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However, the question arises what are the principles that a lender of last resort is supposed to follow. As far back as 1873, Bagehot (1873), based on the work by Thornton (1802), formulated rules of a lender of last resort policy. He suggested that in a crisis, the lender of last resort should lend freely, at a penalty rate, on the basis of collateral that is marketable in the ordinary cause of business when there is no panic.2 Especially, to discourage risk taking by individual institutions the view holds that the lender of last resort should lend whenever possible only to the market at penalty rate and only against good collateral. By this maxim the doctrine of what a lender of last resort should do today is still well-captured besides coming under some criticism by authors like Goodhart (1999) or Giannini (1999).3 In this paper, we take a ﬁrst step to investigate if such a ”one size ﬁts all”-approach with respect to lender of last resort policy makes much sense having in mind the diﬀerences between ﬁnancial systems of various countries. This issue while very important is highly complex because as the literature on comparative ﬁnancial systems shows, there are many dimensions in which ﬁnancial systems diﬀer.4 However, we focus our very simple analysis on one dimension, namely the diﬀerences in the importance of relationship banking in market-oriented and bank-dominated ﬁnancial systems.
More speciﬁcally, we build our analysis on the Diamond/Rajan-framework and use this modelling structure as our starting point to incorporate certain stylized facts on diﬀerences between bank- and market-based ﬁnancial systems.5 The approach will be extended to explore what happens to the functioning of a ﬁnancial system if there is an aggregate shortage of liquidity - if the supply of liquid assets is small relative to aggregate liquidity demand. We are able to deﬁne diﬀerent cases for the resulting equilibrium on the market for liquidity and thus develop a taxonomy of crises situations.
This gives us some hints on the probabilities and welfare consequences of certain crises situations in the respective ﬁnancial systems. In turn this allows us to give a ﬁrst assessment of the type of interventions a lender of last resort should follow. Especially, See for instance Fischer (1999), Giannini (1999) and Goodhart (1999) for a discussion of these rules.
See for instance Fischer (1999).
See Allen and Gale (2001) for a recent survey. This literature includes theoretical analysis, e.g.
Allen and Gale (2000), as well as more empirically oriented work such as Franks and Mayer (1995) and Hackethal, Schmidt, and Tyrell (2002) See Diamond and Rajan (2001) for the basic framework and Diamond and Rajan (2002) for an application to banking crises.
the question when - if at all - the lender of last resort should charge a penalty interest rate and if the lender of last resort should lend only to the market or to individual institutions, will be analyzed with regard to the diﬀerent ﬁnancial systems. Our main result is that under reasonable assumptions individual liquidity assistance to banks is preferable in bank-dominated ﬁnancial system while in market-oriented systems a policy following Bagehot’s rules should be pursued.
Of course, we are not the ﬁrst who discuss optimal lender of last resort policy and especially the classical market doctrine of the lender of last resort.6 But to our knowledge we are the ﬁrst who analyze in a theoretical framework the interrelationship between characteristic diﬀerences of ﬁnancial system conﬁgurations and adequate lender of last resort policies.
The remainder of the paper is organized as follows. Section 2 presents our framework. In section 3 the stability of an individual bank will be investigated. It follows an analysis of the equilibrium in the liquidity market in section 4. In section 5 we describe the optimal lender of last resort policy. Section 6 concludes.
2 The framework
2.1 The setup Following Diamond and Rajan (2001) we consider an economy with three dates (t = 0, 1, 2) and a large number of entrepreneurs, bankers and investors. Entrepreneurs are wealthless, however each of them has a project at his disposal which requires an investment I = 1 at t = 0. Each investor is endowed with a small amount of consumption good in comparison to the required investment size, hence we need many investors to fund a project. In addition, we assume that the aggregate endowment of all investors in the economy is lower than the total investment possibilities. Because of this shortage of investment capital at date 0 entrepreneurs and bankers must oﬀer an expected return as high as possible to attract funding. Entrepreneurs, investors and bankers, whose role will be clariﬁed below, are risk-neutral but diﬀer in their preferences: Investors and bankers have a strong preference for consumption at date 1, i.e. they have a very high discount rate ρ for consumption at date 2, whereas entrepreneurs value consumption at each date equally. Investors can storage their See for instance Rochet and Vives (2002) for a very interesting model that shows how a lender of last resort can avoid ineﬃcient liquidation of banks. Freixas, Parigi, and Rochet (forthcoming) discuss how the optimal LOLR policy is aﬀected by moral hazard problems on side of the banks.
initial endowment earning a return of 1 for every unit invested, or they can invest it in the project.
Financing the projects includes some diﬃculties which have to be overcome. Entrepreneurs have speciﬁc abilities vis-a-vis their projects, i.e. the cash ﬂow each entrepreneur can generate from his project exceed what anyone else can get out of it.
