Finance and Economics Discussion Series: Accessible versions of figures for 2016-009

The Risky Steady State and the Interest Rate Lower Bound

Accessible version of figures


Figure 1: Policy Functions from the Stylized Model

Five panels in this figure show policy functions for the model's key variables (nominal interest rate, inflation, output, real wage, and real interest rate). In all panels, dashed and solid black lines are for deterministic and stochastic models, respectively. y-axis is for the model's variables, while the x-axis is for the model's state variable, the discount factor shock.

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Figure 2: Unconditional Distribution of Inflation in the Stylized Model

This histogram shows the unconditional distribution of inflation from the stylized model. Dashed black, solid black, and solid red verical lines are for the inflation target, the risky steady-state inflation, and the average inflation.

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Figure 3: Conditional and Unconditional Averages of Inflation in the Stylized Model

Black, red, and blue lines in the left panel show how the conditional average of inflation away from the ELB, the unconditional average inflation, and the risky steady-state inflation, vary with the probability of being at the ELB, respectively, in the perfect-foresight version of the stylized model. The dashed black line in the right panel shows how the conditional average of inflation at the ELB vary with the probability of being at the ELB.

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Figure 4: The Risk-Adjusted Fisher Relation and the Taylor Rule

Solid and dashed balck lines represent the standard and risky-adjusted Fisher relation, respectively, while the solid red line represents the Taylor rule. x-axis is for inflation and y-axis is for the policy rate.

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Figure 5: Output Gap, Inflation, and Policy Rate

Year Output Gap (%) Inflation (Annualized %) Policy Rate (Annualized %)
1995Q3 -1.1024 1.8681 5.80
1995Q4 -0.8934 2.0071 5.72
1996Q1 -0.7307 1.5967 5.37
1996Q2 -0.3459 1.8680 5.24
1996Q3 -0.0762 1.8241 5.31
1996Q4 0.3284 2.2611 5.28
1997Q1 0.5560 1.5669 5.28
1997Q2 0.7784 2.0612 5.52
1997Q3 1.1100 0.9021 5.53
1997Q4 1.2190 1.2493 5.51
1998Q1 1.3348 1.1081 5.52
1998Q2 1.5218 1.2126 5.50
1998Q3 1.6796 1.3942 5.53
1998Q4 2.1750 1.2290 4.86
1999Q1 2.3928 1.2882 4.73
1999Q2 2.4137 1.2406 4.75
1999Q3 2.5808 1.3715 5.10
1999Q4 2.9474 1.8177 5.30
2000Q1 3.0564 2.2057 5.68
2000Q2 2.9695 1.3105 6.27
2000Q3 2.7756 1.8268 6.52
2000Q4 2.2418 1.9268 6.47
2001Q1 1.9196 2.2645 5.60
2001Q2 1.1536 1.5571 4.33
2001Q3 0.0954 1.1424 3.50
2001Q4 -0.6639 2.0329 2.13
2002Q1 -0.5469 1.1426 1.73
2002Q2 -0.5692 2.3385 1.75
2002Q3 -0.7025 2.0691 1.74
2002Q4 -0.8748 1.3905 1.44
2003Q1 -1.3850 0.9736 1.25
2003Q2 -1.3001 1.4501 1.25
2003Q3 -0.6777 1.6204 1.02
2003Q4 -0.3770 1.3986 1.00
2004Q1 -0.2096 2.1666 1.00
2004Q2 -0.0592 2.4260 1.01
2004Q3 0.2309 1.8416 1.43
2004Q4 0.1861 1.8728 1.95
2005Q1 0.3483 2.5510 2.47
2005Q2 0.5029 2.1348 2.94
2005Q3 0.5965 1.6607 3.46
2005Q4 0.9895 2.6186 3.98
2006Q1 1.7380 2.0368 4.45
2006Q2 1.6366 2.6948 4.91
2006Q3 1.6256 2.1482 5.25
2006Q4 1.8730 1.6825 5.24
2007Q1 1.6530 2.8440 5.25
2007Q2 1.6045 1.4099 5.25
2007Q3 1.1378 1.9644 5.07
2007Q4 0.6053 2.7013 4.50
2008Q1 -0.2612 2.3063 3.18
2008Q2 -1.0208 2.0161 2.08
2008Q3 -2.3962 1.8074 1.94
2008Q4 -4.8304 0.3994 0.51
2009Q1 -6.7935 0.4756 0.18
2009Q2 -7.6821 1.9484 0.18
2009Q3 -7.8556 1.1257 0.15
2009Q4 -7.3819 2.0853 0.12
2010Q1 -7.2879 1.0213 0.13
2010Q2 -6.7868 1.0584 0.19
2010Q3 -5.9754 0.9805 0.19
2010Q4 -5.6557 0.8085 0.19
2011Q1 -5.7566 1.3539 0.15
2011Q2 -5.5174 2.4281 0.09
2011Q3 -5.2421 2.0157 0.08
2011Q4 -4.6046 1.5983 0.07
2012Q1 -3.8440 2.2372 0.10
2012Q2 -3.7782 1.8751 0.15
2012Q3 -3.8045 1.2353 0.14
2012Q4 -3.4665 1.7195 0.16
2013Q1 -3.3672 1.7312 0.14
2013Q2 -2.9928 1.2134 0.12
2013Q3 -2.6829 1.3868 0.09
2013Q4 -2.1906 1.6787 0.09
2014Q1 -2.3117 1.4212 0.07
2014Q2 -1.7074 1.9565 0.09
2014Q3 -1.0186 1.3796 0.09
2014Q4 -0.5422 0.9831 0.10
2015Q1 -0.6543 0.9585 0.11
2015Q2 -0.6159 1.8279 0.13

