2015-12-01 0.24 Frequency: Monthly observation_date FEDFUNDS 2006-01-01 4.29 200
ID: 3255619 • Letter: 2
Question
2015-12-01
0.24
Frequency: Monthly observation_date FEDFUNDS 2006-01-01 4.29 2006-02-01 4.49 2006-03-01 4.59 2006-04-01 4.79 2006-05-01 4.94 2006-06-01 4.99 2006-07-01 5.24 2006-08-01 5.25 2006-09-01 5.25 2006-10-01 5.25 2006-11-01 5.25 2006-12-01 5.24 2007-01-01 5.25 2007-02-01 5.26 2007-03-01 5.26 2007-04-01 5.25 2007-05-01 5.25 2007-06-01 5.25 2007-07-01 5.26 2007-08-01 5.02 2007-09-01 4.94 2007-10-01 4.76 2007-11-01 4.49 2007-12-01 4.24 2008-01-01 3.94 2008-02-01 2.98 2008-03-01 2.61 2008-04-01 2.28 2008-05-01 1.98 2008-06-01 2.00 2008-07-01 2.01 2008-08-01 2.00 2008-09-01 1.81 2008-10-01 0.97 2008-11-01 0.39 2008-12-01 0.16 2009-01-01 0.15 2009-02-01 0.22 2009-03-01 0.18 2009-04-01 0.15 2009-05-01 0.18 2009-06-01 0.21 2009-07-01 0.16 2009-08-01 0.16 2009-09-01 0.15 2009-10-01 0.12 2009-11-01 0.12 2009-12-01 0.12 2010-01-01 0.11 2010-02-01 0.13 2010-03-01 0.16 2010-04-01 0.20 2010-05-01 0.20 2010-06-01 0.18 2010-07-01 0.18 2010-08-01 0.19 2010-09-01 0.19 2010-10-01 0.19 2010-11-01 0.19 2010-12-01 0.18 2011-01-01 0.17 2011-02-01 0.16 2011-03-01 0.14 2011-04-01 0.10 2011-05-01 0.09 2011-06-01 0.09 2011-07-01 0.07 2011-08-01 0.10 2011-09-01 0.08 2011-10-01 0.07 2011-11-01 0.08 2011-12-01 0.07 2012-01-01 0.08 2012-02-01 0.10 2012-03-01 0.13 2012-04-01 0.14 2012-05-01 0.16 2012-06-01 0.16 2012-07-01 0.16 2012-08-01 0.13 2012-09-01 0.14 2012-10-01 0.16 2012-11-01 0.16 2012-12-01 0.16 2013-01-01 0.14 2013-02-01 0.15 2013-03-01 0.14 2013-04-01 0.15 2013-05-01 0.11 2013-06-01 0.09 2013-07-01 0.09 2013-08-01 0.08 2013-09-01 0.08 2013-10-01 0.09 2013-11-01 0.08 2013-12-01 0.09 2014-01-01 0.07 2014-02-01 0.07 2014-03-01 0.08 2014-04-01 0.09 2014-05-01 0.09 2014-06-01 0.10 2014-07-01 0.09 2014-08-01 0.09 2014-09-01 0.09 2014-10-01 0.09 2014-11-01 0.09 2014-12-01 0.12 2015-01-01 0.11 2015-02-01 0.11 2015-03-01 0.11 2015-04-01 0.12 2015-05-01 0.12 2015-06-01 0.13 2015-07-01 0.13 2015-08-01 0.14 2015-09-01 0.14 2015-10-01 0.12 2015-11-01 0.122015-12-01
Date (Year/Month) Dollars per barrel 2015/12 37.19 2015/11 42.44 2015/10 46.22 2015/09 45.48 2015/08 42.87 2015/07 50.9 2015/06 59.82 2015/05 59.27 2015/04 54.45 2015/03 47.82 2015/02 50.58 2015/01 47.22 2014/12 59.29 2014/11 75.79 2014/10 84.4 2014/09 93.21 2014/08 96.54 2014/07 103.59 2014/06 105.79 2014/05 102.18 2014/04 102.07 2014/03 100.8 2014/02 100.82 2014/01 94.62 2013/12 97.63 2013/11 93.86 2013/10 100.54 2013/09 106.29 2013/08 106.57 2013/07 104.67 2013/06 95.77 2013/05 94.51 2013/04 92.02 2013/03 92.94 2013/02 95.31 2013/01 94.76 2012/12 87.86 2012/11 86.53 2012/10 89.49 2012/09 94.51 2012/08 94.13 2012/07 87.9 2012/06 82.3 2012/05 94.66 2012/04 103.32 2012/03 106.16 2012/02 102.2 2012/01 100.27 2011/12 98.56 2011/11 97.16 2011/10 86.32 2011/09 85.52 2011/08 86.33 2011/07 97.3 2011/06 96.26 2011/05 