Corridor Systems and Overnight Rate Control

Why an Overnight Rate Corridor Matters

A central bank can announce a policy rate, but banks still need to settle payments and manage their reserve balances overnight. The overnight market rate depends on how many reserves are available relative to banks’ demand for them. A corridor system helps guide that market rate by setting rates at which eligible institutions can deposit reserves with, or borrow reserves from, the central bank.

The key distinction is between the facility rates, which provide a lower and upper reference point, and the market rate, which reflects the balance of reserve supply and demand between those reference points. The corridor does not, by itself, imply that the market rate is the midpoint. The market rate’s position depends on reserve conditions.

Definition: A corridor system is an operating framework in which the central bank sets a deposit-facility rate $i_D$ and a standing lending-facility rate $i_L$, with $i_D < i_L$. Eligible institutions can place overnight funds at the deposit facility or obtain overnight funds through the lending facility, subject to the facilities’ terms. The overnight market rate is denoted $i_{ON}$.

How Facility Rates Bound the Market Rate

Start with the benchmark model: eligible banks can use both facilities; the facilities and market loans have the same overnight term; transactions are settled reliably; and there are no material fees, quantity limits, collateral constraints, or differences in credit risk that overturn the interest-rate comparison. Rates are annualized, and any comparison concerns the same overnight principal and accrual period.

Under these assumptions, the lending facility limits how high a bank would rationally pay to borrow overnight. If $i_{ON}$ exceeded $i_L$, an eligible bank could borrow from the central bank at $i_L$ and lend those funds in the overnight market at the higher rate. The difference would be positive. That arbitrage incentive would put downward pressure on the market rate.

Similarly, if $i_{ON}$ fell below $i_D$, an eligible bank could borrow in the market at the lower rate and deposit the funds with the central bank at $i_D$. The difference would again be positive. This incentive would put upward pressure on the market rate. Thus, in the benchmark model:

i_D \leq i_{ON} \leq i_L

This is an arbitrage-bound result, not a claim that every observed transaction must fall inside the corridor under all circumstances. Some market participants may not have access to the facilities, and some banks may face collateral, balance-sheet, or counterparty constraints. Market rates can therefore deviate from the facility rates when the benchmark assumptions do not hold. The direction and size of any deviation depend on the relevant frictions.

Worked Example: Deriving the Corridor Bounds

A central bank pays 2.25% on overnight deposits and charges 4.25% on overnight standing loans. In the benchmark model, determine the range in which the overnight market rate is constrained. Then assess a proposed market rate of 4.60%.

Method. Apply the facility-arbitrage argument, comparing rates for the same overnight term and assuming facility access and no material frictions.

The deposit rate is $i_D=2.25\%$, and the lending rate is $i_L=4.25\%$. Therefore, the benchmark bounds are:

2.25\% \leq i_{ON} \leq 4.25\%

At a proposed market rate of 4.60%, a bank could borrow overnight from the central bank at 4.25% and lend overnight in the market at 4.60%. The gross annualized rate difference is $4.60\%-4.25\%=0.35$ percentage points. For an overnight principal of $1,000,000, using a 360-day money-market convention, the one-day interest difference is:

\$1{,}000{,}000 \times 0.0035 \times \frac{1}{360} = \$9.72\text{ (to the nearest cent)}

The positive difference creates an incentive to borrow at the facility and lend in the market. Under the stated benchmark assumptions, 4.60% is not a stable market rate. Common mistake avoided: treating 4.25% as a target the market must equal. It is the upper facility bound in this model; the market rate can be anywhere within the corridor.

Reserve Supply and the Position Within the Corridor

To analyze the market rate within the corridor, consider a simplified overnight market in which aggregate reserve supply is fixed for the period being analyzed. Banks collectively demand reserves to settle payments and to hold a liquidity buffer. In the usual model, the marginal value of an additional reserve balance falls as reserves become more abundant. Consequently, reserve demand is downward sloping when the overnight interest rate is plotted against the quantity of reserves.

A bank that has few reserves may be willing to pay a relatively high rate to obtain an additional balance. When reserves are plentiful, banks are less willing to pay a high rate. At a sufficiently abundant quantity, the deposit facility offers a return on reserves, so the market rate cannot fall below that return in the benchmark model. At the other end, when reserves are very scarce, banks can use the lending facility, limiting how high they need to bid in the benchmark model.

