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Finance and Economics Discussion Series: 2008-37 Screen Reader version

Estimating the common trend rate of inflation for consumer prices and consumer prices excluding food and energy prices

Michael T. Kiley1
July 16, 2008



Figure 1: Estimates of trend for PCE inflation from IMA(1,1) models (percent, annual rate)
Year/QuarterModel 1 (Bivariate)Model 2 (PCE prices)Model 3 (PCE prices excl. food and energy)
1974Q49.64529210.090519.48182
1975Q17.4222747.9402947.54904
1975Q26.012415.3724676.333189
1975Q36.313067.1168176.044604
1975Q46.4987696.7976676.438615
1976Q15.7200144.7893156.033527
1976Q24.4113183.6400494.768561
1976Q36.2752145.6337046.242828
1976Q46.2645266.1251486.271359
1977Q16.58796.8712536.501197
1977Q25.9105736.8253315.804323
1977Q36.5161626.14076.592761
1977Q45.8384965.7747955.891701
1978Q16.4851176.5388666.420559
1978Q26.8772627.9279146.640025
1978Q36.4937137.0966956.429487
1978Q47.0457047.3962186.966941
1979Q15.2870047.3839574.95076
1979Q28.69319110.116278.170754
1979Q37.7868069.7636347.170701
1979Q48.3896689.5335318.006352
1980Q19.96745211.321889.389673
1980Q28.9676079.9161288.739513
1980Q38.9107649.340368.793279
1980Q49.6555519.6820539.615981
1981Q19.0990410.087418.728645
1981Q27.3666997.437197.527154
1981Q37.2196716.7138867.397878
1981Q46.9357086.1886737.171234
1982Q15.8072485.2629746.048142
1982Q25.1770284.0731295.49365
1982Q36.2189895.7605416.250993
1982Q45.5598014.7651695.777718
1983Q15.2076563.7327745.569043
1983Q23.3220553.6743663.353548
1983Q35.6657014.8794615.794319
1983Q43.4433213.2169263.762403
1984Q13.9143493.982233.879312
1984Q24.3307893.8945944.499759
1984Q33.6844493.2910533.939499
1984Q42.9230092.7018683.142005
1985Q14.3711133.8675544.48447
1985Q23.3568613.2466813.500684
1985Q33.1612512.746473.427228
1985Q43.2036253.0322473.309064
1986Q13.6948692.9114514.039645
1986Q22.7327220.9250893.618993
1986Q33.3927932.4324883.75741
1986Q43.5059782.7406693.7863
1987Q13.6654254.0251623.505692
1987Q23.4785123.5856663.447243
1987Q33.8551893.9015633.792859
1987Q43.8335633.5481143.944242
1988Q13.9296813.482354.124779
1988Q24.4580644.0827414.588795
1988Q34.4637554.5529384.425001
1988Q44.3045274.1013534.354557
1989Q14.4833274.5041024.471659
1989Q24.0085424.9026913.887276
1989Q33.482993.5601423.499712
1989Q43.6106953.3993693.652068
1990Q14.2518774.8305214.162161
1990Q24.7005394.5028084.691318
1990Q34.4174094.7858654.338243
1990Q44.0211364.9916233.815911
1991Q14.1098093.8757264.166131
1991Q23.4327522.9079353.630536
1991Q33.4810642.8543273.687123
1991Q43.5060483.0434243.664714
1992Q13.6080243.0702493.768891
1992Q23.1226422.7723873.305877
1992Q32.9379562.7807553.044262
1992Q42.7707912.6333232.863393
1993Q12.5120392.305382.628401
1993Q22.7132092.459962.809303
1993Q32.16171.8786562.318951
1993Q42.0375051.9957092.09833
1994Q11.9721641.7696252.057198
1994Q22.3042811.9915812.368406
1994Q32.7991922.8798232.752432
1994Q42.2907322.2597012.315479
1995Q12.1526412.0810532.189318
1995Q22.1937822.1491662.212804
1995Q32.073681.9407162.10822
1995Q41.9578391.858572.019629
1996Q12.0007652.0988081.967589
1996Q21.9868892.2540491.880044
1996Q31.8510582.0312391.799195
1996Q41.9968842.2372251.901993
1997Q11.8544282.0982091.773484
1997Q21.7440941.6661491.79715
1997Q31.4730881.4672251.526277
1997Q41.4106091.4156871.439658
1998Q11.2590031.0077761.399531
1998Q21.2033580.8788531.293267
1998Q31.2852671.0352161.347088
1998Q41.432151.1973641.473623
1999Q11.3355081.1303291.381608
1999Q21.5682261.6566931.496157
1999Q31.5612091.8939021.465959
1999Q41.728682.0878021.630909
2000Q12.1449842.6901071.987248
2000Q21.7531312.360261.662421
2000Q31.4070592.1539861.329564
2000Q41.458271.9682791.397968
2001Q12.1508932.4855581.987874
2001Q22.1833442.4975642.010985
2001Q31.7443841.7819421.762977
2001Q41.9530981.2355232.080756
2002Q11.6429481.0888821.763341
2002Q21.784961.7702151.789193
2002Q31.8179251.7636151.812044
2002Q41.5919911.718831.582852
2003Q11.5275852.2106311.402912
2003Q21.3803851.6522381.353484
