BUSN5000 HW 7 Part B

10/30/23, 7 : 35 PM Assignment 7: Potential Outcomes Page 1 of 17 https://chris-cornwell.shinyapps.io/Assignment7/#section-b-empirical-analysis B: Empirical Analysis Here, we will extend the analyses we started in Homework 5 to consider the questions of covariate balance and potential confounding. As we’ve stated, if Project STAR really was a clean RCT, the answers to these questions should be clear. We will limit our analysis to the kindergarten class. Overlap Let’s start by creating a table of summary statistics for the test score variable and key student and teacher characteristics. First, create the test score variable and new female , white and freelunch indicators using the information in gender , ethnicity and lunchk . Note : Although ethnicity has six categories, all but a few students are either White or Black. Next, use the st function to construct a table of summary statistics for the test-score variable and controls (teacher experience, student gender, race, and eligibility for free lunch. R Code ! Start Over ▶ Run Code STAR2 <- STAR2 %>% mutate( white =ifelse(ethnicity=="white", 1, 0) female= ifelse(gender=="female", 1, 0), freelunch = ifelse(lunchk=="freelunch", ) R Code ! Start Over ▶ Run Code st(STAR2, digits = 2, fixed.digits = TRUE, vars=c('scorek', 'experiencek','female',' group='stark', title="Table 1. Summary Statistics for th ) 1 2 3 4 5 6 1 2 3 4 5 Assignment Assignment 7: Potential 7: Potential Outcomes Outcomes A: Short Answer (https://chris- cornwell.shinyapps.io/Assignment7/#section- a-short- answer) B: Empirical Analysis (https://chris- cornwell.shinyapps.io/Assignment7/#section- b- empirical- analysis) Submission Start Over

10/30/23, 7 : 35 PM Assignment 7: Potential Outcomes Page 2 of 17 https://chris-cornwell.shinyapps.io/Assignment7/#section-b-empirical-analysis Using Table 1, answer the following questions. Question 1: The di ! erence between small and regular-class mean scores for The di ! erence between small and regular-class mean scores for kindergarteners is about _____ points (report one decimal kindergarteners is about _____ points (report one decimal place). place). 13.9 Correct! Question 2: Under _____ assignment of students to class type, this can be Under _____ assignment of students to class type, this can be regarded as the _____ of small class size on test scores. regarded as the _____ of small class size on test scores. random, average treatment effect Correct! Question 3: Warning in st(STAR2, digits = 2, fixed.digits Warning in st(STAR2, digits = 2, fixed.digits = TRUE, numformat = NA, vars = = TRUE, numformat = NA, vars = c("scorek", : fixed.digits is deprecated and w c("scorek", : fixed.digits is deprecated and w ill be removed in a future ill be removed in a future version in favor of a setting in version in favor of a setting in Table 1. Summary Statistics for the test-score variable and controls stark stark regular regular small small regular+aid regular+aid Variable Variable N Mean Mean SD SD N Mean Mean SD SD N Mean Mean scorek 2005 918.04 73.14 1738 931.94 76.36 2043 918.36 experiencek 2194 9.07 5.73 1900 8.92 5.81 2210 9.74 female 2194 0.49 0.50 1900 0.49 0.50 2231 0.48 white 2192 0.67 0.47 1899 0.68 0.47 2231 0.66 freelunch 2187 0.48 0.50 1892 0.47 0.50 2222 0.50

10/30/23, 7 : 35 PM Assignment 7: Potential Outcomes Page 4 of 17 https://chris-cornwell.shinyapps.io/Assignment7/#section-b-empirical-analysis First, a question about the basic set-up. Question 7: The CEF that captures the simple class-size treatment e ! ects The CEF that captures the simple class-size treatment e ! ects on test scores equivalent to the di ! erences in means obtained on test scores equivalent to the di ! erences in means obtained from Table 1 is from Table 1 is small, regular+aide Correct! Now, use regression to estimate class-size e ! ects, incrementally adding controls to the model specification. You will report the default standard errors, which do not correspond to the standard error calculation used by Krueger. Fortunately, the inference for the main findings is una ! ected. Start by replicating the di ! erence-in-means result from Table 1. Assign those results to regk_1 . Then add teacher experience ( regk_2 ), school “e ! ects” ( regk_3 ), and finally gender, race and free-lunch eligibility ( regk_4 ). Then, use modelsummary create a table of your findings. Construct a coe ! icient map with variable labels of your choosing. E ( ___, ___) = + ___ + ___. y i 0 1 2 R Code ! Start Over ▶ Run Code regk_1 <- lm(scorek ~ , data = STAR2) regk_2 <- lm(scorek ~ + , data = STAR2) regk_3 <- lm(scorek ~ + + , data = STAR2) regk_4 <- lm(scorek ~ + + schoolidk + + + , data = STAR2) R Code ! Start Over ▶ Run Code # Coefficient map cm <- c( 'starksmall' = 'Class size (small 'starkregular+aide' = 'Class size (regul 'experiencek' = 'Teacher experienc 1 2 3 4 5 1 2 3 4 5

