Finance and Economics Discussion Series: Accessible versions of figures for 2015-093

Regime-Switching Models for Estimating Inflation Uncertainty

Accessible version of figures


Figure 1: U.S. Consumer Inflation Measures

Q4/Q4 percent change

Year CPI PCE price
1947 8.86 7.04
1948 4.53 3.39
1949 -2.12 -2.04
1950 4.37 4.24
1951 6.57 5.52
1952 1.44 1.24
1953 0.72 1.52
1954 -0.5 -0.06
1955 0.37 1.11
1956 2.58 2.68
1957 3.09 2.88
1958 1.91 1.46
1959 1.47 2.25
1960 1.4 1.49
1961 0.71 0.66
1962 1.3 1.36
1963 1.39 1.28
1964 1.27 1.39
1965 1.78 1.51
1966 3.57 3.18
1967 2.99 2.57
1968 4.63 4.29
1969 5.83 4.73
1970 5.6 4.62
1971 3.54 3.75
1972 3.33 3.37
1973 8.42 7.18
1974 12.05 11.51
1975 7.38 6.84
1976 5.19 5.13
1977 6.59 6.6
1978 8.93 7.58
1979 12.64 9.83
1980 12.54 10.64
1981 9.58 7.63
1982 4.44 4.99
1983 3.23 3.82
1984 4.15 3.49
1985 3.51 3.57
1986 1.35 1.71
1987 4.41 3.75
1988 4.31 4.18
1989 4.63 3.85
1990 6.28 4.98
1991 2.97 2.44
1992 3.12 2.65
1993 2.77 2.3
1994 2.6 2.11
1995 2.63 1.9
1996 3.23 2.35
1997 1.89 1.26
1998 1.53 0.73
1999 2.62 1.93
2000 3.44 2.49
2001 1.87 1.29
2002 2.25 1.93
2003 2 1.82
2004 3.38 2.87
2005 3.67 3.1
2006 1.97 1.78
2007 4.03 3.34
2008 1.6 1.47
2009 1.49 1.2
2010 1.23 1.29
2011 3.34 2.66
2012 1.91 1.64
2013 1.23 1.04
2014 1.2 1.12

Return to text


Figure 2: Historical Inflation Regime Probabilities Estimated using the CPI

Probability of HIgh-Variance, HIgh-Persistence State

Year One sided probabilities Two sided probabilities
1948 100.000 100.000
1949 100.000 100.000
1950 94.070 99.750
1951 100.000 100.000
1952 84.170 97.630
1953 84.590 97.780
1954 99.040 97.940
1955 97.770 84.550
1956 81.010 41.130
1957 64.520 25.250
1958 37.300 16.900
1959 24.180 14.660
1960 16.050 14.530
1961 25.850 16.300
1962 19.230 16.090
1963 13.190 17.290
1964 10.930 20.810
1965 6.190 26.720
1966 8.800 42.270
1967 6.050 59.150
1968 44.170 95.260
1969 99.900 100.000
1970 99.980 100.000
1971 92.490 99.240
1972 83.060 99.200
1973 100.000 100.000
1974 100.000 100.000
1975 100.000 100.000
1976 99.930 100.000
1977 100.000 100.000
1978 100.000 100.000
1979 100.000 100.000
1980 100.000 100.000
1981 100.000 100.000
1982 96.480 98.970
1983 84.870 97.540
1984 92.380 97.580
1985 85.420 96.240
1986 53.990 95.700
1987 81.520 98.830
1988 92.110 99.620
1989 98.260 99.930
1990 100.000 99.990
1991 85.660 42.440
1992 71.630 20.480
1993 43.650 7.680
1994 23.110 3.240
1995 10.930 1.550
1996 9.190 1.020
1997 4.120 0.530
1998 3.870 0.480
1999 2.870 0.450
2000 5.670 0.600
2001 3.190 0.360
2002 2.260 0.330
2003 2.180 0.490
2004 3.940 0.970
2005 9.520 1.390
2006 4.780 0.990
2007 11.740 1.200
2008 3.330 0.460
2009 3.020 0.520
2010 4.140 0.740
2011 4.250 0.880
2012 2.030 1.130
2013 3.920 2.920
2014 5.240 5.240

