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Comment on: “A model of a systemic bank run” by Harald Uhlig
ARTICLE IN PRESS Journal of Monetary Economics 57 (2010) 97–100
Contents lists available at ScienceDirect
Journal of Monetary Economics journal homepage: www.elsevier.com/locate/jme
Discussion
Comment on: ‘‘A model of a systemic bank run’’ by Harald Uhlig$ Todd Keister Research and Statistics Group, Federal Reserve Bank of New York, 33 Liberty Street, New York, NY 10045, USA
a r t i c l e in fo Available online 17 November 2009
1. Introduction One of the most common narratives told about the current financial crisis is that it is analogous to an old-fashioned bank run. The cast of players has clearly changed—instead of depositors running to withdraw from their local banks, the current crisis has largely seen financial institutions withdrawing from other financial institutions. Nevertheless, according to this view of events, the fundamental forces at work are the same as in earlier crises. This claim has been made repeatedly in the popular press and elsewhere. Uhlig (this issue) attempts to formalize this view in the language of modern economic theory and asks what can be learned from this exercise. The paper begins by laying out a set of six stylized facts that together summarize this particular view of the crisis. These facts include institutional features and market arrangements the model should incorporate as well as properties that the equilibrium of the model should satisfy. Of particular interest are the two stylized facts about equilibrium asset prices: the price of the securities held by distressed institutions should fall below their fundamental value during a crisis, and this discount should become larger when the number of distressed institutions increases. The latter fact reflects the view that the crisis has been systemic in nature, in the sense that a run on some financial institutions has depressed the prices of certain assets and, in the process, made other institutions more susceptible to a run. The paper builds on the canonical bank runs model of Diamond and Dybvig (1983). It constructs a substantially richer version of this model in which there is tiering in the financial sector: households place their funds in local banks, who in turn deposit funds with a set of core banks. All banks are assumed to offer standard deposit contracts in which depositors are entitled to withdraw their funds at face value on demand.1 If core banks experience an unexpectedly high level of withdrawals, they are forced to sell their securities to some outside investors in order to pay off their depositors. The paper considers two distinct approaches to modelling the market where these securities are sold and shows that they yield different predictions for equilibrium asset prices. The paper argues that one of these specifications fits the stylized facts better than the other and, hence, provides a better platform for evaluating policy proposals. The paper then discusses the possible effects of government intervention, including a large-scale purchase of troubled assets, in this framework. In this discussion, I highlight what I see as the most important results in the paper. I use a simple model to illustrate these results and show how they relate to the existing literature. I then offer some comments on the policy conclusions drawn from the paper. $ The views expressed herein are those of the author and do not necessarily reflect those of the Federal Reserve Bank of New York or the Federal Reserve System. Tel.: + 1 212 720 2267; fax: +1 212 720 8363. E-mail address: [email protected] 1 The paper follows much of the literature in assuming that banks offer simple deposit contracts even though such contracts are not optimal in the environment studied. Some recent papers follow the early work of Wallace (1990) and examine optimal contractual arrangements in the Diamond– Dybvig model. See, for example, Green and Lin (2003), Peck and Shell (2003), Andolfatto et al. (2007), and Ennis and Keister (2009a).
0304-3932/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jmoneco.2009.11.002
ARTICLE IN PRESS 98
T. Keister / Journal of Monetary Economics 57 (2010) 97–100
2. A simple model While the paper constructs a rich model that is designed to match some salient features of the modern financial system, its main conclusions can be illustrated in the context of the standard Diamond–Dybvig model. I will briefly sketch the standard model (which is similar to that in Cooper and Ross, 1998) and use it to discuss the key issues studied in the paper.
