Assignment 2 2022
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Assignment 2
2022
1. (25 points) Load the STAR small data set and the MASS data set into R. Consult table 9.2 from the Week 2 lecture slides (slide 5, package 2). Select the column number from the table above that corresponds to the 6th digit in your Ryerson student number.1 Replicate the results for that column given in the table and then generate the same regression using the STAR (small) dataset and the combined STAR and MASS data sets (three regressions in total). Screenshot the results from R showing the commands and the output from the three regressions. Make sure the three regressions are clearly labeled which is which.
2. (25 points) Now run two versions of your assigned regression from (1) on the Massachusetts data using grade 4 and grade 8 standardized test scores as the dependent variables (i.e. two separate multiple regressions, but one is just a repeat from question 1). Screenshot the results of the regressions in R. How do the regression results differ when you use test scores from younger vs. older students as y? Why do you think you see the similarities and differences you do? Do the differences suggest a threat to the external validity of the regressions?
3. (25 points) Suppose now we are interested in understanding how resources are allocated to schools. Using the combined district-level STAR and MASS data sets, regress total expenditure per student on the natural log of average income in the district, the share of English second language students in the district, a dummy variable for California, and the interaction of the state dummy with share of ESL students. Screenshot the output from R and interpret what it says. Do we need to worry about simultaneity bias with any of the independent variables in this regression?
4. (25 points) Suppose now we want to regress average elementary school test scores in the district (y) on average income in the district (北) to identify the causal effect of local wealth on school performance. But we worry that income may be measured with error, leading to errors in variables bias. Assuming that the measurement error in 北 is classical, an instrumental variables strategy could solve the problem. Let the instrument be z where z corresponds to the eighth number of your Ryerson student number from the table above (and use the cor- responding sample, from either Mass or Cali). Run the 2SLS using the “by hand” method from tutorial #4 (don’t worry about adjusting the standard errors for now) and screenshot the output in R. Do you think your instrument is valid? Explain why or why not.
2022-07-14