Determining subsidies for banks in policy loans to innovative SMEs

In this paper, we develop theoretical game models to determine the level of government subsidies for banks to provide policy loans to innovative SMEs (small and medium sized enterprises) through banks, which otherwise would not finance them for the sake of their own profitability. For this, we compare net cash flows of each bank using different strategies against high risk innovative SMEs. A bank can decide whether to provide them loans or not in each period. Following Kim's(2003) infinite horizon model on the soft budget constraint, we introduce a situation in which banks compete against each other for higher net long-term payoffs from their loans to innovative SMEs and non-innovative SMEs. From the models, we show that competition among banks in general leads to a tighter decision against innovative SMEs, as a Nash equilibrium. It is not because the government bank is simply loose in providing loans, but because competition among commercial banks for fewer riskier borrowers results in tighter loan decisions against innovative SMEs. Thus, the competitive market for policy loans to innovative SMEs fails to reach the socially optimal level of loans for innovative SMEs. Commercial banks in the competitive market may require additional supports from the government to make up for the differences in their payoffs to support innovative SMEs, possibly much riskier due to moral hazards and poor discounted cash flows. The monopolistic government bank might also request such supports from the government to fund otherwise unqualified SMEs. We calculate an optimal level of governmental support for banks to guarantee funding such high-risk innovative SMEs over periods without deviating from their optimal Nash equilibrium policies.