POLYTECHNIC OF NAMIBIA SCHOOL OF MANAGEMENT SCIENCES DEPARTMENT OF ACCOUNTING, ECONOMICS AND FINANCE ECONOMETRICS. Mr.

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1 POLYTECHNIC OF NAMIBIA SCHOOL OF MANAGEMENT SCIENCES DEPARTMENT OF ACCOUNTING, ECONOMICS AND FINANCE COURSE: COURSE CODE: ECONOMETRICS ECM 312S DATE: NOVEMBER 2014 MARKS: 100 TIME: 3 HOURS NOVEMBER EXAMINATION: QUESTION PAPER Examiner: Moderator: Mr. Muine Samahiya Dr. Blessing Chiripanhura INSTRUCTIONS: 1. There are 4 questions in this paper 2. Candidates must answer All the Questions 3. Candidates are allowed to use a calculator 4. Write clearly and legibly 5. This paper is applicable to full-time, part-time and distance students

2 QUESTION 1 [44] 1.1 Assume that X, the daily sale of bread in a bakery, follows a normal distribution with a mean of JJ = 70 loaves and variance,y = 9, that is X-N(J-Ix, u/). (a) What are the properties of the normal distribution? [5] (b) What is the probability that on any given day the sale of bread is greater than 75? Use Table A.1 to answer this question. [5] 1.2 Given a two-variable model: z, = rr 0 + rr 1 P, +!li a) State the Sample Regression Function [1] b) Derive the first least squares equation. Show all the steps. [7] 1.3 A researcher collected the following information on labour-hours (X) and output (Y). Use a table to answer the questions below. Labour hours (X) a) Estimate the regression line from the given sample observations. [20] b) Compute the standard error of the regression (SER). [4] c) On the basis of the SER you computed in (b) above, is the regression model a good fit? Explain. [2] QUESTION 2 [20] 2.1 The manager of MS Fashion House wants to know whether average monthly salary is different for males and females in her firm. She obtains data on monthly salary (in hundreds of N$) and experience (in months) for each of the 9 employees. She runs the following regression model in Microsoft Excel and obtains the results below: Where S = monthly salary, EX = experience in months, 0 = dummy variable for gender (0 = 0 if male and 0 =1 if female) and u =error term. s, = D EX, D *EX, (0.000) (0.1968) (0.000) (0.839) Note: numbers in parentheses are p-values. a) What is the average salary for a male employee holding experience constant? [ 1] b) What is the average salary for a female employee holding experience constant? [1] c) Depict your answer in a) and b) above in a graph [6] 2

3 d) What is the predicted average monthly salary for a female employee with 6 months of experience? [2] e) Is there a statistical difference in monthly salary in this particular firm? Explain. [2] 2.2 Mr. Samahiya is convinced that there was a structural break in the relationship between savings and income in 2009 in Namibia due to the World Financial Crisis from 2007 to He collects data on the two variables from 1980 to 2013 and runs a regression in Microsoft Excel and obtained the following results. Both savings and income are measured in natural logarithms. D= 0: 1980 to 2008, D = 1: 2009 to =dummy variable, Log= logarithms, Inc= Income, Adf" rnbm ウアセ M]@ PNUSXLM ヲセウ M エ ゥウエヲ ZG[Z[M , F p-value = a) Test for a structural break in Namibia in 2009 to validate Mr. Samahiya's claim. [6] b) What is the interpretation of the coefficient of Log inc? [2] QUESTION 3 [20] 3.1 Assume we have Z; = a 0 + a 1 P; + a 2 Y; +!1; and P; = 4Y; a) Explain why the model cannot be estimated. Show all your calculations. [5] b) What is meant a "dummy variable trap"? [3] 3.2 Given the Eviews regression output below, answer the questions that follow Dependent Variable: M2 Method: Least Squares Included observations: 21 Variable Coefficient Std. Error t-statistic Prob. INFR GDP ,5407 BR ,0000 c , ,0000 R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) 0, Note: M2 =broad money supply, INFR = infiation rate, GOP= real GOP growth rate, BR =bank rate 3

4 Evaluate the preceding model in terms of: a) R 2 [2] b) Autocorrelation [5] c) Overall significance of the model (use 1% significance level) [5] QUESTION 4: [15] 4.1 The output below shows Augmented Dickey-Fuller Test results on Namibia's consumer price index (CPI). NAMIBIA'S CONSUMER PRICE INDEX Null Hypothesis: CPI NAhas a unit root Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=9) Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level *MacKinnon (1996) one-sided p-values. t-statistic Prob.* (a) Explain the meaning of the following terms: [6] i. Stationary variable ii. Autoregressive models iii. Co-integration (b) Critically analyse the outputs on Namibia's consumer price index (CPI), presented above and provide a convincing explanation of how an econometrician can detect whether or not unit roots are present in the data. [5] (c) Explain what an econometrician should do in order to make data that contain unit roots stationary. [4] TOTAL MARKS =

5 @ セi ' STATISTICAL TABLES 1 TABLE A.1 Cumulative Standardized Normal Distribution A(z) is the integral of the standardized normal distribution from -"'to z (in other words, the area under the curve to the left of z). It gives the probability of a normal random variable not A(z) being more than z standard deviations above its / mean. Values of z of particular importance: z z A(z) Lower limit of right 5% tail Lower limit of right 2.5% tail Lower limit of right 1% tail Lower limit of right 0.5% tail Lower limit of right 0.1% tail Lower limit of right 0.05% tail z