2003Q31.565231.8864631.506959
2003Q41.5713791.7466581.543319
2004Q11.9887482.365711.872906
2004Q22.3363642.9876632.198529
2004Q32.0475292.5589621.998417
2004Q42.2246162.7278052.039639
2005Q12.2650062.5108432.228393
2005Q22.2446832.758992.163824
2005Q32.1379263.2235831.96802
2005Q42.2059033.0640522.108895
2006Q12.1176772.6690562.073295
2006Q22.4156133.0858162.361799
2006Q32.3658672.9287472.322852
2006Q42.1793862.2079922.179361
2007Q12.2370422.4091292.237343
2007Q22.0358572.6381292.006232
2007Q32.0245872.5113322.002965
2007Q42.1553292.6933512.126832
Return to Figure 1
Figure 2: RMSE for overall PCE prices (rolling 16-quarter estimates) (percentage points, annual rate)
Year/quarterAtkeson/OhanianModel 1 (Bivariate)Model 2 (PCE prices)
1974Q42.9167133.1076762.471289
1975Q13.0659683.1236752.522397
1975Q23.1295953.1092942.506519
1975Q33.1688163.1190362.544876
1975Q43.1941973.1293732.578711
1976Q13.1940273.1273152.586447
1976Q23.1797123.1247122.632908
1976Q33.131273.0535192.573636
1976Q43.0190792.8617242.408606
1977Q12.7372712.5250582.181651
1977Q22.4785932.3440912.090512
1977Q32.2024322.0115431.943815
1977Q41.9995621.5803691.849556
1978Q12.0041181.5253321.842455
1978Q22.0131841.5092361.71345
1978Q31.9427641.3751371.580278
1978Q41.7220631.2869311.411661
1979Q11.6080531.773491.517309
1979Q21.5389331.8040881.51694
1979Q31.4565271.8635171.436833
1979Q41.4106531.8740731.373713
1980Q11.4212031.8755051.416476
1980Q21.4284811.7989371.24245
1980Q31.4513661.8048311.251104
1980Q41.5656481.8946651.379121
1981Q11.801832.0406761.702567
1981Q22.0105152.0933211.779162
1981Q32.1445612.1472721.805957
1981Q42.2193622.1769311.794619
1982Q12.2343722.1877791.789649
1982Q22.215772.1736071.791462
1982Q32.1793232.1555391.783202
1982Q42.1401062.1285171.73649
1983Q12.0167851.7310211.565493
1983Q21.9570581.702971.567671
1983Q31.9433611.7032751.606044
1983Q41.936121.6515331.601528
1984Q11.9320181.6542851.553648
1984Q21.9194771.6773431.543268
1984Q31.8740051.6764061.521111
1984Q41.7477641.5760381.41132
1985Q11.501261.4282031.016611
1985Q21.2338321.368250.912549
1985Q30.997921.2963760.845529
1985Q40.8247071.2144330.804605
1986Q10.7278281.1975730.7834
1986Q20.7565891.1965780.999996
1986Q30.7886071.0876480.974053
1986Q40.8382220.9927660.979758
1987Q10.8602490.9421990.984545
1987Q20.8586010.9306070.982869
1987Q30.8419820.7516680.917508
1987Q40.8409250.7551270.927302
1988Q10.8582020.756280.947782
1988Q20.8597570.7049730.942836
1988Q30.8549750.6959990.94893
1988Q40.8552860.6973480.939829
1989Q10.8465730.5958190.910802
1989Q20.8229240.5213390.901562
1989Q30.8100260.5528830.932526
1989Q40.8202850.6170191.002442
1990Q10.8184430.5586561.00732
1990Q20.7589780.5725680.804811
1990Q30.750150.6330890.828218
1990Q40.8511510.6977090.954094
1991Q10.9028370.7676810.983216
1991Q20.9268910.7738860.981419
1991Q30.9291840.7865440.981207
1991Q40.9266020.8065220.973657
1992Q10.9053920.8448190.955231
1992Q20.8888580.8586050.947982
1992Q30.9091850.8767040.954474
1992Q40.9249880.8912670.965445
1993Q10.9343820.901590.967959
1993Q20.9361190.9295280.955061
1993Q30.928350.8871440.925882
1993Q40.8855470.810520.828917
1994Q10.8919440.815740.833137
1994Q20.9017140.7866080.821447
1994Q30.8469320.7680190.771385
1994Q40.6363370.7125390.551881
1995Q10.5164250.6371160.48579
1995Q20.4666170.6240750.485944
1995Q30.4582310.6070250.486945
1995Q40.471420.5828960.494688
1996Q10.4648160.5116560.472403
1996Q20.4628860.4911360.486394
1996Q30.4387530.4530030.472219
1996Q40.483370.4537780.511277
1997Q10.5627140.4935220.587944
1997Q20.5781050.4923730.600701
1997Q30.5994980.509990.605359
1997Q40.601260.5199210.61292
1998Q10.5941030.5122610.595917
1998Q20.6077260.5217330.615912
1998Q30.6395320.4899960.598746
1998Q40.6894570.5029860.628052
1999Q10.7853710.6015510.735467
1999Q20.8137090.6441430.764601
1999Q30.8256390.6779650.77457
1999Q40.8197210.684730.766994
2000Q10.8271510.6837330.776687
2000Q20.822180.6961830.764643
2000Q30.8184110.7099780.756963
2000Q40.7844250.6879780.717965
2001Q10.7620990.6898030.73027
