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Unformatted text preview: University of California, Davis ARE 106 - Winter 2011 Homework 6 The material covered in this homework will be on the midterm exam held Thursday, February 17, 2011. Conceptual Questions 1. Suppose we believe that the primary determinant of starting salary for Managerial Economics graduates is their grade in ARE 106. We estimate the following model: SALARY i = β 1 + β 2 GRADE i + β 3 GRADE 2 i . (a) What is the marginal effect of GRADE on SALARY ? The marginal effect is the derivative of salary with respect to grade: ∂SALARY ∂GRADE = β 2 + 2 β 3 GRADE (b) What sign do you expect the coefficients β 2 and β 3 to have? What do these signs imply about the relationship between grade and starting salary? There isn’t necessarily a correct answer to this question, so long as your expected signs and their implication work together. For example, if we thought that higher grades meant higher salaries and that the effect of grade on salary was greater for those who earned the highest grades, then we would expect the coefficients on β 2 and β 3 to be positive. If we thought that the effect diminished at higher grade levels, then we would expect β 3 to be negative. (c) Suppose we collect data, estimate the model, and find that b 2 = 0 . 250 and b 3 = . 005. Interpret the effect of GRADE on SALARY , given these numbers. In this case, higher grades imply higher salaries - the marginal effect will be positive. Having a positive estimate of β 3 implies that the effect is strongest for those with the highest grades. (d) What econometric problem might we worry about when estimating this model? There is likely to be collinearity between GRADE and GRADE 2 . Remember that collinearity doesn’t bias the coefficient estimates, but it does inflate their variance, so we may find that our estimates, b 2 and b 3 are not significant. 2. When referring to models containing dummy variables, what is the reference group? If we change the reference group, how does our interpretation of the regression coefficients change? The reference group is the group for which we omit the dummy variable. We interpret the coefficient on a dummy variable as being the effect of that variable relative to the reference group. For example, if we have dummies that indicate the state in which a person lives, and we exclude the California state dummy, then the coefficients on the other state dummies are interpreted as the effect relative to individuals in California. 1 University of California, Davis ARE 106 - Winter 2011 If we change the reference group, our interpretation of the coefficients on the dummy variables are now relative to the new reference group. 3. What is the dummy variable trap?...
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This note was uploaded on 03/18/2011 for the course ARE 106 taught by Professor Havenner during the Spring '09 term at UC Davis.
- Spring '09