Collateral Constraints and the Interest Rate
| DOI | http://doi.org/10.1111/sjpe.12227 |
| Date | 01 May 2020 |
| Published date | 01 May 2020 |
| Author | Donal Smith |
COLLATERAL CONSTRAINTS AND THE
INTEREST RATE
Donal Smith*
ABSTRACT
This paper develops a model in which an increase in financial frictions leads to a
fall in the steady-state rate of interest. A perpetual youth overlapping genera-
tions (OLG) model is extended to incorporate a collateral constraint, this
results in a transmission mechanism in which an interest rate fall occurs endoge-
nously from a disruption to the credit market. It is found that that non-lineari-
ties exist in the relationship between changes in financial frictions and the
interest rate. By specifying the mechanism by means of which this occurs, the
model provides an explanation for why low interest rates have been observed
with such persistence since the financial crisis.
II
NTRODUCTION
This paper focuses on the connection between two key macroeconomic issues
that have become prominent in the literature following the global financial cri-
sis: financial frictions and the zero lower bound (ZLB). The financial frictions
literature developed from a credit view of the economy which stresses the
importance of credit market imperfections and variables such as net worth,
debt, and asset prices in explaining economic fluctuations (Iacoviello, 2005).
This literature provided a natural framework for research motivated by the
2008 crisis. With respect to the second strand of research, the ZLB literature
has sought to explain an economy characteristics and policy options when the
policy interest rate is close or equal to zero, as was the case in a number of
economies for a prolonged period after the 2008 crisis (Williams, 2014).
The motivation for this paper is that the vast majority of papers in the
financial frictions literature rely on an infinite horizon representative agent
framework in which the steady-state interest rate is fixed in accordance with
the rate of time preference. The consequence of this is that, in these papers,
although the motivation for the research is attempting to model the financial
crisis, and so entails substantial dislocations in credit markets with large and
persistent increases in financial frictions between borrowers and lenders and
considerable swings in asset values, the steady-state interest rate is always
*OECD Economics Department & Trade and Agriculture Directorate
Scottish Journal of Political Economy, DOI: 10.1111/sjpe.12227, Vol. 67, No. 2, May 2020
©2019 Scottish Economic Society.
137
fixed. In the ZLB literature, falls in the steady-state interest rate are typically
caused by sudden changes in agent rate of time preference. This paper pre-
sents a model that endogenises the real steady-state interest rate. In this struc-
ture, the interest rate can be influenced by changes in the credit market. The
model allows an answer to the question as to what is the implication of large
financial disruptions for the steady-state interest rate; the model also shows
the short-run dynamic response to such a shock. The mechanism implies a
link to the ZLB literature as persistent changes to the steady-state interest rate
would constrain monetary policy by dragging down the intercept term in, for
example, a standard Taylor rule. By linking aspects of the two literatures, this
paper derives a general equilibrium model that seeks to explain one of the
salient features of many post-crisis economies: that of persistently low interest
rates.
Two important elements of the model are a framework that permits an
endogenous steady-state interest rate and a financial friction; to this end, this
paper constructs a discrete-time perpetual youth model containing durable
goods and an endogenous financial friction in the form of a collateral con-
straint. The motivation for the choice of collateral constraints is similar to
that of Gerali et al. (2010), who use this approach to capture the quantity of
credit supply. The credit quantity should be explicitly measured in relation to
financial friction. Credit can then enter into the aggregate consumption func-
tion and thus influence steady-state interest rate levels through supply and
demand. This allows for interactions that are not possible in a market charac-
terised by a perfectly elastic credit supply curve. With respect to the second
element required in the model namely, variation in the steady-state rate of
interest –a perpetual youth model is used. This model provides a straightfor-
ward synthesis of representative agent models and OLG models, allowing fea-
tures of both to be employed in the analysis (Obstfeld and Rogoff, 1996).
The model shows that a tightening of financial frictions results in a fall in
the steady-state interest rate. The mechanism works through the supply and
demand of credit. When households have a perpetual youth structure and
entrepreneurs are infinitely lived, the steady-state rate of interest in the model
is not determined by the rate of time preference alone. Credit suppliers, the
households, no longer have a perfectly elastic supply curve as in the infinite
horizon case; therefore, a reduction in credit demand lowers the market clear-
ing interest rate. This occurs endogenously in the model, subsequent to a
change in the constraint. It is also shown that non-linearities exist in this rela-
tionship and that it is possible for an economy to experience larger falls in the
interest rate at higher debt levels for the same interest rate. Stylised calibra-
tions confirm that the interest rate falls by up to 1.9% points for a 30%
increase in the friction and that this fall in the interest rate increases the fur-
ther the model is from the infinite horizon case. The short-run dynamics of
the model are shown through the simulation of a financial shock. This is done
through the addition of a stochastic process to the borrowing constraint along
with a sticky price mechanism and monetary authority. The shock leads to a
lower interest rate, a reduction in borrowing, a fall in asset prices and a
138 DONAL SMITH
Scottish Journal of Political Economy
©2019 Scottish Economic Society
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