Plate xi in print

The Contagion

systemic externalities; the risk one firm's gamble visits on the whole, financial contagion, and the case for taxing fragility.

The risk can travel farther than the balance sheet.

— the argument of this plate, after Brunnermeier (2009) and Korinek (2011)

A bank can keep every promise due this morning and still make the afternoon more dangerous for its neighbors. It can sell the securities needed to meet a withdrawal, reduce its borrowing to satisfy a lender, and close a position before its own capital is exhausted. Each action repairs something within its balance sheet. Together, the sales may depress the price of assets that other institutions own and pledge, requiring those institutions to make the same retreat. The risk has crossed a boundary. Some connections are contractual: one firm’s unpaid obligation is another firm’s missing receipt. Others run through a common market, joining institutions that have never lent to each other. A shared exposure can make many banks lose money at once; their responses can then enlarge the original loss. The first fact concerns the shock. The second concerns the machinery that carries it onward. This is the systemic externality: a decision whose consequences for the financial system extend beyond the loss the decision-maker and its immediate creditors have priced.1

1. Markus K. Brunnermeier, “Deciphering the Liquidity and Credit Crunch 2007–2008”, Journal of Economic Perspectives 23, no. 1 (2009), pp. 91–98, especially the loss and margin spirals and the separate counterparty network mechanism. The discussion here uses these mechanisms without treating every common loss as contagion.

The arithmetic of a leveraged balance sheet gives the first movement its force. Suppose a bank owns assets worth 100 and owes 70. Its equity is 30, and its lender permits debt up to three quarters of the value of its assets. A fall in asset value to 90 leaves equity of 20, but the debt now exceeds that ceiling. If the bank can obtain no fresh equity or replacement funding, it must sell assets and use the proceeds to repay debt. Selling 10 leaves assets of 80 and debt of 60, restoring the permitted ratio. A larger initial fall, to 80, requires a sale of 40: the remaining assets of 40 support debt of 30. These figures hold the sale price fixed, assume repayment at par, and leave interest and transaction costs aside. They show how an asset loss of 20 can require a balance-sheet contraction twice as large. If many banks attempt those sales into a market with limited buying capacity, the price can fall further and the calculation must be done again. With entirely equity-financed assets, the same price fall reduces the owners’ wealth but creates no such contractual need to sell. The amplification belongs to the combination of financing and market conditions.2

2. The figures are an illustrative balance sheet. For a sale s at the prevailing price, the binding condition is 70 − s = 0.75(A − s). Brunnermeier, pp. 91–95, distinguishes difficulty raising funds from difficulty selling assets, and shows how their interaction can amplify losses.

The falling price has to be followed into the uses of the assets before it can be counted as a social cost. A buyer who can wait may welcome the sale; the seller’s lower receipt is partly the buyer’s improved bargain. Ordinary competition continually changes prices and redistributes gains in this way. The further difficulty arises when the price also governs access to finance. A productive owner may be forced to surrender an asset because its future income cannot be pledged to meet today’s payment, while a less productive buyer has the cash to acquire it. A reduction in market value can therefore tighten constraints, displace productive activity, and cause additional sales elsewhere. The relevant comparison includes the output that this displacement sacrifices, alongside the gains to purchasers. A decline that simply records worse expected earnings has a different meaning from a decline enlarged by forced liquidation. The inquiry must establish the constraint and the lost use; a chart of falling prices supplies neither by itself.

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Anton Korinek’s model makes this distinction precise by giving bankers a productive asset, a payment due before its final return, and a limit on their ability to borrow against that return. When current resources fall short, they sell to buyers whose marginal productivity declines as they acquire more. A banker deciding how much insurance to buy takes the future selling price as given. A planner also counts the way fewer forced sales would support the prices at which other constrained bankers sell. Liquidity in distress consequently has a social value above its private value, and privately chosen insurance leaves excessive exposure to fire sales. The result depends on the specified financing restrictions and costly risk sharing. When constraints remain loose, the model’s private and social valuations coincide. Allowing the productive owners to borrow freely against the final return removes this route to inefficient liquidation. The argument identifies a particular failure of coordination within financial markets, with conditions under which the failure disappears.3

3. Anton Korinek, “Systemic Risk-Taking: Amplification Effects, Externalities, and Regulatory Responses”, ECB Working Paper 1345 (June 2011), §§1–2, 3.1 and 4, pp. 6–16 and 20–28. In this model the later buyers cannot supply risk-neutral insurance at the initial date; that restriction also matters to the result.

The corresponding levy belongs at the point where the exposure is chosen. A lender and borrower already have reasons to price the losses each may suffer. The additional charge concerns the marginal harm their financing arrangement would impose on others when distress arrives. Its size therefore depends on the states in which payments become due. An obligation that demands cash precisely when many institutions are constrained can have a different systemic cost from an obligation of the same average size that falls mainly in prosperous states. A claim that brings resources into a distressed institution can instead relieve the pressure. Korinek’s externality price is zero in unconstrained states and positive where the financing mechanism magnifies losses; under his assumptions, a state-contingent tax, with compensating transfers, can implement the constrained efficient allocation. This is the financial counterpart of the levy on smoke: the privately attractive transaction is made to face a consequence beyond its own accounts. It is also a demanding measurement problem. Neither the face value of a loan nor the volatility of an asset alone reveals that consequence.4

4. Korinek, §5.2, pp. 30–34, defines the externality price as the difference between social and private valuations of liquidity and derives the charge on a claim’s state-dependent payments. The implementation is a result within that model, including its transfer and information assumptions; it supplies no numerical tax rate for an actual bank.

The practical instruments address different parts of the chain. More equity can absorb a loss before a borrowing limit binds; dependable funding can reduce the amount that must be raised at once; liquid assets can meet a payment without an immediate sale of the less liquid book. Information about connected obligations can reveal exposures that an institution’s own accounts leave obscure. These arrangements have costs, and the useful provision of credit still requires someone to bear risk. Their economic case rests on how much harmful amplification they avert relative to the resources they use and the activity they displace. Timing matters as well. Requiring a protective position before distress and demanding an immediate sale during distress act on different margins. Korinek’s extension on new equity finds a further gap: a bank can undervalue recapitalization because part of its benefit reaches other sellers through the asset price. That result gives a reason to examine collective action; the actual instrument must still be matched to the constraint it can relax.5

5. Brunnermeier, pp. 91–98, supplies the funding, liquidity and network distinctions. Korinek, §5.3 and conclusion, pp. 34–36, studies costly equity issuance and explains the model’s limits, including extensions in which falling collateral values further restrict borrowing. The comparison of instruments here follows these distinct mechanisms.

Who should pay to make the bank safe is therefore a question about responsibility at the margin, followed by a question about who ultimately bears the charge. The institution’s contribution to fragility gives the first inquiry its object; the response of borrowers, investors and competitors determines how a particular rule distributes its burden. A bank’s survival is one outcome. The continuation of useful financing across the system is the wider purpose. The network that conveys funds can also convey the pressure to withdraw them, and a private precaution can deepen the collective danger when everyone takes it together. The last plate carries the boundary farther. Financial contagion travels through claims, prices and constraints that institutions can alter. Carbon enters a physical stock whose effects outlast both the bargain that released it and many of the people who made the bargain. In The Atmosphere, the absent parties include other nations and the future itself.