بانک ها به عنوان هماهنگ کننده رشد و ثبات اقتصادی: میکرو شالوده ای برای اقتصاد کلان با بیگانگی

Competition among banks promotes growth and stability for an economy with production externality. Following Arrow and Debreu (1954) [6], I formulate a standard growth model with externality—a two-period version of Romer (1986) [39]—as a game among consumers, firms, and intermediaries. The Walrasian equilibrium, with an auctioneer, does not achieve the social optimum. Without an auctioneer or intermediaries, I show that no Nash equilibrium exists. With several banks strategically intermediating capital, a Nash equilibrium emerges with a realistic institution, i.e., an interbank market with a negotiation process in the loan market. The equilibrium outcome is uniquely determined and socially optimal.

I formally identify an essential role that banks play: A strategically competitive banking sector serves as a decentralized mechanism to internalize positive production externality among firms, thereby facilitating economic growth. To clarify this role, I shut down banksʼ roles that have been considered in the banking literature. The model does not assume any exogenous stochastic shocks, informational problems, illiquid projects, and transaction costs. 2 The strategically competitive banking sector also brings stability in an economy with production externality by supporting a Nash equilibrium. Without any financial intermediaries, I show that an economy with production externality, which often appears in the economic growth literature, faces serious instability because a Nash equilibrium does not exist. To support an equilibrium, I further find that an additional institutional setup among banks is necessary: an interbank market with a negotiation process in the loan market. This institutional setup can be viewed as an optimal mechanism to internalize the externality. My model is based on a canonical growth model with externality, essentially the same as in Romer [39].3 In his model, investment of a firm is assumed to raise marginal products of other firms. Because of this Marshallian externality, the competitive equilibrium is not Pareto optimal: Investment is lower and the growth is slower. This result has been supporting a case for subsidies (e.g., transportation and R&D) or patents for firms to increase their investments. In Romer [39] and many other growth papers, the capital market is assumed to be competitive in the Arrow–Debreu sense: Financial activity is conducted only by a security market. But, what happens if banks intermediate the capital market? I first formulate a two-period version of the Romer growth model in the spirit of Arrow and Debreu [6]: An economy is a game among consumers, firms, and an auctioneer. The auctioneer, as an abstraction of a security market, intermediates the financial transaction and converts savings to capital. Not surprisingly, the equilibrium allocation is the same as in Romer [39]: The Walrasian equilibrium is not Pareto optimal. I then modify the model so that banks clear the capital market. An economy becomes a game among consumers, firms, and banks. Banks strategically compete with each other in deposit and loan markets. I find that, with an additional institutional setup, a Nash equilibrium exists, and it is Pareto optimal. Banks, in this paper, are different from the Walrasian auctioneer in Arrow and Debreu [6]. While the auctioneer offers only price, a bank can post a contract that specifies both price and quantity (e.g., loan rate and amount). With this more realistic contract space, every bank has an incentive to become a monopoly lender, because, if a bank becomes a monopoly lender, it can tailor the loan contracts to extract all the rents from all firms, including any external effects. Knowing this, banks will compete aggressively for deposits by driving the deposit rate up to the return that a monopoly lender would obtain. In the equilibrium, many banks and firms operate at zero profit under the interest rate that equals the socially optimal level. Also, in the equilibrium, savings and loan amounts become equal to the socially optimal levels. There is a caveat, however. To be clear, the other allocation cannot be an equilibrium: The interest rate below the monopoly lenderʼs return would be upset by a rival bank, and the interest rate above the monopoly lenderʼs rate cannot be technically feasible to prevail. Yet, there is a profitable deviation at the identified equilibrium candidate. The private marginal return is lower than the social marginal return so that a bank-firm pair would want to invest less than the socially optimal amount and share extra profits by free riding on investments of other firms. As a consequence, no Nash equilibrium exists in an economy in which an auctioneer is simply replaced by banks. The problem lies in the discontinuity of banksʼ profit function. Banks are willing to bid the deposit rate up to the monopolistʼs loan rate that internalizes externality. But, at this socially optimal interest rate, banks suddenly have to worry about their fund positions being too large and thereby want to limit deposit amounts. Therefore, the only remedy to support an equilibrium in a decentralized economy is to introduce an institutional setup that allows banksʼ loan market behaviors to be somewhat independent from their collected deposits (a weak link between sources and uses of funds). Apparently, introducing the interbank market is necessary to break the constraint that forces each bankʼs loan to be strongly tied to its collected deposits. In addition, some sort of price adjustment mechanism is necessary for the interbank market to clear. I propose a simple, realistic mechanism: Banks are allowed to have a free-recontracting opportunity in the loan market so that they can adjust quotes on loan terms. For example, if there were two sessions in a day (e.g., morning and afternoon), banks could freely change their loan offers once before the settlement at the end of the day. This mechanism is sufficient to support the identified Nash equilibrium. Note that potential instability may still remain if a more refined equilibrium than a Nash equilibrium is required. However, the instability is not created by banks but deeply rooted in the economy. 4 In one strand of the literature on linkages between a macroeconomy and its financial system, many studies argue that banks are superior to a market allocation by their more active involvement in investments, especially in the phase of economic development. They are, however, mostly based on historical descriptions (e.g., [24], [15], [5], [2] and [27]).5 Also, there are formal modeling attempts on finance and growth (e.g., [25], [9] and [26]), but banksʼ specific roles in economic growth with production externality have not been clearly delineated or argued, at best, in a partial-equilibrium setting (e.g., [19]). In another strand of the literature on finance-macroeconomy linkages, instability is the key issue. Instability is associated with riskiness of loans in banking theories, while instability means amplification of cycles by financial frictions in macroeconomic models. In contrast, this paper deals with more fundamental instability, i.e., possible nonexistence of an equilibrium. In the banking literature, several studies consider bank competition as the primary suspect that brings instability (e.g., [28]), though some question this speculation (e.g., [13]). Many of these theories are, however, based on a partial-equilibrium setting, or with little connection to formal macroeconomic theories, and thus difficult to apply to growth and stability issues at the macroeconomic level.6 Moreover, any of these theories assume some frictions: private information, limited liability, or transaction costs. Also, in macroeconomic models with financial amplification (e.g., [10] and [30]), bank behaviors are mostly hidden in assumptions on financial frictions. Again, as this paper does not rely on any of those frictions, this paper brings a new perspective on the debate on bank competition and stability. From a technical point of view, this paper can be regarded as an extension of the literature on strategic intermediation to a general equilibrium growth model with production. This literature has attempted to replace the Walrasian auctioneer with strategic firms or middlemen. Townsend [45], Stahl II [42], and Yanelle [47] study the strategic competition of middlemen in a frictionless economy.7 Their common concern is whether strategic intermediaries achieve the Walrasian equilibrium. Results are mixed. Townsend [45] shows positive results in an exchange economy.8 In a partial equilibrium framework, given traditional demand and supply functions, Stahl II [42] shows mixed results that depend on specification of the game, and Yanelle [47] reports a negative result, i.e., the allocation is inefficient. In Section 2, I describe the general model setup for an economy with intermediaries. In Section 3, I further develop the model in detail to describe the strategically intermediated economy with free recontracting opportunity. I then show the existence of an equilibrium and the uniqueness of the equilibrium outcome. In Section 4, I explain nonexistence of an equilibrium in an economy without intermediaries. This case is isomorphic to an economy with intermediaries but without further institutional setup, such as free recontracting opportunity. Section 5 concludes.