For numerical work, it is useful to represent the market’s inverse reserve-demand schedule between the facility bounds by a simple downward-sloping function. Let $R$ be aggregate reserves, measured in billions of dollars, and let $g(R)$ be the rate implied by the interior demand schedule. The corridor rate is then:

i_{ON} = \min\!\left(i_L,\ \max\!\left(i_D,\ g(R)\right)\right)

This expression means: use the demand-schedule rate if it lies between the facility rates; otherwise, apply the relevant floor or ceiling. A particular linear function $g(R)$ is a model assumption used for a calculation, not a universal law about reserve demand. Outside the specified range, the schedule may be flat at a facility rate or may require a more detailed model.

Model condition: A calculation using $g(R)$ requires a stated reserve-demand schedule, the applicable facility rates, and a reserve quantity measured in the same units as the schedule. A change in reserve supply moves the market to a different point on a given demand schedule. A change in banks’ desired reserves shifts the demand schedule itself.

Worked Example: Locating the Rate From Reserve Supply

A hypothetical central bank sets a deposit-facility rate of 3.00% and a lending-facility rate of 5.00%. Between the facility bounds, the inverse reserve-demand schedule is $g(R)=3.00\%+0.04(100-R)$, where $R$ is in billions of dollars. Aggregate reserves are $75 billion. Find the overnight rate and explain whether a facility rate is binding.

Method. Substitute the reserve supply into the interior demand schedule, then check the result against both facility rates.

First calculate the reserve difference: $100-75=25$ billion. The rate implied by the schedule is:

g(75)=3.00\%+0.04(25) =3.00\%+1.00\% =4.00\%

The result is between the deposit and lending rates:

3.00\% < 4.00\% < 5.00\%

Therefore, neither facility bound is binding, and $i_{ON}=4.00\%$ in this model. The rate is 1.00 percentage point above the deposit rate and 1.00 percentage point below the lending rate, but that midpoint is a result of these particular numbers—not a general property of a corridor. Common mistake avoided: assuming that the market rate must be halfway between the facility rates without using the reserve-demand schedule.

Why Demand Shifts Differ From Reserve Injections

An increase in reserve supply and an increase in reserve demand have opposite effects on the rate, all else equal. With a fixed demand schedule, adding reserves moves the market down that schedule toward a lower rate. With fixed reserve supply, an increase in banks’ desired reserves shifts the demand schedule outward: banks compete more strongly for a given quantity of reserves, raising the rate.

A demand shift may reflect a greater need for settlement balances or a larger desired liquidity buffer. It should not be confused with a reserve-supply change. For example, a payment outflow could reduce reserves available to some banks without changing the total quantity supplied by the central bank. The market outcome depends on how that event changes aggregate supply, demand, or both.

Worked Example: Separating a Reserve Injection From a Demand Shift

Use the same corridor and schedule as in the previous example: $i_D=3.00\%$, $i_L=5.00\%$, and $g(R)=3.00\%+0.04(100-R)$. First, the central bank injects reserves, raising $R$ from $75 billion to $85 billion without changing demand. Later, banks’ desired reserves rise by $10 billion at every rate. Calculate the rate after each change, treating the second change as a demand shift from the original $75 billion reserve position.

Method. For the injection, change $R$ while holding the schedule fixed. For the demand shift, represent the higher desired quantity by replacing the original reference quantity of 100 with 110.

Before either change, the rate is $3.00\%+0.04(100-75)=4.00\%$. After the reserve injection, $R=85$, so:

g(85)=3.00\%+0.04(100-85) =3.00\%+0.60\% =3.60\%

The injection lowers the rate by $4.00\%-3.60\%=0.40$ percentage points. The result remains within the corridor.

For the demand shift, use the original reserve position of $75 billion and the shifted schedule $g_{\text{new}}(R)=3.00\%+0.04(110-R)$:

g_{\text{new}}(75) =3.00\%+0.04(110-75) =3.00\%+1.40\% =4.40\%

The rate rises by $4.40\%-4.00\%=0.40$ percentage points, again staying within the corridor. Check: the injection and the demand shift are each 10 billion in this linear model, so they produce equal-sized rate changes in opposite directions. Common mistake avoided: calling both events an “increase in reserves.” One increases supply; the other increases the quantity banks want to hold.

