Examine the residuals of your estimated equation/Managerial Economics
1. Present your data in a table showing the names of the variables. Make sure the full definitions and sources of each variable are given.
2. The first equation to be estimated is:
SR i = b0 + b1 GDPi+ b2 PINFi+ ui
where u is a disturbance term and the subscript i represents country.
Answer these questions:
(i) In terms of economic theory what sign would you expect to find for the coefficients in the regression equation?
(ii) It is possible (with a little algebra) to obtain the marginal propensity to consume from this model. Work out an expression for this figure.
(iii) Why is there a constant term in the equation with no variable attached?
(iv) Why do these types of equations have a ‘u’ term?
3. Estimate equation (1) by OLS and present the results in a suitable table (n.b. marks will be lost for simply pasting over the computer output)
(i) Comment on the results for the coefficients on the GDP and PINF variables.
(ii) Comment on the R squared statistic.
(iii) Is the estimated value of b0 positive or negative? Does it matter for the reliability of your estimates for b1 and b2 whether b0 is positive or negative?
(iv) Examine the residuals of your estimated equation to determine whether any of your countries is a regression residual.
4. Carry out the following hypothesis tests:
(i) b0 = 0 against the two sided alternative at the 1% level
(ii) b1 = 0 against the two sided alternative at the 5% level
(iii) b2 = 0 against the two sided alternative at the 10% level
(iv) b1 = b2 = 0 against the one sided alternative at the 5% level
5. You are now required to estimate the following form of the model using OLS:
SR i = b0 GDPi b1PINF b2 exp u (2)
where u is a classical disturbance term and exp is the value of exponential.
(i) Write down the estimating equation you need to use to estimate (2) by OLS.
(ii) Explain why the disturbance term enters equation (2) in a different form from equation (1)
(iii) What does the coefficient of b2 now represent?
(iv) Explain how the impact of a one unit change in PINF on the savings ratio would be calculated
6. You must now estimate equation (2) Compare your results for equations (1) and (2).
7. You should now write a short report of 450-600 words. This should briefly summarize your findings but most of your answer should consist of further exploration of your data and suggestions for improvement of the model you have estimated.
