (PCE prices excl. food and energy) |
1974Q4 | 2.440902 | 1.910788 | 2.215827 |
1975Q1 | 2.549753 | 1.917877 | 2.218431 |
1975Q2 | 2.606189 | 1.885152 | 2.192767 |
1975Q3 | 2.595953 | 1.877557 | 2.185878 |
1975Q4 | 2.595147 | 1.876791 | 2.181483 |
1976Q1 | 2.586505 | 1.850776 | 2.158819 |
1976Q2 | 2.587841 | 1.897066 | 2.182626 |
1976Q3 | 2.58119 | 1.888633 | 2.172414 |
1976Q4 | 2.560825 | 1.842031 | 2.120052 |
1977Q1 | 2.477094 | 1.77153 | 2.021535 |
1977Q2 | 2.354627 | 1.765813 | 2.000708 |
1977Q3 | 2.116501 | 1.657262 | 1.852408 |
1977Q4 | 1.753966 | 1.413391 | 1.499232 |
1978Q1 | 1.433805 | 1.357908 | 1.327499 |
1978Q2 | 1.327947 | 1.327463 | 1.3107 |
1978Q3 | 1.325607 | 0.999629 | 0.939355 |
1978Q4 | 1.170274 | 0.645615 | 0.601597 |
1979Q1 | 1.000917 | 0.940543 | 0.970743 |
1979Q2 | 0.831497 | 0.943359 | 0.963255 |
1979Q3 | 0.8868 | 0.96893 | 1.042581 |
1979Q4 | 1.006395 | 0.97471 | 1.072465 |
1980Q1 | 1.018001 | 1.005962 | 1.077939 |
1980Q2 | 1.015872 | 0.904589 | 1.01678 |
1980Q3 | 1.018258 | 0.918636 | 1.025074 |
1980Q4 | 1.086291 | 1.049488 | 1.139431 |
1981Q1 | 1.193791 | 1.17418 | 1.220154 |
1981Q2 | 1.309023 | 1.18955 | 1.240047 |
1981Q3 | 1.40689 | 1.215417 | 1.273757 |
1981Q4 | 1.471448 | 1.230129 | 1.303392 |
1982Q1 | 1.501332 | 1.228745 | 1.304674 |
1982Q2 | 1.534996 | 1.227835 | 1.307376 |
1982Q3 | 1.552221 | 1.253084 | 1.331571 |
1982Q4 | 1.582913 | 1.280291 | 1.368371 |
1983Q1 | 1.555532 | 1.075441 | 1.146855 |
1983Q2 | 1.507515 | 1.11332 | 1.18288 |
1983Q3 | 1.464115 | 1.174506 | 1.212096 |
1983Q4 | 1.382464 | 1.161288 | 1.175964 |
1984Q1 | 1.372332 | 1.133673 | 1.171818 |
1984Q2 | 1.386833 | 1.14213 | 1.189339 |
1984Q3 | 1.382847 | 1.131094 | 1.185332 |
1984Q4 | 1.327218 | 1.028724 | 1.084378 |
1985Q1 | 1.237679 | 0.902503 | 1.01764 |
1985Q2 | 1.114298 | 0.876423 | 0.982988 |
1985Q3 | 0.988276 | 0.850568 | 0.939675 |
1985Q4 | 0.884133 | 0.822351 | 0.890226 |
1986Q1 | 0.832422 | 0.822542 | 0.893789 |
1986Q2 | 0.764898 | 0.85108 | 0.889761 |
1986Q3 | 0.718657 | 0.810953 | 0.847186 |
1986Q4 | 0.636441 | 0.768432 | 0.785611 |
1987Q1 | 0.488194 | 0.719189 | 0.701433 |
1987Q2 | 0.489963 | 0.681688 | 0.668772 |
1987Q3 | 0.411725 | 0.528848 | 0.486374 |
1987Q4 | 0.416087 | 0.541895 | 0.50127 |
1988Q1 | 0.443683 | 0.559893 | 0.508291 |
1988Q2 | 0.390882 | 0.541304 | 0.478035 |
1988Q3 | 0.407611 | 0.564122 | 0.493652 |
1988Q4 | 0.445949 | 0.55181 | 0.501882 |
1989Q1 | 0.466981 | 0.543371 | 0.478398 |
1989Q2 | 0.466939 | 0.541831 | 0.484135 |
1989Q3 | 0.489979 | 0.574572 | 0.532045 |
1989Q4 | 0.510607 | 0.577134 | 0.538939 |
1990Q1 | 0.526269 | 0.576735 | 0.528564 |
1990Q2 | 0.540759 | 0.58862 | 0.582989 |
1990Q3 | 0.57433 | 0.615926 | 0.607058 |
1990Q4 | 0.589337 | 0.618005 | 0.606896 |
1991Q1 | 0.608476 | 0.629271 | 0.616452 |
1991Q2 | 0.588197 | 0.598747 | 0.582843 |
1991Q3 | 0.567589 | 0.587422 | 0.574485 |
1991Q4 | 0.565492 | 0.580216 | 0.583158 |
1992Q1 | 0.590733 | 0.609293 | 0.63818 |
1992Q2 | 0.624113 | 0.6131 | 0.646031 |
1992Q3 | 0.641642 | 0.603141 | 0.644342 |
1992Q4 | 0.644065 | 0.597222 | 0.640697 |
1993Q1 | 0.625666 | 0.573507 | 0.624128 |
1993Q2 | 0.643644 | 0.591656 | 0.644003 |
1993Q3 | 0.625584 | 0.546322 | 0.601227 |
1993Q4 | 0.608825 | 0.527907 | 0.585138 |
1994Q1 | 0.598581 | 0.540551 | 0.592363 |
1994Q2 | 0.588223 | 0.480183 | 0.538989 |
1994Q3 | 0.563708 | 0.480091 | 0.541548 |
1994Q4 | 0.555343 | 0.479343 | 0.545768 |
1995Q1 | 0.541015 | 0.462527 | 0.528141 |
1995Q2 | 0.551441 | 0.469563 | 0.534814 |
1995Q3 | 0.547275 | 0.472751 | 0.531458 |
1995Q4 | 0.520319 | 0.458965 | 0.509828 |
1996Q1 | 0.470954 | 0.398599 | 0.431806 |
1996Q2 | 0.425495 | 0.388966 | 0.406102 |
1996Q3 | 0.378576 | 0.377895 | 0.38447 |
1996Q4 | 0.347488 | 0.391401 | 0.380411 |
1997Q1 | 0.341853 | 0.404828 | 0.38039 |
1997Q2 | 0.341812 | 0.402738 | 0.373036 |