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Figure 6: 10-Year Inflation Expectations

Year 10-yr Inflation Expectations
1991Q4 4.00
1992Q1 3.70
1992Q2 3.90
1992Q3 3.75
1992Q4 3.60
1993Q1 3.50
1993Q2 3.70
1993Q3 3.45
1993Q4 3.45
1994Q1 3.45
1994Q2 3.50
1994Q3 3.50
1994Q4 3.50
1995Q1 3.30
1995Q2 3.35
1995Q3 3.20
1995Q4 3.00
1996Q1 3.00
1996Q2 3.00
1996Q3 3.00
1996Q4 3.00
1997Q1 3.00
1997Q2 2.85
1997Q3 3.00
1997Q4 2.65
1998Q1 2.60
1998Q2 2.50
1998Q3 2.50
1998Q4 2.50
1999Q1 2.30
1999Q2 2.50
1999Q3 2.50
1999Q4 2.50
2000Q1 2.50
2000Q2 2.50
2000Q3 2.50
2000Q4 2.50
2001Q1 2.50
2001Q2 2.50
2001Q3 2.50
2001Q4 2.55
2002Q1 2.50
2002Q2 2.50
2002Q3 2.50
2002Q4 2.45
2003Q1 2.50
2003Q2 2.50
2003Q3 2.50
2003Q4 2.50
2004Q1 2.50
2004Q2 2.50
2004Q3 2.50
2004Q4 2.50
2005Q1 2.45
2005Q2 2.50
2005Q3 2.50
2005Q4 2.50
2006Q1 2.50
2006Q2 2.50
2006Q3 2.50
2006Q4 2.50
2007Q1 2.35
2007Q2 2.40
2007Q3 2.40
2007Q4 2.40
2008Q1 2.50
2008Q2 2.50
2008Q3 2.50
2008Q4 2.50
2009Q1 2.40
2009Q2 2.50
2009Q3 2.50
2009Q4 2.26
2010Q1 2.39
2010Q2 2.40
2010Q3 2.30
2010Q4 2.20
2011Q1 2.30
2011Q2 2.40
2011Q3 2.40
2011Q4 2.50
2012Q1 2.30
2012Q2 2.48
2012Q3 2.35
2012Q4 2.30
2013Q1 2.30
2013Q2 2.30
2013Q3 2.21
2013Q4 2.30
2014Q1 2.30
2014Q2 2.25
2014Q3 2.20
2014Q4 2.20
2015Q1 2.10
2015Q2 2.14

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Figure 7: Long-Run Interest Rates and the Risky Steady State

In the top-left panel,the black line shows how the probability of being at the ELB varies with the detereministic steady-state policy rate. In the top-right panel, the solid and dashed black lines show how the risky steady-state inflation rates vary with the detereministic steady-state policy rate in the model with and without the ELB constraint, respectively. In the bottom-left panel, the solid and dashed black lines show how the risky steady-state output gaps vary with the detereministic steady-state policy rate in the model with and without the ELB constraint, respectively. In the bottom-right panel, the solid and dashed black lines show how the risky steady-state policy rates vary with the detereministic steady-state policy rate in the model with and without the ELB constraint, respectively. In all panels, x-axis is for the deterministic steady-state policy rate.\

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Figure 8: Alternative Policy Parameters\

Five panels in this figure show how the risky steady-state inflation and the ELB frequency depend on key parameters governing monetary policy: From the top-left to the bottom middle panel, x-axis is for inflation coefficient, output gap coefficient, interest-rate smoothing parameter, inflation target, and the effective lower bound.

