Taylor rule estimation by OLS

Ordinary Least Squares (OLS) estimation of monetary policy rules produces potentially inconsistent estimates of policy parameters. The reason is that central banks react to variables, such as in ation and the output gap, which are endogenous to monetary policy shocks. Endogeneity implies a correlation between regressors and the error term, and hence, an asymptotic bias. In principle, Instrumental Variables (IV) estimation can solve this endogeneity problem. In practice, IV estimation poses challenges, as the validity of potential instruments depends on various unobserved features of the economic environment. We argue in favor of OLS estimation of monetary policy rules. To that end, we show analytically in the three-equation New Keynesian model that the asymptotic OLS bias is proportional to the fraction of the variance of regressors accounted for by monetary policy shocks. Using Monte Carlo simulation, we then show that this relationship also holds in a quantitative model of the U.S. economy. As monetary policy shocks explain only a small fraction of the variance of regressors typically included in monetary policy rules, the endogeneity bias is small. Using simulations, we show that, for realistic sample sizes, the OLS estimator of monetary policy parameters outperforms IV estimators.