Do Estimated Taylor Rules Suffer from Weak Identification?

Over the last decade, applied researchers have estimated forward looking Taylor rules with interest rate smoothing via Nonlinear Least Squares. A common empirical finding for post-Volcker samples, based on asymptotic theory, is that the Federal Reserve adheres to the Taylor Principle. We explore the possibility of weak identification and spurious inference in estimated Taylor rule regressions with interest rate smoothing. We argue that the presence of smoothing subjects the parameters of interest to the Zero Information Limit Condition analyzed by Nelson and Startz (2007, Journal of Econometrics). We demonstrate that confidence intervals based on standard methods such as the delta method can have severe coverage problems when interest rate smoothing is persistent. We then demonstrate that alternative methodologies such as Fieller (1940, 1954), Krinsky and Robb (1986), and the Anderson-Rubin (1949) test have better finite sample coverage. We reconsider the results of four recent empirical studies and show that the evidence supporting the Taylor Principle can be reversed over half of the time.