Applied Econometrics (5AEC) Specimen Test PDF - The London Institute of Banking & Finance

FHEQ Level 5 APPLIED ECONOMETRICS (5AEC) Specimen Test 1 HOUR Test start time XX Test finish time XX The answers to exams should be input into the Brightspace quiz section via the ProctorFree student portal. INFORMATION FOR CANDIDATES 1. This question paper consists of 20 questions wh...

FHEQ Level 5 APPLIED ECONOMETRICS (5AEC) Specimen Test 1 HOUR Test start time XX Test finish time XX The answers to exams should be input into the Brightspace quiz section via the ProctorFree student portal. INFORMATION FOR CANDIDATES 1. This question paper consists of 20 questions which are mandatory. All questions are worth 5 marks. 2. You may use a scientific calculator, but it must not be programmable, nor have a wireless-communications capability, nor be capable of storing textual information. It must also not require a mains electricity supply. Calculators with any further functions are not allowed. 3. A formula sheet and present value tables are provided at the end of the question paper in the appendix. INSTRUCTIONS TO CANDIDATES 1. The guidance on how to sit and submit your online exams is now available in the assessment resources, please ensure to read through this before your upcoming exams. 2. Answer ALL questions. Answer all twenty questions. The following information refers to questions 1 to 10 A multiple linear regression model was calculated to determine the average hourly earnings of workers in a country for a particular period of time. The variables involved are 𝒂𝒉𝒆 Represents worker’s average hourly earnings in US Dollars per hour 𝒃𝒂𝒄𝒉𝒆𝒍𝒐𝒓 A dummy variable that takes the value 1 for bachelor and 0 for non-bachelor 𝒇𝒆𝒎𝒂𝒍𝒆 A dummy variable that takes the value 1 for female and 0 for male 𝒂𝒈𝒆 Represents worker’s age in years The result of the regression was Question 1 The standard error of the coefficient of the regressor 𝑎𝑔𝑒 is: a) 0.045 b) 22.187 c) 6.263 d) 1.96 (5 marks) Answer: 𝛽1 𝑡= 𝑠𝑒(𝛽1 ) 0.5313 11.788 = 𝑠𝑒(𝛽1 ) Page 2 of 9  𝑠𝑒(𝛽1 ) = 0.045 Question 2 The 95% confidence interval estimator for the coefficient of the regressor 𝑏𝑎𝑐ℎ𝑒𝑙𝑜𝑟 is: a) [9.58 , 10.10] b) [9.84 , 10.50] c) [9.33 , 10.36] d) [9.33 , 10.21] (5 marks) Answer: The 95% confidence interval estimator for the coefficient of the regressor 𝑏𝑎𝑐ℎ𝑒𝑙𝑜𝑟 is 9.8456 ± 1.96 × 0.262 [9.33 ,10.36] Question 3 Which of the following can cause the usual OLS 𝒕 statistics to be invalid, that is, not to have the 𝒕 distribution under 𝑯𝟎 ? a) Heteroscedasticity b) Including an unimportant explanatory variable. c) A sample correlation coefficient of 0.095 between two independent variables that are in the model. d) All of the above. (5 marks) Question 4 Which of the following is not a Gauss-Markov assumption of the multiple linear regression model? a) In the sample (and therefore in the population) none of the independent variables is constant and there are no exact linear relationships. b) We have a random sample of 𝑛 observations. c) The error term 𝑢 has an expected value of zero given any values of the independent variable. d) The error term 𝑢 has zero variance given any values of the explanatory variable (5 marks) Question 5 The correct interpretation of the coefficient for the regressor 𝑏𝑎𝑐ℎ𝑒𝑙𝑜𝑟 in the regression is a) An individual with bachelor’s degree is expected to earn US$ 26.2 more in average hourly earnings than individuals without bachelor's degree. b) An increase in one unit in the variable 𝑏𝑎𝑐ℎ𝑒𝑙𝑜𝑟𝑠 is expected to increase 9.84% in average hourly earnings. c) An individual with bachelor’s degree is expected to earn US$ 9.84 more in average hourly earnings than individuals without bachelor's degree.  d) The average hourly earnings for individuals with a bachelor's degree is US$ 9.84. (5 marks) Question 6 Suppose you wish to estimate the effect of age in a worker’s average hourly earnings. We believe that an increase in one year of age increases the average hourly earnings by a constant percentage. To estimate this relationship we should: a) Run a regression with log of age as independent variable and average hourly earnings as a dependent variable b) Run a regression with age as independent variable and log of average hourly earnings as a dependent variable c) Run a regression with age as independent variable and average hourly earnings as a dependent variable d) Run a regression with log of age as independent variable and log of average hourly earnings as a dependent variable (5 marks) Question 