ECOM30002 : Econometrics - Economics Assignment

Internal Code -  MAS3128

Economics Assignment

Question 1 - (a) Do your simulation results suggest that the OLS estimator is unbiased for ?1? Explain why this should (or should not) be so using the parameter values specified for the data generating process. (b) Explain how your simulation results suggest that the OLS estimator is consistent or inconsistent for ?1. (c) Discuss the simulated coverage rates for the confidence intervals and how they vary with n, ? and the distribution of Ui. (d) Discuss the average confidence interval lengths and how they vary with n, ? and the distribution of Ui. Question 2 - Repeat the simulations from question 1, except with the one difference that now ?3 = 1, and report the same set of results as in question 1. (a) Explain how and why there are both similarities and differences between the two sets of results. (b) How do you think the results from question 2(a) would change if you re-ran the simu-lation with ?3 = 0? It is not necessary to run this extra simulation, but you should be be able to describe qualitatively what should happen. Question 3- Repeat the simulations from question 2 (with ?3 = 1), except now replace the OLS estimator with a 2SLS estimator in which Z1,i is used as an IV for X1,i while X2,i is treated as exogenous. (a) Is Z1,i a valid IV in this case? Explain. (b) Explain how the results from the simulations match with what you would expect in this case. How does the validity/invalidity of Z1,i as an IV influence the results? If there are unexpected results, identify these and attempt to explain what is going on1 Question 4- Set n = 200, ? = 1, Ui ? Normal, ?3 = 1, ?3 = 1 and consider the range of values for ?1: ?1 = 0.8, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0. For these 8 cases, carry out simulations of the same properties of the 2SLS estimator (bias and standard deviation) and confidence interval (coverage rate and length) as in the previous question. Explain the results in terms of the validity/invalidity of Z1,i as an IV for X1,i.Again identify any unexpected results and attempt to describe what is happening. Question 5 - Specify the following values ?3 = 0, ?1 = 1, ?3 = 1, ? = 1, n = 200 and Ui ? Normal. Carry out 5 simulations of the OLS estimator and confidence intervals for the following values of ?2: ?2 = 0, 2, 4, 6, 8. Present and explain the results for the properties of the OLS estimator (bias and standard deviation) and its confidence interval (coverage rate and length).