An economy with production externality is a key conceptual laboratory for many theoretical and empirical macroeconomic research, especially in the growth literature (see the review by Klenow and Rodríguez-Clare [31]). I have found that such an economy is unstable without financial intermediaries in the sense that a Nash equilibrium does not exist. Using a game theoretic microfoundation, I have also confirmed that a Walrasian capital market, although it supports an equilibrium, does not bring the socially optimal allocation because of externality. I have introduced strategic competition among banks in an economy with production externality. The strategic competition among banks turns out to support a Nash equilibrium. More importantly, it serves as a decentralized mechanism to internalize production externality and brings the Pareto-optimal allocation. Specifically, banks compete for deposits to obtain potential monopoly profits, taking externality into account. Then, using loan contracts that specify both price and quantity, banks control firmsʼ investment decisions and implement the socially optimal capital allocation. It was not straightforward to identify an equilibrium in the economy with banks, because the economy inherently lacks a Nash equilibrium without a further institutional setup. First, I have presented an example of institutions that establish an equilibrium. The example, strategic tâtonnement, is not far from reality: Banks should be able to negotiate loan terms (free recontracting) with firms and adjust their fund positions in an interbank market. This institutional setup can be viewed as an optimal mechanism to internalize production externality. Second, I have proven that the equilibrium outcome is uniquely determined regarding the deposit contract for each household and the loan contract for each firm under a general condition called a weak link of sources and uses of funds. This condition allows banks to compete for deposits without worrying about their fund positions in the competitive loan market. In the equilibrium, each bank appears to form a firm group endogenously, as the equilibrium loan contract is exclusive (i.e., a firm borrows only from one bank).43 Then, each bank internalizes externality directly within a firm group and indirectly across firm groups. In other words, this paper successfully explains an origin of expansion of bank control and formation of competing firm groups, which are identified by various researchers as salient features of industrial development as well as of contemporary financial systems in many countries (e.g., [29]). At the same time, such seemingly tightly connected business groups are sometimes accused of creating over-investment and crisis.44 This paper justifies over-investment from the viewpoint of the private marginal product of capital. However, even with the proposed institutional setup, the equilibrium is fragile against equilibrium refinements (e.g., subgame perfection). Although this is not the case in the limit of infinite recontracting, the economy is not perfectly free from the intrinsic instability in this sense. Still, it is important to note that this instability is not brought by banks but deeply rooted in the economy with production externality. Moreover, this instability (i.e., possible nonexistence of an equilibrium) is a deeper problem than the main focuses of the literature on bank competition and stability so far, which concentrate on either banksʼ risk taking (in an equilibrium) or financial amplification due to financial frictions (on a dynamic equilibrium path). Understanding banksʼ roles in macroeconomic growth and stability has been a key interest in economics, at least since the Great Depression. Even with burgeoning literature after the recent financial crisis, none is yet to point out either deeply rooted instability in an economy with production externality or implications of having competing banks in such an economy. Therefore, the presented theory brings a new perspective and complements existing micro and macro theories of financial sectors based on informational problems and transaction costs. Moreover, the presented framework can readily serve as a microfoundation for future studies on linkages between a macroeconomy and its financial system, as it formulates strategic behaviors of financial intermediaries interwoven with a standard macroeconomic model.