This paper draws attention to inconsistencies in estimating simple monetary policy rules and their implications for policy advice. We simulate a macroeconomic model with a backward reaction function similar to Taylor (1993). We estimate different versions of a policy rule, using these simulated data. Under certain circumstances, estimations document an illusionary presence of a lagged interest rate, or of forward-looking behavior. Our results are consistent with the fact that several authors found very different versions of monetary policy rules, all fitting the U.S. data well. We also survey the literature, providing a list of issues complicating practical use of Taylor rules.