In recent years, central banks have tested the limits of
lowering monetary policy rates to expand economic activity. The ‘zero
lower bound’ was challenged as many central banks went below zero, and
the question arose of whether there was actually an ‘effective lower
bound’. The important contribution of Brunnermeier and Koby (2018),
henceforth ‘BK’, extends this debate and explores theoretically the
possible existence of a ’reversal interest rate’ below which further
reduction in policy rates are in fact counterproductive. The term
‘reversal rate’ has now become part of the jargon used by both central
bankers and analysts to discuss the monetary policy stance.
In BK a reversal rate exists as lower rates have a
negative effect on bank profitability which erodes the banks’ equity
capital, and in the presence of a capital constraint leads to lower
lending. In a recent paper (Repullo 2020), I present a critical review
of this mechanism.
It should be noted that in BK’s model, a reduction in the
policy rate has two opposite effects on bank capital. On the one hand,
there is a positive effect due to the increase in the value of long-term
mark-to-market assets. On the other hand, there is a negative effect on
profitability. The negative profitability effect is key for the
existence of a reversal rate, while the positive revaluation effect
works in the opposite direction. Since the revaluation effect weakens
BK's result, and in their model banks do not have such assets in their
balance sheet, I focus my review on the profitability channel.
Brunnermeier and Koby’s model of the reversal rate
BK’s model features a local monopoly bank
which is the single provider of loans and deposits in a local market,
but is a perfect competitor in an economy-wide securities markets. The
bank has a given amount of equity capital and faces an upward sloping
supply of deposits and a downward sloping demand for loans. The bank can
also invest in debt securities whose interest rate is taken to be the
monetary policy rate set by the central bank. BK assume that the bank's
maximisation problem is subject to two financial frictions: a capital
constraint and a liquidity constraint.
The liquidity constraint requires the bank
to invest a fraction of their deposits in (liquid) debt securities. This
constraint plays a key role for their results. In particular, a binding
liquidity constraint makes lending equal to the sum of a proportion of
its deposits (those not invested in debt securities) and the exogenous
capital. This means that what happens to lending following a reduction
in the policy rate is driven by what happens to deposit taking. I show
that if the liquidity constraint is binding, lower policy rates lead to
lower deposits and, hence, lower lending. However, this is not the
narrative of the reversal rate in BK, which is linked to the effect of
lower rates on bank profitability. For this reason, I focus my review on
the effect of the policy rate on lending in the presence of only a
capital constraint.
In B, the capital constraint requires the
bank to back a fraction of its lending with equity capital. They argue
that this constraint captures “economic and regulatory factors”.
However, their constraint features the future value of the bank's
capital, not the current value as it should be if it were to capture a
regulatory capital requirement. Moreover, their constraint is not
implied by a standard forward-looking collateral constraint.
At any rate, I review the possible existence
of a reversal rate in the presence of BK's capital constraint, showing
the following results. First, if the capital constraint is not binding,
lower policy rates always lead to higher lending. Second, if the capital
constraint is binding, a reversal rate exists if and only if the bank is
a net investor in debt securities, a condition that is typically
satisfied by high deposit banks (those with more deposits than loans).
Third, there is no single reversal rate, since whenever it exists it
depends on bank-specific characteristics, in particular their relative
advantage in raising deposits versus granting loans.
These results are very much in line with the
empirical results in Heider et al. (2019), who state that “[t]he
introduction of negative policy rates by the European Central Bank in
mid-2014 leads to (...) less lending by euro-area banks with a greater
reliance on deposit funding.” They are also consistent with the results
in Eggertsson et al. (2019) showing that Swedish banks that rely more
heavily on deposit financing experienced lower credit growth after the
policy rate became negative.
It should be noted that BK's specification
of the capital constraint in terms of the future value of the bank's
capital has a simple justification: no reversal would exist if lending
is constrained by the current (exogenous) value of the bank's capital,
since the constraint would just set an upper bound on lending. However,
this misses their intuition that bank profitability should matter for
lending, because if shareholders do not get an adequate return from
their investment they might not want to contribute their capital to the
bank or shift it to other uses.
An alternative model
To capture this intuition, I then consider
an alternative model in which the bank's equity capital is not
exogenous, but it is endogenously provided by shareholders that demand a
return on their investment that incorporates a positive excess cost of
capital. In this model, there is a profitability constraint that
requires the future value of the bank's capital to be greater than or
equal to the opportunity cost of the funds provided by shareholders. The
future value of the bank's capital is driven by two components: profits
from lending, equal to the spread between the loan rate and the policy
rate multiplied by the total amount of loans, and profits from deposit
taking, equal to the spread between the policy rate and the deposit rate
multiplied by the total amount of deposits. While the former are always
positive, the latter can be negative when (i) the policy rate becomes
negative, and (ii) there is a zero lower bound on deposit rates.
The question is: Is it possible to get a
reversal rate when the losses from deposit taking become very large?
Unfortunately, the answer is no. In this setup, the profitability
constraint does not bring about a reversal rate, except in the extreme
form of banks closing down – or stopping to take deposits, as in Ulate-Campos
(2019) – when shareholders do not get the required return from their
investment. The intuition for this result is straightforward. Lower
policy rates always increase the bank's profits from lending, since they
reduce the weighted average cost of deposits and capital. For the same
reason, with a downward sloping demand for loans, they increase bank
lending. At some point, the losses from deposit taking may exceed the
profits from lending, but until we get to that point the bank will
continue to expand its lending, as this maximizes its profits.
Conclusion
The conclusion that follows from this
analysis is that policy makers should not assume that lower negative
rates will, at some point, be contractionary for lending. Negative rates
may bring about some problems, in the banking system and the broader
economy, but the expectation should be that they will increase lending.
I would like to end with a few remarks.
First, I have used a setup in which the bank is a monopolist in lending
and deposit taking in a local market but has access to a competitive
debt market. The local monopoly assumption simplifies the analysis, but
all the results can be obtained in a setup in which several banks
compete (for example à la Cournot) in a local market and have access to
a competitive debt market.
Second, in addressing the effects of low
profitability on bank lending it is natural to think about a process
that takes time, with shareholders gradually reducing their capital
until the capital constraint becomes binding. The alternative model
tries to capture this process in a reduced form manner by assuming that
the initial bank capital is endogenously provided by bank shareholders.
Still, dynamic models of banking that address these issues would be most
welcome.
Finally, it is important to stress that
partial equilibrium models like the ones in my paper have obvious
limitations in capturing general equilibrium effects of monetary policy
actions. However, they can be useful as building blocks for
macroeconomic models with a solid microfoundation of the banking
system.
References
Brunnermeier, M and Y Koby (2018), “The
Reversal Interest Rate,” NBER Working Paper No. 25406.
Eggertsson, G, R Juelsrud, L Summers and E
Getz Wold (2019), “Negative Nominal Interest Rates and the Bank Lending
Channel,” NBER Working Paper No. 25416.
Heider, F, F Saidi, and G Schepens (2019),
“Life below Zero: Bank Lending under Negative Policy Rates,” Review
of Financial Studies 32: 3728-3761.
Repullo, R (2020), “The
Reversal Interest Rate: A Critical Review,”
CEPR Discussion Paper No. 15367.
Ulate-Campos, M (2019), “Going Negative at
the Zero Lower Bound: The Effects of Negative Nominal Interest Rates,”
Federal Reserve Bank of San Francisco Working Paper 2019-21.