On Instrumental Variable Regression Method for Estimating Econometric Model Perturbed with Endogenous Variable

Abstract

Regression techniques are essential tools utilized to formulate, describe and evaluate econometric models. These techniques rely on some assumptions which, if one or more are violated the naive approach of estimating econometric models will be characterized with one problem or the other. Most often in real life situations, one or more of these assumptions cannot go unfulfilled while modelling econometric data. This study therefore, focuses on the consequences of violation of the assumption that error terms are linearly independent of explanatory variables in classical linear econometric model. For the Ordinary Least Squares (OLS) estimator to be sufficient, the expected value of the error term given the explanatory variable should be zero. And for OLS estimator to be consistent, the covariance between the error term and any of the explanatory variables should be zero. Endogeneity is one of the major challenges of econometric analyses. The effect of endogeneity is bias in estimates and therefore inducing the likelihood of committing the Types I and II errors more rapidly. To examine the behaviours of OLS estimators in the presence of endogeneity and compare its performances with Two-Stage Least Squares (2-SLS) as an alternative method of estimation, data were simulated in the environment of R statistical package in which endogeneity problem was infused into the data. It was discovered that relative to OLS, 2-SLS is consistent and less biased when modelling econometric data that are perturbed with endogeneity problem. Although, the 2-SLS might not be more efficient than the OLS under certain condition, but when there is problem of endogeneity in the model, the choice between OLS and 2-SLS depends on whether the Analyst is willing to trade-off efficiency for biasedness or vice versa in finite sample and asymptotically.