ECOM5000 - Introductory Econometrics Data Analysis Project

Assignment Task

Suppose that you have a summer internship with one of the WA state government offices and your supervisor have asked you to model the gross value added (GVA) of the mining sector in Australia. Using quarterly data over the period between the 1st quarter of 1975 and the 4th quarter of 2015 (included in the data file used for modules 9‐10 tutorial exercises), perform appropriate data analyses on R and answer Questions 1 through 7 below.

Question

1. Using appropriate functions on R, create (i) a time variable, t, that starts at 1 in the first period and increases by 1 every period, and (ii) three dummy variables, D1,t , D2,t and D3,t , which take a value 1 if the observation t is in the corresponding quarter and 0 otherwise (e.g., 1, 1 D t  if the period t is in the 1st quarter and 0 otherwise). Then, estimate a linear trend model with seasonality. Provide a summary output from R.

2. State the sample regression equation estimated.

3. Using no more than a few sentences, provide interpretations of the coefficients for t, D1, D2, and D3 estimated in Question 1.

(i) Interpret the estimated coefficient for t.

(ii) Interpret the estimated coefficients for D1, D2, and D3.

4. Interpret the reported R‐square value and briefly comment on the adequacy of the model.

5. Calculate the forecasted value of GVA for the 2nd quarter of 2016 as implied by the estimated regression model.

6. Construct a 95% confidence interval of true population coefficient for t manually (that is, based on the estimated coefficient, standard error, and the relevant critical values). Interpret the obtained confidence interval.

7. Suppose that you want to test whether there is no seasonal variation in the GVA after controlling for a linear trend. Please answer the following questions and describe how you would implement this test.

(i) State the null and alternative hypothesis of this test.

(ii) What test‐statistics would you use to test the hypotheses formulated in part (i)? How would you calculate this statistics? State an additional regression model that needs to be estimated (if any) to calculate this test statistics.

(iii) Describe how you would find the critical value to implement the above test. When would you reject the null hypothesis established in part (i)?

8. State the estimated regression equation.

9. State what is the reference or base case in regards to the three dummy variables included in the regression model.

10. Interpret the estimated coefficients for INTERCEPT, DIS, NIGHT, and PM. Briefly comment if it makes sense and/or has the sign that you would expect:

(i) INTERCEPT

(ii) DIS

(iii) NIGHT

(iv) PM

11. Following the steps below, perform a one‐sided significance test for the coefficient for SOVER against the alternative hypothesis that the coefficient is negative at a 5% significance level. 

(i) Establish a null and alternative hypothesis.

(ii) Calculate an appropriate test statistics to test the hypothesis established in (i).

(iii) Obtain the relevant critical value and complete the test, i.e., state whether you reject or do not reject the null hypothesis.

12. Answer the following questions regarding the F‐statistics and Significance F figures reported at the bottom of the R’s summary output.

(i) What hypothesis is tested by the F‐statistic and corresponding p‐value?

(ii) Sketch (roughly) the F distribution and indicate the relative locations of the F‐statistics, the critical value and the rejection region for an F‐test on this model.

(iii) Based on your answers to part

(ii) Do you reject or not reject the hypothesis stated in (i)?

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