2001Q20.7848370.6968030.771952
2001Q30.7777560.6850550.762432
2001Q40.7741740.6766110.765124
2002Q10.8234980.6952390.822126
2002Q20.8141070.6880130.801922
2002Q30.7882770.6752460.778357
2002Q40.7389690.6612990.749804
2003Q10.6352560.5832620.647071
2003Q20.643930.6367080.67188
2003Q30.653940.6598560.687194
2003Q40.7138270.7433560.758221
2004Q10.728060.7654570.753401
2004Q20.7281080.7539990.759361
2004Q30.7331290.7895560.773957
2004Q40.7210480.8178220.777651
2005Q10.6753250.8001350.712827
2005Q20.6309620.7999170.645806
2005Q30.6237440.8153070.650213
2005Q40.6952040.8179040.700851
2006Q10.6566260.8027820.638824
2006Q20.6805550.8032450.66791
2006Q30.6949170.8053050.697138
2006Q40.7801830.850590.748655
2007Q10.8173530.8862480.781304
Return to Figure 2
Figure 3: RMSE for PCE prices excluding food and energy prices (rolling 16-quarter estimates) (percentage points, annual rate)
Year/quarterAtkeson/OhanianModel 1 (Bivariate)Model 3 (PCE prices excl. food and energy)
1974Q42.4409021.9107882.215827
1975Q12.5497531.9178772.218431
1975Q22.6061891.8851522.192767
1975Q32.5959531.8775572.185878
1975Q42.5951471.8767912.181483
1976Q12.5865051.8507762.158819
1976Q22.5878411.8970662.182626
1976Q32.581191.8886332.172414
1976Q42.5608251.8420312.120052
1977Q12.4770941.771532.021535
1977Q22.3546271.7658132.000708
1977Q32.1165011.6572621.852408
1977Q41.7539661.4133911.499232
1978Q11.4338051.3579081.327499
1978Q21.3279471.3274631.3107
1978Q31.3256070.9996290.939355
1978Q41.1702740.6456150.601597
1979Q11.0009170.9405430.970743
1979Q20.8314970.9433590.963255
1979Q30.88680.968931.042581
1979Q41.0063950.974711.072465
1980Q11.0180011.0059621.077939
1980Q21.0158720.9045891.01678
1980Q31.0182580.9186361.025074
1980Q41.0862911.0494881.139431
1981Q11.1937911.174181.220154
1981Q21.3090231.189551.240047
1981Q31.406891.2154171.273757
1981Q41.4714481.2301291.303392
1982Q11.5013321.2287451.304674
1982Q21.5349961.2278351.307376
1982Q31.5522211.2530841.331571
1982Q41.5829131.2802911.368371
1983Q11.5555321.0754411.146855
1983Q21.5075151.113321.18288
1983Q31.4641151.1745061.212096
1983Q41.3824641.1612881.175964
1984Q11.3723321.1336731.171818
1984Q21.3868331.142131.189339
1984Q31.3828471.1310941.185332
1984Q41.3272181.0287241.084378
1985Q11.2376790.9025031.01764
1985Q21.1142980.8764230.982988
1985Q30.9882760.8505680.939675
1985Q40.8841330.8223510.890226
1986Q10.8324220.8225420.893789
1986Q20.7648980.851080.889761
1986Q30.7186570.8109530.847186
1986Q40.6364410.7684320.785611
1987Q10.4881940.7191890.701433
1987Q20.4899630.6816880.668772
1987Q30.4117250.5288480.486374
1987Q40.4160870.5418950.50127
1988Q10.4436830.5598930.508291
1988Q20.3908820.5413040.478035
1988Q30.4076110.5641220.493652
1988Q40.4459490.551810.501882
1989Q10.4669810.5433710.478398
1989Q20.4669390.5418310.484135
1989Q30.4899790.5745720.532045
1989Q40.5106070.5771340.538939
1990Q10.5262690.5767350.528564
1990Q20.5407590.588620.582989
1990Q30.574330.6159260.607058
1990Q40.5893370.6180050.606896
1991Q10.6084760.6292710.616452
1991Q20.5881970.5987470.582843
1991Q30.5675890.5874220.574485
1991Q40.5654920.5802160.583158
1992Q10.5907330.6092930.63818
1992Q20.6241130.61310.646031
1992Q30.6416420.6031410.644342
1992Q40.6440650.5972220.640697
1993Q10.6256660.5735070.624128
1993Q20.6436440.5916560.644003
1993Q30.6255840.5463220.601227
1993Q40.6088250.5279070.585138
1994Q10.5985810.5405510.592363
1994Q20.5882230.4801830.538989
1994Q30.5637080.4800910.541548
1994Q40.5553430.4793430.545768
1995Q10.5410150.4625270.528141
1995Q20.5514410.4695630.534814
1995Q30.5472750.4727510.531458
1995Q40.5203190.4589650.509828
1996Q10.4709540.3985990.431806
1996Q20.4254950.3889660.406102
1996Q30.3785760.3778950.38447
1996Q40.3474880.3914010.380411
1997Q10.3418530.4048280.38039
1997Q20.3418120.4027380.373036
1997Q30.3476960.3995270.37618
1997Q40.3458280.3873970.36704
1998Q10.3398750.3706490.354602
1998Q20.3472150.3787190.358743
1998Q30.3368520.3313930.313004
1998Q40.3234960.3262640.305491
1999Q10.3249130.3471190.32215