2.1. The standard model There are three time periods, t ¼ 0; 1; 2. Each depositor has an endowment in period 0 but does not discover until period 1 whether she is impatient and desires to consume in period 1 or patient and desires consumption in period 2. A known fraction j of all depositors will be impatient. Endowments can be placed into two assets in period 0. The short-term asset yields a return of 1 in either period 1 or period 2. The long-term asset yields R 4 1 if held until period 2 but only q r 1 if liquidated in period 1. In addition, there is an unlikely, ‘‘bust’’ state of nature in which the period-2 return on the long-term asset is lower than R. There is a set of banks that can accept deposits and divide these funds between the two assets. As is well known, a bank offering demand-deposit contracts can give its depositors a higher level of expected utility than they can attain in autarky. However, this contract also opens the door to two distinct types of bank runs: self-fulfilling runs in which patient depositors rush to withdraw because they fear withdrawals by others will exhaust the bank’s funds, and fundamental runs in which the ‘‘bust’’ state occurs and the bank cannot honor its period-2 obligations even if all patient depositors wait.2 The paper focuses on the latter type of run.
2.2. A reinterpretation The standard model can be made more directly applicable to current events by relabelling the agents. The fact that the current crisis has (for the most part) featured runs by financial institutions on other financial institutions, rather than of retail depositors on their local banks, can be captured by calling the depositors in this model ‘‘local banks’’ and calling the banks in this model ‘‘core banks.’’ A story can then be told in which each local bank represents a group of depositors who will all have the same preference type, but formally the model remains the same. The paper does much more than simply relabel agents, of course. It constructs a model with many locations that leads to a natural form of tiering of the financial system. Nevertheless, many of the points made in the paper can be seen in the context of the simpler model described above. In particular, I would argue that the primary contribution of the paper is its handling of the asset market, and I will focus my discussion on this issue.
2.3. The asset market In the standard model, the liquidation value q is taken as a primitive. One could imagine that q represents the price at which banks can sell the long-term asset to some outside investors, but in the standard model this price is determined outside the model and is assumed to be independent of the quantity of investment being liquidated. The stylized facts presented in the paper suggest that this price has played a central role in the crisis and deserves more careful study. In particular, the paper claims that during the crisis q has been significantly below the fundamental value of the assets and that q falls even further when more long-term assets are sold. In other words, the stylized facts point to a payoff externality that is absent in the standard model: when one bank liquidates assets, it decreases the short-run value of the assets of all other banks. This decrease in assets, in turn, makes each of these other banks more susceptible to a run.3 Matching the model to these stylized facts requires incorporating an explicit asset market in period 1 and deriving an equilibrium pricing function qðLÞ, where L denotes the total quantity of the long-term asset liquidated in period 1. Some frictions must be present in the asset market for the equilibrium price of the long-run asset to fall below its fundamental value. To help generate these frictions, the paper assumes that long-term assets become heterogeneous in the ‘‘bust’’ state. While these assets all yield the same return in normal times, when the ‘‘bust’’ state occurs each bank is left holding a range of distinct assets, some of which offer a very low return in period 2 and others of which offer a higher return. The quality of each asset is privately observed by the bank holding the asset. The paper then presents two distinct models of the asset market in which this heterogeneity in returns causes the price of the assets to fall below their fundamental value. 2 Papers focusing self-fulfilling runs include, among many others, Cooper and Ross (1998), Peck and Shell (2003), and Ennis and Keister (2009b). Fundamental runs have been studied by Allen and Gale (1998) and others. See Ennis (2003) for a discussion of both approaches and how they relate to historical data. 3 While the idea that a decline in q makes the remaining banks more likely to experience a run is intuitively quite plausible, this does not necessarily occur in the standard Diamond–Dybvig model. Some of the more complex aspects of Uhlig’s model are designed to deliver precisely this property.
