7ECON001W Data Analysis Empirical Assignment Questions June 2025 | UoW

7ECON001W Submission Instructions

Only an electronic copy should be handed in via the Blackboard site of the module by 1 p.m. (13:00) UK time on July 9 2025. This copy will automatically be scanned through a text-matching system (designed to check for possible plagiarism and collusion).

To avoid a mark penalty for late submission, ensure you submit your coursework in time according to the deadline above. See the module handbook for details on mark penalisation for late submission and step-by-step online submission instructions.

The name and the registration number of the student should be clearly shown on the first page of the assignment.

7ECON001W General Instructions

This assignment is INDIVIDUAL.

Provide and explain all calculations and relevant EViews outputs.

Use a significance level of 5% for all tests.

Presentation is worth 10% of the total coursework marks —note that a good presentation requires clear and concise answers, avoiding redundant information.

Word limit: 3,000

The EA is worth 40% of the total module mark. A qualifying mark of a minimum of 40% is required in this piece of assessment to pass the module.

Question

The EViews file "Resit_EA_Data.wf1" in the Blackboard folder Assessment contains cross-sectional data on the logarithm of annual household expenditure on food eaten at home, LGFDHO, the logarithm of total annual household expenditure, LGEXP, and the logarithm of the number of persons in the household, LGSIZE, for a sample of 90 households in the 2005 Consumer Expenditure Survey.

Using this data set, answer all the following questions:

1. Regress the variable LGFDHO on variables LGEXP and LGSIZE (remember to include a constant in the model). [7 marks]

• Interpret the coefficient estimates of that regression, including the estimated intercept. Does the estimated intercept an economic meaning? Explain your answer.
• Perform tests for the statistical significance of the parameters of the independent variables using the critical value of the corresponding t-distribution and the test p-value. Provide an interpretation of the test results.

Questions 2 to 14. Below, refer to the Model in question 1:

2. Perform a joint significance test for the independent variables of the model using both the p-value and the critical value of the F-distribution. [6 marks]

• Comment on the goodness-of-fit of the model.
• What are the consequences of the results of this F-test, together with those of the t-tests (in question 1) for the specification of the model? Explain your answer.

3. Test the hypothesis that the variable LGEXP is one-third the effect of the variable LGSIZE on the variable LGFDHO. [8 marks]

• Use the command available in EViews to test for the corresponding coefficient restriction.
• Perform the test analytically, providing all steps to obtain the restricted model and the final test conclusion.
• Explain/interpret the test results.

4. Answer the subquestions below on multicollinearity analysis in the model. [8 marks]
 
Test for multicollinearity between variables LGEXP and LGSIZE using regression analysis. Explain your answer using EViews outputs.

Assuming that there is multicollinearity between those variables:

• Explain how you would resolve this problem using regression analysis. Explain your answer using EViews outputs.
•  What are the consequences of multicollinearity for the OLS estimator properties and its standard error?

5. Perform a graphical analysis to detect the presence of heteroscedasticity in the model using two different types of plots. [5 marks]

• Do you find evidence of heteroscedasticity?  
• Explain your answer using the information obtained from each type of plot.
• Explain the consequences of heteroscedasticity on the properties of the OLS estimator.

6. Perform a White test for heteroscedasticity. [7 marks]

• Explain and interpret the meaning of the null hypothesis of this test.
• Why is the White test preferred to the Breusch-Pagan test for heteroscedasticity? Explain your answer.
• Would the Goldfeld-Quandt test for heteroscedasticity provide more accurate results than the White test? Explain your answer.

7. Assume that there is heteroscedasticity of the form: σ2 = σ2 • (LGSIZEt)1/2. How would you resolve the problem of heteroscedasticity? Explain your answer analytically. [6 marks]

8. Estimate the model using White's autocorrelation and heteroscedasticity-consistent standard errors. [5 marks]

• Compare the results of that estimation (parameter estimates and their standard errors) with the estimation results obtained in question 1.
• When do we use White standard errors? Explain your answer.

9. Provide a graphical analysis of the residuals to detect the presence of autocorrelation using different types of plots. [5 marks]

• Do you find evidence of autocorrelation? Explain your answer using the information obtained from each type of plot.
• Explain the consequences of autocorrelation on the OLS estimator properties.

10. Test for autocorrelation in the residuals of the model using an appropriate procedure. What conclusion on the specification of the model could you extract from your results? Explain your answer. [6 marks]

11. Assuming that there is autocorrelation in the residuals of the model: [7 marks]

• Use EViews to perform the Cochrane-Orcutt (C-O) procedure to resolve autocorrelation of order 1. Comment on the results in the EViews output, estimates and standard errors concerning their counterparts in question 1, AR(1) coefficient and iterations to convergence.
• Explain analytically, step by step, the C-O procedure to resolve first-order autocorrelation in the model of question 1, assuming that the coefficient of autocorrelation in the residuals is unknown.