1999Q20.307930.3391950.315096
1999Q30.3019320.3309150.305646
1999Q40.2973660.3334530.303075
2000Q10.2961320.3533250.312249
2000Q20.295680.3489370.312745
2000Q30.3025550.3659260.342231
2000Q40.3262230.3767580.371624
2001Q10.3138410.3619760.356508
2001Q20.2748410.346170.323667
2001Q30.267510.3451660.320137
2001Q40.3136440.3602670.347475
2002Q10.3234270.3608890.353556
2002Q20.3269090.3679920.365244
2002Q30.3499620.3832040.382014
2002Q40.3497620.3843230.383488
2003Q10.336110.3677820.376713
2003Q20.379110.4067880.415698
2003Q30.4216320.426680.438526
2003Q40.4640050.4523890.468161
2004Q10.4763730.4367260.467781
2004Q20.4760230.4403480.467055
2004Q30.4687820.4203980.442642
2004Q40.4369420.3778560.395699
2005Q10.4373470.3738340.396961
2005Q20.4381040.359360.392562
2005Q30.4434680.3627440.404566
2005Q40.4127250.3480530.383313
2006Q10.4137580.3514720.38437
2006Q20.404880.3518090.380853
2006Q30.3996250.3502330.376732
2006Q40.4020770.3493030.3761
2007Q10.4058440.3487650.369527
Return to Figure 3
Figure 4: Estimates of trend for CPI inflation from IMA(1,1) models (percent, annual rate)
Year/QuarterModel 1 (Bivariate)Model 2 (CPI)Model 3 (CPI excl. food and energy)
1974Q411.8445511.8450411.7674
1975Q18.8609629.2901918.9897
1975Q25.5520785.1579556.344839
1975Q36.4631047.4508535.196659
1975Q47.038827.3382436.793479
1976Q16.1135615.1702547.417973
1976Q24.5466663.816415.46896
1976Q36.3326465.7953876.459165
1976Q45.6661025.779555.533522
1977Q16.7812966.9458816.47729
1977Q26.6640456.9270226.431281
1977Q35.6766925.8165415.720217
1977Q45.6006945.8437315.402107
1978Q16.8117896.6215286.898905
1978Q28.4314868.5622618.061814
1978Q38.8348939.1043278.539464
1978Q48.9569189.1785688.767154
1979Q19.495269.8268279.150954
1979Q210.6450812.156769.330867
1979Q311.2539412.6281510.20059
1979Q412.1698112.4848211.90362
1980Q115.0642815.212614.5216
1980Q213.2556113.554813.18342
1980Q36.0467437.8008825.940703
1980Q410.8054210.548511.03429
1981Q110.3519710.826639.811798
1981Q28.9578388.900559.077708
1981Q311.1947310.4523211.8888
1981Q48.0516687.6445119.243652
1982Q15.0134564.4590676.463737
1982Q26.0272865.4338167.031063
1982Q36.6032826.4996346.797119
1982Q42.7348162.8129123.393714
1983Q11.6848080.8610432.756716
1983Q23.5464353.5007793.510422
1983Q34.1752473.7648484.425369
1983Q44.3863763.9124434.896451
1984Q15.2329935.1116485.274613
1984Q24.5428664.1709345.03233
1984Q34.2188153.6820354.988727
1984Q43.8805043.512434.368769
1985Q13.9739153.6105144.364479
1985Q23.8925723.6185924.251704
1985Q33.2197122.8225573.79714
1985Q44.0052243.6799114.302748
1986Q13.3815822.5745924.301479
1986Q21.519385-0.6413073.672105
1986Q32.7507451.4682163.723614
1986Q43.1848662.3426413.794461
1987Q13.7444793.9684873.430474
1987Q24.4074864.2921974.297596
1987Q34.0878064.2329753.933247
1987Q44.134093.9138474.331844
1988Q13.6841243.4165574.044267
1988Q24.3707944.1247484.516862
1988Q34.5575764.5712244.462771
1988Q44.5905524.4320634.674367
1989Q14.4179334.4855274.396135
1989Q24.7857785.6774244.336871
1989Q34.0748144.1005174.072004
1989Q44.3561464.0642394.461026
1990Q15.0792735.7717324.775662
1990Q24.9251924.6418844.999088
1990Q35.6489716.0052145.487166
1990Q45.380756.4560264.990666
1991Q15.1321964.3584085.400463
1991Q24.024013.1084044.435645
1991Q33.968153.064554.371236
1991Q43.7474533.2131354.016459
1992Q13.4458972.8968713.731
1992Q23.3920893.0008733.594267
1992Q33.2164943.0260423.33582
1992Q43.4073843.2965913.469681
1993Q13.3501943.0656133.470679
1993Q23.2741772.960533.413125
1993Q32.7149852.3565642.909415
1993Q42.95972.8691093.021688
1994Q12.6887992.4041982.823098
1994Q22.6752752.3288342.780341
1994Q32.9393413.0919452.877162
1994Q42.6626632.6711652.728329
1995Q13.0752772.7998013.029405
1995Q23.168193.058033.169743
1995Q32.7934092.5002442.878004
1995Q42.7450462.3722522.82985
1996Q12.775522.8939042.715616
1996Q22.595572.9813382.590886
1996Q32.6340752.7905042.640277
1996Q42.5069652.9684922.576248
1997Q12.4029832.8264722.525201
1997Q22.3820392.0519722.484864
1997Q31.9816972.1208682.065968
