1 Empirical Exercise In this problem, you will use data from the UK to study the impact of education on earnings and health. To do so, you are going to exploit a change in compulsory schooling age law (i.e., the minimum age someone could drop out of school). Students in the 1940s and 1950s, if they were born before April 1st 1933, could drop out when they reached age 14. If they were born April 1st, 1933 or later, they could not drop out untl they reached age 15. To estimate the effect of compulsory schooling law, you can compare individuals born before or after April 1st, 1933. The dataset you will use is UK.csv and contains the following variables: agelfted=age left full time schooling learnings=log of earnings health= continuous measure of health that takes values between 0 and 1 (1 being perfectly healthy) yob=year of birth male=1 if male, 0 otherwise 1. Estimate the linear regression of schooling (measured by the agelfted) on log earnings and on health. Discuss your findings. Do you believe these estimates to be unbiased estimates of the average treatment effect of schooling on earnings and health? 2. Create a dummy variable D indicating the observations who were subject to the new compulsory schooling law. Check the effect of the law on average age of leaving full time schooling by estimating the following equation education = ay + a1 D + agbirthyear + a3z D * birthyear + What is the effect of the law change on age when left full time schooling? 3. Given the results in the previous question and the nature of the law, explain how you can estimate the effect of schooling on earnings and health using an instrumental variable approach. What is the instrument used? Report the IV instruments for both outcomes. 4. Compare the OLS and IV results. 5. In class, you learned about regression discontinuity design. Explain how you can use this approach in this context. What are the advantages and disadvantages of using RDD in this context? 6. Produce the graphical evidence that is usually presented in an RDD. Estimate the effect using the RDD approach. Use both Sharp and Fuzzy designs (based on the graphical evidence which design seems more appropriate) and use different bandwidth around the threshold. Additional Empirical Exercises (Wooldridge): Chapter 15, exercises C2, C4, and C8. Theoretical and Conceptual Exercises . Consider the basic bivariate regression model y=P0+biz+u Elulz] #0 Let z be a valid instrument. First we would like to derive the 2SLS estimator for this simple bivariate case. (a) Write the first stage regression of the 2SLS estimation. Write the OLS estimator of the first stage regression parameters (no need to derive the OLS estimators, you already know them from class). (b) write & the fitted values of the first stage regression as function of the data (z and z). (c) Write the second stage regression of the 2SLS estimation. Write the OLS estimator of 3, as function of the data (y, = and z). Now we will derive the IV estimator using the method of moment method. (d) Show that E[u] =0 and E[zu] =0 (e) Using the moment conditions above write 3y and ; as function of population mo- ments. (f) Show that the IV estimator of 8;, derived using the method of moment, is equal to the 2SLS estimator derived in question c). Note: This exercise contains a lot of algebra. The answer is simple but you need to proceed in a neat way to be able to see the answer. In some cases doing intermediate steps on the side could be helpful. . Suppose you are interested in estimating the following model Y=a+8X"+te Ele|X*] =0 Suppose you observe X* with some measurement error (i.e. you observe X = X* + v, where v is an iid measurement error). Let Var(X*) = %. and Var(v) = o2. Since you only observe X and estimate the following model Y=a+bX +u (a) Write u as function of e and v. (b) Does your model satisfy the zero mean condition? What does that imply about the OLS estimate of b7 (c) Compute the bias in the OLS estimator as a result of the measurement error. (d) Suppose there is another variable X = X* + w. This is another measurement of X* with error. Someone suggests that X can be used as an instrumental variable to fix the bias issue we found above. Explain intuitively why this is possible. What is the necessary condition for that to be true? (e) Show formally that the IV estimator will be a consistent estimator of 3. Note 1: Measurement errors are a very common issue in application. Whenever you are doing empirical work you should consider if you have such problem in your context. Note 2: Think about the case where the measurement error v is not iid. Imagine the measurement error was correlated with X*. How much worse will the bias be? Do you think an IV can resolve this problem? . Compulsory military service is a common practice in many countries and the impact of this policy on young men is often debated. Some people argue that it is harmful for both their education and employment, while others believe it improves national cohesion. In Lebanon, a compulsory military service was put in place in 1983, which required able-bodied men who reach the age of 18 to serve one year in the military forces. The law remained in effect until February 2005. On the 4th of February 2005, the parliament passed law number 665, which decreed that military service be abolished in two years after the publication of the law. Moreover, the law reduced the military service to six months until cancellation of the military service. (a) Your parents inform you that men who were at school in Lebanon or abroad were able to postpone their military service. They also tell you that a commonly adopted strategy was to continue education to avoid military service. If you collect a survey data on young men born between 1980 and 1990, how would you check this claim? (Describe any plot or regression you would use to support or refute this claim.) (b) Suppose your parents' claim was confirmed by the data. If you are interested in measuring the impact of education on earnings, describe how you could use an RD design to quantify the impact of years of education on earnings. (c) If you find a zero effect (insignificant coefficient), can you claim that education does not improve earnings on average? (d) Now suppose you wish to test the theory that military service improves national cohesion. List a number of questions you could include in a survey to obtain some measures of national cohesion in the context of Lebanon. Explain how you could take advantage of law number 665 to do so in a difference-in-differences framework. Who would you use as a control group