12. Perform a Box-Cox test for the model functional form (linear, semi-logarithmic and logarithmic). [8 marks]

13. Test the assumption of normality in the residuals of the selected model in question 12 by using the Jarque-Bera (JB) tests. Comment on the implications of your JB test results on the properties of the OLS estimator. [7 marks]

14. For what purpose could your model in this coursework be used by the director of a multinational chain of restaurants? [5 marks]

Exercise 1

The Excel file "SP500_Prices.xlsx" contains closing prices (in 8) {Pt}Tt=1 of the stocks constituents of the Standard and Poor's 500 (S&P500) index. All data series were downloaded from Datastream.

For the series randomly allocated to you (see surnames in the first row of the Excel sheet) answer the following questions:
 
1. Apply the Box and Jenkins methodology to select an appropriate specification for the conditional mean of the series. Include plots of the level of the series in each step, as well as the correlograms to show and illustrate your answers.
2. Test for ARCH effects in the residuals of your selected conditional mean model. Include and interpret the corresponding EViews output.

3. What is the difference between heteroscedasticity and ARCH? Use an example to explain your answer.

4. Answer both parts:

• Define ARIMA-GARCH-type specifications you know that may be appropriate to explain the conditional variance of your chosen series.
• Fit the ARIMA-GARCH-type models defined above. Interpret the results pointing to the main differences between the estimated models. Provide the corresponding EViews outputs.

5. Using the estimation results from question 4, answer both parts:

• Compare the goodness-of-fit of the models in the previous question. Select the most appropriate specification. Explain your answer using appropriate tests and statistics.
• Does your series return volatility present the "leverage effect"? Explain your answer using your estimation results from the previous question.

6. Using your selected model in question 5, calculate a one-day-ahead forecast of the conditional variance of the returns using an appropriate GARCH-type model under the normal distribution, as well as a 95% confidence interval for the conditional mean forecast.

7. Define VaR and calculate a one-day-ahead 1% Value-at-Risk forecast under Normal errors.

8. Explain the implications for regulatory capital of underestimating or overestimating VaR.

9. Do the residuals of the model estimated in question 4 come from a normal distribution? Perform an appropriate test to answer the question.

Notes: (1) Describe all tests in detail, step by step. (2) For each question, provide the relevant EViews outputs or/or plots.

Exercise 2

Consider the following model:
SLEEPi = βO + βTOTWRKi + β2EDUCi + β3AGEi + β4Y RSMARRi + ui

where

SLEEP = time spent sleeping by worker i (in minutes per week)
TOTWRK    = time spent working by worker i (in minutes per week) 
EDUC    = time invested in education by worker i (in years) 
AGE    = age of worker i (in years)
YRSMARR = years married of worker i

1. Perform a Goldfeld-Quandt (G-Q) test for heteroscedasticity in the residuals of the model above.

2. Why is the White test preferred to the Goldfeld-Quandt test for heteroscedasticity? Explain your answer.

3. Explain the rationale behind the ordinary least squares (OLS) estimation method in the context of a simple linear regression model for SLEEP versus TOTWRK. Explain your answer with the aid of an X-Y diagram, placing SLEEP in the Y-axis and TOTWRK in the X-axis. Note: You need to use equations together with explanations to answer this question. Also, there is no EViews output involved in the answer to this question.

4. Test the hypothesis that two extra years of age have the same effect as one extra year of education, on SLEEP.

5. Analyse whether variable Y RSMARR ought to be included in the model. Explain your answer referring to the EViews outputs used for your analysis.

Notes: (1) The EViews file "sleep.wf1" provides a dataset of 706 workers from the public and private sectors in the UK. (2) Describe the implementation of all tests in detail, step by step. (3) For each question, provide the relevant EViews outputs or/or plots.

Exercise 3

Consider the analysis of quarterly data, from 1980 to 2018, of the variables GDPt (income), CAPt (stock of capital) and LABt (stock of labour).

1. Employ the Engle and Granger (EG) procedure to find out whether the model below constitutes a cointegrating relationship.

GDPt = rO + r1CAPt + r2LABt + ot
 
2. Explain the consequences of the result of the EG test for the reliability of the regression above.

3. Specify the equation of the error correction model (ECM) using the model above as an example. How can one interpret the sign and magnitude of this ECM error correction coefficient? You should use equations to illustrate your answer.

Notes (1) The dataset for this exercise is "output.wf1". (2) Describe the implementation of all tests in detail, step by step. (3) For each test, provide the relevant EViews outputs or/or plots.