IMF Working Paper No. 11/295
Dec 16, 2011
Summary: We study versions of a general equilibrium banking model with moral hazard under either constant or increasing returns to scale of the intermediation technology used by banks to screen and/or monitor borrowers. If the intermediation technology exhibits increasing returns to scale, or it is relatively efficient, then perfect competition is optimal and supports the lowest feasible level of bank risk. Conversely, if the intermediation technology exhibits constant returns to scale, or is relatively inefficient, then imperfect competition and intermediate levels of bank risks are optimal. These results are empirically relevant and carry significant implications for financial policy.
The theoretical literature offers contrasting results on the relationship between bank competition and financial stability. Yet these results arise from models with three important limitations: they are partial equilibrium set-ups; there is no special role for banks as institutions endowed with some comparative advantage in screening and/or monitoring borrowers; and bank risk is not determined jointly by the borrower and the bank. This paper contributes to overcome these limitations. A more general assessment of the relationship between bank competition, financial stability and welfare is not only important per se, but it is also essential to evaluate whether “granting” banks the ability of earning rents may reduce their risk-taking incentives.
We study the relationship between bank competition, financial stability and welfare in versions of a general equilibrium banking model with moral hazard, where the choice of “systematic” risk by either banks or firms is unobservable. In our set-up, risk-neutral agents specialize in production at the start date, choosing to become entrepreneurs, bankers, or depositors, and at a later date they make their financing and investment decisions. In this risk-neutral world, the welfare criterion is total surplus, defined as total output net of effort costs. We consider two versions of the model. In the first version, called “basic”, the bank is a coalition of entrepreneurs that are financed by depositors. In the second version, called “extended”, the “firm” is a coalition of entrepreneurs that is financed by the “bank”, which is a coalition of bankers financed by depositors. The firm, the bank and depositors can be also viewed as representing the business sector, the banking sector and the household sector.
In both versions, we consider two specifications of the bank’s screening and/or monitoring technology, called the “intermediation technology”. In the first specification, the intermediation technology exhibits constant returns to scale: the effort cost of screening and/or monitoring is proportional to the size of investment. In the second specification, this technology exhibits increasing returns to scale: the effort cost of screening and/or monitoring is independent of investment size. This second specification captures in a simple form the essential role of banks in economizing on monitoring and screening costs identified by a well-known literature briefly reviewed below.
In the basic model the bank chooses (systematic) risk, this choice is unobservable to outsiders, and there is competition in the deposit market only, indexed by the opportunity costs of depositors to invest in the bank. The results of this model differ strikingly depending on whether the intermediation technology exhibits constant or increasing returns to scale. Under constant returns to scale, as competition in the deposit market increases, bank risk increases, bank capital declines, and welfare is maximized for some intermediate degree of competition. Thus, perfect deposit market competition is sub-optimal, as it entails excessive bank risk-taking and sub-optimally low levels of bank capitalization. However, allocating large shares of surplus (or rents) to banks is not optimal either, as it results in sub-optimally low levels of bank-risk taking and excessive bank capitalization.
When the intermediation technology exhibits increasing returns to scale, however, results are totally reversed: as competition increases, bank risk declines, capitalization increases, perfect deposit market competition is optimal, and the lowest feasible level of bank risk is best. This reversal is simply explained as follows. As competition increases, a ceteris paribus increase in the cost of funding induces the bank to take on more risk. But at the same time the increase in the supply of funds to the bank reduces the costs of the intermediation technology owing to increasing returns to scale: this offsets the negative impact of higher funding costs on bank’s expected profits, inducing the bank to take on less risk. This result is remarkable for two reasons: it is obtained under a standard assumption about the bank’s intermediation technology, and without modeling loan market competition. Thus, introducing loan market competition, as in Boyd and De Nicolo’ (2005), is not necessary—albeit it may be sufficient—to yield a positive relationship between bank competition and financial stability.
The extended model depicts the more realistic case in which there is competition in both lending and deposit markets, bank risk is jointly determined by borrowers and banks, and setting up the intermediation technology entails set-up costs. Here, bank competition is indexed by the opportunity costs of depositors to invest in the bank, and the opportunity costs of the firm to be financed by the bank. In this model, the relationship between bank competition, financial stability, and welfare becomes complex in a substantial economic sense, since double-sided competition determines how total surplus, whose size is endogenous, is shared by three sets of agents, rather than two, as in the basic model. When the degree of competition in lending and deposit markets differs, we illustrate several results suggestive of a rich comparative statics, which in some cases overturn simple conjectures on the relationship between bank risk, firm risk and capital.
