Monetary policy rule parameters estimated with conventional estimation techniques can be severely biased if the estimation sample includes periods of low interest rates. Nominal interest rates cannot be negative, so that censored regression methods like Tobit estimation have to be used to achieve unbiased estimates. We use IV-Tobit regression to estimate monetary policy responses for Japan, the US and the Euro area. The estimation results show that the bias of conventional estimation methods is sizeable for the inflation response parameter, while it is very small for the output gap response and the interest rate smoothing parameter. We demonstrate how IV-Tobit estimation can be used to study how policy responses change when the zero lower bound is approached. Further, we show how one can use the IV-Tobit approach to distinguish between desired policy responses, that the central bank would implement if there was no zero lower bound, and the actual ones and provide estimates of both.