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We use quantile regressions to model monetary policy reaction functions in three small open economies: Australia, Canada and New Zealand. Focusing on Taylor-type rules, we find evidence of asymmetric interest rate responses for all the countries considered, with monetary policy reacting more strongly to inflation when interest rates are high than when they are low. This is consistent with previous research suggesting that central bankers place more weight on positive deviations of inflation from its target than negative ones. In contrast, the interest rate response to the output gap is largely symmetric and small.