7 A low regression 𝑅 2 means that: a) The regression is bad b) There are other factors influencing the independent variable c) There are other important factors that influence the dependent variable d) The SSR is low relative to the total variation in 𝑌 (5 marks) Question 8 If multicollinearity is present in a model, you should: a) add an additional predictor to the model which is uncorrelated to the dependent variable b) remove highly correlated predictors from the model. c) keep predictors with high correlation but remove predictors with low correlation d) drop the intercept from the model specification. (5 marks) Question 9 A Jarque-Bera Test was performed on the residuals of the regression and was presented in the OLS regression results table above. The conclusion of the test is a) We can reject the null hypothesis that the residuals are normally distributed at a significance level of 5% b) We cannot reject the null hypothesis that the residuals are normally distributed at a significance level of 5% c) We can reject the null hypothesis that the residuals are heteroskedastic at a significance level of 5% d) We cannot reject the null hypothesis that the residuals are autocorrelated at a significance level of 5% (5 marks) Page 4 of 9 Solution: The Jarque-Bera statistic for the normality test of the regression residuals can be found at the bottom right corner of the summary. The Jarque-Bera value for the normality test is 11294.166 with a p-value of 0. This result suggests that we can reject the null hypothesis that the residuals are normally distributed at a significance level of 5%. Question 10 For a male individual with 36 years of age and bachelors degree the expected average hourly earnings is: a) $19.13 b) $31.02 c) $26.87 d) $17.03 (5 marks) Solution: The estimated regression equation is ̂ = 2.0448 + 9.8456 × 𝑏𝑎𝑐ℎ𝑒𝑙𝑜𝑟 − 4.1435 × 𝑓𝑒𝑚𝑎𝑙𝑒 + 0.5313 × 𝑎𝑔𝑒 𝑎ℎ𝑒 Therefore, ̂ = 2.0448 + 9.8456 × 1 − 4.1435 × 0 + 0.5313 × 36 = 31.02 𝑎ℎ𝑒 The following information refers to questions 11 to 20 A multiple linear regression model was calculated to determine the logarithm of the median salary for new law school graduates. The variables involved are 𝒍𝒐𝒈(𝒔𝒂𝒍𝒂𝒓𝒚) Log of the median salary for new law school graduates (salary measured in $1000s) 𝑳𝑺𝑨𝑻 Median LSAT score for the graduating class 𝑮𝑷𝑨 Median college GPA for the class 𝒍𝒐𝒈(𝒍𝒊𝒃𝒗𝒐𝒍) Log of the number of volumes in the law school library 𝒍𝒐𝒈(𝒄𝒐𝒔𝒕) Log of the annual cost of attending law school (cost measured in $1000s) 𝒓𝒂𝒏𝒌 Law school ranking (=1 is the best) 𝒇𝒂𝒄𝒖𝒍𝒕𝒚 The number of faculty in the law school The result of the regression is presented in the summary picture. Question 11 The correct interpretation of the coefficient for the regressor 𝑙𝑐𝑜𝑠𝑡 in the regression is a) An increase in $1,000 dollars in the cost of a law school is predicted to increase in approximately 4.9% the median salary of new law school graduates. b) A 1% increase in the cost of a law school is predicted to increase in approximately 4.9% the median salary of new law school graduates. c) An increase in $1,000 dollars in the cost of a law school is predicted to increase in approximately $49.4 the median salary of new law school graduates. d) A 1% increase in the cost of a law school is predicted to increase in approximately $49.4 the median salary of new law school graduates. (5 marks) Question 12 Omitted variable bias is a potential problem because it a) Creates perfect multicollinearity between regressors. b) Increases the standard error of the estimated effects. c) Prevents accurately estimating true marginal effects. d) Prevents the OLS method from achieving an estimation of the parameters. (5 marks) Page 6 of 9 Question 13 In the Python OLS summary, we have information on the following OLS hypothesis test conducted 𝐻0 : 𝛽1 = 𝛽2 = 𝛽3 = 𝛽4 = 𝛽5 = 0 𝑣𝑠 𝐻1 : 𝑎𝑡 𝑙𝑒𝑎𝑠𝑡 𝑜𝑛𝑒 𝛽𝑘 ≠ 0 𝑓𝑜𝑟 𝑘 = 1, … ,5 Based on the p-value for the F-Test in the Summary we can conclude that a) We cannot reject the null hypothesis that none of the variables have an impact in 𝑙𝑠𝑎𝑙𝑎𝑟𝑦 since the p-value is less than 5%. b) We can reject the null hypothesis that none of the variables have an impact in 𝑙𝑠𝑎𝑙𝑎𝑟𝑦 since the p-value is less than 5%. c) We cannot reject the null hypothesis that none of the variables have an impact in 𝑙𝑠𝑎𝑙𝑎𝑟𝑦 since the p-value is more than 5%. d) We can reject the null hypothesis that all of the variables have an impact in 𝑙𝑠𝑎𝑙𝑎𝑟𝑦 since the p-value is less than 5%. (5 marks) Solution: The F-statistic for this test can