1997Q3 | 0.347696 | 0.399527 | 0.37618 |
1997Q4 | 0.345828 | 0.387397 | 0.36704 |
1998Q1 | 0.339875 | 0.370649 | 0.354602 |
1998Q2 | 0.347215 | 0.378719 | 0.358743 |
1998Q3 | 0.336852 | 0.331393 | 0.313004 |
1998Q4 | 0.323496 | 0.326264 | 0.305491 |
1999Q1 | 0.324913 | 0.347119 | 0.32215 |
1999Q2 | 0.30793 | 0.339195 | 0.315096 |
1999Q3 | 0.301932 | 0.330915 | 0.305646 |
1999Q4 | 0.297366 | 0.333453 | 0.303075 |
2000Q1 | 0.296132 | 0.353325 | 0.312249 |
2000Q2 | 0.29568 | 0.348937 | 0.312745 |
2000Q3 | 0.302555 | 0.365926 | 0.342231 |
2000Q4 | 0.326223 | 0.376758 | 0.371624 |
2001Q1 | 0.313841 | 0.361976 | 0.356508 |
2001Q2 | 0.274841 | 0.34617 | 0.323667 |
2001Q3 | 0.26751 | 0.345166 | 0.320137 |
2001Q4 | 0.313644 | 0.360267 | 0.347475 |
2002Q1 | 0.323427 | 0.360889 | 0.353556 |
2002Q2 | 0.326909 | 0.367992 | 0.365244 |
2002Q3 | 0.349962 | 0.383204 | 0.382014 |
2002Q4 | 0.349762 | 0.384323 | 0.383488 |
2003Q1 | 0.33611 | 0.367782 | 0.376713 |
2003Q2 | 0.37911 | 0.406788 | 0.415698 |
2003Q3 | 0.421632 | 0.42668 | 0.438526 |
2003Q4 | 0.464005 | 0.452389 | 0.468161 |
2004Q1 | 0.476373 | 0.436726 | 0.467781 |
2004Q2 | 0.476023 | 0.440348 | 0.467055 |
2004Q3 | 0.468782 | 0.420398 | 0.442642 |
2004Q4 | 0.436942 | 0.377856 | 0.395699 |
2005Q1 | 0.437347 | 0.373834 | 0.396961 |
2005Q2 | 0.438104 | 0.35936 | 0.392562 |
2005Q3 | 0.443468 | 0.362744 | 0.404566 |
2005Q4 | 0.412725 | 0.348053 | 0.383313 |
2006Q1 | 0.413758 | 0.351472 | 0.38437 |
2006Q2 | 0.40488 | 0.351809 | 0.380853 |
2006Q3 | 0.399625 | 0.350233 | 0.376732 |
2006Q4 | 0.402077 | 0.349303 | 0.3761 |
2007Q1 | 0.405844 | 0.348765 | 0.369527 |
Figure 4: Estimates of trend for CPI inflation from IMA(1,1) models (percent, annual rate)
Year/Quarter | Model 1 (Bivariate) | Model 2 (CPI) | Model 3 (CPI excl. food and energy) |
1974Q4 | 11.84455 | 11.84504 | 11.7674 |
1975Q1 | 8.860962 | 9.290191 | 8.9897 |
1975Q2 | 5.552078 | 5.157955 | 6.344839 |
1975Q3 | 6.463104 | 7.450853 | 5.196659 |
1975Q4 | 7.03882 | 7.338243 | 6.793479 |
1976Q1 | 6.113561 | 5.170254 | 7.417973 |
1976Q2 | 4.546666 | 3.81641 | 5.46896 |
1976Q3 | 6.332646 | 5.795387 | 6.459165 |
1976Q4 | 5.666102 | 5.77955 | 5.533522 |
1977Q1 | 6.781296 | 6.945881 | 6.47729 |
1977Q2 | 6.664045 | 6.927022 | 6.431281 |
1977Q3 | 5.676692 | 5.816541 | 5.720217 |
1977Q4 | 5.600694 | 5.843731 | 5.402107 |
1978Q1 | 6.811789 | 6.621528 | 6.898905 |
1978Q2 | 8.431486 | 8.562261 | 8.061814 |
1978Q3 | 8.834893 | 9.104327 | 8.539464 |
1978Q4 | 8.956918 | 9.178568 | 8.767154 |
1979Q1 | 9.49526 | 9.826827 | 9.150954 |
1979Q2 | 10.64508 | 12.15676 | 9.330867 |
1979Q3 | 11.25394 | 12.62815 | 10.20059 |
1979Q4 | 12.16981 | 12.48482 | 11.90362 |
1980Q1 | 15.06428 | 15.2126 | 14.5216 |
1980Q2 | 13.25561 | 13.5548 | 13.18342 |
1980Q3 | 6.046743 | 7.800882 | 5.940703 |
1980Q4 | 10.80542 | 10.5485 | 11.03429 |
1981Q1 | 10.35197 | 10.82663 | 9.811798 |
1981Q2 | 8.957838 | 8.90055 | 9.077708 |
1981Q3 | 11.19473 | 10.45232 | 11.8888 |
1981Q4 | 8.051668 | 7.644511 | 9.243652 |
1982Q1 | 5.013456 | 4.459067 | 6.463737 |
1982Q2 | 6.027286 | 5.433816 | 7.031063 |
1982Q3 | 6.603282 | 6.499634 | 6.797119 |
1982Q4 | 2.734816 | 2.812912 | 3.393714 |
1983Q1 | 1.684808 | 0.861043 | 2.756716 |
1983Q2 | 3.546435 | 3.500779 | 3.510422 |
1983Q3 | 4.175247 | 3.764848 | 4.425369 |
1983Q4 | 4.386376 | 3.912443 | 4.896451 |
1984Q1 | 5.232993 | 5.111648 | 5.274613 |
1984Q2 | 4.542866 | 4.170934 | 5.03233 |
1984Q3 | 4.218815 | 3.682035 | 4.988727 |
1984Q4 | 3.880504 | 3.51243 | 4.368769 |
1985Q1 | 3.973915 | 3.610514 | 4.364479 |
1985Q2 | 3.892572 | 3.618592 | 4.251704 |
1985Q3 | 3.219712 | 2.822557 | 3.79714 |
1985Q4 | 4.005224 | 3.679911 | 4.302748 |
1986Q1 | 3.381582 | 2.574592 | 4.301479 |
1986Q2 | 1.519385 | -0.641307 | 3.672105 |
1986Q3 | 2.750745 | 1.468216 | 3.723614 |
1986Q4 | 3.184866 | 2.342641 | 3.794461 |
