Financial Networks and Contagion

"Financial Networks and Contagion," a recent paper by Matthew Elliott, Benjamin Golub, and Matthew Jackson, uses network theory to study how financial interdependencies among governments, central banks, investment banks, and other institutions can lead to cascading defaults and failures.

Source: Elliott et al. 2013

While the model is quite technical, the main theoretical findings are fairly intuitive. They define two key concepts, integration and diversification. Integration refers to the level of exposure of institutions to each other through cross-holdings. Diversification refers to how spread-out the cross-holdings are; in other words, whether a typical organization is held by many others or just a few. The key finding is that at very low or very high levels of integration and diversification there is lower risk of far-reaching cascades of financial failures. The risk of a far-reaching cascade is highest at intermediate levels of integration and diversification. The authors explain:

"If there is no integration then clearly there cannot be any contagion. As integration increases, the exposure of organizations to each other increases and so contagions become possible. Thus, on a basic level increasing integration leads to increased exposure which tends to increase the probability and extent of contagions. The countervailing effect here is that an organization's dependence on its own primitive assets decreases as it becomes integrated. Thus, although integration can increase the likelihood of a cascade once an initial failure occurs, it can also decrease the likelihood of that first failure... 

With low levels of diversification, organizations can be very sensitive to particular others, but the network of interdependencies is disconnected and overall cascades are limited in extent. As diversification increases, a "sweet spot" is hit where organizations have enough of their cross-holdings concentrated in particular other organizations so that a cascade can occur, and yet the network of cross-holdings is connected enough for the contagion to be far-reaching. Finally, as diversification is further increased, organizations' portfolios are sufficiently diversified so that they become insensitive to any particular organization's failure."

Near the end of the paper, they illustrate the model using cross-holdings of debt among six European countries. The figure above is their representation of financial interdependencies in Europe. They conduct something akin to stress tests, simulating cascades of failures under various scenarios that very roughly approximate conditions in 2008. The simulations find that, following a first failure in Greece, Portugal is fails from contagion. After Portugal fails, Spain fails due to its large exposure to Portugal. The high exposure of France and Germany to Spain causes them to fail next in most simulations. Italy is always last to fail due to its low exposure to others' debt. They emphasize that this is intended only as an illustrative exercise at this stage, but could eventually be refined and incorporated into analysis of failure and contagion risk.

*Edited to fix my mistake pointed out by Phil.

Possible Futures for the European Banking Union

In September 2012, the European Commission proposed a single supervisory mechanism (SSM) for banks as a preliminary step towards a European banking union. Plans for the union continue this week, as European Union leaders meet in Brussels to set new rules regarding how future bank bailouts will be paid for.

 Earlier this year, I attended the Future of the Euro Conference at UC Berkeley. One of the conference panels was about banking unions. The panelists all draw upon economic history to discuss the possible future of a European banking union. Here are videos of their talks:   

Underneath the Bankers' New Clothes

Anat Admati and Martin Hellwig are the authors of a new book called The Bankers’ New Clothes. This book has been favorably reviewed by John Cochrane and mostly-favorably reviewed by Matthew Yglesias at Slate, though he has a few qualms about it:

Admati and Hellwig say... we should make [banks] fund a much larger share of investment—20 to 30 percent—with equity... Conventional wisdom both in the industry and among the regulatory establishment is that this would be economy-killing madness leading to huge increases in borrowing costs. Brookings Institution fellow Douglas Elliott, in one of the milder critiques, says borrowing costs would rise by about 2 percentage points... The authors’ partially persuasive reply is that this involves confusing social costs with private costs... 

Less convincing is the authors’ claim that imposing stricter capital regulation would have no costs. They analogize their proposal to rules preventing firms from engaging in excessive pollution but fail to explore the analogy deeply enough.

Admati and Hellwig, along with Peter DeMarzo and Paul Pfleiderer, have in fact studied their claim more deeply than they get into in the book. They have two papers from 2010 and 2012 which provide the technical background for the book. We discussed the 2012 paper, "Debt Overhang and Capital Regulation," in the Berkeley macroeconomics reading group this week. I'll try and walk through it here.