Return to text


Figure 3: Historical Inflation Regime Probabilities Estimated using the PCE price index

Probability of HIgh-Variance, HIgh-Persistence State

Year One sided probabilities Two sided probabilities
1949 100.000 100.000
1950 100.000 100.000
1951 98.990 99.960
1952 100.000 100.000
1953 82.460 61.810
1954 55.630 49.650
1955 85.260 46.590
1956 66.100 25.030
1957 52.200 15.030
1958 46.560 8.790
1959 20.800 3.320
1960 8.530 1.740
1961 3.670 1.520
1962 7.930 2.430
1963 4.580 2.590
1964 3.380 3.940
1965 2.680 7.470
1966 2.210 16.690
1967 7.380 42.580
1968 5.380 61.140
1969 80.380 99.140
1970 99.960 100.000
1971 99.980 100.000
1972 99.230 99.960
1973 97.320 99.900
1974 100.000 100.000
1975 100.000 100.000
1976 100.000 100.000
1977 100.000 100.000
1978 100.000 100.000
1979 100.000 100.000
1980 100.000 100.000
1981 100.000 100.000
1982 100.000 100.000
1983 100.000 100.000
1984 99.080 99.940
1985 97.790 99.790
1986 98.030 99.470
1987 65.210 97.910
1988 92.840 99.720
1989 99.690 99.990
1990 99.460 99.980
1991 100.000 99.980
1992 79.040 32.800
1993 63.460 15.120
1994 32.110 4.840
1995 14.580 1.800
1996 5.670 0.750
1997 3.650 0.520
1998 2.680 0.500
1999 6.080 0.700
2000 2.960 0.380
2001 3.060 0.360
2002 2.480 0.300
2003 1.770 0.280
2004 1.670 0.460
2005 3.800 1.070
2006 9.610 1.510
2007 4.170 1.040
2008 11.830 1.330
2009 3.670 0.500
2010 3.190 0.460
2011 2.780 0.470
2012 3.210 0.610
2013 1.870 0.780
2014 3.130 1.860

Return to text


Figure 4: Long Run (Next 10-Year Average) CPI Inflation Forecasts

Q4/Q4 Percent Change

Year SPF, 4th qtr Markov Switching Model
1979 6.9 7.52
1980 8.25 7.87
1981 7.05 7.33
1982 5.65 5.57
1983 5.2 4.90
1984 5.2 4.59
1985 4.55 4.03
1986 4 2.73
1987 4.5 4.00
1988 4.35 3.16
1989 4.2 4.30
1990 4.15 4.13
1991 4 3.25
1992 3.6 3.23
1993 3.45 2.55
1994 3.5 2.43
1995 3 2.28
1996 3 2.30
1997 2.65 2.22
1998 2.5 2.24
1999 2.5 2.26
2000 2.5 2.26
2001 2.55 2.22
2002 2.45 2.25
2003 2.5 2.24
2004 2.5 2.27
2005 2.5 2.26
2006 2.5 2.21
2007 2.4 2.34
2008 2.5 2.19
2009 2.2627 2.25
2010 2.2 2.24
2011 2.5 2.29
2012 2.3 2.22
2013 2.3 2.23
2014 2.2 2.24