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Figure 9: Conditional Averages of Inflation Away From the ELB

Countries 10-yr Inflation Expectations
United States 1.8152
Canada 1.6339
Euro Area (19 countries) 1.5371
United Kingdom 1.4120
Sweden 0.7316
Switzerland 0.8272

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Figure E.1: Expected Time Until Liftoff

Blue Chip Economic Indicators

Date E[ELB_Duration] (in quarters)
2009-01-10 2.5644
2009-02-10 2.2247
2009-03-10 1.9178
2009-04-10 2.5041
2009-05-10 2.1753
2009-06-10 2.7945
2009-07-10 2.4658
2009-08-10 2.1260
2009-09-10 2.8274
2009-10-10 2.4986
2009-11-10 2.1589
2009-12-10 2.8932
2010-01-10 2.5534
2010-02-10 2.2137
2010-03-10 1.9068
2010-04-10 2.4932
2010-05-10 2.1644
2010-06-10 1.8247
2010-07-10 2.4548
2010-08-10 3.1562
2010-09-10 3.8849
2010-10-10 3.5562
2010-11-10 4.1370
2010-12-10 3.8082
2011-01-10 3.4685
2011-02-10 3.1288
2011-03-10 2.8219
2011-04-10 2.4822
2011-05-10 3.1123
2011-06-10 2.7726
2011-07-10 2.4438
2011-08-10 4.1479
2011-09-10 .
2011-10-10 7.0027
2011-11-10 .
2011-12-10 .
2012-01-10 6.4932
2012-02-10 7.1507
2012-03-10 6.8329
2012-04-10 6.4932
2012-05-10 6.1644
2012-06-10 .
2012-07-10 .
2012-08-10 .
2012-09-10 .
2012-10-10 6.9808
2012-11-10 .
2012-12-10 .
2013-01-10 .
2013-02-10 .
2013-03-10 8.8219
2013-04-10 .
2013-05-10 .
2013-06-10 .
2013-07-10 7.5910
2013-08-10 7.2411
2013-09-10 7.0767
2013-10-10 6.4712
2013-11-15 7.0659
2013-12-10 7.1545
2014-01-10 6.6323
2014-02-10 6.0569
2014-03-10 5.8192
2014-04-10 5.4795
2014-05-10 5.1507
2014-06-10 4.8110
2014-07-10 4.4822
2014-08-10 3.5906
2014-09-10 3.1815
2014-10-10 3.4740
2014-11-10 2.5805
2014-12-10 2.3206
2015-01-10 1.9814
2015-02-10 1.9365
2015-03-10 1.8192
2015-04-10 1.6469
2015-05-10 1.4719
2015-06-10 1.2040
2015-07-10 0.8827
2015-08-10 0.5713

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Figure E.1: Expected Time Until Liftoff

Blue Chip Financial Forecasts

Date E[ELB_Duration] (in quarters)
2009-01-01 3.5890
2009-02-01 4.2082
2009-03-01 3.9014
2009-04-01 4.6027
2009-05-01 4.2740
2009-06-01 3.9342
2009-07-01 3.6055
2009-08-01 3.2658
2009-09-01 2.9260
2009-10-01 3.6603
2009-11-01 3.3205
2009-12-01 2.9918
2010-01-01 2.6521
2010-02-01 2.3123
2010-03-01 2.9315
2010-04-01 2.5918
2010-05-01 2.2630
2010-06-01 2.8822
2010-07-01 2.5534
2010-08-01 3.2548
2010-09-01 3.9836
2010-10-01 3.6548
2010-11-01 4.2356
2010-12-01 3.9068
2011-01-01 4.5260
2011-02-01 4.1863
2011-03-01 3.8795
2011-04-01 3.5397
2011-05-01 3.2110
2011-06-01 2.8712
2011-07-01 3.5836
2011-08-01 3.2438
2011-09-01 .
2011-10-01 .
2011-11-01 .
2011-12-01 7.4301
2012-01-01 .
2012-02-01 .
2012-03-01 .
2012-04-01 .
2012-05-01 .
2012-06-01 8.4164
2012-07-01 .
2012-08-01 .
2012-09-01 .
2012-10-01 .
2012-11-01 .
2012-12-01 8.9041
2013-01-01 .
2013-02-01 .
2013-03-01 .
2013-04-01 8.3314
2013-05-01 8.4853
2013-06-01 7.9068
2013-07-01 7.0776
2013-08-01 7.2719
2013-09-01 6.8435
2013-10-01 7.0906
2013-11-01 7.2400
2013-12-01 6.9041
2014-01-01 6.8658
2014-02-01 6.2001
2014-03-01 5.9678
2014-04-01 5.2017
2014-05-01 5.0189
2014-06-01 4.9096
2014-07-01 4.1549
2014-08-01 3.5061
2014-09-01 3.0869
2014-10-01 2.7344
2014-11-01 2.7050
2014-12-01 2.9041
2015-01-01 1.9900
2015-02-01 1.8799
2015-03-01 1.6910
2015-04-01 1.5427
2015-05-01 1.4441
2015-06-01 1.9014
2015-07-01 0.9774
2015-08-01 0.7188

