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Econ 122A Problem Set 4 Due in class on Mar 1 Name(Print)______________________ UCI ID______________________________ 1-8, Multiple-Choice Questions (Choose the best answer, and briefly explain your reasoning.) 1. Suppose you are interested in the effect of class attendance on college performance, and plan to estimate the following model: colGPA= α + β attendance+ u , where colGPA is current GPA and attendance is a student’s class attendance rage (percentage of classes attended among all the classes he or she needs to attend) Due to lack of information, students’ inherent laziness or lack of motivation is omitted from the regression. Assume that lazier students tend to have a lower attendance rate. OLS estimator of the coefficient for attendance will most likely a) be biased away from zero, so that the impact of attendance on colGPA is overestimated. b) be biased toward zero, so that the impact of attendance on colGPA is underestimated. c) be unbiased. d) be biased, but not enough information to determine if the impact is overestimated or underestimated. Questions 2-4 are based on the following information: Consider the following population model for household consumption: cons = α + β1inc + β 2 educ +β3 hhsize + u , where cons is consumption, inc is income, educ is the education level of household head, hhsize is the size of a household. 2. Suppose a researcher estimates the model and gets the predicted value, cons_hat, and then runs a regression of cons_hat on inc, educ, and hhsize. One can a) be certain that the R2 is equal to 1 b) be certain that the R2 is equal to 0 c) be certain that the R2 is less than 1 but greater than 0. d) not be certain 1 3. Suppose that the variable for consumption is measured with error, so conss = cons + e, where conss is the mismeaured variable, cons is the true variable, e is random, i.e., e independent of all the regressors. We would expect that: a) OLS estimators for the coefficients will all be biased b) OLS estimators for the coefficients will all be unbiased c) all the standard errors will be bigger than they would be without the measurement error d) both b) and c) 4. Suppose the data were collected through a telephone survey, and the last 4 digits of the households’ telephone number was accidentally coded as something else and included in the regression. Denote the coefficient as β̂ 4 .We would expect a) the OLS estimators βˆ , βˆ , βˆ , and βˆ are all unbiased. 1 2 3 4 b) OLS estimator β̂ 4 is biased, but βˆ1 , βˆ2 ,and βˆ3 are all unbiased. c) the OLS estimators βˆ1 , βˆ2 , βˆ3 , and βˆ4 are all biased. d) the OLS estimators βˆ , βˆ , βˆ , and βˆ are more precise. 1 2 3 4 5. In the case of question no. 4, we would be certain that a) Adjusted R2 will get larger. b) Adjusted R2 will not change. c) R2 will get larger. d) R2 will get smaller. 6. Under multicollinearity a) the OLS estimator cannot be computed. b) two or more of the regressors are highly but not perfectly correlated. c) the OLS estimator is biased. d) there is a perfect linear relationship among two or more covariates. 2 7. Imagine you regress earnings of individuals on a constant, a binary variable ("Male") which takes on the value 1 for males and is 0 otherwise, and another binary variable ("Female") which takes on the value 1 for females and is 0 otherwise. Because females typically earn less than males, you would expect a) the coefficient for Male to have a positive sign, and for Female a negative sign. b) the coefficient for Male to have a negative sign, and for Female a positive sign. c) none of the OLS estimators to exist because there is perfect multicollinearity. d) both the coefficient for Male and that for Female to have positive signs.