Causal Analysis using R Instrument Variables

Readme.txt

This R script is a step by step tutorial on how to do instrument variable analysis using R.   It contains a brief overview of Instrument Variables including what IVs are, the Two Critical Criteria for IV, Two Stage Least Squares, implementation in R using the ivreg function in the AER package and how to interpret the ivreg outputs. 
For a step by step video demonstration, please visit: https://youtu.be/nVDgLE2ILn4 

R Script

### Causal Analysis using R   Instrumental Variables

## Instrumental variables (IVs) are special variables used in statistics and econometrics 
## to estimate causal effects when ordinary regression methods would be biased due to 
## endogeneity—meaning the explanatory variable is correlated with unobserved factors or the error term.

## Two Key Criterias of IVs
## It is correlated with the problematic (endogenous) explanatory variable.
## It is not correlated with the error term and only affects the outcome through 
## the explanatory variable (called the exclusion restriction).


## Instrumental variables (IV) address bias when explanatory variables correlate with error terms, 
## causing endogeneity.

## A valid instrument is strongly correlated with the endogenous variable (relevance) but uncorrelated 
## with the error term and affects the outcome only through the endogenous variable 
## (exclusion restriction).

## IV estimation typically uses two-stage least squares: first predicting the endogenous 
## variable with the instrument, then estimating the effect on the outcome.

## IVs correct biases from omitted variables, measurement errors, and simultaneous causality.

## Strong instruments improve estimate precision; weak instruments can lead to unreliable results.

## IVs emulate randomized experiments in observational data to infer causal effects.

## Common instruments come from natural or policy variations unrelated directly to the outcome 
## except through the treatment.


### Generate a simulated data set for IV analysis
set.seed(11152025)  # For reproducibility
n <- 200  # Sample size

# Instrument variable (Z), randomly assigned
Z <- rbinom(n, 1, 0.5)

# Unobserved confounder (U)
U <- rnorm(n)

# Endogenous explanatory variable X depends on Z and U
X <- 0.8 * Z + 0.5 * U + rnorm(n)

# Outcome variable Y depends on X and U
Y <- 2 * X + U + rnorm(n)

# Create a data frame
iv_data <- data.frame(Y = Y, X = X, Z = Z)

# View first few rows
head(iv_data)

### Perform an Instrument Variable Analysis

# Install and load the AER package if not already installed



if (!require(AER)) {
  install.packages("AER")
  library(AER)
}

# Assuming 'iv_data' is the dataset with Y, X, and Z
# Perform IV regression with Y as outcome, X as endogenous regressor, and Z as instrument
# using two stage least square (2SLS) estimation

iv_model <- ivreg(Y ~ X | Z, data = iv_data)

# Display summary of IV regression results
summary(iv_model)

## The stimated effect of X on Y after accounting for endogeneity using 
## Z as instrument. This coefficient is 1.784 with a standard error of 0.226, 
## highly significant (p < 0.001).

VideoDemo

For a step by step video demonstration, please visit: https://youtu.be/nVDgLE2ILn4 

For a step by step video demonstration, please visit: https://youtu.be/nVDgLE2ILn4