ARTICLE IN PRESS T. Keister / Journal of Monetary Economics 57 (2010) 97–100
99
3. Adverse selection vs. uncertainty aversion One model of the asset market is based on an adverse selection, or ‘‘lemons,’’ problem. A core bank experiencing a run must sell its assets in the market to meet withdrawal demand. Depending on the market price, a core bank not experiencing a run may choose to opportunistically sell its lowest-quality assets into the market. In equilibrium, there is a single price in the asset market that reflects the average quality of the assets being sold. Because of opportunistic selling by other banks, a distressed bank that is forced to sell assets receives a price that is below their fundamental value. In this way, the model delivers the stylized fact that distressed banks must sell assets at a discount during a crisis. Notice, however, what happens if the crisis becomes deeper and more core banks experience a run. When more banks are forced to sell assets, their actions improve the average quality of assets being sold in the market and, hence, raise the market price. In other words, the liquidation value q is increasing in L in this version of the model, so that liquidation by one bank makes the remaining banks less susceptible to a run. This effect runs counter to the stylized fact about the systemic nature of the crisis.4 This result is perhaps the most interesting aspect of the paper. Informal discussions of the crisis have frequently referred to bank runs and lemons problems as the primary forces at work. The paper shows that combining these two elements in the context of a standard model has a surprising implication, and this implication runs counter to the accepted view of events. There must be more to the story than a simple combination of these two well-known effects. In the second model of the asset market, the outside investors are characterized by uncertainty aversion. A fixed mass of these investors are experts who can determine asset quality; these investors are willing to pay up to the fundamental value for an asset. The remaining investors are unable to determine the quality of an asset and are assumed to be uncertainty averse in the sense that they value assets according to the worst-case scenario. Such an investor’s maximum willingness to pay for an asset is equal to the fundamental value of the worst asset being sold. In this setup, if only a few banks need to sell assets, the marginal investor will be an expert and all assets will trade at their fundamental value. Suppose, however, that more core banks experience a run and are forced to sell assets. If the run becomes large enough, the expert investors exhaust their funds and the marginal investor will instead be an uninformed agent. Uncertainty aversion will then drive the equilibrium price for all assets down to the fundamental value of the worst asset. In other words, when the share of troubled core banks rises past a certain threshold, the price received by all core banks for their assets falls, leaving each of them more susceptible to a run. This version of the model matches all of the stylized facts. 4. Policy implications A wide range of policy responses have been proposed over the course of the current crisis. One proposal that has received a great deal of attention, particularly during the Fall of 2008, is for the government to purchase large quantities of troubled assets at above-market prices. Some observers believe that doing so would have both helped the troubled banks that needed to sell the assets and provided the taxpayers with an above-average return on their investment. The model presented in this paper provides a framework for analyzing the effects and the desirability of proposals such as this one. In the model with adverse selection, a government purchase program would be problematic and most likely of limited value. In this version of the model, high-quality assets trade at a discount to their fundamental value, but low quality assets trade at a premium; this premium is what leads to the opportunistic selling of ‘‘lemons.’’ Much of the benefit of government purchases in this case would accrue to those banks who are not experiencing a run but are selling opportunistically, and the taxpayers would likely realize a low return. In this view, other policies, such as a capital injection for distressed banks, are more likely to prove effective. The model based on uncertainty aversion yields a very different result. In this case, investors are behaving as if every asset is of the lowest quality. If the government can buy a representative sample of all assets, its portfolio should earn the average return. The government could, therefore, pay a price that is somewhere between the fundamental value of the lowest-quality asset and that of the average asset. This above-market price would help the distressed banks that are selling assets while assuring the taxpayers of an above-average return. The main policy conclusion offered in the paper is the following: Since . . . the uncertainty averse scenario is more plausible than the adverse selection scenario, the analysis here provides some support for the argument that an outright purchase of troubled assets by the government at prices above current market prices can both alleviate the financial crisis as well as provide taxpayers with returns above those for safe securities. (Uhlig, this issue) I am skeptical of this conclusion for several reasons. Some of these reasons are related to particular features of the model. The paper is too quick, in my view, to resort to uncertainty aversion instead of exploring other types of frictions in the standard, expected-utility framework. It also jumps quickly to a discussion of government asset purchases when other, potentially better solutions seem possible. What, for example, prevents expert investors from taking deposits from 4
This type of effect also appears in Eisfeldt (2004), which studies adverse selection and liquidity in asset markets.
