1. Consider the multiple regression model Y XB where standard matrix notations apply. Derive the estimator for error variance O^2 by OLS method.

2. Consider the following two-equation system:

Y1 =a1 a2Y2 u1
Y2 =B1 B2Y1 B3Z1 B4Z2 u2

Estimate the the first equation with a view to obtain possible bias, inconsistency and efficiency through the following methods

OLS

Indirect Least Squares

Instrumental variables with Z1 as instrument

3. Explain the underlying idea behind the linear probability model. What are its limitations Explain how probit model takes care of these limitations.

4. What is meant by stationarity in a time series In what respects is the unit root problem related to stationarity? How do you test for stationarity?

5. Explain how GLS method can be used to deal with the problems of heteroscedasticity and autocorrelation.

6. What is meant by multicollinearity? How do you detect it? Suggest remedial measures.

7. Derive the coefficient of determination How do you interpret it

8. Consider the production function Y A K^aL^B e^u. Derive OLS estimator for the parameters and interpret the model.

9. What is meant by heteroscedasticity Explain one of the remedial measures for the problem of heteroscedasticity.

10. While estimating a regression model you found that the explanatory variable is measured with certain error. Specify the model. What are its consequences on the parameters?

11. Explain the concept of identification in a simultaneous equation system. Specify the rank and order conditions in identification of parameters.

12. Write short notes on the following:

RESET Test

Chow Test