10/30/23, 7 : 35 PM Assignment 7: Potential Outcomes Page 5 of 17 https://chris-cornwell.shinyapps.io/Assignment7/#section-b-empirical-analysis Table 2. Regresison Results (1) (1) (2) (2) (3) (3) (4) (4) starksmall 13.899 14.006 15.933 15.901 (2.409) (2.395) (2.167) (2.090) starkregular+aide 0.314 − 0.601 1.215 1.765 (2.310) (2.306) (2.093) (2.019) experiencek 1.469 0.743 0.661 (0.167) (0.168) (0.162) 'experiencek' = 'Teacher experienc 'female' = 'Gender(female)', 'white' = 'Race(white)', 'freelunch' = 'Free lunch eligib '(Intercept)' = 'Intercept' ) # Row stating whether regression included row <- tribble( ~term, ~regk_1, ~regk_2, ~regk_3, ~regk_ "School Effects", "No", "No","Yes", "Yes ) attr(row, 'position') <- c(15, 15) # Create table modelsummary( list(regk_1, regk_2, regk_3, regk_4), type="html", coef_map = , coef_omit = c("Intercept"), add_rows = row, gof_omit = 'DF|Deviance|R2 Adj.|AIC|BIC stars = FALSE, title="Table 2. Regresison Results " ) 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

10/30/23, 7 : 35 PM Assignment 7: Potential Outcomes Page 7 of 17 https://chris-cornwell.shinyapps.io/Assignment7/#section-b-empirical-analysis schoolidk13 36.435 37.232 (11.733) (11.310) schoolidk14 − 32.964 7.821 (13.788) (13.609) schoolidk15 − 51.949 − 10.378 (11.893) (11.840) schoolidk16 − 76.829 − 32.130 (10.241) (10.337) schoolidk17 − 18.900 − 12.604 (11.142) (10.781) schoolidk18 − 51.424 − 24.668 (10.853) (10.668) schoolidk19 − 29.031 14.772 (10.413) (10.473) schoolidk20 − 24.413 1.698 (10.896) (10.888) schoolidk21 16.309 32.271 (10.998) (10.763) schoolidk22 − 16.033 26.502 (9.851) (9.951) schoolidk23 31.210 51.962 (11.059) (10.937) schoolidk24 − 39.174 − 15.808

10/30/23, 7 : 35 PM Assignment 7: Potential Outcomes Page 8 of 17 https://chris-cornwell.shinyapps.io/Assignment7/#section-b-empirical-analysis (11.474) (11.415) schoolidk25 − 33.916 − 12.193 (11.887) (11.510) schoolidk26 − 65.901 − 27.261 (12.279) (12.192) schoolidk27 20.344 59.902 (9.786) (9.895) schoolidk28 − 43.699 − 2.791 (9.847) (9.951) schoolidk29 − 19.793 22.808 (12.007) (12.006) schoolidk30 73.697 113.912 (11.734) (11.684) schoolidk31 5.703 50.724 (12.221) (12.158) schoolidk32 − 76.597 − 32.636 (10.258) (10.334) schoolidk33 − 74.895 − 30.474 (10.448) (10.510) schoolidk34 − 43.062 − 47.791 (11.216) (10.812) schoolidk35 − 46.238 − 41.470 (11.616) (11.194)

10/30/23, 7 : 35 PM Assignment 7: Potential Outcomes Page 10 of 17 https://chris-cornwell.shinyapps.io/Assignment7/#section-b-empirical-analysis (11.771) (11.458) schoolidk48 − 4.983 1.025 (11.440) (11.039) schoolidk49 9.272 12.282 (11.769) (11.338) schoolidk50 − 3.353 1.944 (11.102) (10.749) schoolidk51 11.627 7.430 (9.766) (9.419) schoolidk52 30.792 17.858 (12.378) (11.939) schoolidk53 − 66.974 − 50.806 (12.014) (11.618) schoolidk54 − 0.463 − 6.461 (12.007) (11.567) schoolidk55 − 35.635 − 37.640 (10.970) (10.572) schoolidk56 − 90.780 − 82.111 (10.408) (10.039) schoolidk57 − 43.141 − 45.725 (11.592) (11.165) schoolidk58 19.694 8.777 (10.450) (10.080)

