Abstract
Conventional wisdom has it that entry barriers in banking (for example, historical branch banking restrictions in the United States) are motivated by special interest groups, with small, local banks playing a central role in lobbying for protection. In particular, it is thought that unit (single-office) banks in the United States favored branching restrictions because they wanted (and needed) protection from competition from large, multi-office banks. Historically, however, branch banking restrictions also had the support of some classes of borrowers. Borrower support for entry barriers varied across states, and varied over time within states. We show that entry barriers affect the terms on which borrowers access credit, and can sometimes be beneficial for some classes of borrowers. While it is true that branch banking tends to increase the overall supply of credit to borrowers, it is also true that in the presence of imperfect capital markets, borrowers may benefit from barriers to entry because such barriers limit the options of the banks in the loan market. We develop a model that shows how branching restrictions (or more generically, barriers to varying the inter-regional allocation of credit by banks) create strategic advantages for borrowers that hold their wealth in the form of immobile factors of production (e.g., land). These advantages tend to be present only when borrowers’ net worth levels are sufficiently high. Our results indicate that bank clients, not just unit bankers themselves, may have supported unit banking laws out of informed self interest. We argue that these results also have broader implications for explaining the economic circumstances under which entry barriers to global banking are erected or removed in emerging market economies today.
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Notes
- 1.
- 2.
The model adapts some features of Calomiris and Hubbard (1990).
- 3.
In a model with a large number of regions, independence of outcomes, rather than negative correlation, would produce similar results.
- 4.
Note that π 1,k(i k , C k) is decreasing in i k.
- 5.
Note that \(i^{switch}_k\) is simply the interest rate that satisfies the following: \(\pi _{1,k}(i^{switch}_k,C_k)=\pi _{2,k}(i^{switch}_k,C_k) \).
- 6.
- 7.
When α < α ∗ the model yields uninteresting or trivial results, especially if α is so low that \(\rho _r > \rho _{i^{max,1}_k} \).
- 8.
Note that \(\frac {\partial (1+i^{max,1}_k)}{\partial C_k} >0\), since R c > (1 + r)X; similarly, \(\frac {\partial (1+i^{max,2}_k)}{\partial C_k}<0\), since pR s < (1 + r)X. It is straightforward to note that \(\frac {\partial (1+i^{switch}_k)}{\partial C_k}>0.\)
- 9.
Specifically, for very high range of collateral values (those in excess of C ∗), where collateral levels are identical across regions, borrowers are indifferent between choosing unit or branch banking.
- 10.
Note that is true even for Type B borrowers, since for \(i_k\leq i^{switch}_k \), \(\pi _{1,k}(i_k,C_k)\geq \pi _{2,k}(i_k,C_k)>\pi _{2,k}(i^{max,1}_k,C_k) \equiv s \).
- 11.
Technically, as Proposition 5.2 indicates, the unit bank will offer loans at \(i^{switch}_k\) and \(i^{max,1}_k\), and randomize among borrowers as to who gets which interest rate. The proportion of borrowers receiving credit at \(i^{switch}_k\) will increase with the degree of risk-aversion of the bank. Thus, even if the bank is not very risk-averse, borrowers will prefer unit banking as long as some of them receive credit at interest rate \(i^{switch}_k\).
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Acknowledgements
We would like to thank, without implicating, Bryan Caplan, Mark Crain, Tyler Cowen, Claudia Goldin, Kyle Kauffman, John Matsusaka, Allan Meltzer, David Moss, Peter Temin, Jeff Williamson, as well as seminar participants at Harvard University, George Mason University, the FDIC, and the 2004 European Business History Association for their helpful comments and suggestions.
Appendix
1. Proof that \(i^{switch}_k < i^{max,1}_k < i^{max,2}_k\) under Case 1:
First, note that \(i^{max,1}_k < i^{max,2}_k\) if:
and \(i^{switch}_k < i^{max,1}_k\) if:
Case 2 can be analogously derived. Q.E.D.