1997Q42.1746332.0998892.195647
1998Q12.2660551.6186362.297699
1998Q22.2355741.492742.271647
1998Q32.3029471.7040362.325123
1998Q42.2508551.7702812.274952
1999Q12.0131951.6594572.041464
1999Q21.9810052.1253211.975464
1999Q32.055972.4267772.035396
1999Q42.1558442.6086732.129953
2000Q12.3883063.1232682.343696
2000Q22.4966713.1234232.43179
2000Q32.6597473.372142.530905
2000Q42.5214893.142372.477173
2001Q12.7768733.3781082.679619
2001Q22.6334373.1638222.571198
2001Q32.5942962.4647382.642185
2001Q42.5198791.2025252.63905
2002Q12.3066541.2355932.415845
2002Q22.2078332.0155772.223485
2002Q32.1488012.0636112.15586
2002Q41.9935782.1688421.967047
2003Q11.7626862.8849291.605235
2003Q21.0313381.6993751.054961
2003Q31.4049192.0978761.368666
2003Q41.2027861.9234191.177441
2004Q11.6937862.3331241.628502
2004Q22.1070562.6292.051795
2004Q31.9439762.6865061.888566
2004Q42.2254973.1108792.150576
2005Q12.3768272.7351062.342761
2005Q22.1614252.6216832.115076
2005Q32.0270793.3891241.742803
2005Q42.2919913.6353452.159093
2006Q12.3478393.012942.317329
2006Q22.9260683.1765082.942271
2006Q32.9182923.3287072.880417
2006Q42.2935952.5650012.310183
2007Q12.2853762.5742612.280637
2007Q22.152772.5984942.121935
2007Q32.3126632.5859112.293679
2007Q42.4161442.8129922.377162
Return to Figure 4
Figure 5: RMSE for overall CPI (rolling 16-quarter estimates) (percentage points, annual rate)
Year/quarterAtkeson/OhanianModel 1 (Bivariate)Model 2 (CPI)
1974Q43.0770123.1008012.559
1975Q13.2534093.1714262.674972
1975Q23.3443473.1675562.677198
1975Q33.4080463.1721072.714577
1975Q43.4466413.2084682.773684
1976Q13.4450823.2033222.76989
1976Q23.4024583.1773572.771458
1976Q33.2875693.051632.631109
1976Q43.0783282.8045732.416143
1977Q12.7669842.5257522.232005
1977Q22.5207822.3326232.153578
1977Q32.3124472.0870592.067941
1977Q42.2279852.0599042.123775
1978Q12.3394062.1254392.223524
1978Q22.4804762.1539042.225654
1978Q32.542152.0501432.178709
1978Q42.4566591.8311451.953942
1979Q12.4076871.9472241.987244
1979Q22.4068082.0705572.007158
1979Q32.3121422.0672411.946576
1979Q42.2537952.0089731.868728
1980Q12.3444962.2876622.182049
1980Q22.5481322.4284812.314327
1980Q32.5798592.6514052.39315
1980Q42.643462.677422.413752
1981Q12.7706762.7805882.563565
1981Q22.8534192.8381842.622835
1981Q33.0625383.1166932.844721
1981Q43.2446443.1664522.883216
1982Q13.2915373.1251032.811942
1982Q23.2921573.1702952.834666
1982Q33.2792193.2846742.965188
1982Q43.1837413.2029072.887296
1983Q13.0365893.1405742.902742
1983Q22.9372013.0657722.891053
1983Q32.9558953.0573182.890833
1983Q42.9641313.0570342.886211
1984Q12.9007352.8828172.681111
1984Q22.724152.7297662.478373
1984Q32.6937182.5243152.400027
1984Q42.6148292.4925032.374521
1985Q12.479362.3844962.209877
1985Q22.4289062.381472.194001
1985Q32.1718571.9762391.860025
1985Q41.8854351.8690061.767371
1986Q11.6525641.8633481.757596
1986Q21.4955621.807711.982839
1986Q31.4072851.5241951.83173
1986Q41.5648021.5459471.894445
1987Q11.6143121.3740941.658805
1987Q21.5936761.3665861.64928
1987Q31.5352111.3665841.646164
1987Q41.519261.3644521.647426
1988Q11.5103421.3187461.627771
1988Q21.5244611.3053581.635977
1988Q31.5134731.2849181.633164
1988Q41.5075531.2805851.633258
1989Q11.5078531.2714581.634657
1989Q21.4394031.1454981.588356
1989Q31.3945741.1275291.595498
1989Q41.3481981.0067511.567877
1990Q11.3228890.9473351.570023
1990Q21.2296260.7878481.150632
1990Q31.1453790.853761.098933
1990Q41.1768521.0135941.321329
1991Q11.2202441.1622381.373751
1991Q21.290831.1819371.370447
1991Q31.3044141.2050411.369786
1991Q41.3047511.2165641.368139
1992Q11.295411.1990111.338686
1992Q21.2643671.1901871.319493
1992Q31.2587021.1951751.320928
1992Q41.2592731.2069381.328261
1993Q11.2616591.2132261.326679
1993Q21.2670861.2324671.301395
1993Q31.2505631.1863041.264419
1993Q41.1885591.1088211.161261
1994Q11.1907951.1091141.154229
1994Q21.2017171.111991.167942
1994Q31.1309771.0121.033397
1994Q40.8080890.8041680.536491
1995Q10.5748020.5733610.382527
1995Q20.3909270.5250580.387914