100.9 2011/04 109.53 2011/03 102.86 2011/02 88.58 2011/01 89.17 2010/12 89.15 2010/11 84.25 2010/10 81.89 2010/09 75.24 2010/08 76.6 2010/07 76.32 2010/06 75.34 2010/05 73.74 2010/04 84.29 2010/03 81.2 2010/02 76.39 2010/01 78.33 2009/12 74.47 2009/11 77.99 2009/10 75.72 2009/09 69.41 2009/08 71.05 2009/07 64.15 2009/06 69.64 2009/05 59.03 2009/04 49.65 2009/03 47.94 2009/02 39.09 2009/01 41.71 2008/12 41.12 2008/11 57.31 2008/10 76.61 2008/09 104.11 2008/08 116.67 2008/07 133.37 2008/06 133.88 2008/05 125.4 2008/04 112.58 2008/03 105.45 2008/02 95.39 2008/01 92.97 2007/12 91.69 2007/11 94.77 2007/10 85.8 2007/09 79.92 2007/08 72.36 2007/07 74.12 2007/06 67.49 2007/05 63.46 2007/04 63.98 2007/03 60.44 2007/02 59.28 2007/01 54.51 2006/12 61.96 2006/11 59.08 2006/10 58.89 2006/09 63.8 2006/08 73.04 2006/07 74.41 2006/06 70.95 2006/05 70.84 2006/04 69.44 2006/03 62.69 2006/02 61.63 2006/01 65.490.24
SECTION 1: Analysis of the Relationship between oil prices and monetary policy using ExCEL 1. (65 points) There is a strong presumption in the financial press that oil prices affect monetary policy. In this question, we use the tools in class to conduct a simple analysis of the relationship between oil prices and monetary policy. You will be responsible for collecting the dataset for this question. Your dataset should consist of monthly data on the federal funds rate, and the 2015. Please use EXCEL for this part of the homework. All the data you need are available on the Federal Reserve Bank of Saint Louis' Federal Reserve Economic Data (FRED) website. Please do the following exercises in EXCEL. Present your final answers in a Microsoft Word or LATEX document processor. As we mentioned in class, one can examine the relationship between two or more variables using regression analysis. The following equations were introduced: (1) (2) MacBook ProExplanation / Answer
a)Data:
Frequency: Monthly
Date (Year/Month)
Dollars per barrel
observation_date
FEDFUNDS
01/01/2006
4.29
2006/01
65.49
01/02/2006
4.49
2006/02
61.63
01/03/2006
4.59
2006/03
62.69
01/04/2006
4.79
2006/04
69.44
01/05/2006
4.94
2006/05
70.84
01/06/2006
4.99
2006/06
70.95
01/07/2006
5.24
2006/07
74.41
01/08/2006
5.25
2006/08
73.04
01/09/2006
5.25
2006/09
63.8
01/10/2006
5.25
2006/10
58.89
01/11/2006
5.25
2006/11
59.08
01/12/2006
5.24
2006/12
61.96
01/01/2007
5.25
2007/01
54.51
01/02/2007
5.26
2007/02
59.28
01/03/2007
5.26
2007/03
60.44
01/04/2007
5.25
2007/04
63.98
01/05/2007
5.25
2007/05
63.46
01/06/2007
5.25
2007/06
67.49
01/07/2007
5.26
2007/07
74.12
01/08/2007
5.02
2007/08
72.36
01/09/2007
4.94
2007/09
79.92
01/10/2007
4.76
2007/10
85.8
01/11/2007
4.49
2007/11
94.77
01/12/2007
4.24
2007/12
91.69
01/01/2008
3.94
2008/01
92.97
01/02/2008
2.98
2008/02
95.39
01/03/2008
2.61
2008/03
105.45
01/04/2008
2.28
2008/04
112.58
01/05/2008
1.98
2008/05
125.4
01/06/2008
2
2008/06
133.88
01/07/2008
2.01
2008/07
133.37
01/08/2008
