Answer all questions, no word limit:
1. a. Define multicollinearity. What is the difference between an exact collinear relationship among the explanatory variables and an approximate (not exact) collinear relationship among the explanatory variables?
b. What are the consequences of multicollinearity for Least Squares estimation? Explain how multicollinearity in your data can be detected (such as pair wise correlations, VIFs, and auxiliary regressions). What can a researcher do to reduce multicollinearity?
2. a. What are the properties of the least squares estimators when relevant explanatory variables are omitted from the regression? Does your answer depend on whether the omitted variables are correlated with the included variables?
b. When important explanatory variables are omitted from the regression, what is usually observed about the signs and magnitudes of the estimated coefficients?
c. What are the properties of the least squares estimators when irrelevant explanatory variables are included in the regression model? Does your answer depend on whether the included irrelevant variables are correlated with the other explanatory variables?
d. Describe the RESET test for determining adequacy of the model specification.
3. a. Define multicollinearity. What is the difference between an exact collinear relationship among the explanatory variables and an approximate (not exact) collinear relationship among the explanatory variables?
b. What are the consequences of multicollinearity for Least Squares estimation? Give two ways of detecting multicollinearity in your data. What can a researcher do to reduce multicollinearity?
4. a. What is heteroskedasticity? Explain in terms of the assumptions made in Ch.2 and Ch. 5 for least squares estimation.
b. What are the consequences of heteroskedasticity? What is the econometrician's response to each of these consequences?
c. What are the properties of the least squares estimators of the regression coefficients in the presence of heteroskedasticity?
d. Explain how a model with heteroskedastic errors can be transformed by using a generalized least squares estimation procedure so as to obtain estimators that are BLUE.
e. How can heteroskedasticity be detected in a given sample of data?
5. a. What is autocorrelation? Explain in terms of the assumptions made in Chs.2 and 5 for least squares estimation. Why does autocorrelation occur in econometric models?
b. What are the properties of the least squares estimators of the regression coefficients in the presence of autocorrelation?
c. Explain the first order autoregressive (AR1) model used for modeling auto-correlated errors.
d. Explain how a model with auto-correlated errors can be transformed by using a generalized least squares estimation procedure so as to obtain estimators that are BLUE.
e. How can autocorrelation be detected in a given sample of data?