High leverage in the banking sector is frequently implicated as a source of systemic risk. After the financial crisis of 2007-2009, regulators sought to require that a greater share of banks' investments be funded by equity. There have been arguments made (including by bankers) that greater equity requirements would be costly to the economy. Admati et al. (2010) argued that this is not the case: the benefits of increased equity financing would be large, while the costs would be small if not negligible. For instance, one common argument is that increased equity requirements would increase banks’ funding costs because equity requires a higher return than debt. Admati et al. say that "This argument is fallacious, because the required return on equity, which includes a risk premium, must decline when more equity is used." The benefits of more increased equity requirements come from the fact that with more equity funding, banks can absorb more losses without becoming distressed, defaulting, requiring government support, or causing a financial crisis.

In their newer 2012 paper, Admati et al. consider the situation in which leverage is already high, and analyze shareholders’ incentives to change the leverage of a firm that already has large debt overhang. Heavy debt overhang incentivizes shareholders to resist reductions in leverage. The reason is that leverage reductions make the remaining debt safer (reduce the default probability), which benefits existing creditors and anyone providing guarantees to the debt, but doesn't benefit shareholders enough to compensate them for the price they have to pay to buy back debt. Shareholder resistance to leverage reduction can persist even if leverage reduction would increase the total value of the bank. This effect is present even without government subsidies of debt (but such subsidies make it worse.) Debt overhang can create an "addiction" to leverage among shareholders. There is a ratchet effect, where shareholders sometimes want to increase leverage, but would never want to reduce it.

Notice, shareholders are resistant to buying back debt because they are not compensated for the ensuing reduction in default probability, which benefits debt holders rather than shareholders. Something that came up during our group discussion of this paper was the fact that, if debt were already perfectly safe (zero default probability), then reductions in leverage would not reduce the default probability, so this effect would not hold. When default probability is quite low, debt buybacks can only reduce the default probability by a small amount, so shareholder resistance to leverage reduction should be relatively small. So from a policy perspective, it makes more sense for recapitalization to be imposed when times are good (when default probability is low), rather than in the midst of a crisis (when default probability is higher.)

The above results come from a model in which a firm has previously made an investment of amount A in risky assets and has funded itself with debt. The total debt claim is D. Investment returns in the future period are a random multiple of A, xA. The payouts of the firm’s securities in the future period depend on taxes, bankruptcy costs, and government subsidies. The firm defaults if xA<D and pays its debt in full otherwise. The payoffs to the shareholders and the debt holders depend on whether or not xA<D. They first consider whether a buyback of debt (pure recapitalization) can be beneficial to shareholders. They find that "Equity holders are strictly worse off issuing securities to recapitalize the firm by repurchasing any class of outstanding debt." This creates an interesting tension:

When default is costly to the firm, the interests of equity holders can be in conflict with maximization of total firm value. For example, if taxes and subsidies are zero while bankruptcy costs are not, then a recapitalization and buyback of risky debt raises the combined wealth of shareholders and debt holders jointly. Yet, shareholders consider such a move harmful to their interests. Thus, debt overhang can give rise to a situation in which shareholders and debt holders jointly would benefit from a recapitalization and debt buyback, but shareholders would not find it in their interest to recapitalize.

In a somewhat random but interesting anecdote in the middle of the paper, they cite the buyback of Bolivian sovereign debt in 1988 as an example of debt buyback benefiting debt holders. Bolivian debt was trading at 6 cents on the dollar, and there was a notion that the international community should buy this debt and forgive it to provide Bolivia with debt relief.  The market price of Bolivian debt after the buyback was 11 cents on the dollar, and debt holders' wealth collectively increased by over $33 million.


In situations where banks are required to reduce their leverage, there are two main alternatives to pure recapitalization. The alternatives prove equally undesirable to shareholders:

A pure recapitalization involves buying (or paying) back debt using new equity funding, without any change in assets. Alternatively, the ratio of equity to assets can be increased by selling assets and using the proceeds to buy back debt, a process often referred to as “deleveraging.” Finally, the firm may increase the equity to asset ratio by issuing new equity and acquiring new assets. 

We obtain a striking “irrelevance” result: If there is one class of debt outstanding and asset sales or purchases do not, by themselves, generate value, then shareholders are indifferent between asset sales, pure recapitalization and asset expansion. All are equally undesirable from the perspective of shareholders.

