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4G 46.16:45 74 Section C: Answer the ONE question 4. We consider a regression model with panel data for i=1..... and t = 1, T: tt = 8+ where Wit = 4+24 Elel, da...]=0 (a) We define 12 Το = Σκα, μ = F1 - F, Show that: [7 (i- ZP) - = 0 (1) and that the associated IV estimator 3 is defined as solution of NT - ΣΣταθά (7 marks) (b) Show that (3 marks) (c) We maintain the rank assumption that: F El is a non-singular matrix. Deduce that for N large enough (and given 7"), the IV (Question 4 continued overleaf) EC9100 estimator 8 is well-defined with -INT (5 marks) (d) Show that is a consistent estimator of 3 (when N +) (5 marks) (e) Show that the rank assumption of question (c) cannot be fulfilled if some of the explanatory variables, components of ta, are time-invariant (5 marks) (f) Explain why it is not surprising that, when is not observed, we cannot estimate coefficients of time-invariant variables. (5 marks) Section D: Answer ONE question 5/8 5. We assume that asset (log)returns can be described as T = a + EXE<t1 = 0 5