3E03_Final_20191__1_

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McMaster University *

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3E03

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Economics

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Jan 9, 2024

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Student Name: Student Number: Economics 3E03 Applied Econometrics DAY CLASS Youngki Shin DURATION: 2.5 HOURS MCMASTER UNIVERSITY FINAL EXAMINATION DECEMBER 2019 THIS EXAMINATION PAPER INCLUDES 10 PAGES (includes the cover page) AND 4 BIG QUESTIONS (Part A - Part D). YOU ARE RESPONSIBLE FOR ENSURING THAT YOUR COPY OF THE PAPER IS COMPLETE. BRING ANY DISCREPANCY TO THE ATTENTION OF YOUR INVIGILATOR. Special Instructions: • Write all your answers on the exam papers . • 8.5 x 11, double sided. • Use of Casio FX-991 MS or MS Plus calculator only is allowed. • The total marks are 100 and the marks for each question are denoted in the parentheses. Page 1 of 10

Student Name: Student Number: Part A. (30, 3 marks each) Answer the following questions. 1. When there are omitted variables in the regression, which are determinants of the dependent variable, then: (a) you cannot measure the e ↵ ect of the omitted variable, but the estimator of your included variable(s) is (are) una ↵ ected. (b) this has no e ↵ ect on the estimator of your included variable because the other variable is not included. (c) this will always bias the OLS estimator of the included variable. (d) the OLS estimator is biased if the omitted variable is correlated with the included vari- able. 2. If you wanted to test, using a 5% significance level, whether or not a specific slope coe ffi cient is equal to one, then you should: (a) subtract 1 from the estimated coe ffi cient, divide the di ↵ erence by the standard error, and check if the resulting ratio is larger than 1.96. (b) add and subtract 1.96 from the slope and check if that interval includes 1. (c) see if the slope coe ffi cient is between 0.95 and 1.05. (d) check if the adjusted R 2 is close to 1. 3. When there are two coe ffi cients, the resulting confidence sets are: (a) rectangles. (b) ellipses. (c) squares. (d) trapezoids. 4. Simultaneous causality bias: (a) is also called sample selection bias. (b) happens in complicated systems of equations called block recursive systems. (c) arises in a regression of Y on X when, in addition to the causal link of interest from X to Y , there is a causal link from Y to X . (d) results in biased estimators if there is heteroskedasticity in the error term. 5. A survey of earnings contains an unusually high fraction of individuals who state their weekly earnings in 100s, such as 300, 400, 500, etc. This is an example of: (a) errors-in-variables bias. (b) sample selection bias. (c) simultaneous causality bias. (d) companies that typically bargain with workers in 100s of dollars. Page 2 of 10 ~ W w v 8. ~ ↑ D

Student Name: Student Number: 6. The interpretation of the slope coe ffi cient in the model Y i = β 0 + β 1 log( X i ) + u i is as follows: (a) a change in X by one unit is associated with a β 1 · 100% change in Y . (b) a change in X by one unit is associated with a β 1 change in Y . (c) a 1% change in X is associated with a β 1 % change in Y . (d) a 1% change in X is associated with a change in Y of 0 . 01 · β 1 . 7. In a prediction problem, there are: (a) specific regressors of interest. (b) control variables. (c) predictors and the variable to be predicted. (d) never situations where OLS overfits data as long as there are a large number of regressors relative to the number of observations. 8. Consider the following regression model: TestScore = β 0 + β 1 inc + β 2 inc 2 + u where inc denotes income. You have variables, testscore , inc , and incsq in the data set. Write the R command to run estimate the above nonlinear regression function. If you have been using a software di ↵ erent from R, write the name of the software (e.g. STATA, Matlab, Python) and write the relevant commands of the software. 9. Consider the following regression model: log( Wage ) = β 0 + β 1 Educ + u where Educ is years of education. We can think individual ability as an omitted variable. When we omit ability, will the estimated value of β 1 be higher (overestimated) or lower (underestimated) than the true e ↵ ect of education on wage? 10. Suppose that you have 1,000 candidate predictors. If you believe that only few predictors are relevant, which methods will you choose between ridge and lasso? Page 3 of 10 ch8 - - v ⑳ - overestimated

Student Name: Student Number: Part B. (20) In this question, we investigate the relationship between rent rates and the student population in a college town. Using some data, we get the following estimation results: log( rent ) = β 0 + β 1 log( pop ) + β 2 log( avginc ) + β 3 pctstu + u where rent is the average monthly rent, pop is the total city population, avginc is the average city income, and pctstu is the student population as a percentage of the total population. 1. (5) Write the null hypothesis that size of the student body relative to the population has no ceteris paribus e ↵ ect on monthly rent. Write the alternative hypothesis that there is an e ↵ ect. 2. (5) We estimate the model with data and get the following results: log( rent ) = . 043 + . 066 log( pop ) + . 507 log( avginc ) + . 0056 pctstu + u ( . 844) ( . 039) ( . 081) ( . 0017) n = 64 , R 2 = . 458 Test the null hypothesis stated in (a) at 1% significance level. (Hint: the critical value of the t-test for 1% level is 2.58). Page 4 of 10 => - - Ho: B3 = 0 Ha:3 FO 0.0056 - 0 t = 0.0017 t = 3.29> 2.58 reject Ho &99%

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