Midterm Exam Ii Answers
Econ 400
B. Brown
Spring 2008
Midterm Exam II: Answers
Answer three of the following questions. You must answer question 5. The questions are weighted equally. You have 75 minutes. You may use a calculator and one side of an 8.5 × 11 as a cheat sheet. Relevant tables are attached. Please return the exams to my office by classtime on Tuesday.
Brevity is recommended.
1. Professor I. M. Economist asked his research assistant to estimate the parameters of the regression model
Yi = α + βXi + γZi + δWi + ui .
He suspected that multicollinearity might be a problem and suggested an analysis of the possibility. Suppose you are the research assistant.
a. Explain exactly what is meant by multicollinearity in this model. Extreme multicollinearity means that one of the RHS variables is perfectly linearly related to the remaining variables. Near extreme means that the correlation between one of the RHS variables and a linear combination of the remaining variables is close to one.
b. What would the consequences of collinearity be for estimation and inference? OLS will still be unbiased, consistent and BLUE (BUE under normality). Likewise the usual statistic, such as the t-ratios, will have the usual distribution, such as the t-distribution, under the null hypothesis. Under the alternative hypothesis, however, there will be loss of power since the variance of the estimates on the collinear terms will become highly variable.
c. How might you go about detecting the presence and severity of collinearity? If the coefficient estimate of the suspected collinear term is significant, then collinearity is not a problem. If the coeffcient is insignificantly different from zero when considered alone but the possible collinear terms reject a test of the null hypothesis that they all are zero, then collinearity is a problem.
d. Given that collinearity is present and poses serious complications, what is a possible approach to solving or circumventing the problem. (i)
B. Brown
Spring 2008
Midterm Exam II: Answers
Answer three of the following questions. You must answer question 5. The questions are weighted equally. You have 75 minutes. You may use a calculator and one side of an 8.5 × 11 as a cheat sheet. Relevant tables are attached. Please return the exams to my office by classtime on Tuesday.
Brevity is recommended.
1. Professor I. M. Economist asked his research assistant to estimate the parameters of the regression model
Yi = α + βXi + γZi + δWi + ui .
He suspected that multicollinearity might be a problem and suggested an analysis of the possibility. Suppose you are the research assistant.
a. Explain exactly what is meant by multicollinearity in this model. Extreme multicollinearity means that one of the RHS variables is perfectly linearly related to the remaining variables. Near extreme means that the correlation between one of the RHS variables and a linear combination of the remaining variables is close to one.
b. What would the consequences of collinearity be for estimation and inference? OLS will still be unbiased, consistent and BLUE (BUE under normality). Likewise the usual statistic, such as the t-ratios, will have the usual distribution, such as the t-distribution, under the null hypothesis. Under the alternative hypothesis, however, there will be loss of power since the variance of the estimates on the collinear terms will become highly variable.
c. How might you go about detecting the presence and severity of collinearity? If the coefficient estimate of the suspected collinear term is significant, then collinearity is not a problem. If the coeffcient is insignificantly different from zero when considered alone but the possible collinear terms reject a test of the null hypothesis that they all are zero, then collinearity is a problem.
d. Given that collinearity is present and poses serious complications, what is a possible approach to solving or circumventing the problem. (i)