انتقال سیاست پولی تحت ساختار بانکی متفاوت: نقش سرمایه و عدم تجانس

This work deals with the transmission of monetary policy through the bank loan market, in the presence of a capital requirement regulation. Unlike standard models, based on the “representative bank” shortcut, we adopt the heterogeneous agents approach: this allows us to explicitly model the strategic interaction between well-capitalized and under-capitalized banks. The main results are the following. (I) The propagation of a monetary policy impulse through the loan market differs considerably, depending on the market structure: under monopolistic competition, strategic complementarity among well-capitalized banks leads to a “multiplier effect”; in the Cournot oligopoly framework, an effect of the opposite sign is at work, due to strategic substitutability. (II) Well-capitalized banks are more important, in shaping the adjustment following a monetary policy shock, than what is implied by their relative number over total; this fact strengthens the monetary policy effectiveness. This result holds under both monopolistic competition and oligopoly, although the interaction among banks, leading to such a result, differs across the two banking structures.

The transmission of monetary policy through the banking channel has been extensively analyzed, both on theoretical and on empirical grounds. This work provides a theoretical contribution in this field, addressing two specific issues: – Which are the implications of the banking structure for the transmission of monetary policy? Does the market structure of the banking sector affect the propagation of a monetary policy impulse through the banking channel? – How does the capital requirement regulation modify the reaction of banks to a monetary policy shock? To what extent the capital constraint, by limiting the scope for expanding the supply of loans, reduces the impact of a monetary policy expansionary intervention?1 The innovation we introduce, relative to the existing literature, relies on the heterogeneity approach, which we adopt for the reasons outlined below. We analyze the transmission of a monetary policy impulse–namely a change of the policy interest rate–through the market for bank loans, allowing for the presence of both well-capitalized and under-capitalized banks. The strategic interaction among them is studied under two quite different specifications of the market structure: (i) monopolistic competition, where banks compete in prices and each of them is negligible; (ii) Cournot oligopoly, where banks compete in quantities and the action of a single agent affects the aggregate outcome. The first environment exhibits strategic complementarity, while the second one is characterized by strategic substitutability. We will show that the propagation mechanism, following a monetary policy impulse, differs considerably across the two market structures: while monopolistic competition exhibits a “multiplier effect”, the opposite holds in the oligopoly context. Moreover, the heterogeneous agents approach allows us to show that the adjustment, taking place in the loan market after a central bank intervention, is more driven by well-capitalized than by under-capitalized banks: this implies a stronger monetary policy effectiveness than simply looking at the proportion of the former to the latter in the population of banks. This result holds under both the different market structures we analyze, although the interaction among banks, leading to such a result, differs somewhat across the two banking structures. 1.1. Why heterogeneity? The models of bank behavior traditionally rely on the “representative bank” shortcut: the analysis is focused on the behavior of a single bank; the conclusions are then extended to the whole banking system. This is equivalent to assuming that all banks behave in the same way: in particular, they show the same reaction to monetary policy. When it is used for analyzing the implications of capital regulation, this approach reveals all his limits. The representative bank may be either well-capitalized or under-capitalized: in the first case, it is able to expand its supply of loans, following an expansionary monetary policy, as the capital constraint is not actually binding; in the second case, it is not able to do so, as its volume of loans is limited by the lack of own equity. By extending this reasoning to the whole banking system, we may reach two alternative and extreme conclusions: (i) if the banking system is well-capitalized, monetary policy is effective through the banking channel; (ii) the opposite holds, if the banking system is poorly capitalized. So the representative bank approach points to the existence of two very different equilibria in the loan market, leading to opposite conclusions regarding the transmission of monetary policy through the banking channel. Now, consider the following issue: what is the impact of monetary policy on the loan market, when both types of banks, well-capitalized and under-capitalized, are present and compete in such a market? The representative agent approach is by definition unable to answer this question, as it relies on the implicit assumption that the capital level is homogeneous across banks. In particular, it is unsuitable to analyze the strategic interaction between well-capitalized and under-capitalized banks: the reaction of each bank to a monetary policy shock, given the presence of both types, will be different from the one it has when only its own type is present in the market. 