طراحی و نقدینگی ارائه شده توسط بانک ها و بازارها در یک اقتصاد پویا

This paper contributes to the literature on financial system design by comparing markets and banks in a dynamic economy. Investors trade off their liquidity needs against the high returns on illiquid investments. Both the banking system and the market can provide partial liquidity insurance to investors. We consider full market participation as well as limited market participation. We demonstrate that the full-participation market with intergenerational trading can provide more liquidity than one without. Insurance is provided through wealth transfer across generations, instead of cross-subsidization across contemporaneous types as is the case in the finite economy. Given a full-participation market that allows trading across generations, only banks with initial capital can provide additional liquidity. In a limited-participation market with uncertainty about trading types, an intergenerational bank (with or without initial capital) provides additional insurance to investors. The need for trade is eliminated. Finally, if there is no uncertainty about trading types, then an intergenerational bank with initial capital eliminates the need for trading and improves welfare for all. An intergenerational bank without initial capital improves welfare for people who do not trade.

The relative merits of financial intermediaries and financial markets in providing liquidity have been examined in an extensive recent literature.1 In their asset allocation decisions, investors trade off their liquidity risk against the high return of long-term investments. Both markets and banks can provide some insurance to individual investors by aggregating liquidity risk. Pioneering work by Bryant (1980) and Diamond and Dybvig (1983), and extension by Jacklin, 1987 and Bhattacharya and Gale, 1987, and others, have been the starting point of an important information-based literature on banking and liquidity. The relative importance of banks and markets as liquidity provision mechanisms has been a central question in this literature. Diamond and Dybvig (1983) model a two-period economy in which ex ante identical agents either consume in period one or in period two and the productive technology is an illiquid two-period investment. Meanwhile, the Arrow–Debreu type of insurance contracts are not available. They show that demand deposits with banks are able to provide partial liquidity insurance by centralizing the asset holding and risk bearing and thus subsidizing the consumers with high liquidity needs. Jacklin (1987) points out that once the trading is introduced, banks cannot provide more liquidity than the market does, questioning banks’ importance. Haubrich and King (1990), von Thadden (1997) and Hellwig (1994) also present models that cast doubt on the liquidity role of banks in the presence of financial markets. Diamond (1997) shows that if there is only limited participation in the financial market, banks and markets coexist and influence each other’s activities. Under various specified conditions, banks are shown to improve the consumption to the full-participation market level or higher. The above articles have all used a single generation static model of intertemporal liquidity risk. These models have been recently extended to dynamic overlapping generations (OLG) economies. Qi, 1994 and Bhattacharya and Padilla, 1996 and Fulghieri and Rovelli (1998) have studied the problem of designing and implementing ex ante optimal stationary allocations in dynamic OLG economies. Qi (1994) examines banks’ liquidity service and stability in an overlapping generations version of Diamond and Dybvig model. He concludes that the intergenerational transfers enable an intergenerational bank to achieve interest rate smoothing and provide depositors with liquidity insurance without Diamond and Dybvig’s assumption of no side trades. Instead, the need for side trades is removed by imposing an incentive-compatible constraint that the long-term interest rate is no less than the long-term real investment return. However, this incentive constraint implicitly assumes a market consumption level that could be achieved in a finite model. Whether or not this constraint will actually eliminate trades in the overlapping generations framework remains an open question. Given two technologies (storage technology and long-term profitable technology), it is not possible for an agent to obtain consumption level higher than the long-term real return in a finite trading model. It is not certain, however, that with intergenerational trading possible, investors cannot obtain higher returns than the returns offered by banks. In this paper, we introduce full-fledged dynamic markets that allow for intergenerational trading. We examine the role of banks in such a dynamic economy. We analyze the role of banks with full participation as well as limited participation in financial markets. The questions this paper tries to answer, in an overlapping generations framework, are: How does a full-participation market perform in providing liquidity to investors who are subject to liquidity shocks? Under what condition do banks provide more liquidity than markets? When do markets do better? How does a limited-participation market perform? What can an intergenerational bank offer when there is limited participation in the financial market? When it comes to market performance, the important difference an overlapping generations model makes is that it introduces the possibility of trading between different generations. Intuitively this results in more liquidity than in the finite model. As it turns out, the agents with high liquidity needs obtain liquidity insurance, while the more patient agents can still enjoy the full amount of the productive investment return. In contrast, in a finite model, a bank provides liquidity insurance only through cross-subsidization. Because intergenerational trading is allowed, wealth is either invested in the productive technology or consumed. No capital is left idle. Therefore the additional liquidity and the resulting higher productivity for the economy together lead to higher consumption levels for all agents than those in a finite model. Based on our analysis on intergenerational market performance and Qi’s results on intergenerational banks with and without initial capital, we conclude that only the banks with initial capital and investments are sustainable and able to provide more liquidity than the free market. This leads to a policy implication that the government should help build the initial capital by taxing the earlier generations. The damages caused by bank runs are beyond those due to the termination of productive investment since a viable bank cannot be built immediately after an equilibrium disruption. In examining the limited-participation market, we consider two alternative models. In the first model, we follow Diamond’s (1997) classification of agent types: ex ante, people do not know their liquidity type or their trading type, i.e., when they need to consume or whether they are able to participate in the market. Those who will not participate in the market are a subset of the patient agents. It is shown that in this particular setting, no trade will occur across generations in free markets. If an intergenerational bank (with and without initial capital) exists, it provides liquidity insurance to all types of agents and eliminates needs for trade. Unlike in the single generation model, there will be no cross-subsidization between those who trade and those who do not. However, it is rather unrealistic that people do not trade across generations. We thus propose an alternative model of limited participation in the market. Here, agents do not know their consumption timing ex ante but they know their trading type. This simple modification allows trading across generations. This model results in surprisingly simple conclusions. Both trading types will benefit from an intergenerational bank with initial capital. When there is no initial capital, the economy is virtually divided into two sectors. One is a full-participation market for those who will trade. And those who do not trade will form an intergenerational bank among themselves. Based on our analysis, we summarize the role of banks in providing liquidity under different scenarios. Bhattacharya and Padilla (1996) also study banks and markets, with and without government intervention, in an overlapping generations economy.2 Government intervention subject to the same informational requirements as those imposed on banks is shown to give rise to market allocations that are no worse than those attained by banks. They do not analyze the initial capital constraint for banks or limited market participation. Allen and Gale (1997) also find that investors are better off depositing in banks than trading in markets, in an overlapping generations model. However, unlike all the papers discussed before including ours, they do not model liquidity risk. Instead, they model technology risk associated with the long-term investment. They show that an intermediary can improve on the market allocation in two ways: allowing intergenerational risk-sharing regardless of the random state when the young are born; intergenerational smoothing after the intermediary has accumulated enough reserve which provides full insurance against technology uncertainty with probability one. However, they also point out that markets can still compete ex post in some of the states, which makes the existence of banking system fragile. In our paper, the intergenerational bank with initial capital dominates the market allocation and hence is stable. In contrast to our emphasis on the importance of the initial capital, Diamond and Rajan (2001) present a model under which a fragile capital structure is required to limit the banker’s ability to hold up depositors. The difference lies in that they model the bank as a pass-through that collects the loan payments from the borrowers and transfers them to the depositors. “its (the bank) skills are used mainly in effecting transfers rather than in creating new values.” While in our model, as in most of other models in this literature, banks are aggregated together with the production sector. There is no additional agency problem. The task of the bank is to centralize the holding of assets, make productive investments and redistribute liquidity effciently. The intergenerational bank thus needs the initial capital investment to generate higher returns than the free market can offer. The rest of the paper is organized as follows. Section 2 sets up the overlapping generations model. Section 3 investigates the market performance without banks. The role of an intergenerational bank is examined in Section 4. In 5 and 6, we relax the assumption that everyone can trade in the market and study two alternative models of limited market participation. We also summarize the results on the role of banks in providing liquidity. Section 7 concludes the paper.

