Dear Team,
I am attaching a new homework that is due march 6. I hope you can help me solve it.
The questions are from this book but the numbers are different:
Introductory Econometrics: A Modern Approach, 4th Edition
Jeffrey M. Wooldridge. 2009.Cengage
ISBN-10: 0324581629 ISBN-13: 9780324581621
================ECON 3320 Applied Econometrics
Critical Values Z0.10 Z0.05 Z0.025 Z0.01
One tail values 1.295 1.645 1.96 2.33
1. PART A: 50 points
The researchers are interested in modeling the birth weight of children. They form the following model:
?log?(bwght)?_i=β_0+β_1 ?CIGS?_i+β_2 ?FEDUC?_i+β_3 ?MEDUC?_i+β_2 ?MAGE?_i+β_2 ?MALE?_i+β_2 ?NPVIS?_i+u_i
where the variables are defined as:
BWGHT: child birth weight (in grams)
CIGS: average number of cigarettes smoked by the mother per day
FEDUC: years of education of the father
MEDUC: years of education of the mother
MAGE: age of the mother (in years)
MALE: 1 if the child is a male, 0 otherwise
NPVIS: total number of prenatal visits
By using an Ordinary Least Square Method (OLS) the following regression model is estimated:
TABLE 1
Dependent Variable: LOG(BWGHT)
Included observations: 1625
Variable Coefficient Std. Error
Constant 7.711289 0.138997
CIGS -0.002397 0.001184
FEDUC 0.003066 0.002673
MEDUC -0.002564 0.002975
MAGE 0.021644 0.009502
MAGE^2 -0.000345 0.000159
MALE 0.025137 0.009748
NPVIS 0.004978 0.001320
R-squared 0.021706
DW 1.56
answer the following questions based on the given estimated model result in Table 1:
We are interested to test whether mother's smoking has a negative effect on child birth weight. Test this hypothesis using a 5% significance level.
What is the effect of 10moreprenatal visits on the child birth weight?
Interpret the coefficient estimate of the MALE dummy variable .
Based on the DW statistic in Table 1, decide whether you reject or not the null of no serial correlation of the error.(From DW critical table: dL = 1.697 dU = 1.841; HINT: create the boundries for positive , negative and inconclusive decision areas)
If there is a perfectly positive autocorrelation in residuals in first order, what is the remedy to eliminate the first order autocorrelation? Explain it briefly. You can use an example.
We estimate the regression model for the squared residuals (RESID^2)(in other words, error terms square: (u ^^2)) shown in the Table 2 (below). How would you implement a test for heteroskedasticity based on this regression results? State the null and alternative hypotheses, and calculate the χ2 test statistics as χ2=T*R2. (use a 5% significance level in your decision).
Hint: White-Test is a heteroscadasticity test which takes error term squares and regresses it on the independent variables, their squares and their interactions. You need to test if all coefficients are jointly equal to zero or not. It is basically an F-test for the significancy for the whole model. If F-test is not given, use χ2=T*R2 where T is the number of observations and R2 of the regression. This will give you the χ2 test statistics to compare it with χ2(k=14) critical value, which is 23.7 from the χ2 critical table.
So compare 23.7 and χ2=T*R2 =1625*0.026298=???
TABLE 2
Dependent Variable: RESID^2(u ^^2)
Variable Coefficient Std. Error
Constant 1.797312 2.044727
CIGS 0.029079 0.032139
CIGS^2 7.82E-05 0.000127
CIGS*MAGE -0.002281 0.002237
CIGS*(MAGE^2) 3.73E-05 3.81E-05
CIGS*MALE 0.000682 0.002298
CIGS*NPVIS 0.000168 0.000205
MAGE -0.266978 0.288828
MAGE^2 0.014901 0.015135
MAGE*(MAGE^2) -0.000337 0.000346
MAGE*MALE 0.003528 0.018641
MAGE*NPVIS -0.004875 0.002625
(MAGE^2)^2 2.62E-06 2.91E-06
(MAGE^2)*MALE -3.66E-05 0.000313
(MAGE^2)*NPVIS 8.25E-05 4.41E-05
MALE -0.067026 0.274525
MALE*NPVIS -0.000336 0.002541
NPVIS 0.050867 0.038389
NPVIS^2 0.000477 0.000115
R-squared 0.026298
Based on the results of the White tests, do you think that OLS is the appropriate estimator? What goes wrong if we use OLS and the errors are heteroskedastic?
Discuss the problem of heteroskedasticity. what is the nature of the problem. Why do you see a heteroscadasticity (non-constant variance) problem? Give an example.
PART B: (50 points):
1. You are given the below model for the stock returns:
?log(microsoft)?_t=α+β*log?(SandP)_t+u_t(1)
TABLE 1:
Dependent Variable: LOG(MICROSOFT)
Method: Least Squares
Date: 04/28/14 Time: 17:22
Sample: 2002M01 2007M04
Included observations: 64
Variable Coefficient Std. Error t-Statistic Prob.