1995Q30.3476260.4698420.398037
1995Q40.37550.4519570.445012
1996Q10.3714080.4458550.441387
1996Q20.392660.4460750.474952
1996Q30.4211320.4457820.493445
1996Q40.526130.4419220.546382
1997Q10.6172910.4529470.627542
1997Q20.6160080.4398130.620749
1997Q30.6349650.4502380.624681
1997Q40.6399970.4695530.637237
1998Q10.637790.4915970.629629
1998Q20.6273440.4840290.621607
1998Q30.6520980.4777920.629818
1998Q40.7049850.4847690.661724
1999Q10.8022690.5631350.766261
1999Q20.8497650.6381730.812622
1999Q30.8905940.7222180.844244
1999Q40.9008350.7773470.842413
2000Q10.9007340.8132750.844365
2000Q20.8916190.8321530.826553
2000Q30.8970420.8250790.83347
2000Q40.9185940.8265580.85021
2001Q10.9995390.8829820.947676
2001Q21.0993920.9209921.048201
2001Q31.1214410.9511391.063669
2001Q41.1216870.939531.084318
2002Q11.1992220.9408841.164315
2002Q21.2041380.9418171.154712
2002Q31.200340.9418721.144875
2002Q41.1716690.938141.127529
2003Q11.1439170.8895131.094377
2003Q21.1234310.9360461.090228
2003Q31.0964830.9286471.071903
2003Q41.1281821.022641.10981
2004Q11.1661391.0440051.119817
2004Q21.1664761.0432081.120749
2004Q31.1804711.1347751.136201
2004Q41.1210251.1810271.099536
2005Q11.0007381.1594190.985126
2005Q20.9075661.1900660.923154
2005Q30.8736741.2036640.895646
2005Q40.9743511.2048880.958363
2006Q10.9294981.1947310.873031
2006Q20.9673281.1962460.884867
2006Q30.9839241.2052250.9189
2006Q41.1025321.2730540.979422
2007Q11.1455441.3505771.013389
Return to Figure 5
Figure 6: RMSE for CPI excluding food and energy prices (rolling 16-quarter estimates)
Year/quarterAtkeson/OhanianModel 1 (Bivariate)Model 3 (CPI excl. food and energy)
1974Q43.1838792.0042362.947946
1975Q13.3236792.0870093.006072
1975Q23.4194762.0825642.993222
1975Q33.4137972.0718893.007636
1975Q43.4137222.0821863.008969
1976Q13.4134682.0797823.028461
1976Q23.4134392.1216733.034554
1976Q33.4141342.1219923.03551
1976Q43.3915462.1004532.987945
1977Q13.3337472.0988162.926653
1977Q23.1990312.0921212.833835
1977Q32.8616381.9949932.557489
1977Q42.5028022.0125082.42392
1978Q12.158842.0149192.163612
1978Q22.1023192.0180122.172957
1978Q32.1421231.7676311.803667
1978Q41.9965161.2454671.326725
1979Q11.7935151.1976141.302703
1979Q21.7657611.2704531.520031
1979Q31.8067211.2707891.512127
1979Q41.8323271.2656471.508821
1980Q11.8595261.7615571.826583
1980Q22.0458982.0069322.089334
1980Q32.0457932.3429082.426092
1980Q42.0899512.3560612.444246
1981Q12.1233122.3882262.459663
1981Q22.1302532.3936622.467144
1981Q32.3605032.620642.76741
1981Q42.5834042.6522172.880145
1982Q12.7160122.6157062.890548
1982Q22.8968942.6817673.006574
1982Q32.9770352.8118363.132721
1982Q42.9416252.8171073.118532
1983Q12.8559182.8849043.108266
1983Q22.7443932.8759233.034733
1983Q32.7410852.8855133.025079
1983Q42.7273352.8825553.023218
1984Q12.7077672.6143872.825509
1984Q22.5764792.3943932.63511
1984Q32.5879742.0659812.338665
1984Q42.5574882.0504872.317213
1985Q12.5316752.0066772.299718
1985Q22.5271781.9999912.292877
1985Q32.2930171.6557491.881217
1985Q41.9716421.4777391.568235
1986Q11.6758411.4715951.498023
1986Q21.1952811.4671931.229995
1986Q30.8245491.2253160.834613
1986Q40.7940481.1959810.817381
1987Q10.8064520.8981580.653163
1987Q20.716320.8079340.513827
1987Q30.541890.7766530.498189
1987Q40.5210240.7730060.499344
1988Q10.5213190.7862090.48445
1988Q20.4898340.7853890.457097
1988Q30.4072870.786910.3916
1988Q40.3739790.7872730.400391
1989Q10.3603580.7861910.397699
1989Q20.3496840.7862910.401353
1989Q30.4231010.8159920.49379
1989Q40.4692630.8398850.51007
1990Q10.4920020.8418230.493895
1990Q20.4954580.5952780.490702
1990Q30.5232440.5891670.541178
1990Q40.5586880.6033580.560144
1991Q10.6594210.6801020.660623
1991Q20.7199840.6823330.682395
1991Q30.7610480.6899920.710647
1991Q40.790070.6898420.725794
1992Q10.7915680.6536720.718666
1992Q20.7957140.6534880.720511
1992Q30.7973530.649950.720006
1992Q40.800140.6506420.720048
1993Q10.81130.6618090.735649
1993Q20.8250840.6765490.750384
1993Q30.7942420.6119030.691483
1993Q40.7677720.579670.672284
