Using stochastic simulations, this article analyses the probability distribution of a country's deficit ratio under fixed exchange rates and a variety of monetary and fiscal policy rules. The purpose is to show how the probability of an 'excessive deficit', defined by Europe's Stability Pact as a deficit to GDP ratio above 3 per cent, varies with different deficit targets and policy rules. Using a macro model, we find that when subject to historically consistent shocks, these fiscal ratios typically have a wide distribution, with fat tails and significantly longer tails on the upper side. That means fiscal targets may have to be country-specific and conservative, and that fiscal policy has to be forward-looking to keep the probability of excessive deficits below acceptable limits.