C -0.930703 0.338686 -2.747978 0.0078
LOG(SANDP) 0.585776 0.048161 12.16285 0.0000
R-squared 0.704670 Mean dependent var 3.187797
Adjusted R-squared 0.699907 S.D. dependent var 0.102948
S.E. of regression 0.056396 Akaike info criterion -2.882103
Sum squared resid 0.197188 Schwarz criterion -2.814638
Log likelihood 94.22731 Hannan-Quinn criter. -2.855525
F-statistic 147.9349 Durbin-Watson stat 0.902327
Prob(F-statistic) 0.000000
1. Interpret the R2 in Table 2.
2. Test if the model as a whole statistically significant or not. Write the null hypothesis. Be clear which test you use. Write your test statistic, critical value at 5% significance level. Write down what is p value of the test statistic. Compare it with your significance level (5%).
4. The below graph is taken from the regression estimation. Do you suspect any autocorrelation in the residual series visually. Explain. If there is no autocorrelation, what type of visual graph you expect to see? Draw it hypothetically.
5. We want to test serial correlationby using the LM Serial correlation test for 2 lags of the residuals. The estimation result is given in Table 3.
a.Specify the null hypothesis of the test,
b. use F-statistic to decide on the null hypothesis at 5 % significance level.
c. calculate the χ2 test statistic and decide whether you reject at 5%. (Hint χ2 test statistic= T*R2 and distributed as χ2 (m), m is number lags for serial correlation.χ2 (2)= 5.99 from the critical table)
TABLE 3:Breusch-Godfrey Serial Correlation LM Test
F-statistic 10.75610 Prob. F(2,60) 0.0001
Obs*R-squared 16.89049 Prob. Chi-Square(2) 0.0002
Test Equation:
Dependent Variable: RESID
Method: Least Squares
Date: 04/28/14 Time: 17:33
Sample: 2002M01 2007M04
Included observations: 64
Presample missing value lagged residuals set to zero.
Variable Coefficient Std. Error t-Statistic Prob.
C -0.037668 0.295718 -0.127378 0.8991
LOG(SANDP) 0.005409 0.042052 0.128633 0.8981
RESID(-1) 0.553291 0.129711 4.265562 0.0001
RESID(-2) -0.079426 0.129790 -0.611959 0.5429
R-squared 0.263914 Mean dependent var -3.38E-17
Adjusted R-squared 0.227110 S.D. dependent var 0.055946
S.E. of regression 0.049185 Akaike info criterion -3.126012
Sum squared resid 0.145147 Schwarz criterion -2.991081
Log likelihood 104.0324 Hannan-Quinn criter. -3.072856
F-statistic 7.170737 Durbin-Watson stat 1.896615
Prob(F-statistic) 0.000341
d. What is your decision for the null hypothesis? Did you reject or not? Is there an autocorrelation in the residuals in second order?
6. The below regression model is given for the excess return of Microsoft return and excess return of the market:
?(R?_t-?RF?_t)=α+β(?RM?_t-?RF?_t)+u_t (2)
where:
R denotes a specific stock return at time t
RF denotes risk free interest rate at time t, generally US Treasury Bill interest rate.
RM denotes the market return at time t. Generally S&P 500 Index, or Dow Jones Index as a proxy for market return (all stocks)
TABLE 4:
Dependent Variable: ERMICROSOFT
Method: Least Squares
Date: 04/28/14 Time: 17:41
Sample (adjusted): 2002M02 2007M04
Included observations: 63 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C -0.320282 0.648445 -0.493923 0.6231
ERSANDP 1.070772 0.182660 5.862098 0.0000
R-squared 0.360347 Mean dependent var 0.121478
Adjusted R-squared 0.349861 S.D. dependent var 6.339973
S.E. of regression 5.111997 Akaike info criterion 6.132288
Sum squared resid 1594.083 Schwarz criterion 6.200324
Log likelihood -191.1671 Hannan-Quinn criter. 6.159047
F-statistic 34.36420 Durbin-Watson stat 2.212775
The claim is the excess return of Microsoft return is less riskier than the market return. Test if slope coefficient is equal to 1 in favor of less than 1.
7. Based on the estimation of the regression (2), we have tested Serial Correlation for lag 2. The result is given in Table 5. Based on the estimation, what do you conclude on the serial correlation of the regression? Is there any autocorrelation in regression (2)
TABLE 5: Breusch-Godfrey Serial Correlation LM Test:
F-statistic 0.906154 Prob. F(2,59) 0.4096
Obs*R-squared 1.877505 Prob. Chi-Square(2) 0.3911
Test Equation:
Dependent Variable: RESID
Method: Least Squares
Date: 04/28/14 Time: 17:46
Sample: 2002M02 2007M04
Included observations: 63
Presample missing value lagged residuals set to zero.
Variable Coefficient Std. Error t-Statistic Prob.
C -0.016228 0.649558 -0.024983 0.9802
ERSANDP 0.018453 0.183465 0.100583 0.9202
RESID(-1) -0.137362 0.129684 -1.059210 0.2938
RESID(-2) -0.123842 0.129873 -0.953560 0.3442
R-squared 0.029802 Mean dependent var 8.46E-17
Adjusted R-squared -0.019530 S.D. dependent var 5.070603
S.E. of regression 5.119879 Akaike info criterion 6.165526
Sum squared resid 1546.577 Schwarz criterion 6.301598
Log likelihood -190.2141 Hannan-Quinn criter. 6.219044
F-statistic 0.604103 Durbin-Watson stat 1.979831
Prob(F-statistic) 0.614932
Requirement:- ECON 3320 Applied Econometrics.docx