#8.28
library(dplyr)
mydir <- "DIRECTORY"
setwd(mydir)
dsURL <- "http://qed.econ.queensu.ca/ETM/data/demand-supply.data"
datedownloaded <- date()
download.file(dsURL,destfile = "ds.txt")
#Manually remove the semi-colon at the end of line 120
ds <- read.table("ds.txt",nrows=120)
ds <- select(ds, -V1)
#Renaming the variables
ds <- rename(ds, q=V2, p = V3, X_2 = V4, X_3 = V5, X_4 = V6, X_5 = V7)
dsfit1 <- lm(q ~ X_2+X_3+p,data=ds)
summary(dsfit1)

#First step of 2SLS, I make the matrix W of instruments
W1 <- cbind(ds$X_2,ds$X_3,ds$X_4,ds$X_5)
X1 <- as.matrix(select(ds,X_2,X_3,p))
#I then manually get the matrix of fitted values from the first stage regression
P_W1 <- W1 %*% solve(t(W1)%*%W1) %*% t(W1)
firstfit <- P_W1 %*% X1
firstfit <- as.data.frame(firstfit)
#Second stage
second <- lm(ds$q ~ firstfit$X_2+firstfit$X_3+firstfit$p)
summary(second)