# On the Effect of Imputation on the 2SLS Variance

## TL;DR

This paper examines how imputation affects the variance estimation in two-stage least squares (2SLS) when dealing with endogeneity and missing data, proposing a robust variance estimator.

## Contribution

It derives an asymptotic variance formula and introduces a heteroskedasticity robust estimator that accounts for imputation in 2SLS, improving inference accuracy.

## Key findings

- Conventional variance estimators are unreliable with imputed data.
- The proposed estimator is heteroskedasticity robust and accounts for imputation effects.
- Monte Carlo simulations validate the theoretical improvements.

## Abstract

Endogeneity and missing data are common issues in empirical research. We investigate how both jointly affect inference on causal parameters. Conventional methods to estimate the variance, which treat the imputed data as if it was observed in the first place, are not reliable. We derive the asymptotic variance and propose a heteroskedasticity robust variance estimator for two-stage least squares which accounts for the imputation. Monte Carlo simulations support our theoretical findings.