ARTICLE IN PRESS 100
T. Keister / Journal of Monetary Economics 57 (2010) 97–100
uninformed investors and using these funds to purchase more distressed assets? The government could also lend to experts and presumably do better than purchasing assets on its own. Assuming that only a fixed amount of wealth is available to expert investors seems unsatisfactory for precisely the same reasons that assuming simple cash-in-the-market pricing is often considered unsatisfactory. The paper also takes an optimistic view of the government’s asset-purchasing capabilities. By paying a price that is higher than the fundamental value of the lowest-quality asset, the government creates an adverse selection problem—even in the uncertainty aversion scenario—because non-distressed banks now have an incentive to opportunistically sell their worst assets. The paper assumes that the government is able to purchase a representative sample of the assets for sale, and shows that this policy can be effective despite the adverse selection problem. I suspect, however, that in practice government purchases would tend to attract the worst assets rather than a representative sample. Governments generally do not have any expertise in buying these types of assets, and acquiring such expertise is a non-trivial task. The private sector would be willing to spend substantial resources attempting to unload their lowestquality assets.5 If these efforts are even partially successful, a government purchase program becomes less attractive. Finally, the main result of the paper also seems sensitive to the particular assumptions about asset returns. When the bust state occurs, there is a distribution of returns across the now-distinct assets, but there is no uncertainty about the return on the aggregate portfolio. The benefit of a government purchase program comes through a diversification effect: an individual investor buying a single asset may fear receiving the lowest quality, but a government buying a large portfolio earns a certain return. During the critical stages of the current crisis, however, there seems to have been a significant amount of aggregate uncertainty about the value of mortgage-related securities in general. In such a case, the rationale for a government purchase program is substantially weaker, particularly if taxpayers share the uncertainty aversion of investors. In the limiting case where all uncertainty is aggregate, so that each asset will yield the same return, the taxpayers as a group would be willing to pay no more for the assets than an individual investor would. In the framework presented here, the benefits of a government purchase program depend crucially on the degree to which the government can diversify risks that private investors cannot. 5. Conclusion Perhaps a way of summarizing the points above is to say that matching the six stylized facts presented in the paper may be a necessary condition for trusting the policy conclusions that come out of the model, but it is clearly not sufficient. I worry that the conclusions drawn in the paper may not be robust to some reasonable changes in assumptions. None of these criticisms should be interpreted as undermining the value of the paper, of course; it represents a substantial contribution to the growing body of crisis-related literature. Perhaps most importantly, it provides a solid framework in which the ideas discussed above can be analyzed formally. Understanding the crisis and the effects of the many different policy proposals is a Herculean task, and there is clearly more work to be done. By bringing the policy debate into the realm of modern economic theory, the paper provides an excellent starting point for future work. References Allen, F., Gale, D., 1998. Optimal financial crises. Journal of Finance 53 (4), 1245–1284. Andolfatto, D., Nosal, E., Wallace, N., 2007. The role of independence in the Green–Lin Diamond–Dybvig model. Journal of Economic Theory 137 (1), 709–715. Cooper, R., Ross, T.W., 1998. Bank runs: liquidity costs and investment distortions. Journal of Monetary Economics 41 (1), 27–38. Diamond, D.W., Dybvig, P.H., 1983. Bank runs, deposit insurance, and liquidity. Journal of Political Economy 91 (3), 401–419. Eisfeldt, A., 2004. Endogenous liquidity in asset markets. Journal of Finance 59 (1), 1–30. Ennis, H.M., 2003. Economic fundamentals and bank runs. Federal Reserve Bank of Richmond Economic Quarterly 89 (2), 55–71. Ennis, H.M., Keister, T., 2009a. Run equilibria in the Green–Lin model of financial intermediation. Journal of Economic Theory 144 (5), 1996–2020. Ennis, H.M., Keister, T., 2009b. Bank runs and institutions: the perils of intervention. American Economic Review 99 (4), 1588–1607. Green, E.J., Lin, P., 2003. Implementing efficient allocations in a model of financial intermediation. Journal of Economic Theory 109 (1), 1–23. Peck, J., Shell, K., 2003. Equilibrium bank runs. Journal of Political Economy 111 (1), 103–123. Uhlig, H. A model of a systemic bank run. Journal of Monetary Economics, this issue, doi:10.1016/j.jmoneco.2009.10.010. Wallace, N., 1990. A banking model in which partial suspension is best. Federal Reserve Bank of Minneapolis Quarterly Review 14 (4), 11–23.