be found at the top right corner of the summary. The F- statistic value for this test is 83.63 with a p-value of 3.98 × 10−31, which is essentially zero. This result suggests that we can reject the null hypothesis that all the coefficients are zero and therefore that none of the independent variables impact the dependent variable. Question 14 Which of the following is true with respect to the coefficient of the regressor 𝐿𝑆𝐴𝑇 at a significance level of 5%? a) The variable is not significant at a 5% level since the t-statistic is equals to 1.13. b) The variable is significant at a 5% level since the t-statistic is greater than 1.96. c) The variable is not significant at a 5% level since the t-statistic is less than 1.96. d) The variable is not significant at a 5% level since the t-statistic is 0.223. (5 marks) Solution: The t-statistic is ̂1 𝛽 0.0068 𝑡= = = 1.13 ̂ 𝑠𝑒(𝛽1 ) 0.006 Since 𝑡 = 1.13 < |𝑡𝑐 | = 1.96 we cannot reject the null hypothesis that 𝛽1 = 0 and therefore, the coefficient for 𝐿𝑆𝐴𝑇 is not significant at a 5% level. Question 15. Which of the following is correct with respect to the fit of the regression a) If the adjusted 𝑅 2 of the regression is 0.823 whereas the adjusted 𝑅 2 of a regression which has 𝑓𝑎𝑐𝑢𝑙𝑡𝑦 as an additional regressor is 0.849, then including an additional regressor has improved the fit of the regression. b) The 𝑅 2 of the regression is 0.833 which implies that the logarithm of the cost of a law school alone explains 83.3% of the variation in the logarithm of the median salary of new law school graduates. c) The 𝑅 2 of the regression is 0.833 which implies that the regressors explain 83.3% of the variation in the median salary of new law school graduates. d) The adjusted 𝑅 2 of the regression is 0.823 whereas the 𝑅 2 of the regression is 0.833 which means that a multiple linear regression has not improved the fit of the regression. (5 marks) Solution: The adjusted 𝑅 2 is useful when comparing two models with the same dependent variable and different number of regressors. An increase in adjusted 𝑅 2 when adding a new regressor suggests that the fit of the regression has improved. When adjusted 𝑅 2 decreases by adding a new regressor, it suggests that the new regressor is statistically insignificant. Question 16 The picture below shows the Residual plot of regressing 𝑙𝑠𝑎𝑙𝑎𝑟𝑦 on 𝑙𝑐𝑜𝑠𝑡. What can be concluded from this diagnostic test? a) The fan shaped pattern of residuals suggest the presence of heteroskedasticity. b) The fan shaped pattern of residuals suggest the presence of homoskedasticity. c) Residuals are scattered around zero and therefore errors are likely to be homoscedastic. d) Residuals are scattered around zero and therefore the variables are likely to be uncorrelated. (5 marks) Page 8 of 9 Question 17 Which of the following characteristics does a normally distributed variable exhibit? a) 𝑀𝑒𝑎𝑛 = 0 and 𝑆𝑘𝑒𝑤𝑛𝑒𝑠𝑠 = 0 b) 𝑆𝑘𝑒𝑤𝑛𝑒𝑠𝑠 = 0 and 𝐾𝑢𝑟𝑡𝑜𝑠𝑖𝑠 = 0 c) 𝑆𝑘𝑒𝑤𝑛𝑒𝑠𝑠 = 0 and 𝐾𝑢𝑟𝑡𝑜𝑠𝑖𝑠 = 3 d) 𝑆𝑘𝑒𝑤𝑛𝑒𝑠𝑠 = 3 and 𝐾𝑢𝑟𝑡𝑜𝑠𝑖𝑠 = 4 (5 marks) Question 18 A Breusch-Pagan heteroskedasticity test was conducted for the regression and the result was a statistic 𝐹 = 2.81 with a p-value of 𝑝 = 0.03. The correct interpretation of this result is a) The null hypothesis of heteroskedasticity can be rejected at the 5% significance level. b) The null hypothesis of heteroskedasticity cannot be rejected at the 5% significance level. c) The null hypothesis of homoskedasticity cannot be rejected at the 5% significance level. d) The null hypothesis of homoskedasticity can be rejected at the 5% significance level. (5 marks) Question 19 Under which of the following, we say that errors are homoscedastic? a) If the random errors are normally distributed b) If the random errors are exogenous c) If the random errors are serially correlated d) If the conditional variance of the errors is constant (5 marks) Question 20 Which of the following statements is correct about testing joint hypothesis: a) The overall regression F-statistic tests the joint hypothesis that joint slope coefficients are different from 0. b) The 95% confident set for multiple coefficients is the set of values not rejected at the 5% confidence level by the F-Statistic for a test of joint hypothesis. c) The 95% confident set for multiple coefficients is the set of values rejected at the 5% confidence level by the F-Statistic for a test of joint hypothesis. d) To test the joint hypothesis about two or more coefficients we must look at their individual significance only. (5 marks)