Interest on reserves, bank runs and investment decisions
| DOI | https://doi.org/10.1108/JFRC-04-2021-0029 |
| Published date | 10 May 2022 |
| Date | 10 May 2022 |
| Pages | 393-411 |
| Subject Matter | Accounting & finance,Financial risk/company failure,Financial compliance/regulation |
| Author | Zhan Wang |
Interest on reserves, bank runs
and investment decisions
Zhan Wang
Business School, Wenzhou University, Wenzhou, China
Abstract
Purpose –This paper aims to study the effects of interest on reserves (IOR) on banks’behavior in a
theoreticalframework.
Design/methodology/approach –This paper introduces IOR into both Cooper and Ross (1998) and
Cooper and Ross (2002) and conducts quantitative analysis. It thoroughly examines the effects of IOR on
banks’resourceallocation decisions under different assumptions.
Findings –In the model withoutdeposit insurance, the results of this paper showthat paying IOR facilitates
the bank to use the run-proofcontract. When the run-admitting contract is adopted, there is a set of conditions
under which the bank is indifferent between holding illiquid asset and excess liquid reserves. In the model
with depositinsurance, the results show that if the riskless illiquid investment is profitableand available, then
paying IOR can hardly influencethe bank’s resource allocation. If the riskless illiquid investment is limited,
then a certainlevel of IOR could fulfill some monetary targets.
Originality/value –Little research has combined IOR and model of bank runs. It helps to extend the
theoreticalanalysis in this perspective.
Keywords Financial intermediaries, Interest on reserves, Bank runs
Paper type Research paper
1. Introduction
After the 2008 financial crisis, the Federal Reserve (Fed) used a few non-traditional
monetary policies, including quantitative easing and the payment of interest on reserves
(IOR). Since October 2008, the Fed has been paying interest on reserves held by depository
institutions. While a large volume of theoretical and empirical research has contributed to
the role of quantitative easing (QE),fewer contributions have been made about IOR. Ireland
(2014) uses a New Keynesian modelwith banks to study the effects of paying IOR on output,
inflation and the conduct of monetary policy. Using the data of daylight overdraft from
Fedwire, Hendrickson (2017) shows that paying IOR increased payment processing
efficiency but limited the ability of monetary policy to influence economic activity.
Dutkowsky and VanHoose (2017) examine the balance-sheet decisions of pro t-maximizing
banks, showing that the choice of the interest on excess reserves can create three different
regimes. Beth and Klee (2011) and Williamson (2019) also have studied the effects of IOR
through the channel of the fed funds market or interbank lending. These works provide
valuable perspectivesfor us to understand the policy of IOR.
This paper studies the effects of the payment of IOR on banks’behavior in two related
models of bank runs. The first model is Cooper and Ross (1998),where the deposit insurance
This paper is based on Chapter 2 of my PhD dissertation. This chapter was written under the
guidance of Dr Joshua Hendrickson and Dr Jaevin Park. I sincerely appreciate their guidance. I also
would like to thank Dr John Conlon, Dr Hailin Sang and anonymous reviewers for their useful
comments.
Interest on
reserves, bank
runs
393
Received14 April 2021
Revised31 July 2021
Accepted14 October 2021
Journalof Financial Regulation
andCompliance
Vol.30 No. 4, 2022
pp. 393-411
© Emerald Publishing Limited
1358-1988
DOI 10.1108/JFRC-04-2021-0029
The current issue and full text archive of this journal is available on Emerald Insight at:
https://www.emerald.com/insight/1358-1988.htm
is absent. The second model is Cooper and Ross (2002), in which the deposit insurance is
analyzed. In the first model, when the run-admittingcontract (RAC) is adopted, the payment
of IOR could crowd out the illiquid investment. I also show that the paymentof IOR propels
the bank to shift to adopt the run-proof contract (RPC). In the model considering deposit
insurance, I show that if the riskless illiquid investments are profitable and available,
paying interest on excess reserves can hardlyinfluence the bank’s resource allocation. If the
riskless illiquid investment opportunities are limited, then without IOR, the bank could still
seek risky investment or leave the excess reserves in the central bank. In this special
situation, a certain levelof interest on excess reserves could fulfill some monetary targets, as
the measures recently taken by the US Fed and the European Central Bank (ECB). These
theoretical results might have significant implications on the real economy. However, those
effects on the real economy are beyond the scope of this paper.
Both Cooper and Ross (1998) and Cooper and Ross (2002) are based on Diamond and
Dibvig (1983).Diamond and Dibvig (1983) constructed a framework in which a bank holds
long-term illiquid capital while facing short-term liquidity shocks. They show that a bank
run is one of the Nash Equilibria caused by the depositors’rational behavior. Cooper and
Ross (1998) extended Diamond and Dibvig (1983)by introducing the exogenous probability
of bank runs into the model, analyzing the response of private banking sector to the
probability of bank runs when deposit insurance is absent.In Cooper and Ross (2002), they
evaluate the trade-offs between providing insurance against bank runs and moral hazard
problems.
The rest of this paper is organized as follows. In Section 2, the settings and environment
of the basic model are introduced. In Section 3, I present the complete bank’s problem (BP)
and discuss its two forms: the RAC and the RPC. In Section 4, some basic results inferred
from RAC are presented and the effects of IOR on the bank’s resource allocation decisions
are examined. In Section 5, the optimal choice of the bank contract when IOR is paid is
investigated. In Section 6, IOR is introduced into the Cooper and Ross (2002) model and its
effects on the bank’s behavior are analyzed.Section 7 concludes.
2. Basic model
The model consists of N agents who live for three periods. In Period 0, all agents are
identical and receive an endowment (normalized to one). Each agent deposits the unit
endowment into a competitive bank. At the beginning of Period 1, a proportion
p
of the
agents discover that they are impatient and only obtain utility from consumingin Period 1.
The other agents learn that they are patient and will get utility from Period 2
consumption. Let U(c) be the utility function over consumption in the appropriate period.
Assume that U(·) is strictly increasing, strictly concave and satisfies U(0) = 0 and U’(0) =
1. For the convenience of calculation, the utility function is assumed t o be Uc
ðÞ¼1
a
c
a
,
where 0 <
a
<1.
There are two types of technologies, illiquid capital and liquid reserves. One unit of
investment into capital in Period 0 yields R>1 units of consumption good in Period 2.
However, if the capital is liquidated in Period 1, then it yields only 1
t
units of
consumption good foreach unit of investment, where
t
[[0, 1] is the liquidation cost.
One unit of liquid reserves receives r
t
1(t= 1, 2) units of consumption good from the
central bank in eachperiod. Specifically, assume the gross interest paid on the bank reserves
saved from Periods 0 to 1 is r
1
1, and the gross interest paid on the reserves saved from
Periods 1 to 2 is r1.1 Therefore,for one unit of excess reserves which is held from Periods
0 to 2, the bank will receive r
1
r
2
1 units of interest from the central bank.
JFRC
30,4
394
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