RMSE

Period SPF: Model:
1979-2004: 1.4 1.2
1990-2004: 0.7 0.5

Return to text


Figure 5: 1-Year Ahead CPI Inflation Forecasts

Q4/Q4 Percent Change

Year SPF, 4th qtr Board Staff, December Markov Switching Model
1981 7.7 7.2 8.2
1982 5.5 5.1 4.4
1983 5.1 5.3 5.0
1984 4.4 4.3 4.5
1985 3.8 4.0 3.9
1986 3.6 3.7 2.0
1987 4.4 4.4 5.7
1988 4.9 4.6 2.3
1989 4.2 4.1 6.1
1990 4.5 4.1 4.6
1991 3.5 3.5 2.7
1992 3.2 2.7 3.6
1993 3.0 3.1 2.3
1994 3.4 3.0 2.5
1995 2.9 3.0 2.3
1996 3.0 2.7 2.4
1997 2.6 1.8 2.2
1998 2.3 2.3 2.2
1999 2.5 2.3 2.3
2000 2.7 2.1 2.3
2001 2.1 1.9 2.2
2002 2.2 1.7 2.3
2003 2.1 1.0 2.2
2004 2.3 1.4 2.4
2005 2.4 2.3 2.3
2006 2.6 3.1 2.2
2007 2.4 2.2 2.6
2008 1.8 0.7 2.1
2009 1.6 1.6 2.2
2010 1.6   2.2
2011 2.0   2.4
2012 2.2   2.2
2013 2.0   2.2
2014 1.9   2.2


RMSE

Period SPF: Model:
1982-2014: 1.2 1.3
1990-2014: 1.0 0.9


1999-2010

Statistic SPF: Board Staff: Model:
RMSE 0.8 1.1 0.9
15th percentile: -0.8 -0.4 -1.0
50th percentile: -0.0 0.3 -0.1
85th percentile: 1.4 2.3 1.3

Return to text


Figure 6: 1-Year Ahead PCE Price Inflation Forecasts

Q4/Q4 Percent Change

Year PCE Price Inflation, 1 year ahead Board Staff/SEP, December/Q4 Markov Switching Model
1997 0.73 1.63 1.79
1998 1.93 1.71 1.78
1999 2.49 1.85 1.88
2000 1.29 1.72 1.87
2001 1.93 1.36 1.79
2002 1.82 1.31 1.86
2003 2.87 0.85 1.84
2004 3.1 1.22 1.92
2005 1.78 2.13 1.92
2006 3.34 2.75 1.81
2007 1.47 2.01 2.09
2008 1.2 0.73 1.75
2009 1.29 1.34 1.83
2010 2.66 1.40 1.82
2011 1.64 1.70 1.91
2012 1.04 1.65 1.81
2013 1.12 1.50 1.81
2014   1.30 1.82


1999-2014

Statistic Board Staff: Model: Random Walk:
RMSE: 0.9 0.7 1.0
15th percentile: -0.5 -0.6 -1.2
50th percentile: 0.3 -0.1 0.1
85th percentile: 1.5 1.1 1.3

Return to text


Figure 7: 2-Year Ahead PCE Price Inflation Forecasts

Q4/Q4 Percent Change

Year PCE Price Inflation, 2 years ahead Board Staff/SEP, December/Q4 Markov Switching Model
1997 1.93 2.01 1.83
1998 2.49 1.70 1.8285
1999 1.29 2.13 1.8597
2000 1.93 1.92 1.8484
2001 1.82 1.24 1.8292
2002 2.87 1.35 1.8515
2003 3.1 1.03 1.841
2004 1.78 1.34 1.8554
2005 3.34 1.70 1.8686
2006 1.47 2.09 1.8248
2007 1.2 1.74 1.9096
2008 1.29 1.02 1.8087
2009 2.66 1.18 1.8422
2010 1.64 1.45 1.8463
2011 1.04 1.75 1.8612
2012 1.12 1.75 1.8282
2013   1.75 1.8373
2014   1.85 1.8466


1999-2014

Statistic Board Staff: Model: Random Walk:
RMSE: 1.0 0.7 1.1
15th percentile: -0.7 -0.7 -1.2
50th percentile: 0.2 -0.0 -0.1
85th percentile: 1.6 1.1 1.4

Return to text