1.2. Which market structure? As we mentioned above, we will carry out our analysis under two market structures, namely monopolistic competition and Cournot oligopoly. Despite the space it requires, we believe such effort is worth taking. Competition in banking is typically far from perfect. In particular–as the literature2 in the banking field has shown–banks are able to segment the loan market by keeping private the information on borrowers and by building up customer relationships with them; therefore, borrowers face significant costs if they wish to switch from an existing lending relationship to a new one. As a consequence, bank loans are not perfect substitutes for borrowers. Then it is reasonable to assume that each bank has some market power in the market for loans: in particular, it faces a downward-sloped demand for loans with finite elasticity. Moreover, the same assumption that loans are “information intensive” assets implies that firms (at least part of them) cannot easily substitute bank loans with alternative sources of funding, like issuing securities in the open market. This makes firms “bank dependent” to some extent, enabling banks to apply on their loans an interest rate possibly higher than the one prevailing in the securities market. Traditionally, the monopolistic competition framework has been seen as the most suitable to describe the market for bank loans: despite the presence of many players in the market, each of them retains the power of setting its own price at the desired level. More recently, the process of concentration, taking place in many countries, has sometimes led to situations where a few large players account for the bulk of the market; in such circumstances, the competitive game is perhaps more adequately described by the oligopoly paradigm. Which of the two models is a more accurate description of reality is ultimately an empirical issue. Where a large number of banks compete with each other, and each of them is able to set a price significantly different from the average loan rate, the monopolistic competition framework seems to be the natural candidate. Where a few large banks get a dominant position and set volume targets in their budget plans, the strategic interaction among them is well described by a Cournot game. We do not aim, in this work, at saying which of the two market structures is likely to prevail. Our purpose is rather to highlight the differences and the common features they exhibit, as far as the propagation of a monetary policy impulse is concerned, in the presence of capital regulation. 1.3. Related literature The present work is related to two streams of literature, dealing respectively with: (i) the transmission of monetary policy through the banking sector; (ii) strategic complementarity and heterogeneity. The first area of research was initiated by the seminal work by Bernanke and Blinder (1988), where the existence of a bank lending channel, complementary to the traditional interest rate channel, was introduced in the macroeconomic framework of the IS-LM model. Following that contribution, several theoretical and empirical studies have stressed the role of the banking system in transmitting monetary policy impulses to the real sector of the economy.3 Among them, we wish to mention here only a few articles, dealing in particular with the role of bank capital in conditioning the way the banking channel works: Thakor (1996), Holmstrom and Tirole (1997), Repullo and Suarez (2000), Van den Heuvel (2001), Tanaka (2001), Chami and Cosimano (2001). From these models, it is possible to draw the following conclusions: (i) the presence of a capital requirement may reduce the effectiveness of monetary policy; (ii) a reduction of the level of equity of the banking system lowers the volume of bank credit available to the economy (so-called “credit crunch”). All these studies rely on the assumption that the banking system may be adequately described by a “representative bank”: under this regard, they share the drawbacks outlined above. The second area of research, related to this paper, points to the analysis of strategic interaction among heterogeneous agents. The article by Cooper and John (1988) opened up the way to the study of strategic complementarity and of its consequences for the properties of Nash equilibria. The article by Haltiwanger and Waldman (1991) analyzes the properties of the aggregate behavior of the economy, where heterogeneous agents interact: basically, there are two groups of agents, differing for their degree of strategic complementarity (or substitutability). It comes out that one group of agents may have a disproportionate importance–relative to its own share over the total number of agents–in shaping the aggregate equilibrium. This result may be applied, for instance, to the explanation of the real effects of monetary disturbances: the presence of even a small number of firms, which do not adjust their price following a nominal shock (because of menu costs and/or near rationality), may cause a significant rigidity of the aggregate level of prices. This creates a fundamental link between the literature on heterogeneity (with strategic complementarity) and the one dealing with money non-neutrality, due to the joint effects of nominal and real rigidities:4 see Akerlof and Yellen (1985) on near rational behavior and Mankiw (1985) on menu costs. 1.4. Plan of the paper The paper is organized as follows. In the next section, we present a model of monopolistic competition in the market for bank loans, where banks are subject to a capital requirement and they may differ among each other with regard to their equity level. The model is used to analyze the impact of monetary policy on the loan market, under three alternative environments: (i) all banks are well-capitalized (so they are not constrained by the capital requirement); (ii) all banks are under-capitalized (constrained); (iii) both types of banks are present and compete in the market for loans. In Section 3, the same type of analysis is done in the context of Cournot oligopoly. In Section 4 we draw the main conclusions from our analysis.

