As households are unable to finance investment directly but most borrow the funds from a bank, the value of the stock of physical capital, qtKt, is equal to the level of bank loans, which, because banks are assumed to hold no other assets, is also equal to bank capital plus deposits 9)  . But bankers must exert (unobservable) effort (λt) per unit of loans each period to ensure that borrowers invest in productive physical capital rather than unproductive status symbols with private benefit and no recovery value for the bank. So in order for monitoring to be incentive compatible, the cost of monitoring must be less than or equal to the gross return on lending, 10) where Rkt and Rt are gross returns on loans and deposits, respectively. Putting these banking sector equations together and recalling that bankers do not consume but pass on their wealth when they die, we have two additional equilibrium conditions, a no-shirking condition for bankers : 11)  where  BIS Review 111/2010  and  ; and a law of motion for bank capital:  25  12)  ,  where τt is a bank levy/subsidy. Equation (11) shows that the leverage ratio is an increasing function of the spread between the return on capital but decreasing in the monitoring cost (λt). Equation (12) shows that bank capital accumulates according to the profits of surviving bankers.
During the current ZLB episode, the FOMC has again explicitly indicated that it expects monetary policy to warrant exceptionally low levels of the Federal Funds rate “for an extended period”. The Bank of Canada and the Riksbank have also made statements that imply they expect policy rates to remain low for a period, though given the nature and relatively short time horizon of those statements, it is a moot point whether these are best thought of as exercises in commitment or exercises in transparency. The second option at the ZLB involves the outright purchases of longer-dated assets, particularly government bonds, financed by the issuance of extra central bank reserves. Such purchases aim to raise the prices of the purchased assets, together with those of a whole range of assets that are imperfect substitutes as the sellers subsequently re-balance their portfolios. This imperfect asset substitutability may be both time-varying – in particular, the scope for asset substitution may be rather greater in the long run than in the short run – and state-contingent, as traders may be less able to arbitrage between assets in times of economic and financial distress. But as long as there is some period of imperfect asset  4  Taylor (2008) advocates the use of a “spread-adjusted” Taylor Rule to set the policy rate in such circumstances. Cúrdia and Woodford (2009) develop a simple model in which credit frictions generate a spread on the interest rate between savers and borrowers.