When a Facility Bound Becomes Binding

If the rate implied by an interior demand schedule is below $i_D$, the floor applies in the benchmark model. If the implied rate is above $i_L$, the ceiling applies. When a facility rate binds, changes in reserve supply may not move the market rate in the same way as they do along the interior part of the schedule. In practice, the exact outcome also depends on facility access, facility terms, and whether participants can respond to the rate difference.

Worked Example: Applying the Floor and Ceiling

A corridor has $i_D=3.00\%$ and $i_L=5.00\%$. Its illustrative interior schedule is $g(R)=3.00\%+0.04(100-R)$, with $R$ measured in billions of dollars. Calculate the model rate at $R=35$ billion and at $R=115$ billion. Assume the facilities have sufficient capacity and all relevant banks can use them.

Method. Calculate the unconstrained schedule rate in each case, then apply the corridor formula.

At $R=35$, the reserve difference is $100-35=65$. The unconstrained rate is:

g(35)=3.00\%+0.04(65) =3.00\%+2.60\% =5.60\%

Because 5.60% exceeds the 5.00% lending rate, the ceiling binds. The model rate is $i_{ON}=5.00\%$.

At $R=115$, the reserve difference is $100-115=-15$. The unconstrained rate is:

g(115)=3.00\%+0.04(-15) =3.00\%-0.60\% =2.40\%

Because 2.40% is below the 3.00% deposit rate, the floor binds. The model rate is $i_{ON}=3.00\%$. Both results satisfy the benchmark bounds $3.00\%\leq i_{ON}\leq5.00\%$. Common mistake avoided: reporting an unconstrained rate outside the corridor as the equilibrium market rate, even though a usable facility would create an arbitrage incentive.

Reading Rate Movements Carefully

When interpreting a change in the overnight rate, identify what changed before attributing a cause. If facility rates are unchanged and reserves become more abundant on a given demand schedule, the rate tends to fall. If reserve demand rises while supply is unchanged, the rate tends to rise. If a facility rate changes, the corridor itself changes; the market rate may move even if the reserve quantity and demand schedule do not.

These are comparative-static conclusions from the benchmark model, not guarantees about every observed market rate. Operational frictions can affect the transmission from facility rates and aggregate reserves to market transactions. A precise diagnosis therefore states the facility rates, reserve-supply condition, demand schedule or shift, and any relevant limitations on access.

Key takeaway: In a benchmark corridor system, the deposit rate supplies a floor and the lending rate supplies a ceiling. Within those bounds, reserve supply determines the market rate’s position on reserve demand. More supplied reserves tend to lower the rate; stronger reserve demand tends to raise it.

Check Your Understanding

For each problem, use the stated benchmark assumptions and check whether the result lies within the facility rates.

A central bank sets a 2.00% deposit rate and a 4.00% lending rate. What benchmark range constrains the overnight rate? (Answer: 2.00% to 4.00%, inclusive.)
Let $i_D=2.50\%$, $i_L=4.50\%$, and $g(R)=2.50\%+0.05(80-R)$, with $R$ in billions. If $R=50$, what is the model overnight rate? (Answer: 4.00%.)
Let $i_D=2.00\%$, $i_L=4.00\%$, and $g(R)=2.00\%+0.03(100-R)$. Reserves rise from $60 billion to $80 billion, with demand unchanged. What is the rate change? (Answer: from 3.20% to 2.60%, a decrease of 0.60 percentage points.)
Let $i_D=1.75\%$, $i_L=3.75\%$, and $g(R)=1.75\%+0.02(120-R)$. At $R=90$, desired reserves then shift upward by $10 billion at every rate. What is the new model rate? (Answer: 2.55%.)
A corridor has $i_D=2.00\%$, $i_L=4.00\%$, and $g(R)=2.00\%+0.04(100-R)$. At $R=35$, the lending facility is available without a binding quantity limit. Find the unconstrained schedule rate and the corridor model rate. (Answer: the unconstrained rate is 4.60%; the corridor model rate is 4.00%, at the lending-rate ceiling.)

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