EC655 – Econometrics Department of Economics Wilfrid Laurier University Fall 2020 Final Exam Date and Time: Saturday December 12, 9:00am – Monday, December 14, 9:00am Structure: • This is a take-home test over 48 hours • You will answer 4 of the following 6 questions • If you answer more than 4 questions, I will grade only the first 4. • Each question has equal weight. The weight of subquestions are noted in the question • It is open book and open internet • You are prohibited from collaborating in any way with other people on the midterm. This means no discussing the questions in person, by phone, using chat services, question boards, email, etc. • If you draw your answer from another source (e.g. the textbook, the internet), you must reference it. The normal rules of plagiarism apply to this exam. • Instructor help on the test will be limited to clarification questions only Submission Instructions: • Submit your midterm to Gradescope when complete. Note that you can submit as many times as you wish before the due date. • You are required to hand-write your responses to each question on paper (i.e. do not use a word processor unless you have accommodations through ALC) o I would suggest answering each sub-question on a separate piece of paper • For questions you choose not to answer, upload a photo of a blank piece of paper or one that says “did not answer this question” • Sign your name below the response to each question • Upload your hand-written responses to Gradescope in one of two ways: a) Take a photo of your response to each question separately, and then upload each image b) Scan your questions into a single PDF, then upload it and tag each question Questions 1) (12 Points) In the recent past, the province of Manitoba ran a program called “healthy baby." Under this program, pregnant women earning less than $32,000 received an income supplement if they applied for it, whereas pregnant women who earned more than $32,000 got no income supplement. Suppose a colleague has a dataset with all women who gave birth in Manitoba during the time period where the healthy baby program was in effect, and plans on estimating the effect of the income supplement on child birthweight using a Regression Discontinuity design. a. (6 Points) Write down an appropriate Regression Discontinuity model for estimating the effect of the income supplement on child birthweight b. (6 Points) Identify any problems you might encounter using a Regression Discontinuity model in this specific context. 2) (12 Points) A friend for his Masters Research Project (MRP) has obtained some unpublished data from his uncle on a job training grant program that was supposed to make the firms receiving the grant more efficient. The data consist of observations from 1987, 1988, and 1989 on 54 firms, some of whom received grants. Each firm observation consists of three dummies indicating whether a grant was obtained, one for each year, three observations on the firm’s sales, one for each year, three observations on the number of employees, one for each year, and three observations on a productivity measure, one for each year. Your friend inspected these data carefully and determined that no firm received a grant in 1987, so these data are not of interest (he found out that the grant program didn’t start until 1988), and that no firm received a grant in 1989 either, so that these data also are not of interest (he found out that the program was discontinued when a new party came to political power in late 1988, something his uncle forgot to tell him). He used the 1988 data to regress the productivity measure on grant, sales and employees, but to his dismay discovered that he gets a negative sign on grant instead of the expected positive sign. Knowing that you are an expert in applied econometrics he has turned to you for advice. What advice would you offer? 3) (12 Points) Consider the following unobserved effects model that relates the fatality rate in a US State (i) in a particular time period (t) to a tax on beer (!") some other time-varying variables that affect the fatality rate in a state (!"), unobserved state-specific factors (!), and time- varying unobserved factors (!"). !" = # + $!" + %!" + ! + !" a. (6 Points) Explain in detail what method you would use to estimate this model. Be clear about the assumptions you are making. b. (6 Points) Suppose that you decide there is a dynamic component to your model, so you augment the equation above by including the lagged fatality rate !" = # + $!" + %!" + &!"'$ + ! + !" Imagine that you want to estimate this model by fixed effects, and also that the version of the model you estimated in (a) meets the necessary assumptions for a consistent estimate of $. Does this augmented model also meet the required assumptions? Explain. 4) (12 Points) Imagine you are interested in estimating the effect of a policy on some generic variable y. You observe two groups of people (Group A and Group B) yearly between 2000 and 2010. You know that Group A receives the treatment in each year from 2006 forward, whereas Group B never gets the treatment. You have access to a dataset that contains 5 variables: • y – the outcome variable • treated – a dummy variable equal to 1 if in Group A and 0 otherwise • after – a dummy variable equal to 1 if year >=2006 and 0 otherwise • treated_after – a dummy variable equal to 1 if in Group A and year >=2006, and zero otherwise • year – the year of the observation You plot out the data and estimate the following Difference in Differences model, with results as follows . regress y treated after treated_after, robust Linear regression Number of obs = 20 F(3, 16) = 345.84 Prob > F = 0.0000 R-squared = 0.9813 Root MSE = 10.099 ------------------------------------------------------------------------------- | Robust y | Coef. Std. Err. t P>|t| [95% Conf. Interval] --------------+---------------------------------------------------------------- treated | 43.86051 6.805223 6.45 0.000 29.43408 58.28693 after | -32.47342 2.809071 -11.56 0.000 -38.42839 -26.51846 treated_after | 130.0013 9.033233 14.39 0.000 110.8517 149.1509 _cons | 99.25563 2.527269 39.27 0.000 93.89806 104.6132 ------------------------------------------------------------------------------- 50 10 0 15 0 20 0 25 0 y 2000 2002 2004 2006 2008 2010 year a. (4 Points) Interpret precisely each coefficient in the regression b. (4 Points) Draw the predicted regression line on the graph above for the treated and untreated groups, and based on the regression lines, indicate on the graph how you would find the difference-in-differences estimate. The treated group are the red dots. c. (4 Points) Does it appear based on the scatterplot that key assumptions of the difference-in- differences model are met? Explain. 