1. (65 points) There is a strong presumption in the financial press that oil pri

Question

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 West Texas Intermediate (wTI crude oil prices in Cushing from January 2006 to December 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: (2) Equation (1) is called the stochastic population regression function (PRF) and equation (2) is called the stochastic sample regression function. ut is called the stochastic error term, and ee is called the residual term. bi is an unbiased estimator for Bi, and t2 is an unbiased estimator for

Explanation / Answer

a)Demo 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

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

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