5 Indeed, much of the discussion surrounding the potential government purchase program in the Fall of 2008 centered on whether or not a mechanism could be designed that would prevent the government from systematically overpaying for low-quality assets.
Contents lists available at ScienceDirect
Journal of Monetary Economics journal homepage: www.elsevier.com/locate/jme
Discussion
Comment on: ‘‘A model of a systemic bank run’’ by Harald Uhlig$ Todd Keister Research and Statistics Group, Federal Reserve Bank of New York, 33 Liberty Street, New York, NY 10045, USA
a r t i c l e in fo Available online 17 November 2009
1. Introduction One of the most common narratives told about the current financial crisis is that it is analogous to an old-fashioned bank run. The cast of players has clearly changed—instead of depositors running to withdraw from their local banks, the current crisis has largely seen financial institutions withdrawing from other financial institutions. Nevertheless, according to this view of events, the fundamental forces at work are the same as in earlier crises. This claim has been made repeatedly in the popular press and elsewhere. Uhlig (this issue) attempts to formalize this view in the language of modern economic theory and asks what can be learned from this exercise. The paper begins by laying out a set of six stylized facts that together summarize this particular view of the crisis. These facts include institutional features and market arrangements the model should incorporate as well as properties that the equilibrium of the model should satisfy. Of particular interest are the two stylized facts about equilibrium asset prices: the price of the securities held by distressed institutions should fall below their fundamental value during a crisis, and this discount should become larger when the number of distressed institutions increases. The latter fact reflects the view that the crisis has been systemic in nature, in the sense that a run on some financial institutions has depressed the prices of certain assets and, in the process, made other institutions more susceptible to a run. The paper builds on the canonical bank runs model of Diamond and Dybvig (1983). It constructs a substantially richer version of this model in which there is tiering in the financial sector: households place their funds in local banks, who in turn deposit funds with a set of core banks. All banks are assumed to offer standard deposit contracts in which depositors are entitled to withdraw their funds at face value on demand.1 If core banks experience an unexpectedly high level of withdrawals, they are forced to sell their securities to some outside investors in order to pay off their depositors. The paper considers two distinct approaches to modelling the market where these securities are sold and shows that they yield different predictions for equilibrium asset prices. The paper argues that one of these specifications fits the stylized facts better than the other and, hence, provides a better platform for evaluating policy proposals. The paper then discusses the possible effects of government intervention, including a large-scale purchase of troubled assets, in this framework. In this discussion, I highlight what I see as the most important results in the paper. I use a simple model to illustrate these results and show how they relate to the existing literature. I then offer some comments on the policy conclusions drawn from the paper. $ The views expressed herein are those of the author and do not necessarily reflect those of the Federal Reserve Bank of New York or the Federal Reserve System. Tel.: + 1 212 720 2267; fax: +1 212 720 8363. E-mail address: [email protected] 1 The paper follows much of the literature in assuming that banks offer simple deposit contracts even though such contracts are not optimal in the environment studied. Some recent papers follow the early work of Wallace (1990) and examine optimal contractual arrangements in the Diamond– Dybvig model. See, for example, Green and Lin (2003), Peck and Shell (2003), Andolfatto et al. (2007), and Ennis and Keister (2009a).
