# Integrating endogeneity in survey sampling using instrumental-variable calibration estimator

## TL;DR

This paper introduces a new method to improve survey sampling when some variables are misleading, using instrumental-variable calibration to reduce bias and increase accuracy.

## Contribution

The novelty lies in proposing instrumental-variable calibrated estimators that outperform conventional methods in the presence of endogenous auxiliary variables.

## Key findings

- Instrumental-variable calibration estimators reduce bias and variance in survey sampling with endogenous variables.
- Simulation and real data examples confirm the improved performance of the proposed estimators.
- The method is more efficient than traditional calibration when auxiliary variables are endogenous.

## Abstract

The endogeneity problem arises when the auxiliary variables correlate to the error terms. In such cases, appropriate instrumental variables ensure efficient estimation. Calibration has recognized itself as an important methodological tool at a large scale to estimate the population total in survey sampling. Which does not offer efficient estimation in the presence of endogeneity. When endogeneity is present in the auxiliary variables, the calibration using endogenous auxiliary variables may produce biasedness and increase variance due to inappropriate model assumptions. In this article, we propose instrumental-variable calibrated estimators by using the classical instrumental-variables approach for the case of exact identification that are more efficient than conventional calibration estimators when some auxiliary variables are endogenous. The necessary properties of the proposed estimators are presented. Our study is backed by both the simulation study and a real data example to check the performance of the proposed estimators.