2
2008/08
116.67
01/09/2008
1.81
2008/09
104.11
01/10/2008
0.97
2008/10
76.61
01/11/2008
0.39
2008/11
57.31
01/12/2008
0.16
2008/12
41.12
01/01/2009
0.15
2009/01
41.71
01/02/2009
0.22
2009/02
39.09
01/03/2009
0.18
2009/03
47.94
01/04/2009
0.15
2009/04
49.65
01/05/2009
0.18
2009/05
59.03
01/06/2009
0.21
2009/06
69.64
01/07/2009
0.16
2009/07
64.15
01/08/2009
0.16
2009/08
71.05
01/09/2009
0.15
2009/09
69.41
01/10/2009
0.12
2009/10
75.72
01/11/2009
0.12
2009/11
77.99
01/12/2009
0.12
2009/12
74.47
01/01/2010
0.11
2010/01
78.33
01/02/2010
0.13
2010/02
76.39
01/03/2010
0.16
2010/03
81.2
01/04/2010
0.2
2010/04
84.29
01/05/2010
0.2
2010/05
73.74
01/06/2010
0.18
2010/06
75.34
01/07/2010
0.18
2010/07
76.32
01/08/2010
0.19
2010/08
76.6
01/09/2010
0.19
2010/09
75.24
01/10/2010
0.19
2010/10
81.89
01/11/2010
0.19
2010/11
84.25
01/12/2010
0.18
2010/12
89.15
01/01/2011
0.17
2011/01
89.17
01/02/2011
0.16
2011/02
88.58
01/03/2011
0.14
2011/03
102.86
01/04/2011
0.1
2011/04
109.53
01/05/2011
0.09
2011/05
100.9
01/06/2011
0.09
2011/06
96.26
01/07/2011
0.07
2011/07
97.3
01/08/2011
0.1
2011/08
86.33
01/09/2011
0.08
2011/09
85.52
01/10/2011
0.07
2011/10
86.32
01/11/2011
0.08
2011/11
97.16
01/12/2011
0.07
2011/12
98.56
01/01/2012
0.08
2012/01
100.27
01/02/2012
0.1
2012/02
102.2
01/03/2012
0.13
2012/03
106.16
01/04/2012
0.14
2012/04
103.32
01/05/2012
0.16
2012/05
94.66
01/06/2012
0.16
2012/06
82.3
01/07/2012
0.16
2012/07
87.9
01/08/2012
0.13
2012/08
94.13
01/09/2012
0.14
2012/09
94.51
01/10/2012
0.16
2012/10
89.49
01/11/2012
0.16
2012/11
86.53
01/12/2012
0.16
2012/12
87.86
01/01/2013
0.14
2013/01
94.76
01/02/2013
0.15
2013/02
95.31
01/03/2013
0.14
2013/03
92.94
01/04/2013
0.15
2013/04
92.02
01/05/2013
0.11
2013/05
94.51
01/06/2013
0.09
2013/06
95.77
01/07/2013
0.09
2013/07
104.67
01/08/2013
0.08
2013/08
106.57
01/09/2013
0.08
2013/09
106.29
01/10/2013
0.09
2013/10
100.54
01/11/2013
0.08
2013/11
93.86
01/12/2013
0.09
2013/12
97.63
01/01/2014
0.07
2014/01
94.62
01/02/2014
0.07
2014/02
100.82
01/03/2014
0.08
2014/03
100.8
01/04/2014
0.09
2014/04
102.07
01/05/2014
0.09
2014/05
102.18
01/06/2014
0.1
2014/06
105.79
01/07/2014
0.09
2014/07
103.59
01/08/2014
0.09
2014/08
96.54
01/09/2014
0.09
2014/09
93.21
01/10/2014
0.09
2014/10
84.4
01/11/2014
0.09
2014/11
75.79
01/12/2014
0.12
2014/12
59.29
01/01/2015
0.11
2015/01
47.22
01/02/2015
0.11
2015/02
50.58
01/03/2015
0.11
2015/03
47.82
01/04/2015
0.12
2015/04
54.45
01/05/2015
0.12
2015/05
59.27
01/06/2015
0.13
2015/06
59.82
01/07/2015
0.13
2015/07
50.9
01/08/2015
0.14
2015/08
42.87
01/09/2015
0.14
2015/09
45.48
01/10/2015
0.12
2015/10
46.22
01/11/2015
0.12
2015/11
42.44
01/12/2015
0.24
2015/12
37.19
Follow these steps:
b) STOCHASTIC means something derived using sample and not the exact population quantities.(exact meaning: having a random probability distribution or pattern that may be analysed statistically but may not be predicted precisely.)
