Instrumental variables estimation

Instrumental Variables Estimation (IV estimation) is a method used in statistics, econometrics, and epidemiology to estimate causal relationships when controlled experiments are not feasible and there is an endogeneity problem due to the correlation between the explanatory variable and the error term in a regression model. This method helps in obtaining consistent estimators when the standard assumptions of ordinary least squares (OLS) regression are violated.

Overview

The key idea behind IV estimation is to use an instrument, or an instrumental variable, which is correlated with the endogenous explanatory variables but uncorrelated with the error term. The instrumental variable should not have a direct effect on the dependent variable, except through its correlation with the endogenous explanatory variables. This allows for the estimation of the causal effect of the explanatory variable on the dependent variable.

Requirements for Instrumental Variables

For an instrumental variable to be valid, it must satisfy two main conditions:

1. Relevance: The instrument must be correlated with the endogenous explanatory variable. This is often tested using the first-stage F-statistic.
2. Exogeneity: The instrument must not be correlated with the error term in the regression model, ensuring that the instrument does not directly affect the dependent variable outside of its relationship with the endogenous variable.

Estimation Techniques

Several techniques are used for IV estimation, including:

• Two-Stage Least Squares (2SLS): This is the most common method, where the first stage involves regressing the endogenous variable on the instrument(s) to obtain predicted values. In the second stage, these predicted values are used as explanatory variables in the regression model.
• Limited Information Maximum Likelihood (LIML): A method that is similar to 2SLS but can be more robust in certain situations.
• Generalized Method of Moments (GMM): A flexible method that can accommodate multiple instruments and endogenous variables.

Applications

IV estimation is widely used in various fields:

• In econometrics, it is used to estimate the effects of education on earnings, where education is endogenous due to factors like ability bias.
• In epidemiology, it can be used to assess the causal impact of a treatment when randomization is not possible, and there is selection bias.
• In political science, it helps in understanding the causal effects of policies when there is endogeneity due to omitted variable bias or reverse causality.

Limitations

While powerful, IV estimation has limitations:

• Finding a valid instrument is often challenging.
• Instruments that are weakly correlated with the endogenous variables can lead to biased and inconsistent estimates.
• Over-reliance on statistical tests for instrument validity can be misleading.

Conclusion

Instrumental Variables Estimation is a crucial tool in the analysis of causal relationships in observational data. Its proper application requires careful consideration of the assumptions underlying the choice of instruments and the estimation technique used.