But entrepreneurs cannot commit their human capital to the project, except on a spot basis. From this it follows that a lender can extract future repayment only by threatening to take away the project from the initial entrepreneur. The project returns C generated by the initial entrepreneur are uncertain in terms of their time structure.
The project pays out C either at t1 if the project produces early or at t2 if the project is delayed. All uncertainty about projects is resolved at date 1.
We consider two alternatives when taking away the project from an entrepreneur.
The project can be restructured at any time until date 1 which will yield a payoﬀ c1 immediately and nothing at date 2, or the entrepreneur can be replaced with assets redeployed to their next-best use, which does not change the timing of the produced cash ﬂow but the level to γC with γ 1. Both alternatives result in a loss of surplus, since c1 1 γC C, (1) However, the big diﬀerence between this two alternative is the following: The second alternative (replacement) can only be implemented by a bank who was the only initial ﬁnancier of the project while restructuring can be done by any investor, irrespective of having been an initial ﬁnancier of the project or not.
How can we interpret these alternatives? Restructuring is an activity which can be understood as changing the original content of the projects so that some immediate cash can be produced without any speciﬁc knowledge. One may think of this strategy as abandoning the uncertain technology and using instead a commonly known technology that produces goods quickly or stopping half-ﬁnished projects and salvaging the production goods. All investors can realize this cash ﬂow, hence c1 is the secondary market value of a project. On the other hand, replacing the entrepreneur and redeploying the assets to their next-best use, which yields γC is an activity which demands speciﬁc skills for replacing the entrepreneur but preserving the original content of the project. It may involve searching for a new entrepreneur who has similar skills to the original one, or abandoning only such aspects of the project that were particulary dependent on the old entrepreneur. Because this implies learning all about the project it takes time, eﬀort and a constant close contact to retain this skills. Therefore, we assume that just one initial ﬁnancier, eﬀectively a ”relationship lender” or banker who collect the savings of the investors, will undertake this costly activity. Accordingly, only the banker knows the next-best use of the project’s assets. To sum up, the bank can realize γ · C from the project, if it takes the project away from the initial entrepreneur, while other investors can only realize c1. Therefore, the initial entrepreneur will oﬀer to repay γ · C to a bank and only c1 to other investors.
How can we grasp the diﬀerences between ﬁnancial systems in this modelling structure? One obvious diﬃculty lies in the fact that this framework taken at face value allows only banks to exist as intermediaries. Capital markets in the literal sense as institutions, where ﬁrms issue stocks and bonds, households buy and trade these securities and the resulting prices incorporate valuable information, are not caught in our modelling structure. Yet what makes the framework attractive is the possibility to grasp certain consequences of market-based and bank-based ﬁnancial systems.
We view a bank-based system as a conﬁguration with a relatively high γ and a low c1 while the reverse, a relatively low γ and a high c1 is true in a market-based system. A high γ points out that usually in a bank-based system the intermediary has a great deal of information about her borrowers and their projects because of a long lasting and close relationship. As a consequence, she can enforce higher repayments from a borrower than a typical lender in a market-based system who does not collect as much knowledge and information. So the banker in a bank-based system can ”replace” the entrepreneur easier, thereby retaining much of the original strategy of the initial entrepreneur. This gives her bargaining power. In our opinion, this is an essential characteristic of a bank with typically ﬁrm-speciﬁc knowledge.
On the other hand, c1 is the payoﬀ of restructuring. Because this restructuring is the best alternative, publicly available use, it can be interpreted as the market value of these projects. A relatively high c1 indicates that much information about the best alternative use is released in the market. In sum, we conclude that the diﬀerence between γC and c1 is rather small in market-based systems.7 The assets are relatively liquid because a great deal of information gets ”externalized ” through the market activities. This reﬂects the notion that there are many analysts working for mutual funds, pension funds and other intermediaries who gather private information and incorporate these through their trading activities in market prices which is the general advantage of a market-based system.
In bank-based systems assets are more illiquid. In countries with bank-based systems, relatively few companies are listed and accounting disclosure requirements are Of course, we maintain the relation γC 1 c1 for a market-based system. Only the diﬀerence is small.
limited, so very little information is incorporated into stock prices. Also the number of analysts who follow stocks is small, so only limited private information is incorporated into stock prices. However, intermediaries have more information available in these systems. The greater prevalence of long term relationships, i.e. the ”hausbank”relationship, in bank-based systems means that the banks are able to acquire considerable information about the ﬁrm they lend to. Typically this information will not be released to the market; instead the information will be used internally to allow a smooth functioning of the long term ﬁnancial relationship and allocate resources eﬃciently.8 Therefore information in a bank-based system is more or less ” internalized ”, outsiders to the ﬁnancial relationship have only a small chance to get valuable information.9 Banks have strong incentives to acquire and use information because they can proﬁt from information which doesn’t leak to outsiders. However, this creates the problem that most of the assets are rather illiquid because only the banker has the relevant information. This means c1 is small and the diﬀerence between γC, the payment a bank can extract, and c1, the market value of a loan, is large.