Question 1 (25%) Suppose we want to investigate the money spending behavior in the US, by using the following model
M2t = fio + PiGDPt + fcFFRt + fij...
W e want to test the seasonality effect to see if the US money supply is larger during the Thanksgiving and Christmas holidays (last quarter of the year). The quarterly dummy variables are defined as 51 = 1 for Quarter 1, = 0 otherwise
S3 =1 for Quarter 3, = 0 otherwise
52 = 1 for Quarter 2, = 0 otherwise
S4 =1 for Quarter 4, = 0 otherwise
After regressing without the dummy variables we get the following results: Dependent Variable: М2 Method: Least Squares Date: 09/05/14 Time: 14:06 Sample (adjusted): 1991Q1 2008Q4 Included observations: 72 after adjustments Variable
Coefficient
Std. Error
t-Statistic
Prob.
С GDP FFR INFLATION
17.35961 0.533719 -106.6752 92.00183
104.2171 0.007350 11.36128 20.81161
0.166572 72.61667 -9.389367 4.420698
0.0000 0.0000 0.0000
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)
Analyze the sign of the coefficients. Are they consistent with what we expect? Analyze the effect of each coefficient to the dependent variable.
W e now apply the seasonal effects (by adding dummy variables) to our model and we get the following outputs in each case Dependent Variable: M2 Method: Least Squares Date: 09/05/14 Time: 14:07 Sample (adjusted): 1991Q1 2008Q4 Included observations: 72 after adjustments Variable
Analyze the signs of the dummy coefficients. Do you think that they are consistent with what we might expect?
C.
Suppose now that you multiply the S4 dummy with the independent variables and you get the following output. Analyze the signs of the dummy coefficients. Do you think that they are consistent with what we might expect?
Dependent Variable: M2 Method: Least Squares Date: 10/14/14 Time: 14:07 Sample (adjusted): 1991Q1 2008Q4 Included observations: 72 after adjustments Variable
Question 2 (25%) Suppose w e w a n t to te s t w h e th e r th e re is any structural break (or change) a fte r th e year o f 1980: Ho: T h ere was no structural break (or change) a fte r 1980 H1: T h e re w as a structural break (or change) a fte r 1980 You g e t th e fo llo w in g th re e outpu ts by doing C how Test. Dependent Variable: Y Method: Least Squares Date: 03/10/14 Time: 13:48
Sample: 1960 1999 Included observations: 40 Variable
Coefficient
Std . Error
t-S tatistic
P rob.
C PC PB YD
27.59394 -0.607160 0.092188 0.244860
1.584458 0.157120 0.039883 0.011095
17.41539 -3.864300 2.311452 22.06862
0. 0000 0.0004 0.0266 0.0000
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)
A. Explain the procedure of the Chow Tests, i.e the steps you have to take in order to make conclusion about the structural stability.
B. Calculate the Chow F-Statistic. According to the F statistic you just calculated do you reject or fail to reject the Null Hypothesis? W hat does that mean for your data?
You are given that Fcriticai(0.05,4,32)=2.6896.
Question 3 (25%) A.
One of the ways to detect multicollinearity is the Variance Inflation Factor (VIF). Define and analyze as much as you can.
B.
Suppose w e used Condition Index (CI) in our model to detect multicollinearity and we found CI=42. W hat is the formula of the Condition Index and w hat this number means for our model?
Question 4 (25%) Suppose w e have th e fo llo w in g regression m odel
PCONi = po + piREG + P2TAX + ut w h e re
PCONi = REGi =
p e tro le u m consum ption in th e ith state (m illions o f BTUs)
m o to r vehicles registration in th e ith state (thousands)
TAXi = th e
gasoline ta x rate in th e ith state (cents per gallon)
T he expected sign o f th e coefficients are P 1 > 0 and P 2 < 0 W e ran th e regression in Eviews and w e o b tain ed th e fo llo w in g o u tp u t.
Dependent Variable: PCON Method: Least Squares Date: 03/15/14 Time: 12:08 Sample: 1 50 Included observations: 50 Variable
Coefficient
Std . Error
t-S tatistic
P rob.
C REG TAX
551 .6880 0.186132 -53.59101
186.2709 0.011719 16.85588
2.961750 15.88302 -3.179365
0. 0048 0.0000 0.0026
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)
A. Discuss the sign of the coefficients and the t-Statistics results. Do they seem fine to you?
B.
W e w ant to check if there exists Heteroscedasticity in our model. One of the ways to do it is to use the Park Test. Suppose we created our auxiliary regression model and we ran it and we obtained the following output below. Test if there is Heteroscedasticity or not. Hint: You can use either the t-Statistic outputs or use the LM test to define the existence or not of Heteroscedasticity. You do not have to use both tests. For the use o f LM test, use as critical value o f Chisquared(0.05,1)=3.841.
Dependent Variable: L0G (R E S ID 01A2) Method: Least Squares Date: 03/15/14 Time: 12:13 Sample: 1 50 Included observations: 50 Variable
Coefficient
Std . Error
t-S tatistic
P rob.
C L0G (R EG )
1.650293 0.951916
2.3 74469 0.308304
0.6 95016 3.087594
0. 4904 0.0033
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)