1987Q1 | 3.744479 | 3.968487 | 3.430474 |
1987Q2 | 4.407486 | 4.292197 | 4.297596 |
1987Q3 | 4.087806 | 4.232975 | 3.933247 |
1987Q4 | 4.13409 | 3.913847 | 4.331844 |
1988Q1 | 3.684124 | 3.416557 | 4.044267 |
1988Q2 | 4.370794 | 4.124748 | 4.516862 |
1988Q3 | 4.557576 | 4.571224 | 4.462771 |
1988Q4 | 4.590552 | 4.432063 | 4.674367 |
1989Q1 | 4.417933 | 4.485527 | 4.396135 |
1989Q2 | 4.785778 | 5.677424 | 4.336871 |
1989Q3 | 4.074814 | 4.100517 | 4.072004 |
1989Q4 | 4.356146 | 4.064239 | 4.461026 |
1990Q1 | 5.079273 | 5.771732 | 4.775662 |
1990Q2 | 4.925192 | 4.641884 | 4.999088 |
1990Q3 | 5.648971 | 6.005214 | 5.487166 |
1990Q4 | 5.38075 | 6.456026 | 4.990666 |
1991Q1 | 5.132196 | 4.358408 | 5.400463 |
1991Q2 | 4.02401 | 3.108404 | 4.435645 |
1991Q3 | 3.96815 | 3.06455 | 4.371236 |
1991Q4 | 3.747453 | 3.213135 | 4.016459 |
1992Q1 | 3.445897 | 2.896871 | 3.731 |
1992Q2 | 3.392089 | 3.000873 | 3.594267 |
1992Q3 | 3.216494 | 3.026042 | 3.33582 |
1992Q4 | 3.407384 | 3.296591 | 3.469681 |
1993Q1 | 3.350194 | 3.065613 | 3.470679 |
1993Q2 | 3.274177 | 2.96053 | 3.413125 |
1993Q3 | 2.714985 | 2.356564 | 2.909415 |
1993Q4 | 2.9597 | 2.869109 | 3.021688 |
1994Q1 | 2.688799 | 2.404198 | 2.823098 |
1994Q2 | 2.675275 | 2.328834 | 2.780341 |
1994Q3 | 2.939341 | 3.091945 | 2.877162 |
1994Q4 | 2.662663 | 2.671165 | 2.728329 |
1995Q1 | 3.075277 | 2.799801 | 3.029405 |
1995Q2 | 3.16819 | 3.05803 | 3.169743 |
1995Q3 | 2.793409 | 2.500244 | 2.878004 |
1995Q4 | 2.745046 | 2.372252 | 2.82985 |
1996Q1 | 2.77552 | 2.893904 | 2.715616 |
1996Q2 | 2.59557 | 2.981338 | 2.590886 |
1996Q3 | 2.634075 | 2.790504 | 2.640277 |
1996Q4 | 2.506965 | 2.968492 | 2.576248 |
1997Q1 | 2.402983 | 2.826472 | 2.525201 |
1997Q2 | 2.382039 | 2.051972 | 2.484864 |
1997Q3 | 1.981697 | 2.120868 | 2.065968 |
1997Q4 | 2.174633 | 2.099889 | 2.195647 |
1998Q1 | 2.266055 | 1.618636 | 2.297699 |
1998Q2 | 2.235574 | 1.49274 | 2.271647 |
1998Q3 | 2.302947 | 1.704036 | 2.325123 |
1998Q4 | 2.250855 | 1.770281 | 2.274952 |
1999Q1 | 2.013195 | 1.659457 | 2.041464 |
1999Q2 | 1.981005 | 2.125321 | 1.975464 |
1999Q3 | 2.05597 | 2.426777 | 2.035396 |
1999Q4 | 2.155844 | 2.608673 | 2.129953 |
2000Q1 | 2.388306 | 3.123268 | 2.343696 |
2000Q2 | 2.496671 | 3.123423 | 2.43179 |
2000Q3 | 2.659747 | 3.37214 | 2.530905 |
2000Q4 | 2.521489 | 3.14237 | 2.477173 |
2001Q1 | 2.776873 | 3.378108 | 2.679619 |
2001Q2 | 2.633437 | 3.163822 | 2.571198 |
2001Q3 | 2.594296 | 2.464738 | 2.642185 |
2001Q4 | 2.519879 | 1.202525 | 2.63905 |
2002Q1 | 2.306654 | 1.235593 | 2.415845 |
2002Q2 | 2.207833 | 2.015577 | 2.223485 |
2002Q3 | 2.148801 | 2.063611 | 2.15586 |
2002Q4 | 1.993578 | 2.168842 | 1.967047 |
2003Q1 | 1.762686 | 2.884929 | 1.605235 |
2003Q2 | 1.031338 | 1.699375 | 1.054961 |
2003Q3 | 1.404919 | 2.097876 | 1.368666 |
2003Q4 | 1.202786 | 1.923419 | 1.177441 |
2004Q1 | 1.693786 | 2.333124 | 1.628502 |
2004Q2 | 2.107056 | 2.629 | 2.051795 |
2004Q3 | 1.943976 | 2.686506 | 1.888566 |
2004Q4 | 2.225497 | 3.110879 | 2.150576 |
2005Q1 | 2.376827 | 2.735106 | 2.342761 |
2005Q2 | 2.161425 | 2.621683 | 2.115076 |
2005Q3 | 2.027079 | 3.389124 | 1.742803 |
2005Q4 | 2.291991 | 3.635345 | 2.159093 |
2006Q1 | 2.347839 | 3.01294 | 2.317329 |
2006Q2 | 2.926068 | 3.176508 | 2.942271 |
2006Q3 | 2.918292 | 3.328707 | 2.880417 |
2006Q4 | 2.293595 | 2.565001 | 2.310183 |
2007Q1 | 2.285376 | 2.574261 | 2.280637 |
2007Q2 | 2.15277 | 2.598494 | 2.121935 |
2007Q3 | 2.312663 | 2.585911 | 2.293679 |
2007Q4 | 2.416144 | 2.812992 | 2.377162 |
Figure 5: RMSE for overall CPI (rolling 16-quarter estimates) (percentage points, annual rate)
Year/quarter | Atkeson/Ohanian | Model 1 (Bivariate) | Model 2 (CPI) |
1974Q4 | 3.077012 | 3.100801 | 2.559 |
1975Q1 | 3.253409 | 3.171426 | 2.674972 |
1975Q2 | 3.344347 | 3.167556 | 2.677198 |
1975Q3 | 3.408046 | 3.172107 | 2.714577 |
1975Q4 | 3.446641 | 3.208468 | 2.773684 |
