Small business loan guarantees as insurance against aggregate risks

Ye (George) Jia

doi:10.1515/bejm-2012-0110

Article

Small business loan guarantees as insurance against aggregate risks

Ye (George) Jia

Published/Copyright: August 28, 2013

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From the journal The B.E. Journal of Macroeconomics Volume 13 Issue 1

Abstract

This paper assesses whether insurance against aggregate risk (such as the current economic downturn) could be an important rationale for popular government operated loan guarantee programs for small and medium enterprises (SMEs). We demonstrate in a model that firms could be credit-constrained due to aggregate uncertainty because financial institutions face high borrowing costs during economic downturns. Since it enjoys relatively lower borrowing costs during recession, the federal government could offer insurance in the form of loan guarantees to ease borrowing constraints for small businesses. Furthermore, we show that a guarantee program with a fixed fee is associated with adverse selection, and leads to the “over-lending” problem. We also show that under certain conditions, a program with a net present value of zero could be socially beneficial. Then, the high cost of obtaining guarantees and thorough qualification requirements can be viewed as tools to mitigate this problem.

Keywords: aggregate Risk; loan guarantee; small business financing

Corresponding author: Ye (George) Jia, University of Prince Edward Island – Department of Economcis, 550 University Ave. Charlottetown Prince Edward Island C1A 4P3, Canada, Tel.: +9025660566, e-mail: georgejia@gmail.com; yjia@upei.ca

¹
Both the US and the Canadian governments define a small business as one that has fewer than 100 employees (<50 if it is service-based in Canada), and a medium-sized business as one with fewer than 500 employees.
²
Most developed countries have some kind of business loan guarantee programs in place, some of them being operated directly by the government and others being provided by trade unions.
³
These subsidy rates are calculated without the inclusion of the agency’s administrative costs. However, the SBA has many other functions related to promoting SMEs. <15% of the agency’s budget goes into the administration of credit programs, and an even smaller amount goes into guarantee programs.
⁴
SBA’s loan guarantee programs maintained a negative estimated subsidy rate during this period, i.e., they were making a profit; for details see Figure 1 (SBA 2010).
⁵
Even in the fiscal year 2009, when the US suffered a severe recession, the estimated program subsidy was still <6% of the loans it guaranteed, despite a 10-fold increase in defaults from the previous In fact, the low default rates of these guaranteed loans in the US have attracted many research interests (Andradey and Lucas 2009).
⁶
Two forces drive up the cost of borrowing for financial institutions: first, the supply of deposits goes down during a recession; second, these institutions have to pay a higher risk premium, due to the increase of the default risk. Evidently, the spread of corporate bonds in the financial sector goes up during economic downturns (Barth, Li, and Phumiwasana 2009). Furthermore, the risk premium would be higher if they increased their exposure to aggregate risks ex-ante.
⁷
The famous paper of Meza (2002) draws a similar conclusion: subsidy programs might lead to over-lending in the aggregate economy and reduce overall economy efficiency due to information asymmetry.
⁸
Newly introduced SBA express program requires much less paperwork and takes less time to process, however it offers lower guarantee and asks for higher fees.
⁹
Even if these loans are secured, the value of collateralized assets in general decreases during a economic downturn. Which means that financial institutions will ration loans due to aggregate uncertainty without third party guarantee.
¹⁰
These fixed assets, being machinery or real estate, must be used as collateral.
¹¹
This represents the quality of the projects. One can view this as the sum of probabilities of all states that the firm has enough to repay their debt, even in the case of collateralized assets being liquidated. In that situation, the more fixed assets a firm has, the higher the quality of the firm.
¹²
If this is a dynamic model, the equivalence of this assumption would be that the cost of capital for financial institution during a downturn is infinity. Discussion about a more general formulation is provided in footnote 13.
¹³
A more general way of modeling the situation is to explicitly state the cost of covering for losses during a downturn. Assuming that it costs the financial institution for every unit of loss that it incurs during a downturn. And the same loss costs the government Here, can be viewed as the borrowing cost for rolling over losses to the next period in a dynamic model. Then, the zero profit condition (1) becomes:
px–(1–γ)(1+)min{0, x–θ_lf(k)}=r(k–s)+(1–p)[β+η(k–s)]
and constraint (3) is omitted. As long as there is a wedge between and such that the borrowing cost is lower for the government, most of the main results remain the same.
¹⁴
A formal proof is provided in Appendix 7 to show that is increasing in s.
¹⁵
In case there are more small business owners in the economy as result of the lowered interest rate, the economy is simply allocating capital from more able entrepreneurs (constrained) to less able ones.
¹⁶
Unless it became the sole provider for all loans in the economy.
¹⁷
Again, this would be much clearer in a dynamic model, however, the goal of this paper is to use the simplest framework to illustrate the intuition of how a government-operated guarantee program as insurance against aggregate risks can improve the efficiency of the economy.
¹⁸
Note that this allocation is not Pareto Superior to the equilibrium allocation without the guarantee program. Because of the increase in demand for credit, the equilibrium interest rate goes up, thus those externally financed entrepreneurs not under the guarantee program pay a higher interest rate and operate smaller projects.
¹⁹
This is a more common case: the individual operating the firm and its associated financial institution usually have more information about the quality of the firm than the government.
²⁰
This level of entrepreneurship is slightly different from the 0.2204 in Li (1998), this is most likely due to the difference in choice of software package and treatment of rounding errors.

I am deeply indebted to James MacGee and Igor Livshits. I want to thank Ahmet Akyol, Simon Parker and anonymous referees for many insightful comments. All errors are mine.

Appendix

A Change of with respect to change in savings

In this section, we will show how does the limit on capital change with saving s. First, equation (11) which is used to determine can be re-written as:

The first and second term on the left side are both increasing in k_{s, p}; but given the assumption that f() is concave, and the region of k we are interested is where the marginal product capital is relatively close to r, such that pθ_lf(k) is not higher than r. Then, the left side has to be increasing in The right side on the other hand, is clearly increasing in s. Thus, the limits on capital k_{s, p} is increasing in s.

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Published Online: 2013-08-28

Published in Print: 2013-01-01

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Keywords for this article

aggregate Risk; loan guarantee; small business financing

Small business loan guarantees as insurance against aggregate risks

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