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H.Keiding: Economics of Banking (Prel.version:September 2013)

Chapter 18, page 1

Chapter 18

Capital Regulation and The Basel Accords

1. Introduction: why capital regulation? 2. Eﬀects of capital regulation

2.2. A model where banks have equity in excess of regulatory demand. There is some empirical evidence that banks choose a composition of funding where the share of equity is larger than what is demanded by regulators. Below we consider a simple model of largely competitive ﬁnancial markets, due to Allen, Carletti and Marquez (2011), where this is the case. We consider a one-period economy with ﬁrms having access to a risky investment and in need of ﬁnancing, and banks that lend ...view middle of the document...

Then the level of monitoring is set so as to maximize expected proﬁts 1 Π = q(rL − (1 − k)rD ) − krE − q2 , 2 and the ﬁrst-order conditions for a maximum gives us the optimal level of q as q = min{rL − (1 − k)rD , 1}. It is seen that monitoring eﬀort is increasing in both loan rate rL and capital ratio k, but it decreases in rD . This suggests that there may be a moral hazard problem, given that monitoring is costly for the bank and cannot be observed by the other agents in the market, so that the bank must be given

H.Keiding: Economics of Banking (Prel.version:September 2013)

Chapter 18, page 2

incentives to monitor in the proper way. This of course presupposes that there is some interconnection between monitoring and competitive loan rates. Assume ﬁrst that there is no deposit insurance. If the depositors expect the probability of success of investments to be q, then qrD = 1. In the case of no regulation of k, if competition assures that all surplus goes to the borrower, we ﬁnd the values of k and the loan rates by maximizing borrower expected proﬁts B = q(y − rL ) subject to q = min{rL − (1 − k)rD , 1}, qrD = 1, together with the constraints that B and Π should be nonnegative and 0 ≤ k ≤ 1. If rE ≥ 1 is kept ﬁxed, we can ﬁnd the solution to this problem. Assume ﬁrst that Clearly, as long as q 0, we have that rL ≤ y. If q < 1, then q = rL − (1 − k)q means that an increase in q will increase Π without decreasing B, so it may be accompanied by a decrease in rL giving a larger B. We conclude that q = 1 in the optimum. It follows that rD = 1, so that the participation constraint for the bank becomes 1 (1) rL − 1 + k − krE − ≥ 0. 2 Also, from 1 = q ≤ rL − (1 − k) 1 . 2rE The above result is formally derived under an assumption of perfect competition, so the conclusions of the model tell us that market by itself will discipline banks so as to hold capital above a certain level. However, the distinctive feature is that k is determined by so as to maximize borrowers’ expected proﬁts, hence the lower bound on k: Too small a value of k would mean that the bank might settle down with q < 1, which would reduce borrowers’ proﬁts. If this is a result of market forces, it must be a market where all bargaining power is left with the borrowers, none with the banks. Therefore, it may be questioned whether the result can be seen as a decision by banks to hold more than the minimal capital required. If instead we introduce a regulator, determining k so as to maximize a social welfare function deﬁned as we get that rL ≥ 2 − k, and inserting this into (1) we get that k ≥ 1 1 B + Π = q(y − rL ) + q(rL − (1 − k)rD ) − krE − q2 = q(y − (1 − k)rD ) − krE − q2 , 2 2 while otherwise everything is as before, then for large enough y (namely y ≥ 2, the capital ratio k may be chosen as 0, since the banks’ gain with rE = 2 is large enough to give incentives for q = 1. If y < 2, the capital ratio must be positive, whereas q may be less than 1.

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