Existing estimates of the macroeconomic effects of Australian monetary policy tend to be based on strong, potentially contentious, assumptions. I estimate these effects under weaker assumptions. Specifically, I estimate a structural vector autoregression identified using a variety of sign restrictions, including restrictions on impulse responses to a monetary policy shock, the monetary policy reaction function, and the relationship between the monetary policy shock and a proxy for this shock. I use an approach to Bayesian inference that accounts for the problem of posterior sensitivity to the choice of prior that arises in this setting, which turns out to be important. Some sets of identifying restrictions are not particularly informative about the effects of monetary policy. However, combining the restrictions allows us to draw some useful inferences. There is robust evidence that an increase in the cash rate lowers output and consumer prices at horizons beyond a year or so. The results are consistent with the macroeconomic effects of a 100 basis point increase in the cash rate lying towards the upper end of the range of existing estimates.