QUESTION A1 (15 marks)
(a) One of the most challenging concepts to master in this module is distinguishing between the stochastic error term and the residual. List three differences between the stochastic
error term and the residual (3)
(b) Explain in detail how Ordinary Least Squares (OLS) works in estimating the coefficients
of a linear regression model. (3)
(c) Demonstrate your understanding of the goodness of fit by referring to the total, explained, and residual sum of squares. (6)
(d) Explain the Gauss Markov Theorem and discuss the importance of this theorem in econometrics.
(3)
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QUESTION A2 (15 marks)
(a) Distinguish between cross-sectional, time series and panel data. Use relevant examples in your response (6)
(b) What is the difference between an estimator and an estimate? Provide examples of each.
(4)
(c) Build a regression model to estimate the gender wage gap in South Africa. What are the dependent and independent variables in your model? (5)
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QUESTION B1 (20 marks)
Student A has estimated the following function to explain interest rates (IRATE):
Variable Coefficient Standard error
of the coefficient Average value of the variable
Constant term -18.26 8.14
RGDP 0.084 0.0432 115
MST -0.0625 0.0062 2700
CPI 0.428 0.241 135
MAF 0.056 0.051 122
3
R-squared =0.45; Durbin-Watson statistic=0.15; n=65
The correlation coefficient rRGDP, MAF=0.85
F-value = 15.78
The variables are as follows:
IRATE: The interest rate is the dependent variable.
RGDP: Index of real gross domestic product at constant prices, 2015=100
MST: Money stock $billion
CPI: Index of consumer prices, 2015=100
MAF: Index of the volume of manufacturing production, 2015=100.
Assume that over the sampling period, the monetary authorities controlled the supply of money (MST), which affected the interest rate. Also, assume that the demand for money, in accordance with conventional economic theory, depends, amongst others, on the volume of economic activity, the general price level, and the interest rate.
Perform all statistical tests at the 5% significance level (unless stated otherwise).
(a) Hypothesise signs and state the appropriate null and alternative hypotheses for the coefficients based on theoretical considerations (provide reasons for your choice). Then, test the individual coefficients for statistical significance. Please present your
answers in table format. (8)
(b) Perform the F-test for the joint significance of coefficients in this model (4)
(c) Test, if possible, for multicollinearity, serial correlation, and heteroscedasticity. (5)
(d) Provide an overall evaluation of this regression model and suggest ways to improve
it. (3)
