ECN 627: Variables to Work with from the Usual Big STAR Data Set - Economics Assignment Help

 Assignment Task:

Task:

The following table gives the variables to work with from the usual big STAR data set. Use x1 = 8, x2 = 2, and y= 1. x1 x2 y
1 freem frac s ed frac lt hs z mathscore
2 frpm frac s hs frac own z mathscore
3 enrollment s ed frac grd z math score
4 edi s med income z math score
5 re asian fracs sex frac male z elarts score
6 te 1yr frac s sex frac female z elarts score
7 ell frac s age frac 75 older z elarts score
8 ms frac now married z rev total d .5 × math score + .5 × elarts score
9 yrcal s te days d .5 × math score + .5 × elarts score
0 te avgyr s te salary avg d .5 × math score + .5 × elarts score

1.(30 points). Conduct a difference in conditional meanst-test of y conditioned on whether or not x2 is above or below x2,25, which isthe value of x2 at the 25th percentile of itssample distribution in theSTARdataset.(Youcanusethecommandsummary(STAR$x2)inRtogetthevaluesof x2 at different percentilesin itssample distribution.) Then conduct the same difference in meanstest for y, except conditionedonwhether or not x2is aboveorbelowx2,75,which isthevalueof x2at the75thpercentileofitssampledistribution.Whatis?inbothcases?Whatdotheresultsfrom the two t-teststell us about the relationship between x2 and y?

2.(20 points). Regress ln(y) on x1 and x2 and show the results of this regression in the R console.
Interpret the coefficients from this regression.
3.(30 points). Now regress ln(y) on x1, x2 and the square and cube of x2. Using the formula from the lecture notes, construct the homoskedasticity-only F statistic for the null hypothesis that the coefficients on x2, x2 squared, and x2 cubed are all equal to zero. (If you want, you can check to make sure you get the same F statistic when you run this same F test in R, but you don’t have to.)
Do we reject the null hypothesis? What does the result of this test tell us?
4.(20 points). Regress y on x1 and x2 and show the results of this regression in the R console. Which estimated coefficient, β
ˆ1 or β
ˆ
2, is more likely to measure a true causal effect and why?
If x1 is your variable interest, choose four control variables from the STAR data set (they can be from the table above, or other variables from STAR) and run a regression of y on x1 plus the four controls. Why did you choose these four variables and how do they help us identify the causal effect of x1 on y?

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