In an overlapping generations framework, we have examined the role of banks in providing liquidity. The main conclusions are summarized in the four propositions and Table 3. We first examine the performance of markets without banks. Then we study whether or not an intergenerational bank can provide additional liquidity and eliminate the need for trading. The main results are as follows. Even in a full-participation market, an intergenerational bank with initial capital increases the returns to both types of agents (with high and low liquidity needs) and eliminates the side trade. An intergenerational bank without initial capital, however, has no beneficial role and is not sustainable. These results suggest that the government has a role in helping accumulate capital and establish an intergenerational bank. We consider a model of limited participation in the market, in which agents are uncertain about their liquidity needs as well as their ability to participate in the market. In this model, we show that intergenerational trading is prevented and the intergenerational banks can provide additional liquidity. In our dynamic economy, we obtain results similar to those obtained by Diamond in his one-generation setting with limited market participation. However, unlike a finitely-lived bank, an intergenerational bank, with or without initial capital, provides full insurance to both types of agents with low liquidity needs (trading and non-trading type), and partial insurance to agents with high liquidity needs through intergenerational transfer. There is no cross-subsidization and the need for trading is eliminated. Finally, we suggest an alternative way to model the limited-participation market: Agents know on date 0 their trading type, but do not know their liquidity needs until date 1. Therefore, intergenerational trades will occur. This is a realistic assumption and results in surprisingly simple conclusion. An intergenerational bank with initial capital can improve the welfare of all types of agents and eliminate the need for trade. If such a bank is not available, the economy is divided into two sections. Those trading on the market will continue to do so. Those who do not trade will form an intergenerational bank and greatly improve their welfare. The scale of the banking sector is the population of those who do not trade. This model captures the reality that different generations do trade even if there is only limited participation in the markets. The liquidity provided by banks is especially important to those who are not active on secondary markets.