1976Q1 | 3.445082 | 3.203322 | 2.76989 |
1976Q2 | 3.402458 | 3.177357 | 2.771458 |
1976Q3 | 3.287569 | 3.05163 | 2.631109 |
1976Q4 | 3.078328 | 2.804573 | 2.416143 |
1977Q1 | 2.766984 | 2.525752 | 2.232005 |
1977Q2 | 2.520782 | 2.332623 | 2.153578 |
1977Q3 | 2.312447 | 2.087059 | 2.067941 |
1977Q4 | 2.227985 | 2.059904 | 2.123775 |
1978Q1 | 2.339406 | 2.125439 | 2.223524 |
1978Q2 | 2.480476 | 2.153904 | 2.225654 |
1978Q3 | 2.54215 | 2.050143 | 2.178709 |
1978Q4 | 2.456659 | 1.831145 | 1.953942 |
1979Q1 | 2.407687 | 1.947224 | 1.987244 |
1979Q2 | 2.406808 | 2.070557 | 2.007158 |
1979Q3 | 2.312142 | 2.067241 | 1.946576 |
1979Q4 | 2.253795 | 2.008973 | 1.868728 |
1980Q1 | 2.344496 | 2.287662 | 2.182049 |
1980Q2 | 2.548132 | 2.428481 | 2.314327 |
1980Q3 | 2.579859 | 2.651405 | 2.39315 |
1980Q4 | 2.64346 | 2.67742 | 2.413752 |
1981Q1 | 2.770676 | 2.780588 | 2.563565 |
1981Q2 | 2.853419 | 2.838184 | 2.622835 |
1981Q3 | 3.062538 | 3.116693 | 2.844721 |
1981Q4 | 3.244644 | 3.166452 | 2.883216 |
1982Q1 | 3.291537 | 3.125103 | 2.811942 |
1982Q2 | 3.292157 | 3.170295 | 2.834666 |
1982Q3 | 3.279219 | 3.284674 | 2.965188 |
1982Q4 | 3.183741 | 3.202907 | 2.887296 |
1983Q1 | 3.036589 | 3.140574 | 2.902742 |
1983Q2 | 2.937201 | 3.065772 | 2.891053 |
1983Q3 | 2.955895 | 3.057318 | 2.890833 |
1983Q4 | 2.964131 | 3.057034 | 2.886211 |
1984Q1 | 2.900735 | 2.882817 | 2.681111 |
1984Q2 | 2.72415 | 2.729766 | 2.478373 |
1984Q3 | 2.693718 | 2.524315 | 2.400027 |
1984Q4 | 2.614829 | 2.492503 | 2.374521 |
1985Q1 | 2.47936 | 2.384496 | 2.209877 |
1985Q2 | 2.428906 | 2.38147 | 2.194001 |
1985Q3 | 2.171857 | 1.976239 | 1.860025 |
1985Q4 | 1.885435 | 1.869006 | 1.767371 |
1986Q1 | 1.652564 | 1.863348 | 1.757596 |
1986Q2 | 1.495562 | 1.80771 | 1.982839 |
1986Q3 | 1.407285 | 1.524195 | 1.83173 |
1986Q4 | 1.564802 | 1.545947 | 1.894445 |
1987Q1 | 1.614312 | 1.374094 | 1.658805 |
1987Q2 | 1.593676 | 1.366586 | 1.64928 |
1987Q3 | 1.535211 | 1.366584 | 1.646164 |
1987Q4 | 1.51926 | 1.364452 | 1.647426 |
1988Q1 | 1.510342 | 1.318746 | 1.627771 |
1988Q2 | 1.524461 | 1.305358 | 1.635977 |
1988Q3 | 1.513473 | 1.284918 | 1.633164 |
1988Q4 | 1.507553 | 1.280585 | 1.633258 |
1989Q1 | 1.507853 | 1.271458 | 1.634657 |
1989Q2 | 1.439403 | 1.145498 | 1.588356 |
1989Q3 | 1.394574 | 1.127529 | 1.595498 |
1989Q4 | 1.348198 | 1.006751 | 1.567877 |
1990Q1 | 1.322889 | 0.947335 | 1.570023 |
1990Q2 | 1.229626 | 0.787848 | 1.150632 |
1990Q3 | 1.145379 | 0.85376 | 1.098933 |
1990Q4 | 1.176852 | 1.013594 | 1.321329 |
1991Q1 | 1.220244 | 1.162238 | 1.373751 |
1991Q2 | 1.29083 | 1.181937 | 1.370447 |
1991Q3 | 1.304414 | 1.205041 | 1.369786 |
1991Q4 | 1.304751 | 1.216564 | 1.368139 |
1992Q1 | 1.29541 | 1.199011 | 1.338686 |
1992Q2 | 1.264367 | 1.190187 | 1.319493 |
1992Q3 | 1.258702 | 1.195175 | 1.320928 |
1992Q4 | 1.259273 | 1.206938 | 1.328261 |
1993Q1 | 1.261659 | 1.213226 | 1.326679 |
1993Q2 | 1.267086 | 1.232467 | 1.301395 |
1993Q3 | 1.250563 | 1.186304 | 1.264419 |
1993Q4 | 1.188559 | 1.108821 | 1.161261 |
1994Q1 | 1.190795 | 1.109114 | 1.154229 |
1994Q2 | 1.201717 | 1.11199 | 1.167942 |
1994Q3 | 1.130977 | 1.012 | 1.033397 |
1994Q4 | 0.808089 | 0.804168 | 0.536491 |
1995Q1 | 0.574802 | 0.573361 | 0.382527 |
1995Q2 | 0.390927 | 0.525058 | 0.387914 |
1995Q3 | 0.347626 | 0.469842 | 0.398037 |
1995Q4 | 0.3755 | 0.451957 | 0.445012 |
1996Q1 | 0.371408 | 0.445855 | 0.441387 |
1996Q2 | 0.39266 | 0.446075 | 0.474952 |
1996Q3 | 0.421132 | 0.445782 | 0.493445 |
1996Q4 | 0.52613 | 0.441922 | 0.546382 |
1997Q1 | 0.617291 | 0.452947 | 0.627542 |
1997Q2 | 0.616008 | 0.439813 | 0.620749 |
1997Q3 | 0.634965 | 0.450238 | 0.624681 |
1997Q4 | 0.639997 | 0.469553 | 0.637237 |
1998Q1 | 0.63779 | 0.491597 | 0.629629 |
1998Q2 | 0.627344 | 0.484029 | 0.621607 |
1998Q3 | 0.652098 | 0.477792 | 0.629818 |
1998Q4 | 0.704985 | 0.484769 | 0.661724 |
