1. Explain what is meant by the following terms:
(i) Unbiasedness
(ii) Efficiency
(iii) Linearity
(iv) Standard error of
(v) Normality and Parallel trends
2. (a) Consider the following cross-sectional regression model which has been estimated using n observations:
yi = + ei, where
Explain briefly the interpretation of the following expression:
Explain how this expression can be used to construct a test of the null hypothesis H0: 2=3=0.
(b) For each of the following assumptions concerning the multiple regression model, describe briefly one method you could use to test the validity of the assumption.
(i) Normality
(ii) Linearity
3. (a) With reference to the multiple regression model:
explain what is meant by the following statement:
“The regression splits the variation in the dependent variable into an explained and an unexplained component”.
Explain how this result can be used to construct a test for the null hypothesis H0: 2=3=…=k=0.
(b) The validity of the hypothesis test you have described in part (a) depends upon the Normality of ui. How would you test for the validity of the Normality assumption?
4. (a) With reference to a regression model that is to be estimated using panel data, explain the distinction between fixed effects estimation and random effects estimation.
(b) What are the factors that you would take into account when deciding whether to use fixed effects or random effects estimation?
5. (a) State and explain briefly the Gauss-Markov Theorem concerning the desirable properties of the ordinary least squares estimators of the coefficients of a linear regression model.
(b) What is a maximum likelihood estimator? What are the desirable properties of maximum likelihood estimators? Under what circumstances are the ordinary least squares estimators identical to the maximum likelihood estimators?