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Figure E.1: Expected Time Until Liftoff

Primary Dealers Survey

DateNum E[ELB_Duration] (in quarters) (mean approach)
2011 5.7315
2011.125 4.7781
2011.25 4.2301
2011.375 4.2301
2011.5 5.1288
2011.625 8.0767
2011.75 8.3397
2011.875 8.0767
2012 10.4329
2012.125 10.2685
2012.25 9.6877
2012.375 9.5781
2012.5 10.3781
2012.625 10.5973
2012.75 11.1014
2012.875 10.3671
2013 10.2904
2013.125 9.7315
2013.25 9.2822
2013.375 8.4384
2013.5 8.2082
2013.625 7.7699
2013.75 7.7808
2013.875 7.5836
2014 7.0137
2014.125 6.1479
2014.25 5.7644
2014.375 5.2932
2014.5 4.0438
2014.625 3.3205
2014.75 2.9808
2014.875 2.3123
2015 2.2137
2015.125 1.3808
2015.25 1.4575
2015.375 1.3151
2015.5 0.9973
2015.625 0.4932

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Figure E.1: Expected Time Until Liftoff

Survey of Professional Forecasters

Date Expected Duration (in quarters)
2009Q1 3
2009Q2 3
2009Q3 3
2009Q4 3
2010Q1 3
2010Q2 2
2010Q3 4
2010Q4 4
2011Q1 5
2011Q2 3
2011Q3 4
2011Q4 6
2012Q1 9
2012Q2 8
2012Q3 11
2012Q4 10
2013Q1 9
2013Q2 8
2013Q3 11
2013Q4 10
2014Q1 9
2014Q2 8
2014Q3 4
2014Q4 4
2015Q1 3
2015Q2 2
2015Q3 2

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Figure F.1: Policy Rates and Inflation in Six Economies