1999Q1 | 0.802269 | 0.563135 | 0.766261 |
1999Q2 | 0.849765 | 0.638173 | 0.812622 |
1999Q3 | 0.890594 | 0.722218 | 0.844244 |
1999Q4 | 0.900835 | 0.777347 | 0.842413 |
2000Q1 | 0.900734 | 0.813275 | 0.844365 |
2000Q2 | 0.891619 | 0.832153 | 0.826553 |
2000Q3 | 0.897042 | 0.825079 | 0.83347 |
2000Q4 | 0.918594 | 0.826558 | 0.85021 |
2001Q1 | 0.999539 | 0.882982 | 0.947676 |
2001Q2 | 1.099392 | 0.920992 | 1.048201 |
2001Q3 | 1.121441 | 0.951139 | 1.063669 |
2001Q4 | 1.121687 | 0.93953 | 1.084318 |
2002Q1 | 1.199222 | 0.940884 | 1.164315 |
2002Q2 | 1.204138 | 0.941817 | 1.154712 |
2002Q3 | 1.20034 | 0.941872 | 1.144875 |
2002Q4 | 1.171669 | 0.93814 | 1.127529 |
2003Q1 | 1.143917 | 0.889513 | 1.094377 |
2003Q2 | 1.123431 | 0.936046 | 1.090228 |
2003Q3 | 1.096483 | 0.928647 | 1.071903 |
2003Q4 | 1.128182 | 1.02264 | 1.10981 |
2004Q1 | 1.166139 | 1.044005 | 1.119817 |
2004Q2 | 1.166476 | 1.043208 | 1.120749 |
2004Q3 | 1.180471 | 1.134775 | 1.136201 |
2004Q4 | 1.121025 | 1.181027 | 1.099536 |
2005Q1 | 1.000738 | 1.159419 | 0.985126 |
2005Q2 | 0.907566 | 1.190066 | 0.923154 |
2005Q3 | 0.873674 | 1.203664 | 0.895646 |
2005Q4 | 0.974351 | 1.204888 | 0.958363 |
2006Q1 | 0.929498 | 1.194731 | 0.873031 |
2006Q2 | 0.967328 | 1.196246 | 0.884867 |
2006Q3 | 0.983924 | 1.205225 | 0.9189 |
2006Q4 | 1.102532 | 1.273054 | 0.979422 |
2007Q1 | 1.145544 | 1.350577 | 1.013389 |
Figure 6: RMSE for CPI excluding food and energy prices (rolling 16-quarter estimates)
Year/quarter | Atkeson/Ohanian | Model 1 (Bivariate) | Model 3 (CPI excl. food and energy) |
1974Q4 | 3.183879 | 2.004236 | 2.947946 |
1975Q1 | 3.323679 | 2.087009 | 3.006072 |
1975Q2 | 3.419476 | 2.082564 | 2.993222 |
1975Q3 | 3.413797 | 2.071889 | 3.007636 |
1975Q4 | 3.413722 | 2.082186 | 3.008969 |
1976Q1 | 3.413468 | 2.079782 | 3.028461 |
1976Q2 | 3.413439 | 2.121673 | 3.034554 |
1976Q3 | 3.414134 | 2.121992 | 3.03551 |
1976Q4 | 3.391546 | 2.100453 | 2.987945 |
1977Q1 | 3.333747 | 2.098816 | 2.926653 |
1977Q2 | 3.199031 | 2.092121 | 2.833835 |
1977Q3 | 2.861638 | 1.994993 | 2.557489 |
1977Q4 | 2.502802 | 2.012508 | 2.42392 |
1978Q1 | 2.15884 | 2.014919 | 2.163612 |
1978Q2 | 2.102319 | 2.018012 | 2.172957 |
1978Q3 | 2.142123 | 1.767631 | 1.803667 |
1978Q4 | 1.996516 | 1.245467 | 1.326725 |
1979Q1 | 1.793515 | 1.197614 | 1.302703 |
1979Q2 | 1.765761 | 1.270453 | 1.520031 |
1979Q3 | 1.806721 | 1.270789 | 1.512127 |
1979Q4 | 1.832327 | 1.265647 | 1.508821 |
1980Q1 | 1.859526 | 1.761557 | 1.826583 |
1980Q2 | 2.045898 | 2.006932 | 2.089334 |
1980Q3 | 2.045793 | 2.342908 | 2.426092 |
1980Q4 | 2.089951 | 2.356061 | 2.444246 |
1981Q1 | 2.123312 | 2.388226 | 2.459663 |
1981Q2 | 2.130253 | 2.393662 | 2.467144 |
1981Q3 | 2.360503 | 2.62064 | 2.76741 |
1981Q4 | 2.583404 | 2.652217 | 2.880145 |
1982Q1 | 2.716012 | 2.615706 | 2.890548 |
1982Q2 | 2.896894 | 2.681767 | 3.006574 |
1982Q3 | 2.977035 | 2.811836 | 3.132721 |
1982Q4 | 2.941625 | 2.817107 | 3.118532 |
1983Q1 | 2.855918 | 2.884904 | 3.108266 |
1983Q2 | 2.744393 | 2.875923 | 3.034733 |
1983Q3 | 2.741085 | 2.885513 | 3.025079 |
1983Q4 | 2.727335 | 2.882555 | 3.023218 |
1984Q1 | 2.707767 | 2.614387 | 2.825509 |
1984Q2 | 2.576479 | 2.394393 | 2.63511 |
1984Q3 | 2.587974 | 2.065981 | 2.338665 |
1984Q4 | 2.557488 | 2.050487 | 2.317213 |
1985Q1 | 2.531675 | 2.006677 | 2.299718 |
1985Q2 | 2.527178 | 1.999991 | 2.292877 |
1985Q3 | 2.293017 | 1.655749 | 1.881217 |
1985Q4 | 1.971642 | 1.477739 | 1.568235 |
1986Q1 | 1.675841 | 1.471595 | 1.498023 |
1986Q2 | 1.195281 | 1.467193 | 1.229995 |
1986Q3 | 0.824549 | 1.225316 | 0.834613 |
1986Q4 | 0.794048 | 1.195981 | 0.817381 |
1987Q1 | 0.806452 | 0.898158 | 0.653163 |
1987Q2 | 0.71632 | 0.807934 | 0.513827 |
1987Q3 | 0.54189 | 0.776653 | 0.498189 |
1987Q4 | 0.521024 | 0.773006 | 0.499344 |
1988Q1 | 0.521319 | 0.786209 | 0.48445 |
1988Q2 | 0.489834 | 0.785389 | 0.457097 |
