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MGDI60301T
1/10
24 Hours
THE UNIVERSITY OF MANCHESTER
RESEARCH SKILLS FOR ECONOMIC DEVELOPMENT 1 (QUANTITATIVE METHODS)
26
th January – 27
th January 2023
14:00 (2pm) – 14:00 (2pm) UK Time
Answer ALL questions from Part A and ONLY ONE question from Part B.
Note:
1. Steps and calculations involved in arriving at the final answer or solution must be typed
and submitted through the Turnitin in Blackboard.
2. Scanned copy of answers or solutions are NOT allowed and would NOT be marked
Please use only the Statistical Tables provided on pages 8/10, 9/10 & 10/10
MGDI60301T
2/10
PART A: Answer ALL the FIVE questions in this Section.
1. For nations listed in the Human Development Report, the:
i. correlation between percentage of people using Internet and per capita gross domestic
product (GDP, a summary description of a nation’s wealth), is 0.888;
ii. correlation between percentage of people using Internet and percentage using mobile
phones is 0.818;
iii. correlation between percentage of people using Internet and literacy rate is 0.669;
iv. correlation between percentage of people using Internet and fertility rate (the mean number
of children per adult woman) is -0.551; and
v. correlation between percentage of people using Internet and per capita emissions of carbon
dioxide is 0.680.
a. Using the correlation coefficient between Internet use and GDP, interpret the
association between Internet use and GDP.
[3 marks]
b. Using the correlation coefficient between Internet use and fertility rate, interpret
the association between Internet use and fertility rate.
[3 marks]
c. For data on nations in the Human Development Report, we want to describe
whether the percentage of people using the Internet is strongly associated with
per capita GDP or with the fertility rate. Can we compare the slopes of GDP and
fertility rate when, GDP and fertility rate, each predict Internet use in separate
regression equations If YES, explain or if NO, explain.
[5 marks]
2. In regression analysis, which of the following statements must be CORRECT and which must be
INCORRECT Explain your answer.
a. 1
2 = 2
2 = 0.8 and
2 1.01 [2 marks]
b. The correlation between 0.10 . [2 marks]
c. For every F test, there is an equivalent test using t distribution. [2 marks]
d. When | β1| > |β2| in a multiple regression prediction equation, we can conclude that x1 has
stronger effect than x2 on y. Where | β1| and |β2| are absolute values of β1 and β2.
[2 marks]
e. Suppose = 31.3 + 0.15 1 0.05 2 0.002 1 2 , with 1 and 2 taking values
between 0 and 100. Then, since the coefficients of 1 2 is so small compared to the
coefficients of 1 and 2, we can conclude that the amount of interaction is insignificant.
[2 marks]
f. The F statistic for testing that all the regression coefficients equal zero has p-value < 0.05, but none of the individual t tests have p-value < 0.05. [2 marks] g. The F test for comparing a complete model to a reduced model can be used to test whether Model 1: = + 1 1 + 2 2 gives a significantly better fit than Model 2: = + 1 1 + 2 3 [2 marks] MGDI60301T 3/10 3. For a test of H0: μ = 0 against H1: μ ≠ 0, n = 1500, t-statistic = 0.92, where n = sample size. Where H0 is null hypothesis and H1 is alternative hypothesis. a. Calculate the p-value and interpret its value. [5 marks] b. Suppose t = -3.60 rather than 0.92. Calculate the p-value for t = -3.60. [2 marks] c. Does the result in part 3b provide stronger, or weaker, evidence against the null hypothesis Explain your answer. [3 marks] 4. The p-value for a test about a mean with sample size (n) = 31 is equal to 0.01 (i.e., p-value = 0.01). a. Find the critical value of t-statistic that has p-value = 0.01 for the following alternative hypothesis: i. H1: μ ≠ 0 ii. H1: μ > 0
iii. H1: μ < 0 [6 marks] b. Does the p-value of 0.01 in 4a provide strong or weaker evidence against the null hypothesis (H0) than p-value = 0.001 Explain. [4 marks] 5. Consider the following model without any regressors. = 1 + , Where the dependent variable Yi is child mortality. a. How would you obtain an estimate of 1 Explain your answer. [2 marks] b. What is the meaning of the estimated value of 1 [2 marks] c. Does the estimated value make sense Explain your answer. [1 mark] Please continue to Part B on the next page. MGDI60301T 4/10 PART B: Answer ONLY ONE question (either 1, or 2a & 2b) from this Section. 