Time US, Policy Rate (in annualized %) US, Core Inflation (in annualized %) (in quarters) Canada, Policy Rate (in annualized %) Canada, Core Inflation (in annualized %) (in quarters) Euro Area (19 countries), Policy Rate (in annualized %) Euro Area (19 countries), Core Inflation (in annualized %) (in quarters) United Kingdom, Policy Rate (in annualized %) United Kingdom, Core Inflation (in annualized %) (in quarters) Sweden, Policy Rate (in annualized %) Sweden, Core Inflation (in annualized %) (in quarters) Switzerland, Policy Rate (in annualized %) Switzerland, Core Inflation (in annualized %) (in quarters)
1995q1 5.83 2.2648 8.22 1.2876     6.45 3.1200 7.80 2.6036 3.89 1.3141
1995q2 6.00 2.1661 6.72 2.4732     6.63 3.4561 8.46 2.7744 3.36 2.0213
1995q3 5.76 2.0774 6.46 2.5874     6.63 3.7090 8.90 2.8255 2.87 2.2820
1995q4 5.71 2.0708 5.54 2.2466     6.58 3.0352 8.91 2.7023 2.14 2.2825
1996q1 5.33 1.9560 5.00 1.6658     6.13 2.6085 8.28 2.6646 1.77 1.3842
1996q2 5.25 1.8476 4.75 1.4660     5.87 1.9202 6.70 1.8061 2.21 0.8591
1996q3 5.25 1.8377 4.00 1.3963     5.69 1.7480 5.48 0.6971 2.32 0.7423
1996q4 5.25 1.9008 3.00 1.5222     5.86 2.4559 4.61 -0.1643 1.92 0.6347
1997q1 5.27 1.8932 3.00 1.7444     5.94 2.0232 4.10 -1.3832 1.82 0.5680
1997q2 5.50 1.9422 3.00 1.8299     6.20 1.8128 4.10 -0.7500 1.64 0.5055
1997q3 5.50 1.7070 3.25 1.6075     6.87 1.8115 4.10 -0.1573 1.50 0.2575
1997q4 5.50 1.4525 4.25 1.2506     7.15 1.7949 4.13 0.7501 1.85 0.1037
1998q1 5.50 1.3366 4.75 1.4532     7.25 1.6893 4.35 0.2986 1.21 0.0043
1998q2 5.50 1.1227 4.75 1.2529     7.33 1.6352 4.29 -0.1265 1.69 0.0664
1998q3 5.49 1.2468 5.50 1.3560     7.50 1.3435 4.10 -0.4754 1.84 0.2610
1998q4 4.92 1.2405 5.00 1.5301     6.86 1.2235 3.82 -1.0847 1.48 0.3063
1999q1 4.75 1.2872 4.75 0.9431 3.00 1.3473 5.69 1.0112 3.27 0.1472 1.28 0.6050
1999q2 4.75 1.2942 4.50 1.5180 2.53 1.1554 5.20 0.7866 2.90 0.3866 1.05 0.7910
1999q3 5.10 1.2885 4.50 1.7452 2.50 1.1025 5.07 0.6449 2.90 0.7948 1.17 0.9479
1999q4 5.38 1.4384 4.75 1.7064 2.81 1.0224 5.41 0.3555 3.07 0.9653 2.07 1.1374
2000q1 5.69 1.6691 5.25 1.7130 3.21 0.9989 5.87 0.1073 3.55 -0.3660 2.27 1.3731
2000q2 6.25 1.6868 5.75 1.5310 3.82 0.9685 6.00 0.0000 3.75 -0.3303 3.14 1.1890
2000q3 6.50 1.8021 5.75 1.6034 4.34 0.9505 6.00 0.0000 3.75 -0.3831 3.44 0.9601
2000q4 6.50 1.8297 5.75 1.8721 4.74 1.2807 6.00 0.2480 3.79 -0.0985 3.49 1.0824
2001q1 5.61 1.8446 5.00 1.9919 4.75 1.3089 5.86 0.4643 4.00 1.1743 3.43 0.8352
2001q2 4.32 1.9072 4.50 2.2671 4.60 1.9110 5.37 1.0642 4.00 1.6851 3.20 1.3372
2001q3 3.56 1.7337 3.50 2.3348 4.34 1.8794 5.06 1.5664 4.16 2.1191 3.08 1.0664
2001q4 2.14 1.7605 2.25 1.7705 3.47 2.2492 4.23 1.2014 3.75 2.2245 2.06 0.8005
2002q1 1.75 1.4767 2.00 1.9211 3.25 2.4787 4.00 1.6353 3.78 1.5577 1.71 0.2966
2002q2 1.75 1.6742 2.50 2.4040 3.25 2.4679 4.00 1.2987 4.16 1.7597 1.38 0.7613
2002q3 1.75 1.9091 2.75 2.8720 3.25 2.4107 4.00 1.2969 4.25 1.5883 0.88 0.2920
2002q4 1.45 1.7462 2.75 3.5291 3.12 2.2601 4.00 1.6760 4.10 1.5740 0.72 0.8948
2003q1 1.25 1.7033 3.00 3.6438 2.68 1.8769 3.85 1.5390 3.71 1.0763 0.52 0.7779
2003q2 1.23 1.4787 3.25 2.6196 2.35 1.8791 3.75 1.2821 3.39 0.4811 0.29 0.4834
2003q3 1.00 1.3655 2.75 1.6586 2.00 1.7069 3.53 1.2803 2.77 -0.0354 0.27 0.2350
2003q4 1.00 1.3676 2.75 1.7945 2.00 1.6993 3.65 1.0302 2.75 -0.3456 0.25 0.2345
2004q1 1.00 1.6692 2.25 1.3993 2.00 1.7832 3.91 1.1368 2.61 -0.7691 0.25 0.3042
2004q2 1.00 1.9163 2.00 1.3973 2.00 1.8685 4.22 1.0606 2.03 -1.0114 0.32 0.8293
