Monetary economics as practiced by central bank modelers has made a great deal of progress in recent years. In a 2002 paper I interviewed research economists at four central banks and surveyed the models in use at those banks. I criticized the models for having lost all touch with statistical inference and with its connection to decision theory. I also criticized them for not following the rational expectations literature by jointly specifying and estimating the equations in their systems. And I pointed out that none of the models had a consistent treatment of asset markets. Since then many central banks, taking advantage of the new computational methods for Bayesian inference that economists are learning to use, have made substantial progress toward meeting the first two of these criticisms. They have still for the most part done little about the third. And academic economists are beginning to question some of the standard assumptions in the rational expectations framework that underlies these models. Recent events in financial markets, and the difficulties that they raise for central banks, make it painfully clear that even the frontier Bayesian DSGE models like that in use at the Swedish Riksbank do not model asset markets in any depth. But the problem goes beyond that: these models, and most academic macro models as well, assume a standard rational expectations framework: there is only one probability measure in play, the "true" probability measure from which nature draws realizations. Agents in the model form expectations using this true distribution, conditioning on information sets that consist of all information in the model dated t and earlier. It is well documented that people do not actually behave this way, and in the literature on behavioral finance there is some suggestion that deviations from this standardized assumption of rational behavior given a common probability distribution may be important. The recent events in financial markets - the dotcom boom, the US house price boom, perhaps the continuing commodity price boom - look to some observers like bubbles that must have fed off some sort of irrational behavior. Many observers think that monetary policy might have somehow fueled these bubble-like episodes in asset markets. These are important questions for monetary policy, and it is disturbing that the monetary policy models in use cannot even be used to pose these questions. In this paper I focus on two particular, and related, deviations from the assumption that all agents have the same probability distribution and that they optimally process all information available up to some date t. I consider the implications of agents' being able to process information only at a limited rate, and the implications of agents' assuming differing probability distriubions. This is part of a series of BIS Working Papers (273 to 278) collecting papers presented at the BIS's Seventh Annual Conference on "Whither monetary policy? Monetary policy challenges in the decade ahead" in Luzern, Switzerland, on 26-27 June 2008. The event brought together senior representatives of central banks and academic institutions to exchange views on this topic. BIS Paper 45 contains the opening address of William R White (BIS), the contributions of the policy panel on "Beyond price stability - the challenges ahead" and speeches by Edmund Phelps (Columbia University) and Martin Wolf (Financial Times). The participants in the policy panel discussion chaired by Malcolm D Knight (BIS) were Martin Feldstein (Harvard University), Stanley Fischer (Bank of Israel), Mark Carney (Bank of Canada) and Jean-Pierre Landau (Banque de France). This Working Paper includes comments by Athanasios Orphanides and Lars E O Svensson.