Focusing on changes of competition in both loan and deposit markets, we obtain the following main results. If the bank intermediation technology is relatively inefficient, as defined as one that entails high monitoring and screening costs but relatively low set-up costs, then a level of competition lower than perfect competition is optimal, corresponding to an “intermediate” optimal levels of bank risk. However, if the bank intermediation technology is relatively efficient, defined as one that entails low monitoring and screening costs but relatively large set-up costs, then perfect competition is optimal, and the optimal level of bank risk turns out to be the lowest attainable. Notably, these results are independent of whether the intermediation technology exhibits constant or increasing returns to scale in screening and/or monitoring effort.
We discuss below the empirical relevance of some of our results. Furthermore, we believe these results throw a new light on the important policy question regarding the desirability of supporting bank profits, or banks’ “charter value”, with some “rents” in order to guarantee financial stability: what seems to matter are not necessarily rents per se, but what are their sources and how banks might exploit them.
We studied versions of a general equilibrium banking model with moral hazard in which the bank’s intermediation technology exhibits either constant or increasing returns to scale. In the basic version of the model under constant returns of the intermediation technology we showed that as deposit market competition increases, bank risk increases, capitalization declines, and “intermediate” degreed of deposit market competition and bank risk are best..The result that the lowest attainable level of bank risk is not optimal echoes Allen and Gale’s (2004b) result that a positive degree of financial ”instability” can be a necessary condition for optimality. Yet, the efficiency of the intermediation technology matters. If this technology exhibits increasing returns to scale, then the implications of this model for bank risk, capitalization and welfare are totally reversed: as competition increases, bank risk declines, capitalization increases, perfect deposit market competition and the lowest attainable level of bank risk are optimal.Source: http://www.imf.org/external/pubs/cat/longres.aspx?sk=25439.0
Subsequently, we studied the more realistic version of the model where there is competition in both lending and deposit markets and bank risk is determined jointly by the bank and the firm. The key results of the extended model pertain to the role of the efficiency of the intermediation technology in relationship to the level of competition in both lending and deposit markets. We showed that independently of whether the intermediation technology exhibits constant or increasing returns, perfect competition and the lowest attainable level of bank risk are optimal if the bank intermediation technology is relatively efficient. When such technology is relatively inefficient, however, perfect competition is suboptimal, and intermediates levels of competition and bank risk are best.
The theoretical results or our study are empirically relevant. Several studies present evidence consistent with a positive relationship between bank competition and financial stability. Jayaratne and Strahan (1998) find that branch deregulation resulted in a sharp decrease in loan losses. Restrictions on banks’ entry and activity have been found to be negatively associated with some measures of bank stability by Barth, Caprio and Levine (2004), Beck (2006a and 2006b), and Schaeck et al. (2009). Furthermore, Cetorelli and Gambera (2001) and Cetorelli and Strahan (2006) find that banks with market power erect an important financial barrier to entry to the detriment of the entrepreneurial sector of the economy, leading to long-term declines in a country’s growth prospect. Lastly, Corbae and D’Erasmo (2011) present a detailed quantitative study of the U.S. banking industry based on a dynamic calibrated version of Boyd and De Nicolo’ (2005) model, finding evidence of a positive association between competition and financial stability. It is apparent that these results are consistent with the predictions of the basic model with increasing returns, and those of the extended model in which banks use relatively efficient intermediation technologies.
Under a policy viewpoint, we believe that our results provide an important insight with regard to the question of whether supporting bank profits with some rents—or, in a dynamic context, supporting banks’ charter values—is a desirable public policy option. A substantial portion of the literature and the policy debate maintains that preserving bank profitability through rents enhancing bank profitability—or banks’ charter values—may be desirable, as it induces banks to take on less risk. As we have shown, however, this argument ignores how these rents are generated, or how they may be eventually used once granted.
Our results suggest that supporting bank profitability (or charter values) with rents that are independent of bank’s actions aimed at improving efficiency may be unwarranted. If rents accrue independently of banks’ efforts to adopt more efficient intermediation technologies and, more generally, to provide better intermediation services, then rents are suboptimal and do not guarantee banking system stability. In this light, competitive pressures may be an effective incentive for banks to adopt more efficient intermediation technologies. In a competitive environment, rents would need to be earned by investing in technologies that provide banks a comparative advantage in providing intermediation services, rather than been derived from some market power enjoyed “freely”.