2004q3 1.42 1.9725 2.25 1.3634 2.00 1.8880 4.65 1.0591 2.00 -0.8532 0.57 0.9062
2004q4 1.94 2.0929 2.50 1.2041 2.00 1.8828 4.75 1.1217 2.00 -0.7963 0.73 1.2905
2005q1 2.44 2.1916 2.50 1.4171 2.00 1.5471 4.75 1.2602 2.00 0.1699 0.75 1.3022
2005q2 2.91 2.1165 2.50 1.2998 2.00 1.4492 4.75 1.5234 1.95 0.0101 0.76 0.9447
2005q3 3.42 2.0717 2.75 1.3245 2.00 1.2961 4.59 1.7579 1.50 -0.4031 0.76 0.7091
2005q4 3.97 2.2600 3.25 1.3851 2.07 1.3617 4.50 1.4790 1.50 -0.2729 0.93 0.6699
2006q1 4.43 2.1283 3.75 1.1410 2.34 1.2645 4.50 1.2782 1.78 0.0254 1.11 0.6413
2006q2 4.90 2.2716 4.25 1.2221 2.57 1.4385 4.50 1.1670 2.03 0.2741 1.40 0.7943
2006q3 5.25 2.3936 4.25 1.1755 2.91 1.4428 4.66 1.1296 2.32 0.8427 1.63 0.8472
2006q4 5.25 2.1577 4.25 1.5505 3.29 1.5386 4.89 1.6231 2.69 0.8560 1.92 0.7006
2007q1 5.25 2.3628 4.25 1.8476 3.57 1.8266 5.22 1.8266 3.11 2.0045 2.21 0.2990
2007q2 5.25 2.0362 4.25 2.1193 3.82 1.9170 5.40 1.9117 3.26 2.8956 2.43 0.5810
2007q3 5.18 1.9906 4.50 2.4638 4.00 1.8887 5.74 1.6097 3.55 3.7190 2.78 0.7985
2007q4 4.52 2.2482 4.25 1.7303 4.00 1.9096 5.69 1.4342 3.91 4.1387 2.77 0.9732
2008q1 3.22 2.1117 3.50 1.0914 4.00 1.8656 5.36 1.2068 4.11 1.9496 2.75 1.3337
2008q2 2.08 2.2659 3.00 0.8945 4.00 1.7586 5.03 1.5200 4.25 1.6576 2.82 1.3859
2008q3 2.00 2.2260 3.00 0.7404 4.24 1.8634 5.00 2.0692 4.53 0.8726 2.77 1.5008
2008q4 1.23 1.6417 1.50 1.5322 3.28 1.9186 3.37 1.6710 3.65 0.6194 1.99 1.4990
2009q1 0.13 1.1791 0.50 1.8374 1.92 1.6073 1.07 1.5147 1.52 0.3266 0.50 1.2998
2009q2 0.13 1.1621 0.25 2.0358 1.10 1.5826 0.50 1.5929 0.61 -0.7938 0.40 1.0328
2009q3 0.13 0.9904 0.25 1.7635 1.00 1.2786 0.50 1.7422 0.27 -0.5638 0.34 0.9142
2009q4 0.13 1.4156 0.25 1.1220 1.00 1.0981 0.50 2.2124 0.25 -0.6924 0.26 0.7874
2010q1 0.13 1.5539 0.25 1.2517 1.00 0.8760 0.50 3.0159 0.25 -1.4654 0.25 0.5340
2010q2 0.13 1.3290 0.50 1.0859 1.00 0.9129 0.50 3.0417 0.25 -0.1921 0.18 0.2506
2010q3 0.13 1.2923 1.00 1.4076 1.00 1.0250 0.50 2.6774 0.55 0.0568 0.16 -0.0101
2010q4 0.13 0.9707 1.00 1.5938 1.00 1.0861 0.50 2.7829 0.95 0.0188 0.17 -0.0777
2011q1 0.13 1.0544 1.00 1.5169 1.00 1.1059 0.50 3.2049 1.38 1.7838 0.17 0.5010
2011q2 0.13 1.3995 1.00 1.4464 1.23 1.5346 0.50 3.2563 1.68 2.2421 0.18 0.2718
2011q3 0.13 1.6613 1.00 1.3205 1.49 1.3362 0.50 3.2444 1.99 2.6856 0.08 0.3921
2011q4 0.13 1.8617 1.00 1.4475 1.28 1.5995 0.50 3.1889 1.97 2.9649 0.04 -0.6646
2012q1 0.13 2.0858 1.00 1.5238 1.00 1.5478 0.50 2.5082 1.64 1.7560 0.08 -1.0684
2012q2 0.13 1.9456 1.00 1.7917 1.00 1.5661 0.50 2.1515 1.50 1.1785 0.11 -1.0920
2012q3 0.13 1.7476 1.00 1.1719 0.76 1.5751 0.50 2.1439 1.45 0.3309 0.06 -0.9356
2012q4 0.13 1.7784 1.00 0.9373 0.75 1.4595 0.50 2.5365 1.23 -0.7141 0.03 -0.6093
2013q1 0.13 1.6503 1.00 0.9473 0.75 1.3661 0.50 2.2721 1.00 0.6421 0.02 -0.4152
2013q2 0.13 1.4829 1.00 0.6178 0.59 1.1048 0.50 2.1639 1.00 0.2146 0.02 -0.3449
2013q3 0.13 1.5213 1.00 0.9264 0.50 1.0668 0.50 2.0414 1.00 0.1091 0.02 -0.1291
2013q4 0.13 1.5100 1.00 0.8235 0.36 0.8309 0.50 1.7344 0.98 0.5758 0.02 -0.0011
2014q1 0.13 1.4317 1.00 1.0730 0.25 0.8404 0.50 1.6520 0.75 0.6341 0.02 -0.0653
2014q2 0.13 1.6205 1.00 1.3236 0.22 0.8144 0.50 1.8638 0.75 0.6466 0.01 -0.0823
2014q3 0.13 1.6187 1.00 1.7422 0.12 0.8266 0.50 1.7752 0.30 0.5379 0.01 -0.0470
2014q4 0.13 1.4436 1.00 2.1087 0.05 0.7148 0.50 1.3136 0.08 0.7800 -0.00 0.0909
2015q1 0.13 1.3267 0.75 2.4529 0.05 0.6608 0.50 1.2328 -0.06 0.9252 -0.72 0.0263
2015q2 0.13 1.2933 0.75 2.4327 0.05 0.7784 0.50 0.8317 -0.25 0.4947 -0.79 -0.4354

