We estimate the parameters of a reputational game of political competition using data from five two-party parliamentary systems. We find that latent party preferences (and party reputations) persist with high probability across election periods, with one exception: parties with extreme preferences who find themselves out of power switch to moderation with higher probability than the equivalent estimated likelihood for parties in government (extreme or moderate) or for moderate parties in opposition. We find evidence for the presence of significant country-specific differences. Notably, we estimate that in the long-term, Australia is less than half as likely to experience extreme policies and Australian governments enjoy significantly longer spells in office as compared to their counterparts in Greece, Malta, New Zealand, and the United Kingdom. The model outperforms alternative naive models on a battery of goodness-of-fit tests.