Let us summarize our results. (1) The propagation of a monetary policy impulse through the loan market differs considerably, depending on the market structure: this is due to the nature of the strategic interaction among banks. Under monopolistic competition, it is characterized by a “multiplier effect” (which is typical of contexts where the interaction among agents exhibits strategic complementarity): the response of each bank to a central bank intervention is increased by the fact that other banks react as well, leading to an amplification of the aggregate outcome. In the oligopoly framework, an effect of the opposite sign is at work, due to strategic substitutability: the incentive of each bank to pass through the monetary policy impulse to their loan supply is decreased by the reaction of the other banks, weakening the impact of central bank action. These different patterns of aggregate response to a monetary policy shock emerge very clearly when we examine the equilibria with (homogeneous) well-capitalized banks, whose behavior is not constrained by the capital requirement. (2) In the heterogeneity context, well-capitalized banks are more important, in shaping the equilibrium prevailing after a monetary policy shock, than what is implied by their relative number over total; in other words, the equilibrium with heterogeneous banks is “distorted” towards the one where only well-capitalized banks are present. Therefore, the aggregate impact of monetary policy through the banking channel is stronger than the one obtained by simply “averaging” the two extreme equilibria (where all banks are either well-capitalized or under-capitalized). Moreover, it is a (decreasing) concave function of the number (n) of under-capitalized banks: it declines less than proportionally for low values of n; however, as n grows large, the marginal reduction of monetary policy effectiveness, due to an additional bank suffering from a lack of equity, becomes greater. We believe such results being relevant both on theoretical and empirical grounds. Under the first regard, our model is able to show the exact propagation mechanism of a monetary policy impulse through the banking sector, highlighting the differences between two quite different market contexts–monopolistic competition and Cournot oligopoly–which are commonly observed in banking. Moreover, thanks to the heterogeneity approach, it provides a correct measure of the monetary policy impact on the loan market in the presence of capital regulation, thus improving upon the traditional representative agent approach. Interestingly enough, result 2 is “robust”, as it holds under both the two above-mentioned market structures, although the underlying mechanisms leading to such a result differ somewhat across them. On empirical grounds, our analysis shows that the implications of capital regulation for the transmission mechanism must be carefully evaluated, particularly when a fraction of the banking system suffers from under-capitalization. Suppose you wish to forecast the impact of a policy rate cut on the average loan rate. If you do that by looking at the typical response of a “representative” well-capitalized bank, weighting it by the share of well-capitalized banks over total, you will get an under-estimation of the true impact. You should instead correctly consider the interaction between well-capitalized and under-capitalized banks; in other words, you have to take into account that each of them behaves differently, depending on the relative number of under-capitalized banks over total. Moreover–since the monetary policy impact is a concave function of such relative number–the amount of under-estimation grows larger as the share of under-capitalized banks increases, it reaches a (interior) maximum and then it converges to zero (look at the distance between the solid and the dashed lines in Fig. 1).