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Figure F.2: Average Inflation Rates Away From the Lower Bound with Alternative Starting Dates

Time US, Average Core Inflation non-ELB era (w/ alternating start dates) US, Standard Error (Average Core Inflation) Canada, Average Core Inflation non-ELB era (w/ alternating start dates) Canada, Standard Error (Average Core Inflation) Euro Area (19 countries), Average Core Inflation non-ELB era (w/ alternating start dates) Euro Area (19 countries), Standard Error (Average Core Inflation) United Kingdom, Average Core Inflation non-ELB era (w/ alternating start dates) United Kingdom, Standard Error (Average Core Inflation) Sweden, Average Core Inflation non-ELB era (w/ alternating start dates) Sweden, Standard Error (Average Core Inflation) Switzerland, Average Core Inflation non-ELB era (w/ alternating start dates) Switzerland, Standard Error (Average Core Inflation)
1995q1 1.8295 0.0447 1.6402 0.0765     1.4778 0.0988 0.7831 0.1392 0.8572 0.0753
1995q2 1.8216 0.0448 1.6448 0.0774     1.4485 0.0961 0.7589 0.1389 0.8489 0.0757
1995q3 1.8152 0.0452 1.6339 0.0776     1.4120 0.0905 0.7316 0.1381 0.8272 0.0744
1995q4 1.8102 0.0457 1.6212 0.0774     1.3694 0.0814 0.7029 0.1370 0.7998 0.0719
1996q1 1.8052 0.0464 1.6127 0.0781     1.3380 0.0765 0.6752 0.1361 0.7712 0.0691
1996q2 1.8023 0.0472 1.6120 0.0797     1.3136 0.0739 0.6472 0.1351 0.7592 0.0691
1996q3 1.8014 0.0481 1.6140 0.0811     1.3017 0.0744 0.6306 0.1359 0.7572 0.0699
1996q4 1.8006 0.0491 1.6171 0.0825     1.2928 0.0754 0.6296 0.1378 0.7575 0.0708
1997q1 1.7985 0.0501 1.6185 0.0841     1.2690 0.0730 0.6413 0.1393 0.7601 0.0718
1997q2 1.7965 0.0511 1.6166 0.0859     1.2533 0.0728 0.6715 0.1385 0.7642 0.0728
1997q3 1.7934 0.0522 1.6135 0.0877     1.2414 0.0733 0.6931 0.1391 0.7698 0.0739
1997q4 1.7953 0.0533 1.6136 0.0896     1.2290 0.0739 0.7061 0.1406 0.7812 0.0749
1998q1 1.8031 0.0539 1.6191 0.0911     1.2164 0.0744 0.7055 0.1427 0.7966 0.0757
1998q2 1.8139 0.0541 1.6216 0.0929     1.2057 0.0753 0.7119 0.1447 0.8150 0.0765
1998q3 1.8304 0.0527 1.6274 0.0945     1.1957 0.0764 0.7254 0.1465 0.8328 0.0773
1998q4 1.8446 0.0520 1.6317 0.0963     1.1922 0.0782 0.7451 0.1477 0.8468 0.0784
1999q1 1.8597 0.0511 1.6333 0.0986 1.5371 0.0532 1.1914 0.0801 0.7756 0.1474 0.8603 0.0796
1999q2 1.8744 0.0502 1.6447 0.0989 1.5403 0.0541 1.1959 0.0820 0.7863 0.1495 0.8668 0.0808
1999q3 1.8897 0.0491 1.6468 0.1013 1.5469 0.0546 1.2064 0.0835 0.7932 0.1518 0.8688 0.0821
1999q4 1.9059 0.0476 1.6451 0.1040 1.5547 0.0550 1.2212 0.0843 0.7931 0.1543 0.8667 0.0832
2000q1 1.9189 0.0471 1.6440 0.1068 1.5642 0.0551 1.2446 0.0832 0.7901 0.1569 0.8592 0.0840
2000q2 1.9260 0.0479 1.6428 0.1098 1.5745 0.0552 1.2762 0.0792 0.8111 0.1585 0.8445 0.0842
2000q3 1.9331 0.0488 1.6448 0.1128 1.5857 0.0550 1.3127 0.0723 0.8322 0.1601 0.8344 0.0848
2000q4 1.9370 0.0501 1.6456 0.1160 1.5977 0.0547 1.3513 0.0630 0.8551 0.1617 0.8305 0.0859