If, however, there are multiple asset classes, shareholders prefer asset sales over recapitalization or asset expansion, because all debt is the same to the shareholders, and junior debt is cheaper:

This also may explain why shareholders would choose to engage in asset sales or “deleveraging” (as opposed to recapitalization or asset expansion) if a decrease in leverage is imposed by regulation and there are no covenants protecting senior debt holders. In this case, if the proceeds of a sale of assets are used to buy back junior debt and perhaps make payouts to equity, the senior debt holders lose to the benefit of the shareholders. Shareholders therefore prefer this over a pure recapitalization or asset expansion.

What determines a firm's ex ante decision about debt and equity financing?  By Modigliani and Miller (1958), the capital structure choice is only relevant to the ex ante value of the firm to the extent that it is affected by frictions including taxes, bankruptcy costs, bailout subsidies, and agency costs. If these frictions change, the effect on capital structure is asymmetrical. One interesting policy implication is:

The total value of banks, net of the value of bailout subsidies, can be increased when regulators force banks to recapitalize because, in effect, the regulators can create a commitment technology that allows banks to overcome the debt overhang agency problem that would otherwise prevent beneficial recapitalizations. In other words, assuming there are no bailout subsidies but there are bankruptcy costs (that are incurred by the firm), regulators who force the firm to recapitalize might enhance its ex ante value by allowing it to raise debt at a lower price than it could absent a way to commit to such recapitalizations.

However, as far as I can tell, the model does not help us understand what level of recapitalization is ideal. Does recapitalization monotonically increase the ex ante value of the firm, all the way up to 100 percent equity? The model tells us that higher equity is better, but does not tell us how high is optimal. So I don't know where the 20 to 30 percent recommendation comes from. The model is two-period. It would be hard, but interesting, to think about longer horizons. Another important point is that the result about shareholders resisting recapitalization holds even in a stripped-down model with no taxes, subsidies, or bankruptcy costs. The taxes, subsidies, and bankruptcy costs can exacerbate the result but do not drive it. It would be interesting to see some analysis of how much they are exacerbating the problem.

The Financial Sector after the Crisis

When Italian Prime Minister Silvio Berlusconi announced Ignazio Visco as his pick for Governor of the Bank of Italy in October 2011, it came as something of a surprise. Berlusconi was under pressure from various ministers to pick their candidates for Governor, but he ended up picking none of their choices and going with Visco. Visco was the third-ranked official at the Bank of Italy before he replaced Mario Draghi when Draghi became President of the European Central Bank. Visco did his PhD at Penn and was chief economist at the Organization for Economic Cooperation and Development from 1997 to 2002.

Based on a lecture he gave in London earlier this month, Visco seems to be a wise choice. Visco's lecture, titled "The Financial Sector after the Crisis," is epically ambitious. The first section of the lecture is called "'Good' finance as a force for good." He is heavily influenced by Amartya Sen, whom he quotes multiple times. The first Sen quote, referring to finance, asks "How is it possible that an activity that is so useful has been viewed as being morally so dubious?" It is apparent that Visco has reflected on this question quite a lot:

One can detect cyclical patterns in the public’s attitude towards finance, affected by the conditions of financial systems and shifts in the political mood about state intervention in the economy. Until the 1970s it was taken for granted that market failures required the presence and response of a regulator to avoid suboptimal results. Then came the great inflation of the 1970s, combined with high unemployment, and the emphasis shifted to government failures. Governments, central banks and other regulators were blamed for failing to prevent these developments. This eventually led to an ideological swing: a push to reduce the extent of state intervention. The failures of the “regulated economy,” the pace of technological advance and the rapid expansion of international trade after the end of the Cold War fuelled a protracted process of financial deregulation that was halted only by the financial crisis that broke out in 2007. The latter triggered a move toward re-regulation – or better regulation – that is still under way. The pendulum keeps swinging and will certainly continue to do so. 

The global financial crisis, with its huge costs for the whole society, has caused a further deep erosion of the trust in financial institutions. Witness to this are the widespread protests against the financial industry, from the Occupy Wall Street movement to the “Indignados” in Spain and their counterparts in other European countries. Anger has been fuelled not only by the discovery of wrongdoings and perverse incentives, but also by a perceived lack of action against those responsible, in a context of exceptionally high remunerations. The integrity of financial intermediaries’ codes of conduct has been called into question under many dimensions: honesty, the ability to manage financial risks and the commitment to take care of the interests of their clients.

