hw6.sol - Page 1 of 3 Stat209/Ed260 D Rogosa 2/20/09...

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Stat209/Ed260 D Rogosa 2/20/09 Solutions Assignment 6. Instrumental variable methods, simultaneous equations see also Lab3 exercises ------------------------ Problem 1. Schneider et al Public School choice reprinted paper also available Jstor Institutional Arrangements and the Creation of Social Capital: The Effects of Public School Choice Mark Schneider; Paul Teske; Melissa Marschall; Michael Mintrom; Christine Roch The American Political Science Review > Vol. 91, No. 1 (Mar., 1997), pp. 82-93 Stable URL: http://links.jstor.org/sici?sici=0003-0554%28199703%2991%3A1%3C82%3AIAATCO%3E2.0.CO%3B2-6 Answers in Freedman text p.262 scan of answer page at http://www-stat.stanford.edu/~rag/stat209/08hw6p1sol.pdf ---------------- Problem 2. simulation described in Freedman text bottom p.191-top p.192 > library(MASS) Warning message: package 'MASS' was built under R version 2.2.1 > ?mvrnorm > # Freedman pp191-2, simulate 100 obs make .3 correlation delta epsilon > zeddelteps = mvrnorm(n=100, mu = c(0,0,0), Sigma= + matrix(nrow = 3, ncol = 3, data = c(3,0,0,0,1,.3,0,.3,1), byrow = T), empirical = TRUE) > cor(zeddelteps) [,1] [,2] [,3] [1,] 1.000000e+00 2.661070e-16 -3.463923e-16 [2,] 2.661070e-16 1.000000e+00 3.000000e-01 [3,] -3.463923e-16 3.000000e-01 1.000000e+00 > # could also just take what I get from mvrnorm to get close go up to 400 at least > xsim = .75*zeddelteps[,1] + zeddelteps[,2] # C = .75 set > cor(xsim, zeddelteps[,1]) [1] 0.7924058 > ysim = .5*xsim + zeddelteps[,3] # beta = .5 set > cor(ysim,xsim) [1] 0.7140388 > ols = lm(ysim ~ xsim) > summary(ols) Call: lm(formula = ysim ~ xsim) Residuals: Min 1Q Median 3Q Max -3.8382 -0.4933 0.0961 0.6177 1.8380 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -2.542e-16 9.881e-02 -2.57e-15 1 xsim 6.116e-01 6.058e-02
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This note was uploaded on 08/20/2011 for the course STATS 209 taught by Professor Rogosa,d during the Winter '09 term at Stanford.

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hw6.sol - Page 1 of 3 Stat209/Ed260 D Rogosa 2/20/09...

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