UNIVERSITY OF BRISTOL
Examination for the Degree of M.Sc. in Economics, Finance and Management Economics, Accounting and Finance and Accounting, Finance and Management
Exam January 2019
ECONOMICS PAPER 47
QUANTITATIVE METHODS FOR ECONOMICS, FINANCE AND MANAGEMENT (Module No. ECONM1012)
Time allowed: TWO AND A HALF hours Answer ALL questions from Section A and Section B.
Should you attempt a question and do not wish it to be marked, delete it clearly.
Statistical tables are attached. Approved electronic calculators are permitted.
Intermediate calculations must be shown. (Maximum marks are shown in parentheses)
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TURN OVER
̅ ̅𝑎𝑐𝑡 ̅ ̅𝑎𝑐𝑡
− 𝜇𝑌,0|].
b. Pr𝐻0 = [|𝑌 − 𝜇𝑌,0| > |𝑌
c. Pr(𝑧 > 1.96).
d. Pr𝐻0 = [|𝑌 − 𝜇𝑌,0| < |𝑌 QUESTION 3. The size of the test
− 𝜇𝑌,0|].
SECTION A
For questions 1-10 write clearly in your answer book the number of the question and the letter (a, b, c, or d) which you think corresponds to the correct answer. In each case write down only ONE letter.
You are not asked to explain your answers to questions 1-10.
You’ll be given +2 for a correct answer, 0 for an incorrect answer and 0, for an unanswered question.
QUESTION 1. The sample average is a random variable and
a. is a single number and as a result cannot have a distribution.
b. has a probability distribution called its sampling distribution.
c. has a probability distribution called the standard normal distribution.
d. has a probability distribution that is the same as for 𝑌 , ... , 𝑌 i.i.d. variables. 1𝑛
QUESTION 2. The p-value is defined as follows:
a. 𝑝 = 0.05
a. is the probability of committing a type I error. b. is the same as the sample size.
c. is always equal to (1-the power of the test). d. can be greater than 1 in extreme examples.
QUESTION 4. The central limit theorem
a. states conditions under which a variable involving the sum of 𝑌 , ... , 𝑌 i.i.d. variables
becomes the standard normal distribution.
̅
b. postulates that the sample mean,Y, is a consistent estimator of the population mean 𝜇𝑌.
c. only holds in the presence of the law of large numbers.
d. states conditions under which a variable involving the sum of 𝑌 , ... , 𝑌 i.i.d. variables
becomes the Student t distribution.
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1𝑛
1𝑛
QUESTION 5. Interpreting the intercept in a simple regression function is
a. reasonable because under certain conditions the estimator is BLUE.
b. not reasonable because economists are interested in the effect of a change in the
explanatory variables on the dependent variable.
c. not reasonable because you never observe values of the explanatory variables around
the origin.
d. reasonable if your sample contains values of the explanatory variables around the origin.
̂
QUESTION 6. When the estimated slope coefficient in the simple regression model, 𝛽1, is
zero, then
a. 0 < 𝑅2 < 1.
2̅ b.𝑅 =𝑌.
c. 𝑅2 = 0
d. 𝑅2 > (SSR/TSS).
QUESTION 7. When there are omitted variables in a regression, which are determinant of the dependent variable, then
a. you cannot measure the effect of the omitted variable(s), but the estimator of your included variable(s) is (are) unaffected.
b. this has no effect on the estimator of your included variable(s) because the other variable(s) is (are) not included.
c. this will always bias the OLS estimator of the included variable(s).
d. the OLS estimator is biased if the omitted variable(s) is (are) correlated with the included
variable(s).
QUESTION 8. The binary variable interaction regression
a. can only be applied when there are two binary variables, but not three or more.
b. is the same as testing for differences in means.
c. cannot be used with logarithmic regression functions because the ln(0) is not defined.
d. allows the effect of changing one of the binary independent variables to depend on the
value of the other binary variable.
QUESTION 9. When testing joint hypothesis, you should
a. use t-statistics for each hypothesis and reject the null hypothesis if all of the restrictions fail.
b. use the F-statistic and reject all the hypotheses if the statistic exceeds the critical value.
c. use t-statistics for each hypothesis and reject the null hypothesis once the statistic
exceeds the critical value for a single hypothesis.
d. use the F-statistic and reject at least one of the hypotheses if the statistic exceeds the
critical value.