5) (12 Points) Imagine that you are interested in estimating the relationship between murder rates in U.S. States and the number of executions a state performs. You model this as follows: !" = # + $!" + %!" + &90" + (93" + ! + !" The index i denotes the state, and t denotes the year. The variable !" is the murder rate, !" is the number of executions in the state in the past 3 years, !" is the unemployment rate, 90" is a dummy variable for the year being 1990, 93" is a dummy variable for the year being 1993, ! is an unobserved state effect, and !" is the error term. In the data, each state is observed in 1987, 1990, and 1993. Suppose you estimate the regression above first by Random Effects, and then by Fixed Effects (using the within transformation). The results are as follows: . xtreg mrdrte exec unem d90 d93, re Random-effects GLS regression Number of obs = 153 Group variable: id Number of groups = 51 R-sq: Obs per group: within = 0.0680 min = 3 between = 0.0731 avg = 3.0 overall = 0.0426 max = 3 Wald chi2(4) = 8.52 corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0743 ------------------------------------------------------------------------------ mrdrte | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- exec | -.0543375 .1595008 -0.34 0.733 -.3669533 .2582784 unem | .3947507 .2848133 1.39 0.166 -.1634732 .9529745 d90 | 1.732981 .7478556 2.32 0.020 .2672106 3.19875 d93 | 1.699913 .7065606 2.41 0.016 .3150796 3.084746 _cons | 4.635132 2.179451 2.13 0.033 .3634863 8.906778 -------------+---------------------------------------------------------------- sigma_u | 8.2056677 sigma_e | 3.5214244 rho | .84447636 (fraction of variance due to u_i) ------------------------------------------------------------------------------ . xtreg mrdrte exec unem d90 d93, fe Fixed-effects (within) regression Number of obs = 153 Group variable: id Number of groups = 51 R-sq: Obs per group: within = 0.0734 min = 3 between = 0.0037 avg = 3.0 overall = 0.0108 max = 3 F(4,98) = 1.94 corr(u_i, Xb) = 0.0010 Prob > F = 0.1098 ------------------------------------------------------------------------------ mrdrte | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- exec | -.1383231 .1770059 -0.78 0.436 -.4895856 .2129395 unem | .2213158 .2963756 0.75 0.457 -.366832 .8094636 d90 | 1.556215 .7453273 2.09 0.039 .0771369 3.035293 d93 | 1.733242 .7004381 2.47 0.015 .3432454 3.123239 _cons | 5.822104 1.915611 3.04 0.003 2.020636 9.623572 -------------+---------------------------------------------------------------- sigma_u | 8.7527226 sigma_e | 3.5214244 rho | .86068589 (fraction of variance due to u_i) ------------------------------------------------------------------------------ F test that all u_i=0: F(50, 98) = 17.18 Prob > F = 0.0000 a. (6 Points) Based on these results, which estimate of the effect of executions on murder rates would you prefer, and why? [note: focus on the coefficient estimates only. Ignore all the other detail, since we have not really covered this in class. Also note that you do not need to know anything about the “xtreg” command to be able to answer this question. Just know that it produces a fixed effects or random effects estimate depending on the option “fe” or “re”.] b. (6 Points) Suppose you are interested in whether state-level average income explains murder rates, so you decide to take the 1990 Census, compute average incomes for each state, and attach these averages to all three observations for each state. You then decide to estimate the model using Fixed Effects and include the state average income variable as an additional regressor. Is this a good strategy? Why or why not? 6) (12 Points) Dobkin, Gil, and Marion (2010) estimate the effect of skipping class in college on final exam performance. They take advantage of a policy they enforced in their own economics classes (they are professors) whereby class attendance was required for students who scored below the median on the midterm, and not required for those who scored above the median. They use a fuzzy regression discontinuity design with the following structural and first stage equations ! = # + $! + !% + (!) + !" ! = # + $! + !% + (!) + !" Here, ! is an outcome variable like the final exam score, ! is each student’s attendance rate, ! is a dummy variable equal to 1 if the student scores above the median on the midterm, ! are student background characteristics like gender, major, and level of study, and (!) and (!) are polynomial functions of the variable !. The authors’ main finding is that for each 10 percentage point increase in the attendance rate the final exam score rises by 0.17 standard deviations (recall from class that economists often measure test scores in standardized units). a. (6 Points) Interpret this result as a Local Local Average Treatment Effect (Local LATE). Be specific about the subgroup of people to whom the estimate applies. b. (6 Points) Do you think there is any reason to believe that students can manipulate which side of the discontinuity they fall on? How would you check for this in practice?
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