1. Table 1 below shows regression results of average hourly wage regressed on gender and other variables using a US Household Survey. The following variables are defined as follows: Wage = average hourly wage Female = binary variable (1 if female, 0 if male) Non-white = binary variable (1 if non-white, 0 otherwise) Union = binary variable (1 if in a union job, 0 otherwise) Education = education level measured in years of schooling Experience = work experience measured in years Table 1 Dependent variable: average hourly wage Regressor Coefficients (SE) Female (X1) -3.07*** (0.36) Non-white (X2) -1.57*** (0.51) Union (X3) 1.10** (0.51) Education (X4) 1.37*** (0.07) Experience (X5) 0.17*** (0.02) Constant (β0) -7.18*** (1.06) Summary Statistics and joint Tests F-statistics 122.61 SER 6.51 R 2 0.32 n 1289 Notes: Numbers in parentheses (i.e. brackets) are heteroskedasticity-robust standard errors (SE) *** (1%) indicate the statistical significance of the coefficients. ** (5%) indicate the statistical significance of the coefficients. Earnings are measured in US $ Please continue on the next page. MGDI60301T 5/10 Using the regression results from the Table 1 above: a. State the population regression equation. [2 marks] b. Suppose you want to test the hypothesis that the true population regression coefficient of the education variable is 1. How would you test this hypothesis at 1% significance level Show all the necessary steps and calculations. [9 marks] c. Would you reject or not reject the hypothesis that the true Union regression coefficient is 1 Show all the necessary steps and calculations. [9 marks] d. Interpret: i. The estimated coefficient of Education (X4) [4 marks] ii. The estimated coefficient of Female (X1) [4 marks] e. Can you take the logs of the nominal variables, such as gender, race and union status Why or why not Explain your answer. [6 marks] f. Discuss Five Control Variables that could be included in the model. [10 marks] g. Would you add the age of the worker as an explanatory variable to the model Why or why not Explain your answer. [6 marks] 2a. Suppose you have been hired by Union that wants to convince workers in clothing firms that joining the union will improve their well-being. As your first assignment, your manager asks you to build a model of wages for workers clothing firms that measures the impact of union membership on those wages. Your first equation (robust standard errors in parentheses) is: = 11.40 + 0.30 + 0.003 2 + 1.00 + 1.20 -------------------------------------2a. (0.100) (0.002) (0.200) (1.000) 2 = 0.25, = 34 Where: = the hourly wage (in dollars) of the i th worker = the age of the i th worker = the number of years of education of the i th worker = the dummy variable = 1 if the i th worker is a union member, 0 otherwise. Please continue on the next page. MGDI60301T 6/10 i. Examine the regression equation 2a. How do the signs and significance of the coefficients (i.e., coefficients of , 2 , , ) compare with your expectations [5 marks] ii. Interpret the causal effect of A 2 on wages. [5 marks] iii. Does inclusion of A and A 2 violate Classical Assumption 4 of no perfect collinearity between two independent variables Explain your answer. [4 marks] iv. Do you think in equation 2a, log(Wi) should have been used as dependent variable instead of Wi Why or why not Explain your answer. [5 marks] v. Even though we have been told not analyse the value of intercept, is -￡11.40 not too low to ignore Discuss what should be done to correct this problem [2 marks] vi. On the basis of regression equation 2a, should workers be convinced that joining the Union will improve their well-being Why or why not Explain your answer. [4 marks] 2b. A recent study of the salaries of primary school teachers in a small school district in Northern California came up with the following estimated regression equation (robust standard in parentheses). = 10.5 0.006 + 0.002 + 0.790 + 0.020 , -----------------------2b.1 (0.0612) (0.0008) (0.3798) (0.0040) 2 = 0.866, = 25 Where: lnSal = log of salary of a teacher emp = the years that a teacher has worked in the school district units = the units of graduate work completed by a teacher lang = a dummy variable equal to 1 if a teacher speaks at least two languages exp = the total years of teaching experience of a teacher. a. i. What is the functional form of equation 2b.1 [2 marks] ii. Does the functional form of equation 2b.1 seem appropriate Explain your answer. [3 marks] Please continue on the next page MGDI60301T 7/10 b. What econometric problems (out of irrelevant variable, omitted variables, and multicollinearity) does the equation 2b.1 appear to have Explain your answer. [4 marks] c. Suppose that you are now told that the simple correction coefficient between emp and exp is 0.89 and that the variance inflation factors (VIFs) for emp and exp are both just a little over 10. Does this change your answer to part b above Explain your answer. [4 marks] d. What solution for the problem you identified in c do you recommend Explain your answer. [4 marks] e. If you drop emp from the regression equation 2b.1, the estimated equation becomes equation 2b.2. i. Use our four specification criteria (i.e., Theory, t-test, R 2 , and Bias) explaining each criterion to decide whether you prefer equation 2b.1 or equation 2b.2. Which equation do you prefer and why Explain your answer. [8 marks] = 10.5 + 0.002 + 0.800 + 0.015 , --------------------------------------2b.2 (2.47) (2.09) (8.65) 2 = 0.871, = 25 (Note: in equation 2b.2, t-statistics in parentheses). END OF QUESTIONS Note: Statistical Tables are on the next pages MGDI60301T 8/10 Appendix: Statistical Tables (Copyright 2009 South-Western/Cengage Learning) MGDI60301T 9/10 MGDI60301T 10/10