1994Q10.7371860.5781890.656961
1994Q20.7392470.5849690.659873
1994Q30.7197560.5175930.617955
1994Q40.6931030.4567720.60078
1995Q10.571520.3133320.446692
1995Q20.4963060.3350520.434755
1995Q30.418960.3115930.373544
1995Q40.366260.3039980.348588
1996Q10.3672010.3145770.345221
1996Q20.3563050.3155650.341611
1996Q30.3600310.327560.351385
1996Q40.3604420.3257830.349852
1997Q10.3382970.3047630.323031
1997Q20.3060740.2754230.282421
1997Q30.2948170.286270.289628
1997Q40.2815030.2817730.280799
1998Q10.2821050.2780410.282502
1998Q20.2714840.2669520.280401
1998Q30.2832610.2779860.291925
1998Q40.2843620.2712880.291418
1999Q10.2844260.2698250.290968
1999Q20.2761860.2519970.274818
1999Q30.2919660.2717250.290819
1999Q40.3004080.2843220.300524
2000Q10.3012120.2784340.301062
2000Q20.3051750.278560.303146
2000Q30.2959120.2644590.29052
2000Q40.2856590.2567560.280173
2001Q10.2822190.2625920.274337
2001Q20.2747570.2635460.265895
2001Q30.2905580.2641430.276519
2001Q40.3308570.2884040.313527
2002Q10.3716330.311870.345366
2002Q20.4358840.3583660.388603
2002Q30.482130.4025660.429488
2002Q40.5239910.4492570.469801
2003Q10.5380270.459650.473024
2003Q20.5366230.4836330.493985
2003Q30.532580.4802750.491365
2003Q40.5687490.5236750.535412
2004Q10.6053550.5385690.553044
2004Q20.6102460.5379480.551761
2004Q30.6131870.5386380.552934
2004Q40.6123370.5381830.550819
2005Q10.6129760.5387230.552793
2005Q20.6157940.5402440.557323
2005Q30.635530.5664470.607996
2005Q40.6285430.5593080.600022
2006Q10.6171880.548680.584592
2006Q20.5757070.5464120.582459
2006Q30.5567640.5461330.57843
2006Q40.5180410.504550.541888
2007Q10.5064380.4927430.537562
Return to Figure 6
Figure 7: Information coefficients for overall PCE prices (a1) and PCE prices excluding food and energy prices (a2)
Year/quartera1a2
1975Q10.2017330.851606
1975Q20.2032070.851287
1975Q30.1903980.859413
1975Q40.1848090.862494
1976Q10.1793670.866025
1976Q20.2214140.851406
1976Q30.1601960.875475
1976Q40.1590940.876045
1977Q10.150690.881076
1977Q20.1216450.900274
1977Q30.1712220.868527
1977Q40.1616850.874562
1978Q10.1617480.874056
1978Q20.1516910.880979
1978Q30.1594360.876153
1978Q40.1351350.891215
1979Q10.1783120.867428
1979Q20.1950670.752258
1979Q30.2210870.696511
1979Q40.2281690.674682
1980Q10.2361950.685184
1980Q20.2257110.689392
1980Q30.2388560.662274
1980Q40.2293250.668584
1981Q10.2419110.649311
1981Q20.1861320.72481
1981Q30.1988370.731696
1981Q40.195710.721501
1982Q10.2111220.706353
1982Q20.1779330.738714
1982Q30.1774220.7357
1982Q40.1647490.738042
1983Q10.1599750.745666
1983Q20.2372340.686232
1983Q30.2718270.596528
1983Q40.2740340.540159
1984Q10.2594750.5405
1984Q20.2664520.535402
1984Q30.2643290.532782
1984Q40.2710180.534897
1985Q10.2668730.520243
1985Q20.2717430.510617
1985Q30.2729260.506109
1985Q40.2675370.508948
1986Q10.2689030.499861
1986Q20.241260.524004
1986Q30.2259350.54205
1986Q40.202140.542709
1987Q10.2311130.542279
1987Q20.2305510.545316
1987Q30.2332740.510948
1987Q40.2040060.498346
1988Q10.2348150.499177
1988Q20.2484810.453214
1988Q30.2055250.431975
1988Q40.1234240.506967
1989Q10.1095460.534913
1989Q20.0880050.470415
1989Q30.0791340.446657
1989Q40.0823890.440269
1990Q10.0644370.44725
1990Q20.0811270.441595
1990Q30.1005590.42525
1990Q40.1219210.428235
1991Q10.1348730.402558
1991Q20.1300580.407922
1991Q30.1302840.408742
1991Q40.1316550.407115
1992Q10.1280130.40908
1992Q20.1473190.402539
1992Q30.1386280.403121
1992Q40.1443680.399627
1993Q10.1454870.404272
1993Q20.1480450.394459
1993Q30.1472420.398369
1993Q40.1360590.404717
1994Q10.1309150.414743
1994Q20.1086690.423694
1994Q30.102780.441666
1994Q40.1127510.417814
1995Q10.1126470.420238
1995Q20.112820.422502
1995Q30.0759560.392741
1995Q40.1241140.31626
1996Q10.1190980.303558
1996Q20.1122010.279695
1996Q30.104040.266868
1996Q40.0997640.260637
1997Q10.1043820.264739
1997Q20.1003470.236337
1997Q30.0978360.231701
1997Q40.0802910.240223
1998Q10.0762480.563379
1998Q20.0670690.315622
1998Q30.071520.329109
1998Q40.0696880.324344
