This paper analyses the impact of asymmetric preferences with respect to inflation and output by policymakers on interest-rate reaction functions and test for their existence. A modified New Keynesian framework which makes it possible to identify the dominant type of asymmetry is developed and related to the precautionary demand of policymakers for expansions and for low inflation. Using data for four G7 economies, the paper shows that, except for Germany, nonlinear and asymmetric behaviour is present. A main finding, for the US, is that after credibility-building and disinflation have been established, the monetary authority develops a greater precautionary demand for output expansions than for low inflation. This may generate a new type of inflation bias. Conversely, where, as is the case in the UK, credibility-building is still a concern for the authorities, managing the business cycle is dominated by concerns of the monetary authorities to keep inflation expectations low.