1988Q3 | 0.407287 | 0.78691 | 0.3916 |
1988Q4 | 0.373979 | 0.787273 | 0.400391 |
1989Q1 | 0.360358 | 0.786191 | 0.397699 |
1989Q2 | 0.349684 | 0.786291 | 0.401353 |
1989Q3 | 0.423101 | 0.815992 | 0.49379 |
1989Q4 | 0.469263 | 0.839885 | 0.51007 |
1990Q1 | 0.492002 | 0.841823 | 0.493895 |
1990Q2 | 0.495458 | 0.595278 | 0.490702 |
1990Q3 | 0.523244 | 0.589167 | 0.541178 |
1990Q4 | 0.558688 | 0.603358 | 0.560144 |
1991Q1 | 0.659421 | 0.680102 | 0.660623 |
1991Q2 | 0.719984 | 0.682333 | 0.682395 |
1991Q3 | 0.761048 | 0.689992 | 0.710647 |
1991Q4 | 0.79007 | 0.689842 | 0.725794 |
1992Q1 | 0.791568 | 0.653672 | 0.718666 |
1992Q2 | 0.795714 | 0.653488 | 0.720511 |
1992Q3 | 0.797353 | 0.64995 | 0.720006 |
1992Q4 | 0.80014 | 0.650642 | 0.720048 |
1993Q1 | 0.8113 | 0.661809 | 0.735649 |
1993Q2 | 0.825084 | 0.676549 | 0.750384 |
1993Q3 | 0.794242 | 0.611903 | 0.691483 |
1993Q4 | 0.767772 | 0.57967 | 0.672284 |
1994Q1 | 0.737186 | 0.578189 | 0.656961 |
1994Q2 | 0.739247 | 0.584969 | 0.659873 |
1994Q3 | 0.719756 | 0.517593 | 0.617955 |
1994Q4 | 0.693103 | 0.456772 | 0.60078 |
1995Q1 | 0.57152 | 0.313332 | 0.446692 |
1995Q2 | 0.496306 | 0.335052 | 0.434755 |
1995Q3 | 0.41896 | 0.311593 | 0.373544 |
1995Q4 | 0.36626 | 0.303998 | 0.348588 |
1996Q1 | 0.367201 | 0.314577 | 0.345221 |
1996Q2 | 0.356305 | 0.315565 | 0.341611 |
1996Q3 | 0.360031 | 0.32756 | 0.351385 |
1996Q4 | 0.360442 | 0.325783 | 0.349852 |
1997Q1 | 0.338297 | 0.304763 | 0.323031 |
1997Q2 | 0.306074 | 0.275423 | 0.282421 |
1997Q3 | 0.294817 | 0.28627 | 0.289628 |
1997Q4 | 0.281503 | 0.281773 | 0.280799 |
1998Q1 | 0.282105 | 0.278041 | 0.282502 |
1998Q2 | 0.271484 | 0.266952 | 0.280401 |
1998Q3 | 0.283261 | 0.277986 | 0.291925 |
1998Q4 | 0.284362 | 0.271288 | 0.291418 |
1999Q1 | 0.284426 | 0.269825 | 0.290968 |
1999Q2 | 0.276186 | 0.251997 | 0.274818 |
1999Q3 | 0.291966 | 0.271725 | 0.290819 |
1999Q4 | 0.300408 | 0.284322 | 0.300524 |
2000Q1 | 0.301212 | 0.278434 | 0.301062 |
2000Q2 | 0.305175 | 0.27856 | 0.303146 |
2000Q3 | 0.295912 | 0.264459 | 0.29052 |
2000Q4 | 0.285659 | 0.256756 | 0.280173 |
2001Q1 | 0.282219 | 0.262592 | 0.274337 |
2001Q2 | 0.274757 | 0.263546 | 0.265895 |
2001Q3 | 0.290558 | 0.264143 | 0.276519 |
2001Q4 | 0.330857 | 0.288404 | 0.313527 |
2002Q1 | 0.371633 | 0.31187 | 0.345366 |
2002Q2 | 0.435884 | 0.358366 | 0.388603 |
2002Q3 | 0.48213 | 0.402566 | 0.429488 |
2002Q4 | 0.523991 | 0.449257 | 0.469801 |
2003Q1 | 0.538027 | 0.45965 | 0.473024 |
2003Q2 | 0.536623 | 0.483633 | 0.493985 |
2003Q3 | 0.53258 | 0.480275 | 0.491365 |
2003Q4 | 0.568749 | 0.523675 | 0.535412 |
2004Q1 | 0.605355 | 0.538569 | 0.553044 |
2004Q2 | 0.610246 | 0.537948 | 0.551761 |
2004Q3 | 0.613187 | 0.538638 | 0.552934 |
2004Q4 | 0.612337 | 0.538183 | 0.550819 |
2005Q1 | 0.612976 | 0.538723 | 0.552793 |
2005Q2 | 0.615794 | 0.540244 | 0.557323 |
2005Q3 | 0.63553 | 0.566447 | 0.607996 |
2005Q4 | 0.628543 | 0.559308 | 0.600022 |
2006Q1 | 0.617188 | 0.54868 | 0.584592 |
2006Q2 | 0.575707 | 0.546412 | 0.582459 |
2006Q3 | 0.556764 | 0.546133 | 0.57843 |
2006Q4 | 0.518041 | 0.50455 | 0.541888 |
2007Q1 | 0.506438 | 0.492743 | 0.537562 |
Figure 7: Information coefficients for overall PCE prices (a1) and PCE prices excluding food and energy prices (a2)
Year/quarter | a1 | a2 |
1975Q1 | 0.201733 | 0.851606 |
1975Q2 | 0.203207 | 0.851287 |
1975Q3 | 0.190398 | 0.859413 |
1975Q4 | 0.184809 | 0.862494 |
1976Q1 | 0.179367 | 0.866025 |
1976Q2 | 0.221414 | 0.851406 |
1976Q3 | 0.160196 | 0.875475 |
1976Q4 | 0.159094 | 0.876045 |
1977Q1 | 0.15069 | 0.881076 |
1977Q2 | 0.121645 | 0.900274 |
1977Q3 | 0.171222 | 0.868527 |
1977Q4 | 0.161685 | 0.874562 |
1978Q1 | 0.161748 | 0.874056 |
1978Q2 | 0.151691 | 0.880979 |
1978Q3 | 0.159436 | 0.876153 |
1978Q4 | 0.135135 | 0.891215 |
1979Q1 | 0.178312 | 0.867428 |
1979Q2 | 0.195067 | 0.752258 |
1979Q3 | 0.221087 | 0.696511 |
