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This paper offers a new approach that estimates the response of interest rates to inflation and the output gap at various points (quantiles) on the conditional distribution of interest rates. This offers an improvement on empirical estimates conducted only at the mean and also allows us to test the propositions that policy shows greater aggression to inflation in the reaction function in terms of a greater response coefficient as interest rates reach low levels, and increasing aggression as the lower bound is approached. We find support for the Taylor principle, a more aggressive response to inflation than under a Taylor rule, but no detectable evidence of increasing aggression as the zero lower bound is approached in the US and Japan. [ABSTRACT FROM AUTHOR]