Endogeneity in Models

Endogeneity arises when explanatory variables are correlated with the error term, posing a serious threat to causal inference in econometric analysis. This chapter addresses endogeneity in the context of nonlinear economic systems, where feedback loops, simultaneity, and coevolution of variables amplify identification challenges. Here, we systematically examine three primary sources of endogeneity: simultaneity bias (mutual causation), omitted variable bias (unobserved confounders), and measurement errors. Using the empirical relationship between inflation and interest rates as a motivating example, we demonstrate how naive ordinary least squares (OLS) estimation produces biased, inconsistent estimates when endogeneity is present. The chapter progresses through formal diagnostic testing (Wu-Hausman, Sargan tests) and linear instrumental variable (IV) methods and extends to nonlinear specifications including quadratic and log-log IV-GMM models. Through hands-on implementation with US macroeconomic data, readers learn not only how to correct for endogeneity but when different specifications are appropriate and why functional form matters for economic interpretation. The comparative analysis reveals how elasticity estimates vary dramatically across specifications, findings with direct implications for monetary policy evaluation in the volatile post-COVID economic environment.