QUESTION10.Intheregressionmodel𝑌=𝛽 +𝛽𝑋+𝛽𝐷+𝛽(𝑋×𝐷)+𝑢,whereXis
𝑖01𝑖2𝑖3𝑖𝑖𝑖
a continuous variable and D is a binary variable, to test that the two regressions are identical, you must use the
a. t-statistic separately for 𝛽2 = 0, 𝛽3 = 0.
b. F-statistic for the joint hypothesis that 𝛽0 = 0, 𝛽1 = 0. c. t-statistic separately for 𝛽3 = 0.
d. F-statistic for the joint hypothesis that 𝛽2 = 0, 𝛽3 = 0.
TURN OVER
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SECTION B
QUESTION 11. The accompanying table shows the joint distribution between the change of the unemployment rate in an election year, ∆u, and the share of the candidate of the incumbent party since 1928. You think of this data as a population which you want to describe, rather than a sample from which you want to infer behaviour of a larger population.
Joint Distribution of Unemployment Rate Change and Incumbent Party’s Vote Share in Total Vote Cast for the Two Major-Party Candidates, 1928-2013.
(Incumbent – 50%) > 0 (Y = 0)
(Incumbent – 50%) ≤ 0 (Y = 1)
T otal
∆u > 0 (X = 0)
0.053
0.211
0.264
∆u ≤ 0 (X = 1)
0.579
0.157
0.736
T otal
0.632
0.368
1.00
a. Compute and interpret E(Y)andE(X). (4 marks)
b. Calculate E(Y | X = 1) and E(Y | X = 0) . Did you expect these to be very different?
Explain. (6 marks)
c. What is the probability that the unemployment rate increases in an election year?
(2 marks)
d. Conditional on the unemployment rate decreasing, what is the probability that an
incumbent will lose the election? (4 marks)
e. Show what the joint distribution would look like if the two variables were independent. (4 marks)
Note: The “incumbent” party is the current holder of a political office.
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QUESTION 12. Adult males are taller, on average, than adult females. Visiting two recent Youth Football Organisation under 12 years old (U12) football matches on a Saturday, you do not observe an obvious difference in the height of boys and girls of that age. You suggest to your little sister that she collects data on height and gender of children in the 4th and 6th grade as part of her science project. The following table shows her findings.
Height of young Boys and Girls, Grades 4-6 (inches)
a. Let your null hypothesis be that there is no difference in height of females and males at this age level. Write (formally) both the null and the alternative hypotheses. (4 marks)
b. Find the difference in height and the standard error of the difference. (6 marks)
c. Calculate a 95% confidence interval for the difference in height. (4 marks)
d. Is the difference between the two means statistically significant at the 1% level? Which critical value did you use? Why would this number be smaller if you had assumed a one- sided alternative hypothesis? Provide the intuition behind this. (6 marks)
Boys
Girls
̅ 𝑌
𝐵𝑜𝑦𝑠
𝑠𝐵𝑜𝑦𝑠
𝑛𝐵𝑜𝑦𝑠
̅ 𝑌
𝐺𝑖𝑟𝑙𝑠
𝑠𝐺𝑖𝑟𝑙𝑠
𝑛𝐺𝑖𝑟𝑙𝑠
57.8
3.9
55
58.4
4.2
57
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TURN OVER
QUESTION 13. You have obtained a sub-sample of 1744 individuals from the Current Population Survey (CPS) and are interested in the relationship between weekly earnings and age. The regression, using heteroskedasticity-robust standard errors, yield the following result:
̂2 𝐸𝑎𝑟𝑛𝑖 = 239.16 + 5.20𝐴𝑔𝑒𝑖 𝑅
= 0.05 𝑆𝐸𝑅 = 287.21 Where 𝐸𝑎𝑟𝑛 and 𝐴𝑔𝑒 are measured in dollars and years respectively.
a. Interpret the estimated coefficients and explain the meaning of the 𝑅2 here. (4 marks)
b. Is the relationship between 𝐴𝑔𝑒 and 𝐸𝑎𝑟𝑛 statistically significant? Explain. (3 marks)
c. Construct a 95% confidence interval for both the slope and the intercept. (3 marks)
d. The variance of the error term and the variance of the dependent variable are related.
