Another look at yield spreads: the role of liquidity

Southern Economic Journal, April, 2008 by Dong Heon Kim

How should one think of the CIA constraint in the light of borrowed reserves? By studying the discount window borrowing by weekly reporting banks disaggregated by Federal Reserve District, Cosimano and Sheehan (1994) show that any single bank seldom visits the discount window and argue that this behavior is consistent either with banks not aggressively managing their discount window borrowings or, more plausibly, with the presence of considerable harassment costs imposed by the discount window officer. Hamilton (1998) states that banks act as if they faced a cost function for borrowing reserves from the Fed, and the cost of borrowing includes nonpecuniary costs in the form of additional regulation, supervision, and inferior credit standing with other banks. From this point of view, banks should not place excessive reliance on the discount window to obtain reserves and fund their loans to the public; thus, they might need to hold excess reserves for liquidity yield purposes. Hence, the CIA constraint that the bank faces might reflect the bank's demand for liquidity.

However, the strict CIA requirement ignores real-life institutions such as credit cards available to consumers or within-day overdraft privileges available to banks on their accounts with the Fed. Even so, the requirement of needing actual cash on hand for certain transactions seems to capture the key idea of what is meant by liquidity and has proven to be a useful framework for thinking about liquidity demand by private households. I propose that it may also be fruitful for seeing how the need for liquidity may impact the rates of return on assets of different maturities held by banks. Thus, I propose that bank j faces a CIA or liquidity constraint such as the following:

[L.sub.j,t] [less than or equal to][R.sub.j,t-1] [L.sub.j,t-n], (3)

where [R.sub.j,t-1] is the reserve balance transferred from the previous period to the start of period t for the bank j. In this case, I assume that the repayment of outstanding loans contributes to the bank's liquidity balances at the beginning of period t. Thus, the bank enters period t with predetermined holdings of reserves, as the liquidity balances and the bank's new loans must obey the CIA constraint. (11)

The Equilibrium

Bank j faces the choice of new loans at the beginning of period t and the choice of federal funds at the end of period t. The state variables that are relevant for the bank's decision of the quantity of federal funds to lend at the end of period t are [L.sub.j,t], [L.sub.j,t-1], ..., [L.sub.j,t-n], [F.sub.j,t-1], [R.sub.j,t-1], and [[bar.D].sub.j,t]. Consider the following value function formulation of the decision at the end of period t:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

subject to

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where [U.sub.j,t](.) denotes the lifetime value of bank j's optimal program as of the second session of period t, whereas [V.sub.j,t 1](L.sub.j,t],[L.sub.j,t-1], ..., [L.sub.j,t- n 1],[F.sub.j,t],[R.sub.j,t],[[bar.D].sub.j,t]) is the value as of the first session of period t 1, and [beta] denotes the discount factor.