Q4
a) Correct STATA output (see do file) (3 marks) Explain correlations (1 mark). Explain that the relation between lcost and lkwh is increasing, monotonic and linear or possibly quadratic. (1 mark)
b) Correct STATA output (including robust standard errors) (4 marks). Explain that the coefficients are different due to omitted variables bias (ideally, use correlation table in part (a) in the answer) (4 marks)
c) Define R-squared and explain that the value is high (2 marks). Explain that R-squared does not tell one anything about correct specification and/or omitted variables bias. (1 mark)
d) Correct STATA output (4 marks). Explain the relevance of the 45 degree line (2 marks). Explain that the fit is better for high values of lcost than low. Moreover, there is systematic deviation from the 45 degree line for both large and small cost, which could also be established using an RVF plot. This suggests that the functional form might not be appropriate. Could also mention heteroscedasticity (4 marks).
e) Correct STATA output (4 marks). The points are more clustered around the 45 degree line than for regression 1, which explains the higher R-squared value. (4 marks)
f) It is useful for inference, particularly with a sample as small as 145. This is because our t- statistics follow an exact t distribution (otherwise t-distribution is an approximation). If the errors are i.i.d. then OLS is equal to MLE and BLUE. (5 marks)
g) The log-transformation does not lead to a linear model, so would need to be estimated by NLS/MLE which might be computationally challenging. Cost can be negative. (3 marks)
h) This model imposes constant returns to scale (r=1) (2 marks), which is overwhelmingly
rejected by the data (this could be shown using a hypothesis test, see do file) (2 marks)
i) Correct STATA output (2 marks). Coefficients change relative to baseline log-linear model
due to omitted variable bias. (2 marks)