SMM466 Applied Empirical Accounting 2019
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MSc International Accounting & Finance
SMM466
Applied Empirical Accounting
2019
Section A
(50 marks total – Answer all questions)
Question A.1
A researcher is interested in assessing the driving factors of the returns on BP. She has collected a sample of monthly data on the returns on BP (BP) and of monthly factors covering the same time period: the MARKET(MARKET) is the excess return on the FTSE100; the size factor (SIZE) is the return on a portfolio of small stocks less the return on a portfolio of large stocks. BP announces its yearly results every October to the shareholders. The researcher wants to find out if, following the announcement, the impact of MARKET on BP changes. She thus generates a dummy variable, OCTOBER, that takes value 1 in October and zero in any other month and she estimates the following multiple linear regression model using OLS and obtains the following estimation output.
Dependent Variable: BP
Method: Least Squares
Sample: 1980M10 2010M12
Included observations: 363
Variable |
Coefficient |
Std. Error |
-Statistic |
Prob. |
C |
0.005379 |
0.001898 |
2.834781 |
0.0048 |
MARKET |
0.669732 |
0.039124 |
17.11797 |
0.0000 |
SIZE |
0.833417 |
0.053539 |
15.56653 |
0.0000 |
MARKET*OCTOBER |
-0.005220 |
0.050715 |
1.877544 |
0.0001 |
R-squared |
0.602309 |
Mean dependent var |
0.010881 |
S.E. of regression |
0.034331 |
Akaike info criterion |
-3.891877 |
Sum squared resid |
0.421937 |
Schwarz criterion |
-3.838235 |
Log likelihood |
711.3757 |
Hannan-Quinn criter. |
-3.870555 |
F-statistic |
135.5493 |
Durbin-Watson stat |
1.584676 |
Prob(F-statistic) |
0.000000 |
|
|
a. Write down the model being estimated and the fitted model.
(4 marks)
b. Is the regression significant in the overall? Justify your answer. Interpret all the coefficients that the researcher has obtained and run the hypothesis tests that you feel are appropriate for understanding the determinants of the returns on BP.
(12 marks)
c. Can you conclude from the regression output above that the impact of MARKET on BP changes in October?
(5 marks)
d. The researcher wants to find out if the model in a) is an improvement with
respect to a simple linear regression model, where the return on BP is expressed only as a function of the MARKET. Therefore she runs the following regression
Dependent Variable: BP
Method: Least Squares
Included observations: 363
Variable |
Coefficient |
Std. Error |
-Statistic |
Prob. |
|
|
|||||
C MARKET |
0.007468 0.873586 |
0.002347 0.050026 |
3.181679 13.26481 |
0.0016 0.0000 |
|
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) |
0.327691 0.325828 0.044451 0.713298 616.0802 175.9553 0.000000 |
Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat |
0.010881 0.054137 -3.383362 -3.361905 -3.374833 1.398702 |
Comment on the change in explanatory power of the model and test if the specification proposed in a) is an improvement relative to this simple linear specification.
(7 points)
e. The researcher wants to test for the presence of a structural break in January
2006. Describe the Chow break test, stating very clearly the null and alternative hypotheses of the test, the restricted and unrestricted model, the test statistics and its distribution under the null hypothesis.
(6 marks)
Question A.2
Write down the Gauss-Markov assumptions for the following simple linear regression model
yi = a + Fxi + ei
Write down the formula for the OLS estimator of β and prove that the estimator is unbiased. Which are the crucial assumptions to guarantee unbiasedness?
(8 marks)
Question A.3
Consider the following multiple linear regression model:
y= βX+ u
Write down the Gauss Markov assumptions for the multiple linear regression model above. Find the variance of the estimator of the parameters β when all the assumptions are satisfied.
(8 marks)
Section B
(50 marks total - choose TWO of the following THREE questions)
Question B.1
a. A researcher is interested in identifying day of the week effects in the returns on Jo Malone London, a luxury candles company. Note that stocks are traded only five days a week. She collects a sample of returns on Jo Malone and a sample of returns on the FTSE100 index for the same time period. Then she creates five dummy variables, D1,t , D2,t , D3,t , D4,t , D5,t , one for each day of the week . D1,t takes value of one on Monday and a zero on any other day of the week and the other dummies are defined similarly for the other days of the week. Explain why the model
rt =α +β rtM + γ1D1t + γ 2D2t + γ3D3t + γ4D4t + γ5D5t + ut
suffers from perfect multicollinearity. Write down two different specifications of the model that allow for seasonality effects without causing perfect multicollinearity. Interpret the parameters of the dummy variables in both models.
(10 marks)
b. Discuss the problem of serial correlation in the multiple linear regression model. Which are its consequences on the OLS estimator? Can the estimator still be used? How can such a problem be remedied?
(10 marks)
c. In a multiple regression model
y = Xβ + u
define the consistency of an estimator. Discuss two possible situations that cause inconsistency in the OLS estimator in the model above.
(5 marks)
Question B.2
A researcher collects data on US investment rates (measured as gross investment divided by GDP) and interest rates (measured in percentage points). She wishes to estimate how sensitive investment rates are to interest rates by running a linear regression. If y is the investment rate and x is the interest rate, the features of her data are as follows:
N=22, = 5.227, = 0. 134, ∑ xt(2) , ∑ xt yt = 15.04 ∑ 2 = 0.011
a. Using the data above, compute the intercept and slope coefficients from a regression of investment rates on interest rates. Give an economic interpretation of your results.
(5 marks)
b. Write down the formulae for the standard errors of the OLS estimator of the slope and the intercept coefficients. Discuss how the sample size, the error variance and the sample variance of x influence the precision of the estimators. Compute the standard errors of the estimates and comment upon the estimates precision. Test the null hypothesis that the slope equals zero against the one-sided alternative that it is less than zero. Interpret your results.
(10 marks)
c. Compute and comment upon the R2 from the regression.
(10 marks)
Question B.3
In the multiple linear regression model
y = Xβ + u
a. Explain what a heteroscedasticity of the disturbances is. Derive the variance of the OLS estimator of the parameters under heteroscedasticity. Will it be bigger or smaller than under homoscedasticity? How can we obtain standard errors in the presence of heteroscedasticity in STATA or in EVIEWS (choose the software you prefer)?
(10 marks)
b. Discuss the problem of serial correlation of the disturbances. Propose a test for serial correlation clearly stating null and alternative hypotheses, auxiliary equation, test statistics and rejection region.
(15 marks)
2022-08-02