The output is:
Regression Statistics
Multiple R
0.169389437
R Square
0.028692781
Adjusted R Square
0.020461364
Standard Error
1.949879791
Observations
120
ANOVA
df
SS
MS
F
Significance F
Regression
1
13.25299
13.25299
3.485764
0.064381
Residual
118
448.6397
3.802031
Total
119
461.8927
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
2.565821738
0.710469
3.611448
0.000448
1.1589
3.972744
1.1589
3.972744
X Variable 1
-0.015897042
0.008515
-1.86702
0.064381
-0.03276
0.000964
-0.03276
0.000964
c) Hence b1=2.565821738 and b2=-0.015897042.
d) Interpretation of b1:
When oil price Wt=0, the federal fund rate Rt=2.565821738.
Interpretation of b2:
When oil price Wt changes by 1 unit, federal fund rate Rt changes by -0.015897042 units.
Now
e_t=R_t-b1-b2*W_t
e) Thus residual sum of squares is 448.6397 and =3.802031
The residual sum of squares is used to measure the deviation of predicted values from actual values.
f)
=835481.5
=80.7795
=52442.22
n=120
var(b1)= 835481.5*3.802031/(120*52442.22)= 0.504766
var(b2)= 3.802031/52442.22=7.24994E-05
We get the standard errors of b1 and b2 from Anova table as:
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
2.565821738
0.710469
3.611448
0.000448
1.1589
3.972744
1.1589
3.972744
X Variable 1
-0.015897042
0.008515
-1.86702
0.064381
-0.03276
0.000964
-0.03276
0.000964
Squaring these values also gives variances which are calculated above using the given formulae for var(b1) and var(b2).
g) Hypothesis testing:
H0: Oil prices have no effect on interest rates. Vs
H1: Oil prices have an effect on interest rates.
Test statistic=-1.86702
p-value=0.064381
As p-value is greater than 0.05, we fail to reject H0(null hypothesis) at 5% los. Thus we conclude that oil prices have no effect on interest rates at 5% los.
Frequency: Monthly
Date (Year/Month)
Dollars per barrel
observation_date
FEDFUNDS
01/01/2006
4.29
2006/01
65.49
01/02/2006
4.49
2006/02
61.63
01/03/2006
4.59
2006/03
62.69
01/04/2006
4.79
2006/04
69.44
01/05/2006
4.94
2006/05
70.84
01/06/2006
4.99
2006/06
70.95
01/07/2006
5.24
2006/07
74.41
01/08/2006
5.25
2006/08
73.04
01/09/2006
5.25
2006/09
63.8
01/10/2006
5.25
2006/10
58.89
01/11/2006
5.25
2006/11
59.08
01/12/2006
5.24
2006/12
61.96
01/01/2007
5.25
2007/01
54.51
01/02/2007
5.26
2007/02
59.28
01/03/2007
5.26
2007/03
60.44
01/04/2007
5.25
2007/04
63.98
01/05/2007
5.25
2007/05
63.46
01/06/2007
5.25
2007/06
67.49
01/07/2007
5.26
2007/07
74.12
01/08/2007
5.02
2007/08
72.36
01/09/2007
4.94
2007/09
79.92
01/10/2007
4.76
2007/10
85.8
01/11/2007
4.49
2007/11
94.77
01/12/2007
4.24
2007/12
91.69
01/01/2008
3.94
2008/01
92.97
01/02/2008
2.98
2008/02
95.39
01/03/2008
2.61
2008/03
105.45
01/04/2008
2.28
2008/04
112.58
01/05/2008
1.98
2008/05
125.4
01/06/2008
2
2008/06
133.88