He also quotes Sen as saying that “finance plays an important part in the prosperity and well-being of nations.” He takes a long historical perspective on financial innovation, from the “letters of exchange” introduced by Italian merchants in the Middle Ages to today's structured finance products and originate-to-distribute intermediation model.

He recognizes that both the distrust of finance and its role in prosperity come from its complexity. He praises financial literacy efforts as a way to alleviate some of the public distrust of finance, but cautions that "as the case of Bernard Madoff and others in the US and elsewhere clearly show – this is no panacea (Madoff’s customers were surely much better educated than average). Therefore, for purposes of consumer protection in the financial services industry, financial regulation and good supervision are the necessary complements to financial education and inclusion." When it comes to regulation, however, he believes that "Complexity was also used, somewhat perversely, as an argument in favour of a sort of benign neglect on the part of regulators."

The big financial players argued successfully that financial innovation was too complex and too opaque for the regulators to get their heads around. Indeed, they said, to safeguard the international financial system from systemic risk, the main priority was promoting an “industry-led” effort to improve internal risk management and related systems. This, in a nutshell, was the view espoused by the Group of Thirty report following the outbreak of the Asian crisis. But this thesis was often accompanied by the argument to the effect that “you, regulators and supervisors, will always be behind financial innovation; it would be better to allow us, the big financial international players, to self regulate; we are grown-ups, we can take care of ourselves...” 

The difficulties in coordinating the regulators’ actions, in the face of a natural tendency to preserve each one’s particular sphere of influence, was a powerful drag on the ability to rise to the challenge posed by a finance gone global... The phenomenon of regulatory capture was a definite reality...Financial regulation and supervision have to keep pace with developments in the financial industry... The coordination of financial supervision across borders and across sectors is a key condition for the stability of the global financial system. More importantly, regulators and supervisors have to pay attention to keeping financial industry lobbies at due distance.

The next section of the lecture, "In search of a better regulatory and supervisory regime," is worth reading for a summary of recent reforms by the Basel Committee on Banking Supervision. But more interesting and surprising is the subsequent section of the lecture, "Observations on the analytical implications of economic and financial instability."  He describes, with more lucidity and in fewer words than I have heard before, the challenges of "non-ergodicity."

Changes in institutional arrangements, technological innovation and revisions in economic policy paradigms continuously reshape the framework in which economic agents (consumers and businesses) make their decisions...When there is marked discontinuity with the past, such changes may be far-reaching and the past fails to provide enough guidance for the present (never mind the future). We should always remember that the financial system is part of a richer social, economic and political environment... 

However, a stationarity assumption of sorts underpins our theoretical and statistical models, in the case of economic forecasting and (macro) policy making as well as in the case of financial analysis and risk management. In general, the basic tenet is that future outcomes will be drawn from the same population that generated past outcomes, so that the time average of future outcomes cannot be persistently different from averages calculated from past observations and future events can be predicted with a certain degree of statistical accuracy. In non-ergodic environments, on the contrary, at least some economic processes are such that expectations based on past probability distribution functions can differ persistently from the time averages that will be generated as the future unfolds.

In case of acute uncertainty, no analysis of past data can provide reliable signals regarding future prospects. The challenges posed by the non-ergodic nature of economic systems may be met by recognizing that our models are by necessity “local” approximations of very complex economic and financial developments.

In the above paragraphs he cites a 1991 paper by Paul Davidson, “Is probability theory relevant for uncertainty? A Post Keynesian perspective." He also cites Charles Kindleberger: “For historians each event is unique. Economics, however, maintains that forces in society and nature behave in repetitive ways.” In conclusion, he adds:

This is not to say that all the analytical efforts of the past and the progress achieved should be disregarded. It means rather that in order to make the best out of them one needs to remember that models are by necessity “local” approximations to very complex phenomena and they should be used with good sense as a framework, not a straightjacket, for our decision-making. Quantitative analysis and modelling can also help to establish institutional and behavioural norms to rein in patterns of instability and developing proper learning devices to deal with major shocks and regime changes. In turn, models should take into account the impact of such norms on economic developments.  