10/30/23, 7 : 35 PM Assignment 7: Potential Outcomes Page 11 of 17 https://chris-cornwell.shinyapps.io/Assignment7/#section-b-empirical-analysis schoolidk59 10.294 8.636 (11.837) (11.459) schoolidk60 − 40.156 − 32.762 (11.341) (10.935) schoolidk61 − 28.758 − 36.561 (11.150) (10.749) schoolidk62 − 36.164 − 33.383 (12.136) (11.703) schoolidk63 18.475 19.345 (10.105) (9.733) schoolidk64 − 24.511 − 22.056 (10.604) (10.248) schoolidk65 17.476 16.197 (12.948) (12.476) schoolidk66 − 36.682 − 39.028 (10.559) (10.202) schoolidk67 − 13.550 − 9.411 (13.157) (12.685) schoolidk68 26.870 38.820 (10.410) (10.043) schoolidk69 24.625 19.159 (11.885) (11.458) schoolidk70 − 20.916 − 14.951

10/30/23, 7 : 35 PM Assignment 7: Potential Outcomes Page 13 of 17 https://chris-cornwell.shinyapps.io/Assignment7/#section-b-empirical-analysis Answer the following questions based on the results reported in Table 2. Question 8: The estimated small-class e ! ect in Column (1) is _____ to the The estimated small-class e ! ect in Column (1) is _____ to the di ! erence in means calculated from Table 1. di ! erence in means calculated from Table 1. Correct! Question 9: The result in Column (1) is statistically significant at the _____- The result in Column (1) is statistically significant at the _____- percent level. percent level. Correct! Question 10: freelunch − 34.882 (2.014) Num.Obs. 5786 5766 5766 5748 R2 0.007 0.020 0.234 0.291 larger, compared ✗ insignificant ✗ smaller, compared ✗ equivalent ✓ di ! erent ✗ 10 ✗ 1 ✓ 5 ✗ N/A ✗

10/30/23, 7 : 35 PM Assignment 7: Potential Outcomes Page 14 of 17 https://chris-cornwell.shinyapps.io/Assignment7/#section-b-empirical-analysis The results in Column (1) indicate that the e ! ect of adding an The results in Column (1) indicate that the e ! ect of adding an aide to a regular class is just under _____ of a point and aide to a regular class is just under _____ of a point and statistically (significant/insignificant) _____. statistically (significant/insignificant) _____. 1/3, insignificant Correct! Question 11: What is the impact of teacher experience on the estimated What is the impact of teacher experience on the estimated class-size e ! ect? class-size e ! ect? Correct! Question 12: The estimated coe ! icient of teacher experience in Column (2) The estimated coe ! icient of teacher experience in Column (2) suggests that an additional year of experience is associated suggests that an additional year of experience is associated with about a _____ with about a _____ point increase (round to one decimal place) point increase (round to one decimal place) in test scores. in test scores. 1.5 Correct! Question 13: The The statistic for the teacher-experience coe ! icient estimate in statistic for the teacher-experience coe ! icient estimate in Column (2) is _____ . (Round to one decimal). Column (2) is _____ . (Round to one decimal). Adding teacher experience to the model has such a large impact on the simple di ! erences-in-means estimate given in Column (1), that it changes our perspective on the e ! ect we were trying to measure. ✗ Adding teacher experience to the model has a large impact on the simple di ! erences-in-means estimate given in Column (1). ✗ Adding teacher experience to the model has essentially no impact on the simple di ! erences-in-means estimate given in Column (1). ✓ Adding teacher experience to the model has an important impact on the simple di ! erences-in-means estimate given in Column (1). ✗ t

10/30/23, 7 : 35 PM Assignment 7: Potential Outcomes Page 16 of 17 https://chris-cornwell.shinyapps.io/Assignment7/#section-b-empirical-analysis Question 16: Based on the results in Column (4), the e ! ect of being assigned Based on the results in Column (4), the e ! ect of being assigned to a small class is roughly the same as having teacher with to a small class is roughly the same as having teacher with _____ years more experience (round to the nearest whole _____ years more experience (round to the nearest whole number). number). Correct! Question 17: Overall, the simple di ! erences-in-means result _____ (is/is not) Overall, the simple di ! erences-in-means result _____ (is/is not) highly robust, holding up even when you _____ for a range of highly robust, holding up even when you _____ for a range of student and school characteristics. student and school characteristics. is, control Correct! Continue Previous Topic Next Topic 7 ✗ 16 ✗ 0.234 ✗ 24 ✓

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