# Instrumental Variables

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Instrumental variables (IV) estimation is quasi-experimental approach to data analysis and impact evaluation that overcomes endogeneity through the use of a valid instrument. IV estimation is a useful method to consistently estimate causal impact when there are omitted variables, measurement errors, or simultaneity. This page gives an general overview of IV estimation and assumptions. For more technical details on implementation, see Additional Information.

• A valid instrument must be correlated with the explanatory variable of interest (X) and uncorrelated with the error term (e).
• `ivreg2` is a Stata command that conducts instrumental variable estimation and runs tests for over-identifying restrictions, under-identification, and weak instruments.

## Overview

Instrumental variables (IV) estimation is quasi-experimental approach to data analysis and impact evaluation that uses a valid instrument to overcome endogeneity (i.e. omitted variables, measurement error, or simultaneity). In cases of endogeneity, an OLS regression of the outcome variable (Y) on the explanatory variable of interest (X) yields an inconsistent estimate due to endogeneity. While randomized control trials (RCTs) ensure exogeneity through randomization, they are not always logistically or ethically feasible. In these situations, quasi-experimental methods like IVs prove useful for measuring causal impact under the exogeneity assumption.

A valid instrument must meet both the relevance and exogeneity conditions. The relevance condition states that the instrument is correlated with the explanatory variable of interest (X). The exogeneity condition states that the instrument is uncorrelated with the error term (e). In other words, the instrument affects the outcome (Y) only through X. To estimate causal impact with the instrumental variable, researchers can use two-stage least squares (2SLS), generalized method of moments (GMM) or k-estimators. For more information on implementing these methods, see Additional Information.

`ivreg2`is a Stata command that implements IV estimation. It provides tests of over-identifying restrictions, under-identification, and weak instruments. To install the command, type `ssc install ivreg2` in Stata; for more information on the command and its options, type `help ivreg2`.