Overheating and the Fed

This article is cross-posted at the Berkeley Blog.

Governor Jeremy Stein of the St. Louis Federal Reserve gave a speech on February 7 called "Overheating in Credit Markets: Origins, Measurement, and Policy Responses." Overheating is a term he uses to describe a credit market with low interest rates, lax lending standards, and high risk-taking by investors "reaching for yield." The problem with overheating is that it can contribute to financial instability. A boom followed by a bust can create harmful spillovers for the economy.

Both monetary policy and regulatory policy can potentially address overheating. In the speech, Stein describes an approach called decoupling, which holds that monetary policy should restrict its attention to the goals of price stability and maximum employment, while supervisory and regulatory tools should be used to safeguard financial stability.  Stein does not completely buy this decoupling approach. He recognizes that low interest rates are a cause of overheating, and that the Fed, by its power to control interest rates, can address overheating in ways that regulators cannot.

I believe it will be important to keep an open mind and avoid adhering to the decoupling philosophy too rigidly... I can imagine situations where it might make sense to enlist monetary policy tools in the pursuit of financial stability...Supervisory and regulatory tools remain imperfect in their ability to promptly address many sorts of financial stability concerns...While monetary policy may not be quite the right tool for the job, it has one important advantage relative to supervision and regulation--namely that it gets in all of the cracks. The one thing that a commercial bank, a broker-dealer, an offshore hedge fund, and a special purpose ABCP vehicle have in common is that they all face the same set of market interest rates. To the extent that market rates exert an influence on risk appetite, or on the incentives to engage in maturity transformation, changes in rates may reach into corners of the market that supervision and regulation cannot.

In the New York Times, Binyamin Applebaum writes that Stein's speech "underscored that the Fed increasingly regards bubbles, rather than inflation, as the most likely negative consequence of its efforts to reduce unemployment by stimulating growth." In fact, the Fed's concern about bubbles is not so new. After the Great Depression, it was widely believed that the stock market overheated in the 1920s, leading to the Great Crash in 1929 and the onset of the Depression. In those days, the word for bubbles or overheating was speculation, and it became a dirty word indeed. After the Great Depression, speculation remained a major concern of the Fed. The Fed very explicitly regarded bubbles as the most likely negative consequence of its efforts to reduce unemployment by stimulating growth.

For example, the United States economy was in a recession in 1953-54. In 1955, as the economy was recovering, the minutes from the Federal Open Market Committee refer multiple times to concerns about "speculative developments" or "speculative excesses." The March 2 minutes note:

The critical problem for credit and monetary policy in the United States, the review [from the Board's Division  of Research  and  Statistics  and  Division  of  International  Finance] said,  was how to thread its way along the narrow ledge that encourages sound economic growth and high employment and, at the same  time, limits speculative developments and discourages financial over commitments by businesses and consumers.

Minutes from May 10, 1955 say:

Business,  financial,  and  consumer  confidence  is  extraordinarily  high--possibly  too  high  for sound  growth.  At  this  stage,  the task  of monetary  and  credit  policy  is  to foster  stable  growth  in  line  with expanding  manpower  and  industrial  resources,  at  the  same  time  restraining financial  over-commitments  and  dampening  speculative  excesses.

In 1958, William Phillips published "The Relation between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom." This really kicked off the now-common idea that inflation is the most likely negative consequence of the Fed's efforts to reduce unemployment. If the Fed is now starting to regard bubbles, rather than inflation, as the most likely negative consequence of its efforts to reduce unemployment, this is not a new trend. It is history of thought repeating itself.

Real Estate Monetary Standard: the New Wildcat Banking?

Michael Sankowski at Monetary Realism suggests that we may be on a "real estate monetary standard." He writes:

Much like how we can use assets like gold to create a commodity money system, it seems like we operate our current monetary system as a real estate standard.
Banks create money against real estate assets. We use this money in our day-to-day transactions, without much thought about what stands behind this money, but most loans are for residential and commercial real estate.

