Using this becomes L=D (5) We can differentiate (5) with respect to bank-loan supply allowing to vary with D, B D: (6) Finally, we can solve for BD: (7) The sign follows from the assumptions made about the functions and Equation (7) shows that f y. the quantity of bonds issued goes down when loan supply increases, and up when decreases. In other D D words, firms substitute between bonds and loans. When banks lend less, bond issuance goes up in response. What about price of bonds? We take the total derivative of with respect to y(B) D: (8) Bond yields go up when the loan supply falls; as firms are getting more funding out of the bond market, the price of bond funding is pushed up. The predictions of the model, as derived in equations (7) and (8), are consistent with the empirical findings in our paper. They key assumption is that the bank lending market is not clearing through price. This may reflect various frictions, including rationing as in Stiglitz and Weiss (1981). However, this is a particularly simple setting and it is reasonable to ask if these predictions are specific to our simple set-up. In fact, they are not. Holmström and Tirole (1997) derive an equilibrium with some similar properties, as can be seen from their equation (9):
Using L=D this becomes (5) We can differentiate (5) with respect to bank-loan supply D, allowing B to vary with D: (6) Finally, we can solve for BD: (7) The sign follows from the assumptions made about the functions f and y. Equation (7) shows that the quantity of bonds issued goes down when loan supply D increases, and up when D decreases. In other words, firms substitute between bonds and loans. When banks lend less, bond issuance goes up in response. What about price of bonds? We take the total derivative of y(B) with respect to D: (8) Bond yields go up when the loan supply falls; as firms are getting more funding out of the bond market, the price of bond funding is pushed up. The predictions of the model, as derived in equations (7) and (8), are consistent with the empirical findings in our paper. They key assumption is that the bank lending market is not clearing through price. This may reflect various frictions, including rationing as in Stiglitz and Weiss (1981). However, this is a particularly simple setting and it is reasonable to ask if these predictions are specific to our simple set-up. In fact, they are not. Holmström and Tirole (1997) derive an equilibrium with some similar properties, as can be seen from their equation (9):
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