1999Q10.0679270.325449
1999Q20.0750940.385162
1999Q30.0815230.391223
1999Q40.073980.412587
2000Q10.0708940.427333
2000Q20.0594750.391424
2000Q30.0553040.407086
2000Q40.0631260.429119
2001Q10.088630.392526
2001Q20.0857540.547629
2001Q30.066960.375123
2001Q40.0701720.35477
2002Q10.0692310.33987
2002Q20.0610670.340359
2002Q30.0947980.469615
2002Q40.0699360.341558
2003Q10.0672790.335745
2003Q20.0638690.340784
2003Q30.0590840.34406
2003Q40.0587110.358989
2004Q10.0499770.393037
2004Q20.0550480.388039
2004Q30.0811530.536277
2004Q40.1154660.371301
2005Q10.0414210.355858
2005Q20.0460010.340603
2005Q30.0462240.338138
2005Q40.0359240.342196
2006Q10.0352130.364646
2006Q20.0240280.350308
2006Q30.0237360.303079
2006Q4-0.0003350.279795
2007Q1-0.0028860.279662
2007Q20.0096330.247136
2007Q30.0106270.240697
2007Q40.009280.230382
Return to Figure 7
Figure 8: Information coefficients for overall CPI (a1) and CPI excluding food and energy prices (a2)
Year/quartera1a2
1975Q10.4906780.388721
1975Q20.4970140.496338
1975Q30.4542780.505539
1975Q40.4768960.473359
1976Q10.4528370.516505
1976Q20.4738080.515062
1976Q30.4369690.512126
1976Q40.4320250.50282
1977Q10.4233050.501085
1977Q20.4223860.500012
1977Q30.4173520.506205
1977Q40.4140670.507875
1978Q10.4289110.490169
1978Q20.4330880.516227
1978Q30.4371930.522831
1978Q40.4340960.536226
1979Q10.4305510.535464
1979Q20.4104720.571509
1979Q30.4170020.574328
1979Q40.4397140.560552
1980Q10.4519460.595518
1980Q20.4095230.56918
1980Q30.541240.558152
1980Q40.4338070.322166
1981Q10.4325470.325249
1981Q20.4010820.340628
1981Q30.4699190.299266
1981Q40.43280.312247
1982Q10.4677910.284908
1982Q20.4587440.290644
1982Q30.4508310.295861
1982Q40.4275040.299606
1983Q10.4006860.311722
1983Q20.3834520.325765
1983Q30.4570070.316122
1983Q40.4085550.310835
1984Q10.4062830.310864
1984Q20.3935640.322656
1984Q30.4344990.36946
1984Q40.3748860.329659
1985Q10.3647850.362101
1985Q20.4007460.323668
1985Q30.3961610.320204
1985Q40.3694350.339414
1986Q10.3726520.33227
1986Q20.3481170.369623
1986Q30.333170.403643
1986Q40.3325850.394589
1987Q10.3402950.38443
1987Q20.3388270.387703
1987Q30.3527260.370339
1987Q40.3497450.3571
1988Q10.3467330.353665
1988Q20.3597220.332808
1988Q30.342210.350999
1988Q40.2976330.398774
1989Q10.2840110.421933
1989Q20.2118240.423813
1989Q30.1878950.396203
1989Q40.1942870.390793
1990Q10.1789230.398372
1990Q20.1669850.408744
1990Q30.1662460.411789
1990Q40.1656280.413685
1991Q10.1680650.407581
1991Q20.1393350.486728
1991Q30.1740410.416483
1991Q40.1744240.415264
1992Q10.1613960.515219
1992Q20.1776850.411352
1992Q30.1648610.398737
1992Q40.1680940.383705
1993Q10.1615950.385887
1993Q20.1621230.380906
1993Q30.1600530.363973
1993Q40.1639440.348068
1994Q10.1487090.356036
1994Q20.1120110.402551
1994Q30.1167890.49441
1994Q40.0762470.563388
1995Q10.0762470.563387
1995Q20.1183710.492869
1995Q30.0938970.510193
1995Q40.0762480.563387
1996Q10.0762470.563387
1996Q20.0360030.479351
1996Q30.0084820.331905
1996Q4-0.0590190.895077
1997Q1-0.0119040.601995
1997Q20.0709480.684132
1997Q30.0762360.563363
1997Q40.0437790.455663
1998Q10.0187270.470613
1998Q20.0197850.471915
1998Q30.0186110.470849
1998Q40.0222640.449672
1999Q10.0221020.439549
1999Q20.018960.440221
1999Q30.0185590.440028
1999Q40.0181340.435857
2000Q10.0180680.442503
2000Q20.0294520.484218
2000Q30.055340.511554
2000Q40.0326660.484101
2001Q10.0519710.461353
2001Q20.0559440.450453
2001Q30.0510910.443511
2001Q40.0349180.468709
2002Q10.0388370.486068
2002Q20.0383570.490626
2002Q30.040430.502165
2002Q40.0350960.48912
2003Q10.0566510.51266
2003Q20.0371590.566869
2003Q30.0267260.547723
2003Q40.0244510.545821
2004Q10.0408830.497513
2004Q20.0294370.536471
2004Q30.0328150.520769
2004Q40.0293150.531482
2005Q10.0425570.562219
2005Q20.0417910.492961
2005Q30.0409710.431468
2005Q40.0346210.477159
2006Q10.0381480.497602
2006Q20.036750.50841
2006Q30.0373310.505862
2006Q40.0092020.496683
2007Q10.0083360.501568
2007Q20.0097710.528005
2007Q30.0128610.480324
2007Q40.0131030.459378
Return to Figure 8