3. (a) What is meant by a fixed effects panel model? (10 marks] (b) Consider the following least squares dummy variable panel model for the volume of imports, In(Mir), estimated on 9 countries using quarterly data from 2000q1 to 2020q4 (84 observations), where the subscripts relate to country i at time t In(Yi:) In(RPmi) Constant Log of real income Log of relative price of imports Coef. 1.725 -0.723 -9.496 Std. Err. 0.253 0.057 0.307 Country dummies Fixed Residual sum of squares 4.627 i) ii) iii) At the 5% significance level, does the log of real income influence the volume of imports? [10 marks] Comment on the estimated coefficient on the log of relative prices. Is it consistent with economic theory? (10 marks] If the dependent variable is reparameterised to ln(Mi Yi) with In(Yi) and in(RPmi) as independent variables, what would happen to the estimated coefficients? Explain why R2 would change. [15 marks) (Alt + A) Explain the dummy variable trap. [5 marks] When quarterly dummies are included in the above equation the residual sum of squares decrease to 4.251. Undertake a test to see if the quarterly dummies can be excluded from the above equation, with the critical value being 2.72. [10 marks] iv) v) (C) It is believed that the relative price of imports is endogenous. i) What impact does this have on the estimated coefficients? [10 marks] ii) Discuss the approaches that could be adopted to overcome the problem of endogeneity. [10 marks] (d) It is argued that the quality of imports compared to domestically produced goods should be included in the regression equation. i) Explain the effect of excluding the relative quality of imports on the estimated coefficients. [10 marks] ii) If the correlation between quality of imports and relative price of imports changes over time, how would you capture the omission of relative quality of imports? (10 marks]