The Federal Reserve Board eagle logo links to home page

Skip to: [Printable Version (PDF)] [Bibliography] [Footnotes]
Finance and Economics Discussion Series: 2007-56 Screen Reader version

Welfare-Maximizing Monetary Policy
Under Parameter Uncertainty
(Figure Data)

Rochelle M. Edge, Thomas Laubach, and John C. Williams *

Figure 1 - Output (y)
QuarterVAR impulse responseVAR response plus 1 std devVAR response minus 1 std devModel impulse response
00.57690.82560.32830.2710
10.53330.86560.20100.4987
20.56640.93000.20280.6841
30.79301.11720.46880.8306
40.91531.25580.57480.9427
50.97571.32890.62251.0257
60.97731.33460.62001.0845
71.02911.39140.66681.1238
81.07471.45080.69851.1477
Return to Text


Figure 1 - Hours (l)
QuarterVAR impulse responseVAR response plus 1 std devVAR response minus 1 std devModel impulse response
0-0.23600.0127-0.4846-0.7290
1-0.25850.0962-0.6132-0.5013
2-0.23250.1836-0.6487-0.3159
3-0.03370.3905-0.4580-0.1694
40.00860.4409-0.4237-0.0573
50.06420.5050-0.37660.0257
60.10170.5396-0.33630.0845
70.12930.5559-0.29740.1238
80.13110.5450-0.28270.1477
Return to Text


Figure 1 - Real wage (w)
QuarterVAR impulse responseVAR response plus 1 std devVAR response minus 1 std devModel impulse response
00.59581.01460.17700.1825
10.76111.24130.28080.3339
20.96531.51550.41510.4593
31.02671.58370.46970.5629
41.02041.57780.46300.6482
51.01071.56760.45370.7183
61.03011.59660.46360.7755
71.04111.61690.46540.8222
81.04701.63220.46180.8601
Return to Text


Figure 1 - Price inflation
QuarterVAR impulse responseVAR response plus 1 std devVAR response minus 1 std devModel impulse response
0-0.8296-0.4093-1.2499-0.6526
1-0.6475-0.3068-0.9882-0.5215
2-0.3221-0.0215-0.6228-0.4146
3-0.15140.1692-0.4720-0.3278
4-0.3581-0.0124-0.7037-0.2576
5-0.4033-0.0735-0.7330-0.2010
6-0.26360.0232-0.5504-0.1556
7-0.08920.1966-0.3749-0.1194
8-0.13230.1573-0.4220-0.0908
Return to Text


Figure 1 - Interest rate
QuarterVAR impulse responseVAR response plus 1 std devVAR response minus 1 std devModel impulse response
0-0.19250.0227-0.4078-0.1254
1-0.23140.1563-0.6191-0.2016
2-0.33050.1108-0.7719-0.2427
3-0.33100.1557-0.8178-0.2592
4-0.27070.1786-0.7201-0.2591
5-0.17430.2217-0.5703-0.2481
6-0.18920.2051-0.5834-0.2306
7-0.25790.1303-0.6460-0.2094
8-0.23410.1113-0.5796-0.1868
Return to Text


Figure 2 - Output(y)
QuarterVAR impulse responseVAR response plus 1 std devVAR response minus 1 std devModel impulse response
00.00000.00000.00000.0000
1-0.1199-0.0282-0.2116-0.2084
2-0.5865-0.4559-0.7171-0.3266
3-0.7305-0.5667-0.8944-0.3833
4-0.7518-0.5738-0.9298-0.3991
5-0.7883-0.5984-0.9782-0.3888
6-0.8012-0.5961-1.0063-0.3628
7-0.7694-0.5533-0.9855-0.3284
8-0.7144-0.4914-0.9373-0.2904
Return to Text


Figure 2 - Hours(l)
QuarterVAR impulse responseVAR response plus 1 std devVAR response minus 1 std devModel impulse response
00.00000.00000.00000.0000
10.00340.0633-0.0564-0.2084
2-0.2568-0.1565-0.3572-0.3266
3-0.4476-0.3140-0.5812-0.3833
4-0.5301-0.3731-0.6870-0.3991
5-0.6051-0.4320-0.7782-0.3888
6-0.6349-0.4462-0.8237-0.3628
7-0.6249-0.4243-0.8255-0.3284
8-0.5932-0.3844-0.8021-0.2904
Return to Text