2. Proof of Lemma 1 (identification of α ∗ ):
Consider first the case when C < C ∗. The bank’s expected gross returns from investing at rate r, and lending at rates \(i^{switch}_k \), and \(i^{max,1}_k \) are:
To establish the proposition, we must show that there is α ∗≥ 0, such that for α ≥ α ∗, \(\rho _{i^{max,1}_k}(\alpha |\alpha \geq \alpha ^*)>\rho _{i^{switch}_k} \), and \(\rho _{i^{max,1}_k}(\alpha |\alpha \geq \alpha ^*)>\rho _r \). This is clearly true for α = 1, since \(i^{switch}_k < i^{max,1}_k \) for C < C ∗, and since \(r<i^{max,1}_k\) (because R c ≥ (1 + r)X). To establish the existence of α ∗ it is enough to notice that \(\rho ^{\prime }_{i^{max,1}_k}(\alpha )>0\), because this implies that the bank’s return from lending at rate \(i^{max,1}_k \) decreases as α declines.
Consider next the case when C ≥ C ∗. In this case, the bank’s expected gross returns from investing at rate r, and lending at rates \(i^{switch}_k \), and \(i^{max,1}_k \) are:
Note that for any α, \(r<i^{max,1}_k \) since R c ≥ (1 + r)X. Also, for any α, it is trivially true that \(\rho _{i^{max,1}_l} > 0\). Q.E.D.
3. Proof of Proposition 1:
Proposition 5.1 establishes that for α ≥ α ∗, \(\rho _{i^{max,1}_k}(\alpha |\alpha \geq \alpha ^*)>\rho _{i^{switch}_k} \), and \(\rho _{i^{max,1}_k}(\alpha |\alpha \geq \alpha ^*)>\rho _r \). Hence, we need to show that for C < C low, \(\rho _r>\rho _{i^{switch}_k}\), and that for C ≥ C low, \(\rho _r \leq \rho _{i^{switch}_k}\); where C low is defined as:
If C < C low, then
An analogous derivation would obtain for the C ≥ C low case. \(\rho _r > \rho _{i^{max,2}_k} \) holds for any C since pR s ≥ (1 + r)X. Q.E.D.
4. Proof of Proposition 4:
-
1.
C 2 < C 1 < C ∗
Under this collateral order, Proposition 5.3 establishes that \(\rho _{i^{max,1}_1} > \rho _{i^{max,1}_2} > \rho _r\). Although loans in Region 1 offer the highest expected return to the bank, this return is risky because Type B borrowers will choose to do Type 2 projects. Investing in loans in Region 2 is also risky for the same reason. However, it is possible to find a loan portfolio combination of the two regions that eliminates all risk since outcomes of Type 2 projects are perfectly negatively correlated across regions. Thus, it is possible to find a loan portfolio that, from a risk-return perspective, strictly dominates investment in government bonds. According to Tobin’s (1958) optimal portfolio allocation model, a risk-averse branch bank will select a portfolio that invests some of its assets in Region 1 and some in Region 2.
-
2.
C 2 < C ∗≤ C 1
According to Proposition 5.3, the branch bank’s loan return is highest in Region 1. Since C 1 ≥ C ∗, Type B borrowers in this region will choose to do Type 1 projects only (as Corollary 5.1 establishes). Thus, investing in loans in Region 1 is riskless. Hence, this investment alternative dominates all other risk-return combinations available to the branch bank.
-
3.
C ∗≤ C 2 < C 1
According to Proposition 5.3, the branch bank’s loan return is highest in Region 1. Since C 1 ≥ C ∗, Type B borrowers in this region will choose to do Type 1 projects only (as Corollary 5.1 establishes). Thus, investing in loans in Region 1 is riskless. Hence, this investment alternative dominates all other risk-return combinations available to the branch bank. Q.E.D.
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Calomiris, C.W., Ramírez, C.D. (2018). The Political Economy of Bank Entry Restrictions: A Theory of Unit Banking. In: Hall, J., Witcher, M. (eds) Public Choice Analyses of American Economic History. Studies in Public Choice, vol 37. Springer, Cham. https://doi.org/10.1007/978-3-319-95819-4_5
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