invalidIV project is a set of R functions for linear instrumental variables analysis with potentially invalid instruments (IVs). Eventually, these R functions will become a comprehensive R package for IV analysis with invalid instruments. The methods in these R functions are based on work by Guo, Kang, Cai, and Small (2016) and Kang, Cai, and Small (2016).
To load these functions into R, run the following commands
source("https://raw.githubusercontent.com/hyunseungkang/invalidIV/master/TSHT.R")
source("https://raw.githubusercontent.com/hyunseungkang/invalidIV/master/JMCode.R")The code example.R has additional working examples.
### Obtain the two-stage hard thresholding (TSHT) code from Github ###
source("https://raw.githubusercontent.com/hyunseungkang/invalidIV/master/TSHT.R")
source("https://raw.githubusercontent.com/hyunseungkang/invalidIV/master/JMCode.R")
### R Packages to Load ###
# The AER and MASS packages are only needed to run the working example.
library(AER)
### Working Low Dimensional Example ###
### n = 500, pz = 10 IVs (s = 3 invalid)
# Y: n by 1 vector of outcomes (must be continuous)
# D: n by 1 vector of treatments (continuous or discrete)
# Z: n by pz vector of instruments (continuous or discrete)
# beta: true treatment effect (set at 1)
# Create data #
library(MASS)
n = 500; L = 10; s = 3
alpha = c(rep(3,s),rep(0,L-s)); beta = 1; gamma = c(rep(1,L))
epsilonSigma = matrix(c(1,0.8,0.8,1),2,2)
Z = matrix(rnorm(n*L),n,L)
epsilon = mvrnorm(n,rep(0,2),epsilonSigma)
D = 0.5 + Z %*% gamma + epsilon[,1]
Y = -0.5 + Z %*% alpha + D * beta + epsilon[,2]
### Oracle Two-Stage Least Squares Estimator ###
# This oracle knows exactly which IVs are invalid
# and should perform very well, with the point estimate
# associated with D close to 1 and the 95% confidence
# interval covering 1
summary(ivreg(Y ~ D + Z[,1:s] | Z ))
confint(ivreg(Y ~ D + Z[,1:s] | Z ))[2,]
### Our TSHT Estimator ###
# Our estimator does not assume which IVs are invalid
# a priori. It should perform as well as the the oracle
# above as sample size increases.
# Output is a list that includes
# VHat: estimated set of valid and relevant IVs
# SHat: estimated set of relevant IVs
# betaHat: point estimate of treatment effect
# varHat: estimate of variance of betaHat
# ci: 1-alpha confidence interval for treatment effect
TSHT(Y,D,Z)
### Working High Dimensional Example ###
### You need the following packages to run the high dimensional code
library(Matrix)
library(glmnet)
library(flare)
### n = 500, pz = 600 IVs (s = 3 invalid, 10 relevant)
# Y: n by 1 vector of outcomes (must be continuous)
# D: n by 1 vector of treatments (continuous or discrete)
# Z: n by pz vector of instruments (continuous or discrete)
# beta: true treatment effect (set at 1)
# Create data #
library(MASS)
n = 500; L = 600; s = 3; nRelevant = 10
alpha = c(rep(3,s),rep(0,L-s)); beta = 1; gamma = c(rep(1,nRelevant),rep(0,L-nRelevant))
epsilonSigma = matrix(c(1,0.8,0.8,1),2,2)
Z = matrix(rnorm(n*L),n,L)
epsilon = mvrnorm(n,rep(0,2),epsilonSigma)
D = 0.5 + Z %*% gamma + epsilon[,1]
Y = -0.5 + Z %*% alpha + D * beta + epsilon[,2]
### Oracle Two-Stage Least Squares Estimator ###
# This oracle knows exactly which IVs are invalid
# and should perform very well, with the point estimate
# associated with D close to 1 and the 95% confidence
# interval covering 1
summary(ivreg(Y ~ D + Z[,1:s] | Z[,1:nRelevant] ))
confint(ivreg(Y ~ D + Z[,1:s] | Z[,1:nRelevant] ))[2,]
### Our TSHT Estimator ###
# Our estimator does not assume which IVs are invalid
# a priori. It should perform as well as the the oracle
# above as sample size increases.
# Output is a list that includes
# VHat: estimated set of valid and relevant IVs
# SHat: estimated set of relevant IVs
# betaHat: point estimate of treatment effect
# varHat: estimate of variance of betaHat
# ci: 1-alpha confidence interval for treatment effect
TSHT(Y,D,Z,method="DeLasso")
Guo, Z., Kang, H., Cai, T. T., and Small, D. S. (2018). Confidence Interval for Causal Effects with Invalid Instruments using Two-Stage Hard Thresholding with Voting. Journal of the Royal Statistical Society: Series B (Statistical Methodology. 80:4. 793-815.