Please write the names of any students you worked with on the first page of your problem set. Attach your
\nR output to your problem set. No credit will be given if you report only the final answers without showing
\nformulas and calculations where appropriate, and no credit will be given if the R output is missing.
\nFor the empirical exercise, you must use the dataset posted on Blackboard and R. Please ask your TA if
\nyou have any questions about coding. You must submit both R output and solutions to the empirical exercise.
\n1. Suppose we sample 197 college-educated individuals and 201 individuals with less than college
\neducation to gather information on income and education. Based on our sample, we calculate that
\nindividuals with a college education earn $25.20 an hour, while individuals with less than a college
\neducation earn $21.90 an hour. The standard deviation of hourly earnings for college-educated individuals
\nis 15.4; the standard deviation of hourly earnings of individuals with less than college education is 12.0.
\na. Define College as a binary variable equal to one if the individual has at least a college education and zero
\nif the individual has less than a college education. Write, in regression form, the regression results you
\nwould obtain from an OLS regression of HourlyWage on College. (Write the numerical coefficients you
\nwould get for \ud835\udefd\u0302
\n0 and \ud835\udefd\u0302
\n1; do not write the standard errors.)
\nb. Using a t-statistic, test the hypothesis that the difference in average hourly wages between college- and
\nnon-college educated individuals is zero. Clearly state your alternative hypothesis.
\nc. Calculate the p-value for the same hypothesis test you conducted in part (b). Explain what this p-value
\nmeans in words.
\nd. Repeat part (a) but instead write the regression results you would obtain if you regressed HourlyWage
\non LessThanCollege, where LessThanCollege = 1 if an individual has less than a college education and =0
\nif an individual has at least a college education.
\n2. (S&W Ch. 6: 6.12) A school district undertakes an experiment to estimate the effect of class size on test
\nscores in second-grade classes. The district assigns 50% of its previous year\u2019s first graders to small secondgrade classes (18 students per classroom) and 50% to regular-size classes (21 students per classroom).
\nStudents new to the district are handled differently: 20% are randomly assigned to small classes and 80%
\nto regular-size classes. At the end of the second-grade school year, each student is given a standardized
\nexam. Let \ud835\udc4c\ud835\udc56 denote the exam score for the ith student, \ud835\udc4b\ud835\udc56 denote a binary variable that equals 1 if the student
\nis assigned to a small class, and \ud835\udc4a\ud835\udc56 denote a binary variable that equals 1 if the student is newly enrolled.
\nLet \ud835\udefd1 denote the causal effect on test scores of reducing class size from regular to small.
\nECO 321
\nSpring 2022
\n2
\na. Consider the regression \ud835\udc4c\ud835\udc56 = \ud835\udefd0 + \ud835\udefd1\ud835\udc4b\ud835\udc56 + \ud835\udc62\ud835\udc56
\n. Do you think that \ud835\udc38(\ud835\udc62\ud835\udc56
\n|\ud835\udc4b\ud835\udc56
\n) = 0? Is the OLS estimator of
\n\ud835\udefd1 unbiased and consistent? Explain.
\nb. Consider the regression \ud835\udc4c\ud835\udc56 = \ud835\udefd0 + \ud835\udefd1\ud835\udc4b\ud835\udc56 + \ud835\udefd2\ud835\udc4a\ud835\udc56 + \ud835\udc62\ud835\udc56
\n. Do you think that \ud835\udc38(\ud835\udc62\ud835\udc56
\n|\ud835\udc4b\ud835\udc56\ud835\udc4a\ud835\udc56) depends on \ud835\udc4b\ud835\udc56? Is
\nthe OLS estimator of \ud835\udefd1 unbiased and consistent? Explain. Do you think that \ud835\udc38(\ud835\udc62\ud835\udc56
\n|\ud835\udc4b\ud835\udc56\ud835\udc4a\ud835\udc56) depends on \ud835\udc4a\ud835\udc56?
\nWill the OLS estimator of \ud835\udefd2 provide an unbiased and consistent estimate of the causal effect of transferring
\nto a new school (that is, being a newly enrolled student)? Explain.
\n3. (S&W Ch. 7: 7.8 part (a) and (b) only)
\na. Calculate the \ud835\udc45
\n2
\nfor each of the regressions.
\nb. Calculate the homoskedasticity-only F-statistic for testing \ud835\udefd3 = \ud835\udefd4 = 0 in the regression shown in
\ncolumn (5). Is the statistic significant at the 5% level?
\n4. S&W Empirical Exercise E5.3, parts (a), (b), and (c), and E6.1 part (b) questions (i) and (ii) only. For
\nthis exercise, use the Birthweight_Smoking.csv data set that is posted on Blackboard. (The scanned
\nexercise from the 4th edition is posted on Blackboard.)
\n5. S&W Empirical Exercise E7.1, parts (a), (c), and (d) only. For this exercise, use the
\nBirthweight_Smoking.csv data set that is posted on Blackboard. (The scanned exercise from the 4th edition
\nis posted on Blackboard.)<\/p>\n","protected":false},"excerpt":{"rendered":"
Please write the names of any students you worked with on the first page of your problem set. Attach your R output to your problem set. No credit will be given if you report only the final answers without showing formulas and calculations where appropriate, and no credit will be given if the R output […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[25],"tags":[],"class_list":["post-48171","post","type-post","status-publish","format-standard","hentry","category-statistics"],"_links":{"self":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/48171","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/comments?post=48171"}],"version-history":[{"count":2,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/48171\/revisions"}],"predecessor-version":[{"id":48173,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/48171\/revisions\/48173"}],"wp:attachment":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/media?parent=48171"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/categories?post=48171"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/tags?post=48171"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}