Ythat you can explain with the IV
Zis related to
Xbut all effects of
X, you’ve isolated a causal effect of
Yby isolating just the causal part of
Xand ignoring all the back doors!
Zis binary, get difference in
Ydivided by difference in
library(AER) #US income and consumption data 1950-1993 data(USConsump1993) USC93 <- as.data.frame(USConsump1993) #lag() gets the observation above; here the observation above is last year IV <- USC93 %>% mutate(lastyr.invest = lag(income) - lag(expenditure)) %>% group_by(cut(lastyr.invest,breaks=10)) %>% summarize(exp = mean(expenditure),inc = mean(income)) cor(IV$exp,IV$inc)
##  0.9993985
Persistence, other things.
RemC) as an instrument for “Actually in remediation” (