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Figure G.1: Moments with Alternative Degrees of Price Indexation

Four panels in this figure show how the unconditional averages (shown by the dashed black lines) and unconditional standard deviations (shown by the solid black lines) of the model's key variables (inflation, output gap, policy rate, and the expected duration of the ELB episode in top-left, top-right, bottom-left, and bottom-right panels, respectively) vary with the degree of price indexation (which is on x-axis).

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Figure G.2: Risky Steady State with Alternative Degrees of Price Indexation

In the top-left panel, the black line shows how the risky steady-state inflation varies with the degree of price indexation (which is on x-axis). In the top-right panel, the black line shows how the risky steady-state output gap varies with the degree of price indexation (which is on x-axis). In the bottom-left panel, the black line shows how the risky steady-state policy rate varies with the degree of price indexation (which is on x-axis).
In the bottom-right panel, the solid black and red lines show how the ELB frequency and the standard deviation of the demand shock vary with the degree of price indexation (which is on x-axis), respectively.

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Figure G.3: Moments with Alternative Degrees of Wage Indexation

Four panels in this figure show how the unconditional averages (shown by the dashed black lines) and unconditional standard deviations (shown by the solid black lines) of the model's key variables (inflation, output gap, policy rate, and the expected duration of the ELB episode in top-left, top-right, bottom-left, and bottom-right panels, respectively) vary with the degree of wage indexation (which is on x-axis).

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Figure G.4: Risky Steady State with Alternative Degrees of Wage Indexation

In the top-left panel, the black line shows how the risky steady-state inflation varies with the degree of wage indexation (which is on x-axis). In the top-right panel, the black line shows how the risky steady-state output gap varies with the degree of wage indexation (which is on x-axis). In the bottom-left panel, the black line shows how the risky steady-state policy rate varies with the degree of wage indexation (which is on x-axis).
In the bottom-right panel, the solid black and red lines show how the ELB frequency and the standard deviation of the demand shock vary with the degree of wage indexation (which is on x-axis), respectively.

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Figure H.1: Unconditional Distribution of Inflation in a perfect-foresight version of the Stylized Model

This histogram shows the unconditional distribution of inflation from the perfect-foresight version of the stylized Model. Dashed black, solid black, and solid red verical lines are for the inflation target, the risky steady-state inflation, and the average inflation.

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Figure H.2: Conditional and Unconditional Averages of Inflation in the Stylized Model

Black, red, and blue lines in the left panel show how the conditional average of inflation away from the ELB, the unconditional average inflation, and the risky steady-state inflation, vary with the probability of being at the ELB, respectively, in the perfect-foresight version of the stylized model. The dashed black line in the right panel shows how the conditional average of inflation at the ELB vary with the probability of being at the ELB.

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