0304-3932/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jmoneco.2009.11.002
ARTICLE IN PRESS 98
T. Keister / Journal of Monetary Economics 57 (2010) 97–100
2. A simple model While the paper constructs a rich model that is designed to match some salient features of the modern financial system, its main conclusions can be illustrated in the context of the standard Diamond–Dybvig model. I will briefly sketch the standard model (which is similar to that in Cooper and Ross, 1998) and use it to discuss the key issues studied in the paper.
2.1. The standard model There are three time periods, t ¼ 0; 1; 2. Each depositor has an endowment in period 0 but does not discover until period 1 whether she is impatient and desires to consume in period 1 or patient and desires consumption in period 2. A known fraction j of all depositors will be impatient. Endowments can be placed into two assets in period 0. The short-term asset yields a return of 1 in either period 1 or period 2. The long-term asset yields R 4 1 if held until period 2 but only q r 1 if liquidated in period 1. In addition, there is an unlikely, ‘‘bust’’ state of nature in which the period-2 return on the long-term asset is lower than R. There is a set of banks that can accept deposits and divide these funds between the two assets. As is well known, a bank offering demand-deposit contracts can give its depositors a higher level of expected utility than they can attain in autarky. However, this contract also opens the door to two distinct types of bank runs: self-fulfilling runs in which patient depositors rush to withdraw because they fear withdrawals by others will exhaust the bank’s funds, and fundamental runs in which the ‘‘bust’’ state occurs and the bank cannot honor its period-2 obligations even if all patient depositors wait.2 The paper focuses on the latter type of run.
2.2. A reinterpretation The standard model can be made more directly applicable to current events by relabelling the agents. The fact that the current crisis has (for the most part) featured runs by financial institutions on other financial institutions, rather than of retail depositors on their local banks, can be captured by calling the depositors in this model ‘‘local banks’’ and calling the banks in this model ‘‘core banks.’’ A story can then be told in which each local bank represents a group of depositors who will all have the same preference type, but formally the model remains the same. The paper does much more than simply relabel agents, of course. It constructs a model with many locations that leads to a natural form of tiering of the financial system. Nevertheless, many of the points made in the paper can be seen in the context of the simpler model described above. In particular, I would argue that the primary contribution of the paper is its handling of the asset market, and I will focus my discussion on this issue.
2.3. The asset market In the standard model, the liquidation value q is taken as a primitive. One could imagine that q represents the price at which banks can sell the long-term asset to some outside investors, but in the standard model this price is determined outside the model and is assumed to be independent of the quantity of investment being liquidated. The stylized facts presented in the paper suggest that this price has played a central role in the crisis and deserves more careful study. In particular, the paper claims that during the crisis q has been significantly below the fundamental value of the assets and that q falls even further when more long-term assets are sold. In other words, the stylized facts point to a payoff externality that is absent in the standard model: when one bank liquidates assets, it decreases the short-run value of the assets of all other banks. This decrease in assets, in turn, makes each of these other banks more susceptible to a run.3 Matching the model to these stylized facts requires incorporating an explicit asset market in period 1 and deriving an equilibrium pricing function qðLÞ, where L denotes the total quantity of the long-term asset liquidated in period 1. Some frictions must be present in the asset market for the equilibrium price of the long-run asset to fall below its fundamental value. To help generate these frictions, the paper assumes that long-term assets become heterogeneous in the ‘‘bust’’ state. While these assets all yield the same return in normal times, when the ‘‘bust’’ state occurs each bank is left holding a range of distinct assets, some of which offer a very low return in period 2 and others of which offer a higher return. The quality of each asset is privately observed by the bank holding the asset. The paper then presents two distinct models of the asset market in which this heterogeneity in returns causes the price of the assets to fall below their fundamental value. 2 Papers focusing self-fulfilling runs include, among many others, Cooper and Ross (1998), Peck and Shell (2003), and Ennis and Keister (2009b). Fundamental runs have been studied by Allen and Gale (1998) and others. See Ennis (2003) for a discussion of both approaches and how they relate to historical data. 3 While the idea that a decline in q makes the remaining banks more likely to experience a run is intuitively quite plausible, this does not necessarily occur in the standard Diamond–Dybvig model. Some of the more complex aspects of Uhlig’s model are designed to deliver precisely this property.
