Working Paper

Taylor Rule Estimation by OLS

Abstract: 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 inflation and the output gap, that are endogenous to monetary policy shocks. Endogeneity implies a correlation between regressors and the error term – hence, an asymptotic bias. In principle, Instrumental Variables (IV) estimation can solve this endogeneity problem. In practice, however, 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 due to monetary policy shocks. Using Monte Carlo simulations, we then show that this relationship also holds in a quantitative model of the U.S. economy. Since monetary policy shocks explain only a small fraction of the variance of regressors typically included in monetary policy rules, the endogeneity bias tends to be small. For realistic sample sizes, OLS outperforms IV. Finally, we estimate a standard Taylor rule on different subsamples of U.S. data and find that OLS and IV estimates are quite similar.

Keywords: Taylor Rule; Ordinary Least Squares (OLS); GMM; endogeneity; bias; weak instruments; New Keynesian models;

JEL Classification: E47; E50; E52; E58;

https://doi.org/10.24148/wp2018-11

Bibliographic Information

Provider: Federal Reserve Bank of San Francisco

Part of Series: Working Paper Series

Publication Date: 2021-09-01

Number: 2018-11

Note: The first version of this paper was September 6, 2018.