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We model how monetary policy shocks affect the lending behavior of small and large banks. Other things being equal, small banks are riskier than large banks since the latter are more likely to be bailed out. Thus, small banks face a higher cost of non-deposit financing and are unable to finance liquidity shocks at a cost below a certain threshold. Consequently, we show that under a tight monetary regime small bank lending is more sensitive to monetary shocks. This relation reverses under loose monetary regimes where large bank lending is more responsive to monetary shocks. Our empirical results strongly support our analysis.