A Toy Instrumental Variable Application

r_instrumental_var.r

# r code to support post: http://econometricsense.blogspot.com/2013/06/an-toy-instrumental-variable-application.html

#   ------------------------------------------------------------------
#  | PROGRAM NAME: R_INSTRUMENTAL_VAR
#  | DATE:6/17/13 
#  | CREATED BY: MATT BOGARD 
#  | PROJECT FILE: P:\BLOG\STATISTICS             
#  |----------------------------------------------------------------
#  | PURPOSE: BASIC EXAMPLE OF IV
#  |
#  | 
#  |------------------------------------------------------------------
 
setwd('P:\\BLOG\\STATISTICS')
 
CAMP <- read.table("mplan.txt", header =TRUE)
 
 
summary(lm(CAMP$RET~CAMP$CAMP + CAMP$INDEX)) # true B1
summary(lm(CAMP$RET~CAMP$CAMP))  #  biased OLS estimate for B1
 
cor(CAMP$CAMP,CAMP$Z) # is the treatment correlated with the instrument?
cor(CAMP$INDEX,CAMP$Z) # is the instrument correlated with the omitted variable
 
cov(CAMP$RET,CAMP$Z)/var(CAMP$Z) # y = bZ
cov(CAMP$CAMP,CAMP$Z)/var(CAMP$Z) # x = bZ
 
# empirical estiamte of B1(IV)
 
(cov(CAMP$RET,CAMP$Z)/var(CAMP$Z))/(cov(CAMP$CAMP,CAMP$Z)/var(CAMP$Z)) # B1(IV)
 
# or
 
(cov(CAMP$RET,CAMP$Z))/(cov(CAMP$CAMP,CAMP$Z)) 
 
# two stage regression with IV substitution
 
# x^ = b1Z
 
CAMP_IV <- predict(lm(CAMP$CAMP~CAMP$Z)) # produce a vector of estimates for x
 
# y = b1 x^

# y = b1 x^
 
lm(CAMP$RET~CAMP_IV)