1979Q4 | 0.228169 | 0.674682 |
1980Q1 | 0.236195 | 0.685184 |
1980Q2 | 0.225711 | 0.689392 |
1980Q3 | 0.238856 | 0.662274 |
1980Q4 | 0.229325 | 0.668584 |
1981Q1 | 0.241911 | 0.649311 |
1981Q2 | 0.186132 | 0.72481 |
1981Q3 | 0.198837 | 0.731696 |
1981Q4 | 0.19571 | 0.721501 |
1982Q1 | 0.211122 | 0.706353 |
1982Q2 | 0.177933 | 0.738714 |
1982Q3 | 0.177422 | 0.7357 |
1982Q4 | 0.164749 | 0.738042 |
1983Q1 | 0.159975 | 0.745666 |
1983Q2 | 0.237234 | 0.686232 |
1983Q3 | 0.271827 | 0.596528 |
1983Q4 | 0.274034 | 0.540159 |
1984Q1 | 0.259475 | 0.5405 |
1984Q2 | 0.266452 | 0.535402 |
1984Q3 | 0.264329 | 0.532782 |
1984Q4 | 0.271018 | 0.534897 |
1985Q1 | 0.266873 | 0.520243 |
1985Q2 | 0.271743 | 0.510617 |
1985Q3 | 0.272926 | 0.506109 |
1985Q4 | 0.267537 | 0.508948 |
1986Q1 | 0.268903 | 0.499861 |
1986Q2 | 0.24126 | 0.524004 |
1986Q3 | 0.225935 | 0.54205 |
1986Q4 | 0.20214 | 0.542709 |
1987Q1 | 0.231113 | 0.542279 |
1987Q2 | 0.230551 | 0.545316 |
1987Q3 | 0.233274 | 0.510948 |
1987Q4 | 0.204006 | 0.498346 |
1988Q1 | 0.234815 | 0.499177 |
1988Q2 | 0.248481 | 0.453214 |
1988Q3 | 0.205525 | 0.431975 |
1988Q4 | 0.123424 | 0.506967 |
1989Q1 | 0.109546 | 0.534913 |
1989Q2 | 0.088005 | 0.470415 |
1989Q3 | 0.079134 | 0.446657 |
1989Q4 | 0.082389 | 0.440269 |
1990Q1 | 0.064437 | 0.44725 |
1990Q2 | 0.081127 | 0.441595 |
1990Q3 | 0.100559 | 0.42525 |
1990Q4 | 0.121921 | 0.428235 |
1991Q1 | 0.134873 | 0.402558 |
1991Q2 | 0.130058 | 0.407922 |
1991Q3 | 0.130284 | 0.408742 |
1991Q4 | 0.131655 | 0.407115 |
1992Q1 | 0.128013 | 0.40908 |
1992Q2 | 0.147319 | 0.402539 |
1992Q3 | 0.138628 | 0.403121 |
1992Q4 | 0.144368 | 0.399627 |
1993Q1 | 0.145487 | 0.404272 |
1993Q2 | 0.148045 | 0.394459 |
1993Q3 | 0.147242 | 0.398369 |
1993Q4 | 0.136059 | 0.404717 |
1994Q1 | 0.130915 | 0.414743 |
1994Q2 | 0.108669 | 0.423694 |
1994Q3 | 0.10278 | 0.441666 |
1994Q4 | 0.112751 | 0.417814 |
1995Q1 | 0.112647 | 0.420238 |
1995Q2 | 0.11282 | 0.422502 |
1995Q3 | 0.075956 | 0.392741 |
1995Q4 | 0.124114 | 0.31626 |
1996Q1 | 0.119098 | 0.303558 |
1996Q2 | 0.112201 | 0.279695 |
1996Q3 | 0.10404 | 0.266868 |
1996Q4 | 0.099764 | 0.260637 |
1997Q1 | 0.104382 | 0.264739 |
1997Q2 | 0.100347 | 0.236337 |
1997Q3 | 0.097836 | 0.231701 |
1997Q4 | 0.080291 | 0.240223 |
1998Q1 | 0.076248 | 0.563379 |
1998Q2 | 0.067069 | 0.315622 |
1998Q3 | 0.07152 | 0.329109 |
1998Q4 | 0.069688 | 0.324344 |
1999Q1 | 0.067927 | 0.325449 |
1999Q2 | 0.075094 | 0.385162 |
1999Q3 | 0.081523 | 0.391223 |
1999Q4 | 0.07398 | 0.412587 |
2000Q1 | 0.070894 | 0.427333 |
2000Q2 | 0.059475 | 0.391424 |
2000Q3 | 0.055304 | 0.407086 |
2000Q4 | 0.063126 | 0.429119 |
2001Q1 | 0.08863 | 0.392526 |
2001Q2 | 0.085754 | 0.547629 |
2001Q3 | 0.06696 | 0.375123 |
2001Q4 | 0.070172 | 0.35477 |
2002Q1 | 0.069231 | 0.33987 |
2002Q2 | 0.061067 | 0.340359 |
2002Q3 | 0.094798 | 0.469615 |
2002Q4 | 0.069936 | 0.341558 |
2003Q1 | 0.067279 | 0.335745 |
2003Q2 | 0.063869 | 0.340784 |
2003Q3 | 0.059084 | 0.34406 |
2003Q4 | 0.058711 | 0.358989 |
2004Q1 | 0.049977 | 0.393037 |
2004Q2 | 0.055048 | 0.388039 |
2004Q3 | 0.081153 | 0.536277 |
2004Q4 | 0.115466 | 0.371301 |
2005Q1 | 0.041421 | 0.355858 |
2005Q2 | 0.046001 | 0.340603 |
2005Q3 | 0.046224 | 0.338138 |
2005Q4 | 0.035924 | 0.342196 |
2006Q1 | 0.035213 | 0.364646 |
2006Q2 | 0.024028 | 0.350308 |
2006Q3 | 0.023736 | 0.303079 |
2006Q4 | -0.000335 | 0.279795 |
2007Q1 | -0.002886 | 0.279662 |
2007Q2 | 0.009633 | 0.247136 |
2007Q3 | 0.010627 | 0.240697 |
2007Q4 | 0.00928 | 0.230382 |
Figure 8: Information coefficients for overall CPI (a1) and CPI excluding food and energy prices (a2)
Year/quarter | a1 | a2 |
1975Q1 | 0.490678 | 0.388721 |
1975Q2 | 0.497014 | 0.496338 |
1975Q3 | 0.454278 | 0.505539 |
1975Q4 | 0.476896 | 0.473359 |
1976Q1 | 0.452837 | 0.516505 |
1976Q2 | 0.473808 | 0.515062 |
1976Q3 | 0.436969 | 0.512126 |
