This article aims to provide a comprehensive guide on performing 2SLS (Two-Stage Least Squares) regression in R, specifically for binary endogenous variables. We will discuss the key concepts, examples, and code snippets to help you understand and implement this technique effectively.
Two-Stage Least Squares (2SLS) Regression
Two-Stage Least Squares regression is an econometric technique used to address the issue of endogeneity in linear regression models. Endogeneity arises when the explanatory variables are correlated with the error term, violating the standard assumption of exogeneity.
2SLS Regression Process:
The 2SLS regression process involves the following two stages:
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In the first stage, the endogenous variables are regressed on the instruments using a linear regression model.
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In the second stage, the original model is re-estimated using the predicted values from the first stage as the explanatory variables.
Example of 2SLS Regression in R
Assumptions:
Suppose we have an outcome variable Y, two binary endogenous variables X1 and X2, and a set of instruments Z1, Z2, and Z3.
The relationship between the variables is given by the following equation:
Y = β0 + β1*X1 + β2*X2 + ε
However, X1 and X2 are correlated with the error term ε, so we need to use 2SLS regression to address this issue.
Instruments Selection:
When selecting instruments, it's essential to ensure that they are strong predictors of the endogenous variables but not correlated with the error term. The validity of the instruments is crucial for the 2SLS regression to provide reliable results.
First Stage:
# First stage regression
first_stage_model_X1 <- lm(X1 ~ Z1 + Z2 + Z3)
first_stage_model_X2 <- lm(X2 ~ Z1 + Z2 + Z3)
In this example, we have estimated two first-stage regression equations, one for each endogenous variable.
Second Stage:
Now, we can use the predicted values from the first-stage regression as explanatory variables in the second stage.
# Predicted values from the first stage
X1_hat <- predict(first_stage_model_X1)
X2_hat <- predict(first_stage_model_X2)
# Second stage regression
second_stage_model <- lm(Y ~ X1_hat + X2_hat)
Finally, we have estimated the 2SLS regression model using R.
- Two-Stage Least Squares (2SLS) regression is a method to address endogeneity in linear regression models.
- 2SLS regression involves two stages: first-stage regression of endogenous variables on the instruments and second-stage regression using the fitted values from the first stage.
- In order to perform a 2SLS regression in R, you can use the
lmfunction twice, first for the first stage and then for the second stage, using the predicted values obtained from the first stage.
References
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Book: Wooldridge, J. M. (2010). Introductory Econometrics: A Modern Approach. Cengage Learning.
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Article: Angrist, J. D., & Krueger, A. B. (1991). Instrumental Variables and the Return to Schooling. The Review of Economic Studies, 58(3), 277-303.
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Online Resource: https://economics.mit.edu/files/3663