In other words, bankers have, by assumption, short horizons. They aim to maximise their reputation in the market at the end of this period. 4 At the beginning of each period, each bank originates a risky asset, the return on which depends on (i) the banker’s ability, which can be high or low, and (ii) the macro state, which can be good or bad. Both are unobservable to the market. The macro state is good with probability . High bank ability and a good macro state increase the probability of positive asset returns. That is, when the macro state is bad, assets turn out to be bad, irrespective of bankers’ ability. But when the macro state is good, both high and low ability bankers achieve high returns with some probability, with high ability types always achieving high returns and low ability types achieving high returns with probability . Asset returns are realised in the middle of each period and are observed only by banks. If the asset is good, banks make a profit (normalised to be a negligible amount). If the asset is bad, banks face a loss of –1. Because of their short horizons, bankers care about both the present value of their asset returns and their reputation in the market, where is the probability assigned by the market to a banker being high ability. The market is unable to observe banks’ actions directly, so instead infers bankers’ ability from observed bank earnings. Banks’ earnings are affected by their choices when returns are low.
A concern for reputation incentivises banks to seek risky ventures (to keep dancing), the more so the better is the market’s prior on the macro state (the louder the music). We also posit as a larger proportion of banks set risky credit policies, the larger the incentive to pursue similarly risky policies. When others are posting positive earnings, the reputational loss from foreclosing and taking losses is that much greater. This is the “Keynes constraint”. It is better for your reputation to fail conventionally than to succeed unconventionally. These conditions generate the potential for credit booms and busts. The better is the macro state, the greater banks’ incentive to pursue risky projects to preserve reputation, as the market attributes low earnings to low ability. But one bank’s announcement of positive earnings encourages others to announce positive earnings by setting risky policies too. In Rajan’s model this strategic complementarity between banks generates multiple equilibria: in sufficiently good states, banks coordinate on risky policies (“credit booms”), while in bad states they coordinate on tight policies (“credit crunches”). In between, either equilibrium is possible. Define the payoff function  . Substituting gives:  This captures the marginal return to adopting a risky policy. It allows us to define the regions of fundamentals over which risky policies and tight policies dominate respectively.