From the dark days when I tried to grasp non-cooperative game theory, I know that there are circumstances that may make randomised (or mixed) strategies individually rational. Even at an abstract level, I have always considered randomised strategies to be bogus, unless there is a natural randomisation mechanism present in the fundamental structure/specification of the non-cooperative game. A coin toss simply won’t do, because there is no reason why, if heads are called but tails materialise, the coin tosser would be able to impose the action dictated by the outcome of the coin toss on the player. In other words, you cannot add randomisation of strategies as a deus-ex-machina to a game where the natural strategies are ‘pure’, that is, non-stochastic functions of (possibly random) state variables (Who tosses the coin? Isn't he also a player in the game? What are his objectives? What instruments does he have to compel the other players to abide by the outcome of the coin toss etc.?)
Even if I disregard my deep conviction that randomised strategies are bogus - mathematical tricks without behavioural content - unless the randomisation device is itself part of the deep structure of the game, I have never, in the field of monetary policy, come across a configuration of circumstances that would make the deliberate creation of noise, uncertainty and ambiguity sensible, let alone optimal.
Central bankers have, however, often argued differently. I have been confronted many times with central bankers singing the praises of the pernicious doctrine of ‘constructive ambiguity’. This means that the central bank deliberately keeps the private sector in the dark about its true intentions or its true reaction function.
One example of alleged beneficial results from constructive ambiguity, is the central bank acting all coy about the circumstances that would induce it to bail out a private financial institution. This is supposed to be an efficient policy for minimising moral hazard. It's wrong. Policy can be stated clearly and conducted transparently without creating moral hazard. For liquidity problems, there is the discount window. For this to function well, the central bank should accept as collateral a much wider range of assets, including non-investment grade and impaired assets, than it currently does. That may involve the central bank acting as Market Maker of Last Resort in order to price the illiquid collateral. In the case of insolvency of a systemically important institution, it has to be made clear that all equity of the insolvent entity is extinguished if any public money goes in and that all creditors of the insolvent institution may take a hit (including, in the case of commercial banks, depositors to the extent that they are not insured). Finally, the entire top management goes without golden handshakes. That ought to take care of most of the moral hazard.
The threat of unexpected and unannounced foreign exchange market intervention intended to inflict pain on exposed private speculators is supposed to be an effective way of discouraging speculation against the currency, is another example of alleged beneficial use of constructive ambiguity. Even the deliberate creation of unnecessary uncertainty about future central bank interest rate decisions has been justified as a way to prevent the private sector from making one-way bets on some asset price or other.
I don’t buy this cloak-and-dagger-stuff. In my view the central bank’s policy objectives are best served by maximal openness and transparency. From this perspective, the Bank of England is making a mistake, if recent reports are accurate, by instructing the banks and building societies that borrow at its discount window (its ‘standing (collateralised) lending facility') not to comment on their use of that facility. The Bank refuses to comment on the identity of the discount window users, on the amount they borrow, and on the collateral they offer.
If secrecy is indeed what the Bank of England has imposed on its standing lending facility counterparties, it is bad policy. It is bad policy, first, because it won’t work. The £1.6bn collateralised (overnight) loan to Barclays Bank transacted on
The only information conveyed by borrowing at the discount window ought be (1) that the loan was made at an interest rate 100bps above the Bank of England’s policy rate (which currently stands at 5.75%) and (2) that the borrower could offer appropriate (eligible) collateral. How punitive 100bps over the Bank of England’s policy rate is, depends on what the market rate is in the overnight money markets (or interbank market). During August, that rate has risen as high as 6.53%, which is only 12bps below the 6.75% rate charged at the Bank of England’s standing collateralised lending facility.
The best way to de-mystify discount window operations is for the Bank of England to report, for each transaction at the standing lending facility, the identity of the borrower, the spread charged over and above the policy rate, the amount borrowed, the nature of the collateral offered, the valuation of the collateral and the ‘haircut’ applied to it.
Secrecy about who borrows at the discount window, how much is borrowed and against what collateral, is an own goal in the struggle to restore orderly markets, as rumours, gossip, suspicion, leaks and strategic misinformation take the place of transparency and accountability – of the Bank of England to Parliament and of the borrower to its shareholders and other stakeholders. Even more dangerously, it reinforces the perception of the central bank in times of crisis as a manipulator of financial markets rather than a transparent strategic operator in the markets. The sooner this secrecy nonsense is ended, the better.
 In Prescottian real business cycle theory, there is, in a competitive setting, a similar triumph of mathematical convenience over behavioural plausibility. When fixed costs create non-convexities which may well preclude the existence of a competitive equilibrium, some deus-ex-machina organises lotteries to convexify the economic environment. Employment lotteries are a favourite example in models with indivisible labour supply. This is an economic nonsense because there is no plausible story as to how any worker could credibly commit himself to accept the outcome of the lottery, as the winners would be, ex-post, better off than the losers (at least which mixed strategies, the utility levels attached to the pure strategies that are subject to randomisation are the same). There is a second major conceptual embarrassment with these deus-ex-machina lotteries. Typically the models in question are complete contingent market models. However, it is not possible, by assumption, to create contracts contingent on the outcome of the convexifying lottery. Permitting such contracts would re-introduce the non-convexities the lotteries are supposed to cure. This is truly bad, tool-driven economics.
© Willem H. Buiter 2007