01/07/2008
2.01
2008/07
133.37
01/08/2008
2
2008/08
116.67
01/09/2008
1.81
2008/09
104.11
01/10/2008
0.97
2008/10
76.61
01/11/2008
0.39
2008/11
57.31
01/12/2008
0.16
2008/12
41.12
01/01/2009
0.15
2009/01
41.71
01/02/2009
0.22
2009/02
39.09
01/03/2009
0.18
2009/03
47.94
01/04/2009
0.15
2009/04
49.65
01/05/2009
0.18
2009/05
59.03
01/06/2009
0.21
2009/06
69.64
01/07/2009
0.16
2009/07
64.15
01/08/2009
0.16
2009/08
71.05
01/09/2009
0.15
2009/09
69.41
01/10/2009
0.12
2009/10
75.72
01/11/2009
0.12
2009/11
77.99
01/12/2009
0.12
2009/12
74.47
01/01/2010
0.11
2010/01
78.33
01/02/2010
0.13
2010/02
76.39
01/03/2010
0.16
2010/03
81.2
01/04/2010
0.2
2010/04
84.29
01/05/2010
0.2
2010/05
73.74
01/06/2010
0.18
2010/06
75.34
01/07/2010
0.18
2010/07
76.32
01/08/2010
0.19
2010/08
76.6
01/09/2010
0.19
2010/09
75.24
01/10/2010
0.19
2010/10
81.89
01/11/2010
0.19
2010/11
84.25
01/12/2010
0.18
2010/12
89.15
01/01/2011
0.17
2011/01
89.17
01/02/2011
0.16
2011/02
88.58
01/03/2011
0.14
2011/03
102.86
01/04/2011
0.1
2011/04
109.53
01/05/2011
0.09
2011/05
100.9
01/06/2011
0.09
2011/06
96.26
01/07/2011
0.07
2011/07
97.3
01/08/2011
0.1
2011/08
86.33
01/09/2011
0.08
2011/09
85.52
01/10/2011
0.07
2011/10
86.32
01/11/2011
0.08
2011/11
97.16
01/12/2011
0.07
2011/12
98.56
01/01/2012
0.08
2012/01
100.27
01/02/2012
0.1
2012/02
102.2
01/03/2012
0.13
2012/03
106.16
01/04/2012
0.14
2012/04
103.32
01/05/2012
0.16
2012/05
94.66
01/06/2012
0.16
2012/06
82.3
01/07/2012
0.16
2012/07
87.9
01/08/2012
0.13
2012/08
94.13
01/09/2012
0.14
2012/09
94.51
01/10/2012
0.16
2012/10
89.49
01/11/2012
0.16
2012/11
86.53
01/12/2012
0.16
2012/12
87.86
01/01/2013
0.14
2013/01
94.76
01/02/2013
0.15
2013/02
95.31
01/03/2013
0.14
2013/03
92.94
01/04/2013
0.15
2013/04
92.02
01/05/2013
0.11
2013/05
94.51
01/06/2013
0.09
2013/06
95.77
01/07/2013
0.09
2013/07
104.67
01/08/2013
0.08
2013/08
106.57
01/09/2013
0.08
2013/09
106.29
01/10/2013
0.09
2013/10
100.54
01/11/2013
0.08
2013/11
93.86
01/12/2013
0.09
2013/12
97.63
01/01/2014
0.07
2014/01
94.62
01/02/2014
0.07
2014/02
100.82
01/03/2014
0.08
2014/03
100.8
01/04/2014
0.09
2014/04
102.07
01/05/2014
0.09
2014/05
102.18
01/06/2014
0.1
2014/06
105.79
01/07/2014
0.09
2014/07
103.59
01/08/2014
0.09
2014/08
96.54
01/09/2014
0.09
2014/09
93.21
01/10/2014
0.09
2014/10
84.4
01/11/2014
0.09
2014/11
75.79
01/12/2014
0.12
2014/12
59.29
01/01/2015
0.11
2015/01
47.22
01/02/2015
0.11
2015/02
50.58
01/03/2015
0.11
2015/03
47.82
01/04/2015
0.12
2015/04
54.45
01/05/2015
0.12
2015/05
59.27
01/06/2015
0.13
2015/06
59.82
01/07/2015
0.13
2015/07
50.9
01/08/2015
0.14
2015/08
42.87
01/09/2015
0.14
2015/09
45.48
01/10/2015
0.12
2015/10
46.22
01/11/2015
0.12
2015/11
42.44
01/12/2015
0.24
2015/12
37.19
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