ECON339
Applied Financial Modelling
Mid-Semester Examination Paper
Spring 2022
Q1. Briefly describe the criterion used to obtain the ordinary least square estimator. [2]
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The model must be linear in the parameters.The Gauss-Markov theorem is applied and the estimator for ols is the best linear unbiased estimate (BLUE).
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Q2. When estimating a regression in a sample why is a large sample observations preferred to a small sample? [2]
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This means that the estimates will converge to their true values when the sample size is larger.
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Q3. Why is an efficient estimator a desirable property of the OLS estimator? [2]
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When the estimate is valid and can minimise the probability of it being far from the true value.
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Q4. State the assumption(s) under the classical linear regression model giving rise to a biased standard error of the coefficient estimates when violated. [2]
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The bias is due to the omission of any of the variables associated with the dependent and independent variables.
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Tt = a + bTM,t + ut (1)
Tt = c + dTM,t + evolt + vt (2)
where Tt is stock returns, TM,t is market returns, and volt is market volatility. State the null hypothesis if regression (1) is nested in regression (2). [2]
Q6. Holding other things constant, what is the effect of (a) sample size and (b) variation in x on the variance of the OLS estimator? [2]
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a ：An increase in sample size will lead to a decrease in the OLS estimator.
b：An increase in variation in x will result in an increase in the OLS estimator.
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Use the following information to answer Q7-Q9.
A researcher runs the following regression with the Eviews output presented below.
nettfa = b0 + b1 inc + b2 age + b3marr + b4male + e (3)
where
nettfa = the net financial wealth (measured in $’000)
inc = income
age = the age of the respondent
marr = a dummy variable equals 1 if the respondent is married and 0 otherwise. male = a dummy variable equals 1 if the respondent is male and 0 otherwise.
Dependent Variable: NETTFA
Method: Least Squares
Date: 08/23/22 Time: 19:06
Sample: 1 9275
Included observations: 9275
Q7. Interpret the coefficient of age. [2]
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Net financial wealth increases by 1.041951 * 1000 per age increase.
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Q8.State the independent variable whose estimate is not statistically significant at the 5% significance level. [2]
Q9. On average is there any gendre bias in the net financial wealth in the sample? [2]
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There are biases and men have more wealth
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Use the following information to answer Q10-Q12.
The researcher estimated a log-log regression and the output is reported below:
log (nettfa) = b0 + b1 log (inc) + b2 age + b3marr + b4male + e (4)
Dependent Variable: LNETTFA
Method: Least Squares
Date: 08/23/22 Time: 19:04
Sample: 1 9275
Included observations: 6029
Q10. Between equations (3) and (4), which model do you prefer? Explain. [2]
[Hint: the included observations in regression 4 are far lesser than the sample in regression 3]
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equations (4) Because in (4) the square of r and the square of the adjusted r are higher
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Q11. Interpret the coefficient of log(inc) . [2]
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Net financial wealth increases by $1,898 with every $1,000 increase in income.
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Q12. Interpret the coefficient of marr . [2]
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For each unit increase in marr ，nettfa will decrease by 0.31% .
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Use the following information to answer Q13-Q14.
The researcher performed diagnostic tests on the residuals of regression (3).
Breusch-Godfrey Serial Correlation LM Test:
Null hypothesis: No serial correlation at up to 2 lags
Q13. Based on the Breusch and Godfrey test, what is the order of the lag of the serial correlation in the null hypothesis? [2]
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Second-order autocorrelation.
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Q14. What can you infer from the Breusch and Godfrey test results? [2]
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There is an autocorrelation problem because the p-value is not significant and reject Null hypothesis
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Use the information below to answer Q15 to Q17.
The researcher is interested in a nonlinear relationship between nettfa and age. The squared of age (denoted agesq) is incorporated in regression (3) and the regression output is shown below.
nettfa = b0 + b1 inc + b2 age + b3 age2 + b4marr + b5male + e (5)
Dependent Variable: NETTFA
Method: Least Squares
Date: 08/23/22 Time: 20:14
Sample: 1 9275
Included observations: 9275
Q15. Between models (3) and (5), which is the preferred model? Explain. [2]
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I chose 3 because 3 has fewer independent variables than 5 and they are significantly correlated
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Q16. At what age is the net financial wealth maximised? Show your working. [2]
Q17. State the name of the test that you can perform. to determine whether a linear regression or a nonlinear regression is a better fit for the data. [2]
Use the information below to answer Q18 to Q20.
The researcher performed a test for heteroskedasticity on residuals of equation (3). The table below shows the results.
Heteroskedasticity Test: White
Null hypothesis: Homoskedasticity
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 08/23/22 Time: 20:24
Sample: 1 9275
Included observations: 9275
Q18. What can you infer from the White test result? [2]
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There is no heteroscedasticity.
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Q19. Which property of the OLS estimator is violated based on the White test result? [2]
Q20. State an alternative method of estimating regression (3) that will address the concern of Q19. [2]
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Weight Least Square （WLS)
Replacing the original model with a logarithmic model
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