Econometrics $-$ Homework $5-$ Regression Discontinuity Designs

General Instructions

$-$ Use RDD to estimate the impact of precalculus on a calculus exam score.

$-$ Do the question in Stata $($or whatever package you are using if not Stata$).$

$-$ Use the dataset, "precalc analysis data $2.$csv$."$ We will use these variables:

$-$ aleks: Score on the ALEKS math placement test

$-$ intent: $1$ if the student scored $70$ or below on the ALEKS placement test, indicating they should take precalculus, $0$ otherwise

$-$ treat: $1$ if the student took precalculus, $0$ otherwise

$-$ hsgpa: High school GPA

$-$ actcon: ACT score or calculated ACT equivalent of SAT score

$-$ Keep only observations for which the variables exam, treat, aleks, intent, actcon, and hsgpa are all not missing.

$-$ Perform analytical steps $1-14$ listed below. These steps are structured to help you complete the work efficiently. Together the do files from homework $3$ and the classes on RDD provide something close to a template you can work from to facilitate doing this assignment.

$-$ You can do more analysis if you would like, e$.$g$.$ taking natural logs$,$ creating other figures, checking other specifications, or including ACTCON or HSGPA, but that is not required.

$-$ Organize your work as a coherent report on the causal effect of precalculus on success in calculus. Don't just provide a list of results$/$answers matching the analytical steps. Your report should include four figures that are neatly labeled and self$-$explanatory and a table with results from four regression models. Make sure to explain why RDD is appropriate, why this is a fuzzy RDD$,$ and what that means.

$-$ Include the do file to replicate your work in Stata and the log file from a clean run of the do file as appendices to your answer to this question.

Analytical Steps

$1.$ Prepare a cross tabulation to gauge compliance with treatment assignment.

$2.$ Create a figure to examine the discontinuity in treatment assignment at the assignment threshold applying a linear fit $($lfit$)$ to the data each on side of the cutoff.

$3.$ Create a figure to examine the discontinuity in treatment assignment at the assignment threshold applying a local mean smoother $($lpoly with degree $0)$ to the data on each side of the cutoff. Try a few reasonable bandwidths. Ten points $($a $20$ point interval$)$ is too wide and $1$ point $($a $2$ point interval$)$ is too narrow. Within that range, find something relatively smooth but no wider than it takes to achieve that.

$4.$ Based on $1-3,$ discuss why this is a fuzzy RDD and whether intent is a good instrument.

$5.$ Create a figure to examine the discontinuity in exam at the assignment threshold using a linear fit $($lfit$)$ to the data each on side of the cutoff.

$6.$ Estimate a regression model of the effect of intent on exam controlling for ALEKS. Store the results as Model $1.$

$7.$ Estimate a model of the effect of intent on exam controlling for aleks and the interaction of intent and aleks, intentXaleks. Store the results as Model $2.$ Econometrics $-$ Homework $5-$ Regression Discontinuity Designs

$8.$ Check the variance inflation factors after the prior regression and use them to explain the problem with interpreting the results of that regression.

$9.$ Estimate a model of the effect of intent on the probability of treatment controlling for aleks. Explain the meaning of the coefficient on intent. Store the result as Model $3.$ Generate predicted values of treatment based on this regression, named predtreat.

$10.$ Use the results of Models $1$ and $3$ to estimate the LATE. Explain your process and interpret the LATE.

$11.$ Estimate a model of the effect of predicted treatment on exam controlling for aleks. Interpret the coefficient on predicted treatment. Save the results as Model $4.$ Explain its relationship to the LATE calculated in step $10.$ Generate predicted values for exam based on this regression, named predexam.

$12.$ Create a figure to examine the discontinuity in exam at the assignment threshold applying a local mean smoother $($lpoly with degree $0)$ to exam on each side of the cutoff. Try a few reasonable bandwidths. Ten points $($a $20-$point interval$)$ is too wide and $1$ point $($a $2$ point interval$)$ is too narrow. Within that range, find something relatively smooth but no wider than it takes to achieve smoothness.

$13.$ How do you interpret the results of the figure from $12?$ How does it compare to the results from $11?$

$14.$ Use the etable command to prepare a neat table of the results from the four estimated regression models to include in your write up$.$