ARTICLE IN PRESS T. Keister / Journal of Monetary Economics 57 (2010) 97–100
99
3. Adverse selection vs. uncertainty aversion One model of the asset market is based on an adverse selection, or ‘‘lemons,’’ problem. A core bank experiencing a run must sell its assets in the market to meet withdrawal demand. Depending on the market price, a core bank not experiencing a run may choose to opportunistically sell its lowest-quality assets into the market. In equilibrium, there is a single price in the asset market that reflects the average quality of the assets being sold. Because of opportunistic selling by other banks, a distressed bank that is forced to sell assets receives a price that is below their fundamental value. In this way, the model delivers the stylized fact that distressed banks must sell assets at a discount during a crisis. Notice, however, what happens if the crisis becomes deeper and more core banks experience a run. When more banks are forced to sell assets, their actions improve the average quality of assets being sold in the market and, hence, raise the market price. In other words, the liquidation value q is increasing in L in this version of the model, so that liquidation by one bank makes the remaining banks less susceptible to a run. This effect runs counter to the stylized fact about the systemic nature of the crisis.4 This result is perhaps the most interesting aspect of the paper. Informal discussions of the crisis have frequently referred to bank runs and lemons problems as the primary forces at work. The paper shows that combining these two elements in the context of a standard model has a surprising implication, and this implication runs counter to the accepted view of events. There must be more to the story than a simple combination of these two well-known effects. In the second model of the asset market, the outside investors are characterized by uncertainty aversion. A fixed mass of these investors are experts who can determine asset quality; these investors are willing to pay up to the fundamental value for an asset. The remaining investors are unable to determine the quality of an asset and are assumed to be uncertainty averse in the sense that they value assets according to the worst-case scenario. Such an investor’s maximum willingness to pay for an asset is equal to the fundamental value of the worst asset being sold. In this setup, if only a few banks need to sell assets, the marginal investor will be an expert and all assets will trade at their fundamental value. Suppose, however, that more core banks experience a run and are forced to sell assets. If the run becomes large enough, the expert investors exhaust their funds and the marginal investor will instead be an uninformed agent. Uncertainty aversion will then drive the equilibrium price for all assets down to the fundamental value of the worst asset. In other words, when the share of troubled core banks rises past a certain threshold, the price received by all core banks for their assets falls, leaving each of them more susceptible to a run. This version of the model matches all of the stylized facts. 4. Policy implications A wide range of policy responses have been proposed over the course of the current crisis. One proposal that has received a great deal of attention, particularly during the Fall of 2008, is for the government to purchase large quantities of troubled assets at above-market prices. Some observers believe that doing so would have both helped the troubled banks that needed to sell the assets and provided the taxpayers with an above-average return on their investment. The model presented in this paper provides a framework for analyzing the effects and the desirability of proposals such as this one. In the model with adverse selection, a government purchase program would be problematic and most likely of limited value. In this version of the model, high-quality assets trade at a discount to their fundamental value, but low quality assets trade at a premium; this premium is what leads to the opportunistic selling of ‘‘lemons.’’ Much of the benefit of government purchases in this case would accrue to those banks who are not experiencing a run but are selling opportunistically, and the taxpayers would likely realize a low return. In this view, other policies, such as a capital injection for distressed banks, are more likely to prove effective. The model based on uncertainty aversion yields a very different result. In this case, investors are behaving as if every asset is of the lowest quality. If the government can buy a representative sample of all assets, its portfolio should earn the average return. The government could, therefore, pay a price that is somewhere between the fundamental value of the lowest-quality asset and that of the average asset. This above-market price would help the distressed banks that are selling assets while assuring the taxpayers of an above-average return. The main policy conclusion offered in the paper is the following: Since . . . the uncertainty averse scenario is more plausible than the adverse selection scenario, the analysis here provides some support for the argument that an outright purchase of troubled assets by the government at prices above current market prices can both alleviate the financial crisis as well as provide taxpayers with returns above those for safe securities. (Uhlig, this issue) I am skeptical of this conclusion for several reasons. Some of these reasons are related to particular features of the model. The paper is too quick, in my view, to resort to uncertainty aversion instead of exploring other types of frictions in the standard, expected-utility framework. It also jumps quickly to a discussion of government asset purchases when other, potentially better solutions seem possible. What, for example, prevents expert investors from taking deposits from 4
This type of effect also appears in Eisfeldt (2004), which studies adverse selection and liquidity in asset markets.