Given the distribution of earnings, do you think it is plausible that the distribution of errors
is normal? Explain your answer. (4 marks)
e. Why should age matter in the determination of earnings? Do the results suggest that there is a guarantee for earnings to rise for everyone as they become older? Do you think that the relationship between age and earnings is linear? Explain your answers.
(6 marks)
(20.24) (0.57)
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QUESTION 14. A dataset contains information from a random sample of high school seniors interviewed in 1980 and re-interviewed in 1986. A researcher is interested to investigate the relationship between the number of completed years of education for young adults and the distance from each student’s high school to the nearest four-year college. (Proximity to college lowers the cost of education, so the students who live closer to a four-year college should, on average, complete more years of higher education). She estimates the following model:
Source | SS df MS ————-+—————————— Model | 93.0256754 1 93.0256754 Residual | 12394.3568 3794 3.266831 ————-+—————————— Total | 12487.3825 3795 3.29048287
Number of obs = F( 1, 3794) = Prob>F = R-squared = Adj R-squared = Root MSE =
3796
[xxx]
0.0000
[xxx]
0.0072
1.8074
—————————————————————————— yrsed | Coef. Std. Err. t P>|t| [95% Conf. Interval] ————-+—————————————————————- dist | -.0733727 .0137498 [xxx] 0.000 -.1003304 -.046415 _cons| 13.95586 .0377241 369.95 0.000 13.88189 14.02982 ——————————————————————————
where the variables yrsed and dist are years of completed education and the distance to the nearest college measured in tens of miles (for example, dist=2 means that the distance is 20 miles), respectively. The homoskedasticity-only standard errors are given in the regression results.
a. Examine the table of output provided above and complete the missing information [xxx]. Give the formulae for them and write the answers in your book. (6 marks)
b. Give an economic interpretation of the coefficients in this model. Does distance to college is an important determinant of years of completed education? (4 marks)
c. Theregressionabovewasestimatedagain,butthistimeitwasincludedsomeadditional regressors to control for characteristics of the student, the student’s family, and the local labour market. The results are
̂
𝑦𝑟𝑠𝑒𝑑𝑖 = 8.83 + −0.03𝑑𝑖𝑠𝑡𝑖 − 0.09𝑏𝑦𝑡𝑒𝑠𝑡𝑖 + 0.15𝑓𝑒𝑚𝑖 + 0.37𝑏𝑙𝑎𝑐𝑘𝑖 + 0.40𝐻𝑖𝑠𝑝𝑖
𝑅2 = 0.28
(0.25) (0.01) (0.00) (0.05) (0.07) (0.08)
+ 0.40𝑖𝑛𝑐𝑖 + 0.15𝑜𝑤𝑛h𝑖 + 0.70𝑑𝑎𝑑𝑐𝑜𝑙𝑖 + 0.02𝑐𝑢𝑒80𝑖 − 0.05𝑠𝑡h𝑤80𝑖 (0.06) (0.07) (0.07) (0.01) (0.02)
𝑆𝐸𝑅 = 1.54
where bytest is the based year composite test, fem is a binary variable that equals 1 if the individual is female and 0 if the individual is male, black is a binary variable that equals 1 if the individual is black and 0 otherwise, Hisp is a binary variable that equals 1 if the individual is Hispanic and 0 otherwise, inc is a binary variable equals to 1 if the family income is $25,000 or less and 0 otherwise, ownh is a binary variable that equals 1 if the family owns home and zero otherwise, dadcol is a binary variable equals 1 if the individual’s father is a college graduate and 0 otherwise, cue80 is the county unemployment rate, and sthw80 is the state hourly wage in 1980.
What is the estimated effect of dist on yrsed? Is the estimated effect of dist on yrsed in this regression substantially different from the regression in (a)? Based on this, does the regression in (a) seem to suffer from important omitted variable bias? Explain. (6 marks)
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d. It has been argued that, controlling for other factors, blacks and Hispanic complete more college than whites. Is this consistent with the regression results in part (c)? Explain.
END OF EXAM
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(4 marks)