Part I - Multiple Choice (24 points in total – 4 points each)...

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Part I - Multiple Choice (24 points in total – 4 points each) 1. You estimate the following sample regression function: π·π‘Žπ‘–π‘™π‘¦Μ‚πΈπ‘Žπ‘Ÿπ‘›π‘–π‘›π‘”π‘  = 80 + 10 βˆ— π‘Œπ‘’π‘Žπ‘Ÿπ‘ _𝑂𝑓_πΈπ‘‘π‘’π‘π‘Žπ‘‘π‘–π‘œπ‘› Josh has 5 years of education and a residual of $20. What are his daily earnings? A. $150 B. $160 C. $180 D. Impossible to tell 2. Which of these could cause a randomized experiment to generate an underestimate? A. No Shows B. Crossovers C. Both A and B D. Neither A nor B 3. Suppose you estimate the following regression ln(π·π‘Žπ‘–π‘™π‘¦Μ‚πΈπ‘Žπ‘Ÿπ‘›π‘–π‘›π‘”π‘ ) = 4.65 + .08 βˆ— ln(π»π‘œπ‘’π‘Ÿπ‘ ) Which of the following statements is approximately correct? A. A 100% increase in hours is associated with an 8% increase in predicted earnings B. A 10% increase in hours is associated with an 8% increase in predicted earnings C. A 1% increase in hours is associated with an 8% increase in predicted earnings D. A 0.1% increase in hours is associated with an 8% increase in predicted earnings 4. Data reveal the following relationship between life expectancy (years) and gender, the number of days per week a person exercises, and the interaction of gender and exercise: 𝐿𝑖𝑓𝑒𝐸π‘₯π‘π‘’π‘π‘‘π‘Žπ‘›π‘π‘¦ Μ‚= 75 βˆ’ 5 π‘€π‘Žπ‘™π‘’ + 3 𝐸π‘₯π‘’π‘Ÿπ‘π‘–π‘ π‘’π·π‘Žπ‘¦π‘  + 4 π‘€π‘Žπ‘™π‘’_𝐸π‘₯π‘’π‘Ÿπ‘π‘–π‘ π‘’π·π‘Žπ‘¦π‘  For men, each additional day of exercise per week is associated with life expectancy A. Increasing by 3 years. B. Increasing by 4 years. C. Increasing by 7 years. D. Decreasing by 5 years 5. Which of the following characteristics of an instrumental variable can be verified with certainty in the data? A. Relevance B. Exogeneity C. Both A and B D. Neither A nor B 6. In a regression with college fixed effects on cross-sectional data, which of these could still be used as a control variable? A. The size of the school’s endowment B. A student’s incoming SAT score C. Both A and B D. Neither A nor B 7. In a regression with country fixed effects, which of these could you also include as controls? A. An indicator for whether the country is landlocked. B. B.A measure of the country’s GDP in 1960. C. Both A and B D. Neither A nor B PART III - Do police responses affect the likelihood of future violence? (35 POINTS) In responding to a domestic violence report, the police can arrest the assailant or just provide a warning. In 1981, the Minneapolis Police Department conducted a study to understand the link between arrests and the likelihood of an assailant re-offending. They analyzed data from 314 initial domestic violence reports. You are asked to provide an assessment of their analysis. They defined two dummy variables: Re-Offend = 1 if the Assailant Commits another Assault within 6 Months = 0 otherwise Arrest = 1 if the Assailant Was Arrested after the First Report = 0 otherwise Table 1: The Relationship between Re-Offend and Arrest Re-Offend LPM Probit (1) (2) Arrest -0.087 -0.340 (0.044) (0.171) Constant 0.219 -0.775 (0.029) (0.104) Observations 314 314 1. (3 points): Interpret the coefficient on Arrest in Column 1 of Table 1 above [1 sentence]. 2. (3 Points) Based only on the information provided in Table 1, the Minneapolis Police Department concludes that the larger probit coefficient on arrest (Column 2) represents a greater marginal effect than the LPM estimate on arrest (Column 1). Is this conclusion true or false? Explain why. [2 sentences]. 3. (3 points): The Police Department tells you that officers often know if an assailant has been incarcerated (sent to prison) in the past. Officers are more likely to arrest people who have been in prison, and people who have spent time in prison are more likely to re-offend. Using the Omitted Variable Bias Formula, explain to the police department whether this would be a positive or negative bias. The Minneapolis police department decided to run a randomized experiment to estimate the causal effect of an arrest on the probability of re-offense. Before they went to investigate an incident, the officers drew either a pink sheet indicating that they were to arrest the assailant or a yellow sheet indicating that they were supposed to just provide advice. Though officers were supposed to follow this randomization device, they were instructed to ignore it if they judged an arrest necessary. Table 2 provides information on whether the officers followed the randomization protocol: Table 2. 4. (3 points): Consider the pink sheet to be the treatment and the yellow sheet to be the control. How many β€œcrossovers” (a.k.a. β€œalways-takers”) are there in this experiment? [1 sentence] Total 92 222 314 1 91 45 136 0 1 177 178 arrest pink yellow Total color . tab arrest color To test whether or not the randomization was done correctly, you create 10 dummy variables using the event reports. You then test whether or not the means are the same for the pink and yellow groups. The results are in Table 3. 5. (4 points) Does Table 3 (on the next page) suggest that the randomization was successful? Does the statistical significance of the mean difference in β€œAssailant is Polite” necessarily determine the success of the randomization? Explain why or why not. [3 sentences] Table 3. Dependent Variables Pink Yellow P-Value for Difference in Mean (1) (2) (3) Involved Drugs 0.67 0.61 0.27 (.47) (.49) Late at Night 0.75 0.68 0.25 (.44) (.47) Assailant is White 0.41 0.47 0.33 (.50) (.50) Used a Weapon 0.28 0.24 0.42 (.45) (.42) Year =1981 0.66 0.65 0.87 (.48) (.48) Victim is White 0.53 0.60 0.25 (.50) (.49) Summer 0.30 0.25 0.34 (.46) (.44) Assailant is Black 0.37 0.35 0.70 (.49) (.48) Victim is Black 0.24 0.23 0.79 (.43) (.42) Assailant is Polite 0.42 0.55 0.06 † (.50) (.50) Observations 92 222 314 Standard deviations in parentheses. † indicates statistical significance at the 10% level. You then perform the following three regressions: Table 4. First Stage Reduced Form IV/2SLS Dependent Variables Arrest Re-Offend Re-Offend (1) (2) (3) Arrest -0.150 (.06) Pink 0.786 -0.118 (0.043) (.047) Instrument Pink Observations 314 314 314 Standard errors in parentheses. where: Pink = 1 if the officers drew a pink sheet = 0 otherwise A) (3 points) Interpret the coefficient in regression 1. Is the instrument relevant? Explain. [2 sentences] B) (3 points) Using the information in Table 2 and Table 4, what was the constant term in regression 1? C) (3 points) Interpret the coefficient in regression 2. Is this the effect of being arrested on reoffending? Explain why or why not. [2 sentences] D) (3 points) Interpret the coefficient in regression 3. How does it relate to the estimates in regression 1 and 2? 6. (4 Points) Compare the IV/2SLS estimate in Table 4 with the OLS estimate in Table 1. Explain whether this relationship makes sense. [4 sentences] 7. (3 points): A local activist claims that the IV results are not internally valid because part of the population would re-offend regardless of the police response. Is this critique correct? Explain. [4 sentences]

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1. A. $150
2. B. Both A and B
3. A 1% increase in hours is associated with an 8% increase in predicted earnings...

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