Figure 2 - Real wage (w)
QuarterVAR impulse responseVAR response plus 1 std devVAR response minus 1 std devModel impulse response
00.00000.00000.00000.0000
1-0.1324-0.0745-0.1903-0.0105
2-0.1490-0.0670-0.2309-0.0190
3-0.1788-0.0747-0.2828-0.0254
4-0.2008-0.0888-0.3128-0.0298
5-0.2136-0.0979-0.3293-0.0324
6-0.2105-0.0887-0.3323-0.0334
7-0.2076-0.0801-0.3351-0.0333
8-0.2043-0.0739-0.3348-0.0323
Return to Text


Figure 2 - Price inflation
QuarterVAR impulse responseVAR response plus 1 std devVAR response minus 1 std devModel impulse response
00.00000.00000.00000.0000
10.15630.26160.0510-0.0719
20.10500.2256-0.0157-0.0707
30.01690.1448-0.1111-0.0681
4-0.10650.0036-0.2166-0.0644
5-0.1194-0.0043-0.2346-0.0599
6-0.2290-0.1019-0.3562-0.0550
7-0.2717-0.1397-0.4037-0.0498
8-0.3001-0.1755-0.4248-0.0447
Return to Text


Figure 2 - Interest rate
QuarterVAR impulse responseVAR response plus 1 std devVAR response minus 1 std devModel impulse response
01.00001.00001.00001.0000
10.95891.04940.86850.7949
20.50130.63400.36860.6292
30.42860.58350.27370.4958
40.38400.54920.21870.3886
50.24370.40790.07950.3027
60.15430.3232-0.01470.2343
70.08910.2641-0.08580.1799
80.01830.1950-0.15840.1369
Return to Text


Figure 3 - Natural Rate of Hours
QuarterPoint estimates Lower 90% CILower 70% CIMedianUpper 70% CIUpper 90% CI
1-0.2995-0.5193-0.5064-0.4525-0.3382-0.2411
2-0.0897-0.2697-0.2564-0.2047-0.1144-0.0582
3-0.0269-0.1401-0.1298-0.0926-0.0387-0.014
4-0.008-0.0727-0.0657-0.0419-0.0131-0.0034
5-0.0024-0.0378-0.0333-0.019-0.0044-0.0008
6-0.0007-0.0196-0.0169-0.0086-0.0015-0.0002
7-0.0002-0.0102-0.0085-0.0039-0.00050
8-0.0001-0.0053-0.0043-0.0018-0.00020
Return to Text


Figure 3 - Natural Rate of Interest
QuarterPoint estimates Lower 90% CILower 70% CIMedianUpper 70% CIUpper 90% CI
1-6.4823-7.1148-6.072-4.1805-2.3728-1.055
2-1.9416-2.1361-2.0584-1.8218-1.151-0.4728
3-0.5816-0.8991-0.8632-0.7677-0.4681-0.1472
4-0.1742-0.4187-0.3969-0.3378-0.1664-0.0332
5-0.0522-0.2034-0.189-0.1513-0.0564-0.0073
6-0.0156-0.1007-0.092-0.0677-0.0189-0.0015
7-0.0047-0.0504-0.0453-0.0305-0.0063-0.0003
8-0.0014-0.0255-0.0224-0.0136-0.002-0.0001
Return to Text


Figure 4 - Certainty Equivalent Policy
QuarterNominal interest rate (annual)Output GapPrice Inflation (annual)Wage Inflation (annual)
1-4.6321-0.0129-0.69110.0606
2-2.3062-0.0181-0.56120.049
3-1.2023-0.0199-0.45570.0396
4-0.6698-0.0199-0.370.0321
5-0.4043-0.0189-0.30040.0262
6-0.2649-0.0172-0.24390.0214
7-0.1863-0.0152-0.1980.0175
8-0.1383-0.0131-0.16060.0144
9-0.1064-0.0111-0.13030.0119
10-0.0837-0.0091-0.10570.0099
11-0.0668-0.0073-0.08570.0083
12-0.0537-0.0058-0.06940.0069
Return to Text


Figure 4 - Optimal Bayesian Policy.
QuarterNominal interest rate (annual)Output GapPrice Inflation (annual)Wage Inflation (annual)
1-5.83870.0272-0.6920.0628
2-2.49880.0088-0.56220.0478
3-1.1585-0.0088-0.45690.0375
4-0.6031-0.0183-0.37130.03
5-0.359-0.0214-0.30170.0242
6-0.241-0.021-0.24520.0196
7-0.1762-0.0189-0.19930.0159
8-0.1356-0.0163-0.1620.0129
9-0.1073-0.0137-0.13160.0105
10-0.0861-0.0114-0.1070.0085
11-0.0695-0.0093-0.08690.0069
12-0.0563-0.0076-0.07070.0056
Return to Text



This version is optimized for use by screen readers. Descriptions for all mathematical expressions are provided in LaTex format. A printable pdf version is available. Return to Top