He makes the comparison to a gold standard, but I suggest another analogy: the Free Banking Era. The Free Banking Era refers to the period from 1837 to 1863. Prior to free banking, opening a bank was a difficult process that involved obtaining a charter from a state legislature, and the Second Bank of the United States required state banks to keep an adequate supply of specie on hand, thereby limiting the amount of notes that they could issue. When the Second Bank closed, states needed to make bank entry easier to fill the void in banking services. New York and Michigan were early adopters of free banking laws, which allowed anyone to operate a bank as long as notes were redeemable on demand and backed by state bonds held at the state auditor's office. Eventually, 18 states adopted free banking laws. I would like to compare the state bond-backed monetary system to what Sankowski calls our real estate monetary standard.

With the passage of the free banking laws, many new banks opened and a plethora of different kinds of banknotes circulated as currency. An expansion of the banking sector in that era has its analogue in the expansion of mortgage lending, including subprime lending, from around 2003-2007, when there was also large growth in non-bank independent mortgage originators. (See Joshua Wojnilower's post on how tax policies created a real estate monetary standard.)

The Free Banking Era is notorious for a large number of bank failures, which often resulted in losses to noteholders. The conventional explanation for the problems of free banking is also a common explanation for the bank failures of recent years: fraud and greed. The evil bankers of those days were called “wildcat bankers." In a well known 1974 paper, Hugh Rockoff explains the link between wildcat banking and free banking laws. Some states allowed banks to issue notes equal to the face value, instead of the market value, of the bonds backing. So wildcat bankers could buy state bonds that had depreciated, deposit them with the state auditor, and issue currency amounting to the face value, rather than the depreciated value, of the bonds. They could then circulate these notes to the public, in exchange for specie and investments worth more than what they paid for the state bonds, forfeit the bonds and run off with the bank’s assets. Sound familiar? Consider Felix Salmon's description of the "enormous mortgage bond scandal."

This is where things get positively evil. The investment banks didn't mind buying up loans they knew were bad, because they considered themselves to be in the moving business rather than the storage business. They weren't going to hold on to the loans: they were just going to package them up and sell them on to some buy-side sucker. In fact, the banks had an incentive to buy loans they knew were bad. Because when the loans proved to be bad, the banks could go back to the originator and get a discount on the amount of money they were paying for the pool. And the less money they paid for the pool, the more profit they could make when they turned it into mortgage bonds and sold it off to investors. 

However, as the Economist notes, there has been "a lot of debate over whether blame [for the recent financial crisis] should be assigned to deliberate fraud by financial-industry actors, or whether the whole phenomenon was simply an unfortunate catastrophe based on systemic miscalculations. General opinion settled on the unfortunate-catastrophe thesis." Likewise regarding the free banking era, later authors such as Gerald Dwyer and Arthur Rolnick and Warren Weber argue that most bank closings and noteholder losses were not caused by fraudulent wildcat banks, but rather by capital losses due to drops in state bond prices. There were systemic miscalculations concerning state bonds like there were with mortgage-backed securities. And in fact, they were eerily similar.

State governments at the time were in the business of building roads and canals, running up big debts to do so. It seemed like a great investment, given New York's success with the Erie Canal. States expected to be able to service debt with the revenue proceeds of an expanding tax base; the land boom of the 1830s seemed to promise growing property tax revenues. Plus, the roads and canals that they were borrowing to build were expected to bring in even more revenue. So state bonds were presumably extremely safe assets. It was very similar to the subprime loans made during the housing bubble: even though borrowers didn't have the income they would need to pay their mortgages, they were allowed to borrow because home values were expected to keep rising. But just as AAA-rated subprime-mortgage-backed securities were downgraded to junk status when borrowers started defaulting, the state bonds also sunk in value when many states went into default.

Then as now, leverage mattered. Nine of the ten states with the highest per capita debts defaulted; none of the states with below median per capita debts defaulted. The defaults of course caused financial turmoil and also adversely impacted the real economy. And although the pros and cons of free banking were not well understood until well over a century later, policymakers were fairly quick to impose new regulations. The Free Banking Era came to an end with the passage of the National Bank Acts of 1863 and 1864, which set up a national system of banking with federally issued charters and a uniform national currency backed by Treasury securities. The Comptroller of the Currency was established as a supervisor in 1863; the Federal Housing Finance Agency was established in 2008 to supervise secondary mortgage market components. The parallels are so interesting--this is why I love economic history!