ARTICLE IN PRESS 100
T. Keister / Journal of Monetary Economics 57 (2010) 97–100
uninformed investors and using these funds to purchase more distressed assets? The government could also lend to experts and presumably do better than purchasing assets on its own. Assuming that only a fixed amount of wealth is available to expert investors seems unsatisfactory for precisely the same reasons that assuming simple cash-in-the-market pricing is often considered unsatisfactory. The paper also takes an optimistic view of the government’s asset-purchasing capabilities. By paying a price that is higher than the fundamental value of the lowest-quality asset, the government creates an adverse selection problem—even in the uncertainty aversion scenario—because non-distressed banks now have an incentive to opportunistically sell their worst assets. The paper assumes that the government is able to purchase a representative sample of the assets for sale, and shows that this policy can be effective despite the adverse selection problem. I suspect, however, that in practice government purchases would tend to attract the worst assets rather than a representative sample. Governments generally do not have any expertise in buying these types of assets, and acquiring such expertise is a non-trivial task. The private sector would be willing to spend substantial resources attempting to unload their lowestquality assets.5 If these efforts are even partially successful, a government purchase program becomes less attractive. Finally, the main result of the paper also seems sensitive to the particular assumptions about asset returns. When the bust state occurs, there is a distribution of returns across the now-distinct assets, but there is no uncertainty about the return on the aggregate portfolio. The benefit of a government purchase program comes through a diversification effect: an individual investor buying a single asset may fear receiving the lowest quality, but a government buying a large portfolio earns a certain return. During the critical stages of the current crisis, however, there seems to have been a significant amount of aggregate uncertainty about the value of mortgage-related securities in general. In such a case, the rationale for a government purchase program is substantially weaker, particularly if taxpayers share the uncertainty aversion of investors. In the limiting case where all uncertainty is aggregate, so that each asset will yield the same return, the taxpayers as a group would be willing to pay no more for the assets than an individual investor would. In the framework presented here, the benefits of a government purchase program depend crucially on the degree to which the government can diversify risks that private investors cannot. 5. Conclusion Perhaps a way of summarizing the points above is to say that matching the six stylized facts presented in the paper may be a necessary condition for trusting the policy conclusions that come out of the model, but it is clearly not sufficient. I worry that the conclusions drawn in the paper may not be robust to some reasonable changes in assumptions. None of these criticisms should be interpreted as undermining the value of the paper, of course; it represents a substantial contribution to the growing body of crisis-related literature. Perhaps most importantly, it provides a solid framework in which the ideas discussed above can be analyzed formally. Understanding the crisis and the effects of the many different policy proposals is a Herculean task, and there is clearly more work to be done. By bringing the policy debate into the realm of modern economic theory, the paper provides an excellent starting point for future work. References Allen, F., Gale, D., 1998. 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5 Indeed, much of the discussion surrounding the potential government purchase program in the Fall of 2008 centered on whether or not a mechanism could be designed that would prevent the government from systematically overpaying for low-quality assets.