2023F_322_Problem Set 5

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Rowan University *

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322

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Economics

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Jan 9, 2024

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Econ 322 - Fall 2023 Problem Set 5 Due December 8th, 2023, 8 pm Please answer each of the questions below. Note that writing only a numeric answer to the ques- tion is not enough to receive full credit unless otherwise stated. Please submit: (1) a PDF/Word Document with your answers (including any plots/tables), and (2) the R (or other language) code you used to answer the questions. You need to submit both files for your problem set to be graded. Total: 60 points. Question 1: Who Buys Health Insurance? (34 Points) According to the Center for Disease Control, about 8.4 percent or 27.6 million Americans of all ages did not have health insurance in 2022. In this exercise, we will study the question of what the determinants for buying health insurance are. We are interested in the following equation: insured i = α + β 1 X 1 + ... + β k X k + ε i (1) where insured is a dummy variable indicating whether an individual has health insurance and { X 1 , ..., X k } is a set of k characteristics of an individual (in other words, a list of independent variables, each of which has a β associated to them). To estimate this equation, we will use the National Health Interview Survey from 2009. In this survey, respondents were asked about their health insurance status and several of their demographic and economic characteristics. Below you can find a list with variable descriptions: • pid : personal identifier (anonymized) • insured : dummy variable for whether respondent has at least some health insurance • health : health index, broadly understood • age : the respondent’s age in years • educ : the respondent’s total years of education • empl : dummy variable for whether the respondent is employed • inc : the respondent’s household/family income Answer the questions below (please round all of your answers to three decimal places): 1

1. (5 points) Estimate Equation 1 by OLS only including the health index as an independent variable. Report the slope coefficient and the associated heteroskedasticity-robust standard error. Interpret this coefficient. Do you think this regression suffers from omitted variable bias (OVB)? Why? 2. (6 points) Estimate the regression in the previous part also including the natural logarithm of household income as a control variable. Report the regression coefficients and their associated heteroskedasticity-robust standard errors. Was the coefficient for the health index upward or downward biased in the previous part? Why (discuss the two conditions of OVB and their sign for this case)? 3. (6 points) Estimate Equation 1 by OLS including the following as independent variables: health index, age, years of education, employment indicator, and the natural logarithm of household income. Report the coefficients and their heteroskedasticity-robust standard errors. Compute the probability that an individual that has health = 5, age = 30, educ = 13, empl = 1, and inc = 45 , 000 is insured. 4. (6 points) Now compute the probability that an individual that has health = 5, age = 21, educ = 10, empl = 0, and inc = 1 , 000 is insured. Does the linear probability model make sense in this case? Why? 5. (6 points) Estimate Equation 1 including the same independent variables as in Part 3 but using a probit model. Compute the probability that an individual that has health = 5, age = 21, educ = 10, empl = 0, and inc = 1 , 000 is insured. Round this numerical answer to four decimal places. Does the probit model make sense in this case? Why? 6. (5 points) What would be the change in the probability of being insured for the average in- dividual in the dataset if they went from being unemployed to being employed? Answer the question using the probit model. Question 2: Crime Exposure and Academic Achievement (26 Points) As Casey and his co-authors put it in their 2018 paper “Local Violence, Academic Performance, and School Accountability”, a growing body of research shows that “ random shocks external to the classroom or school environment (e.g., spikes in air pollution on testing days) may affect measured test performance ”. Since school evaluation systems heavily rely on test performance, we want to understand a little bit more how some of these external shocks can distort student test performance. In this question, we will revisit the main question in the paper: what is the effect of exposure to crime on test performance? We will depart a little bit from the paper in that we will only focus on the effect of property crime taking place within 0.1 miles of a school on their students’ performance. For this exercise, we will use (a subset of) their dataset, “ crime and schools.csv ”. Below you can find a list with variable descriptions: • schoolid : school identifier (denoted by s ) • nhoodid : identifier for the neighborhood where the school is located (denoted by n ) • year : calendar year (denoted by t ) • mathpct : share of students who exceed or meet their math test growth goals during the year • crime exposure : number of property crimes within 0.1 miles of school s in year t Page 2

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