1976Q4 | 0.432025 | 0.50282 |
1977Q1 | 0.423305 | 0.501085 |
1977Q2 | 0.422386 | 0.500012 |
1977Q3 | 0.417352 | 0.506205 |
1977Q4 | 0.414067 | 0.507875 |
1978Q1 | 0.428911 | 0.490169 |
1978Q2 | 0.433088 | 0.516227 |
1978Q3 | 0.437193 | 0.522831 |
1978Q4 | 0.434096 | 0.536226 |
1979Q1 | 0.430551 | 0.535464 |
1979Q2 | 0.410472 | 0.571509 |
1979Q3 | 0.417002 | 0.574328 |
1979Q4 | 0.439714 | 0.560552 |
1980Q1 | 0.451946 | 0.595518 |
1980Q2 | 0.409523 | 0.56918 |
1980Q3 | 0.54124 | 0.558152 |
1980Q4 | 0.433807 | 0.322166 |
1981Q1 | 0.432547 | 0.325249 |
1981Q2 | 0.401082 | 0.340628 |
1981Q3 | 0.469919 | 0.299266 |
1981Q4 | 0.4328 | 0.312247 |
1982Q1 | 0.467791 | 0.284908 |
1982Q2 | 0.458744 | 0.290644 |
1982Q3 | 0.450831 | 0.295861 |
1982Q4 | 0.427504 | 0.299606 |
1983Q1 | 0.400686 | 0.311722 |
1983Q2 | 0.383452 | 0.325765 |
1983Q3 | 0.457007 | 0.316122 |
1983Q4 | 0.408555 | 0.310835 |
1984Q1 | 0.406283 | 0.310864 |
1984Q2 | 0.393564 | 0.322656 |
1984Q3 | 0.434499 | 0.36946 |
1984Q4 | 0.374886 | 0.329659 |
1985Q1 | 0.364785 | 0.362101 |
1985Q2 | 0.400746 | 0.323668 |
1985Q3 | 0.396161 | 0.320204 |
1985Q4 | 0.369435 | 0.339414 |
1986Q1 | 0.372652 | 0.33227 |
1986Q2 | 0.348117 | 0.369623 |
1986Q3 | 0.33317 | 0.403643 |
1986Q4 | 0.332585 | 0.394589 |
1987Q1 | 0.340295 | 0.38443 |
1987Q2 | 0.338827 | 0.387703 |
1987Q3 | 0.352726 | 0.370339 |
1987Q4 | 0.349745 | 0.3571 |
1988Q1 | 0.346733 | 0.353665 |
1988Q2 | 0.359722 | 0.332808 |
1988Q3 | 0.34221 | 0.350999 |
1988Q4 | 0.297633 | 0.398774 |
1989Q1 | 0.284011 | 0.421933 |
1989Q2 | 0.211824 | 0.423813 |
1989Q3 | 0.187895 | 0.396203 |
1989Q4 | 0.194287 | 0.390793 |
1990Q1 | 0.178923 | 0.398372 |
1990Q2 | 0.166985 | 0.408744 |
1990Q3 | 0.166246 | 0.411789 |
1990Q4 | 0.165628 | 0.413685 |
1991Q1 | 0.168065 | 0.407581 |
1991Q2 | 0.139335 | 0.486728 |
1991Q3 | 0.174041 | 0.416483 |
1991Q4 | 0.174424 | 0.415264 |
1992Q1 | 0.161396 | 0.515219 |
1992Q2 | 0.177685 | 0.411352 |
1992Q3 | 0.164861 | 0.398737 |
1992Q4 | 0.168094 | 0.383705 |
1993Q1 | 0.161595 | 0.385887 |
1993Q2 | 0.162123 | 0.380906 |
1993Q3 | 0.160053 | 0.363973 |
1993Q4 | 0.163944 | 0.348068 |
1994Q1 | 0.148709 | 0.356036 |
1994Q2 | 0.112011 | 0.402551 |
1994Q3 | 0.116789 | 0.49441 |
1994Q4 | 0.076247 | 0.563388 |
1995Q1 | 0.076247 | 0.563387 |
1995Q2 | 0.118371 | 0.492869 |
1995Q3 | 0.093897 | 0.510193 |
1995Q4 | 0.076248 | 0.563387 |
1996Q1 | 0.076247 | 0.563387 |
1996Q2 | 0.036003 | 0.479351 |
1996Q3 | 0.008482 | 0.331905 |
1996Q4 | -0.059019 | 0.895077 |
1997Q1 | -0.011904 | 0.601995 |
1997Q2 | 0.070948 | 0.684132 |
1997Q3 | 0.076236 | 0.563363 |
1997Q4 | 0.043779 | 0.455663 |
1998Q1 | 0.018727 | 0.470613 |
1998Q2 | 0.019785 | 0.471915 |
1998Q3 | 0.018611 | 0.470849 |
1998Q4 | 0.022264 | 0.449672 |
1999Q1 | 0.022102 | 0.439549 |
1999Q2 | 0.01896 | 0.440221 |
1999Q3 | 0.018559 | 0.440028 |
1999Q4 | 0.018134 | 0.435857 |
2000Q1 | 0.018068 | 0.442503 |
2000Q2 | 0.029452 | 0.484218 |
2000Q3 | 0.05534 | 0.511554 |
2000Q4 | 0.032666 | 0.484101 |
2001Q1 | 0.051971 | 0.461353 |
2001Q2 | 0.055944 | 0.450453 |
2001Q3 | 0.051091 | 0.443511 |
2001Q4 | 0.034918 | 0.468709 |
2002Q1 | 0.038837 | 0.486068 |
2002Q2 | 0.038357 | 0.490626 |
2002Q3 | 0.04043 | 0.502165 |
2002Q4 | 0.035096 | 0.48912 |
2003Q1 | 0.056651 | 0.51266 |
2003Q2 | 0.037159 | 0.566869 |
2003Q3 | 0.026726 | 0.547723 |
2003Q4 | 0.024451 | 0.545821 |
2004Q1 | 0.040883 | 0.497513 |
2004Q2 | 0.029437 | 0.536471 |
2004Q3 | 0.032815 | 0.520769 |
2004Q4 | 0.029315 | 0.531482 |
2005Q1 | 0.042557 | 0.562219 |
2005Q2 | 0.041791 | 0.492961 |
2005Q3 | 0.040971 | 0.431468 |
2005Q4 | 0.034621 | 0.477159 |
2006Q1 | 0.038148 | 0.497602 |
2006Q2 | 0.03675 | 0.50841 |
2006Q3 | 0.037331 | 0.505862 |
2006Q4 | 0.009202 | 0.496683 |
2007Q1 | 0.008336 | 0.501568 |
2007Q2 | 0.009771 | 0.528005 |
2007Q3 | 0.012861 | 0.480324 |
2007Q4 | 0.013103 | 0.459378 |