Credit Markets and the Propagation of Monetary Policy Shocks

Certificates of deposits are remunerated at the nominal rate R^B .Banksarerisk
neutral and the financial sector is competitive. So, the problem of a representative
bank is to maximize profits from intermediation

max Π^I = R^LL + R^BB^d - R^DD
L,B^d,D,H^d

subject to

D = L + H^d + B^d

and

H^d = ρD.                             (3)

Because of the financial constraint imposed on borrowers, banks face no risk. Also,
the problem of the bank shows the role of government liabilities. Reserves are used
to expand deposits. On the other hand, certificates of deposits deviate units of
accounts from the private sector’s financing of firms to the central bank. This
implies that some of the assets deposited in the financial intermediary will remain
idle in the sense that they will not be used by entrepreneurs to acquire productive
capital. Bank optimization implies

D

R— = RB = RL.

1-ρ

Finally, the central bank decides on the composition of its nominal liabilities.
At the beginning of each period, the central bank supplies the economy with
H units of liquid assets (reserves) and B units of illiquid assets (certificates of
deposits). Call X = H + B, the total liabilities of the central bank. We assume
the central bank increases government liabilities to pay for the interest rates of its
certificates of deposits. The budget constraint of the central bank is then,

X⁰ = X + R^BB.

The decision of the central bank is the composition of the new liabilities, that is,
how to split X⁰ between H⁰ and B⁰ .

3.1 The stationary equilibria

We first look at the determination of the stationary equilibria. Since nominal
variables are growing, it will be convenient to normalize them by the total level

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