Does the
Interest Rate Form Business Cycle?
�
Bijan Bidabad
B.A., M.Sc., Ph.D., Post Doc.
Professor of
Economics and Chief Islamic Banking Advisor
Bank Melli Iran,
Tehran, Iran����� ��
Email: [email protected]
Abul Hassan
Lecturer and Senior Research Fellow
Markfield Institute of Higher
Education
University of Gloucestershire
Ratby Lane, Markfield,
Leicestershire LE67 SY, UK.
Email: [email protected]
Abstract
Dynamic structural
behavior of depositor, bank and borrower and the role of banks in forming
business cycle are investigated. We test the
hypothesis that does banks behavior make oscillations in the economy through the
interest rate. By dichotomizing banking activities into two markets of deposit
and loan, we show that these two markets have non-synchronized structures, and
this is why the money sector fluctuation starts. As a result, the fluctuation
is transmitted to the real economy through saving and investment functions.
Empirical results assert that in the USA, the banking system creates
fluctuations in the money sector and real economy as well through short-term
interest rates
Keywords: Business cycle,
Interest rate,
Banking Sector.
JEL: E32, E43, G01
1. Introduction
There
are several studies on business cycles from different points of view. The essence
of these studies was to find out a solution on how to reform monetary and
banking structure and overcome the economic crisis. The purpose of this paper
is to examine the relationship between interest rates and business cycle
formation. In the area of the business cycle, Fisher�s (1933) �Theory of Credit
Cycles� is one of the interesting theories discusses elaborately the causes of
business cycles. He argues that credit cycles are the main reasons for economic
cycles. Minsky (1992) puts forward the financial instability hypothesis, and in
the line of Fisher�s theory, he further argues on credit bubbles and their
burst effects on economic cycles. While discussing the �Austrian Business Cycle
Theory�, Block and Barnett (2007) state that banking structure is one of the factors
to create a crisis. Some other researches have
also touched different aspects of the relation between interest rate and
business cycle (Beaudry and Guay, 1996; Blankenau et al.,2001; Ivanova et al.,(2000);
but none of these studies look at the fluctuation of bank interest rates which
is one of the causes of business cycle in the economy. Therefore, this study attempted
to show the co-movements between interest rates and output.
This study highlights
on money market by bifurcating bank's behavior into two markets, namely saving-deposit
and investment-credit markets in line with the studies of Bidabad (2004, 2010).
In one hand, the demand of bank for deposits is kept at one side, which
intersects with the supply of deposits (saving) and fixes deposit interest
rate. On the other hand, the bank creates another market by supplying credit funds
that intersects demand for credit and creates the loan interest rate. In view
of this, the bank stands between two markets of supply and demand for funds in the
money market.
In case the consumption increases, the
supply of bank deposits will fall. As a result, there will be an increase in
the deposit interest rate. The increase in deposit interest rate cannot
instantly increase credit-lending interest rate because credit contracts have
been fixed for a period, and the bank has to wait for contract maturity to increase
the rate. Therefore, the bank will face loss during this period, and thereafter,
it will be compensated by increasing the loan interest rate by a time lag. This
lag, from an economic point of view, creates a special dynamic relationship
between supply and demand for money. In the following lines, mathematically
shown that because of this lag, the relationship between these two variables (supply
and demand for money) is a second order difference equation. Second order
difference equations have the ability to create the cycles. In other words,
fluctuation of the real economy is induced by fluctuations in the money market.
The most important effect of elimination of interest rate (Islamic banking) is
to bridge between investment and saving. This analysis is shown in the
following graph:
Saving Demand
for loan Loan interest rate Saving supply Bank demand for deposit Saving interest rate Supply
of bank loans ����������������� Loan
�����������
�
Figure 1
Where:
Bank�s revenue
at the time t is equal to:
At equilibrium, we have:
In case the demand for loans decreases, DtL moves
from the left side to Dt+1L. In the new equilibrium, if the
bank�s revenue turns negative, we will get the following equations:
Or:
�
Therefore, in respect of the time-based loan
contract, the bank has to compensate losses during the period t+1from other
sources until the next period when DB curve moves to the left-hand side. It is
shown below:
�����
By
generalizing this hypothesis, we clearly see that whenever shocks occur in
deposit supply or demand for banks' loans, because of time-based contracts,
these shocks will be transferred to the other market in the next period. These
fluctuations will effect from one market to another market and finally extend
to other markets in the real economy as well.
By considering the sign of three
equations of (1), (5) and (7), we can clearly see that the behavior of variable
R is alternative in different periods. The behavior of the above-mentioned two
markets may be similar to the Cob-Web model, which creates different
fluctuation according to the gradient of different parts of supply and demand schedules.
The interest rates in the two markets are:
�������������������������������������������������������������������������������������������������������
������������������������(9)
According to the
above assumptions, if we adjust the relationship of the two markets with one
time-lag, we will have:
By replacing (8)
and (9) in (10), we have:
�
In
other words, the interest rate in the deposit market is a function of the interest
rate in the loan market in the previous period. The adjustment takes place when
the return movement occurs in the next period which means that the interest
rate of the loan market is itself a function of the interest rate of the deposit
market in the previous period, or:
�
By replacing
(10) in (12), we will have:
This is a second-order
difference equation which is characterized to fluctuate easily in time,
(Baumol,1958; Baumol and Turvey,1951). This is also true in the case of interest
rates. By replacing (12) in (10), we have:
�
�����������
����������������������������������������������������������������������(15)
Since equations
(15) and (11) are function of mt-1S and mt-1B
these two variables may be considered completely oscillatory according to (14)
and (13). Hence, both loans and deposits markets may fluctuate due to interest
rates and the amount of deposits and loans fluctuations. Considering the
equilibrium at the macro level and its relationship with interest rate
fluctuations induced by the banking behavior, we can go through the following
national accounting relationship equations:
gdp
= con + inv + gov + ex � im
gde
= con + sav + tax + tr����������������� �������������������������������������������������������������������������������������������������(16)
gdp
= gde
In which:
gdp = gde� ���������Gross domestic product = Gross domestic
expenditure
con������������������� ��Consumption
inv���������������������� Investment
gov��������������������� Government expenditures
ex����������������������� Exports
im���������������������� �Imports
sav���������������������� Savings
tax���������������������� Tax
tr����������������������� �Transfer payments to outside
By solving equation (16), macroeconomic
equilibrium condition will be as follow:
(inv-sav) +
(gov-tax) + (ex-im-tr) = 0����������������������������������������������������������������������������������������
�����������������(17)�������������
In order to make simplification, we will
only consider the two variables of investment and saving as functions of
interest rates of saving deposits and loans (rS and rL). The
equilibrium condition in the economy at time t will be the following:
�
By replacing rtS
and rtL from equations (15) and (11) in equilibrium
condition, we will have:
In case the government has balanced
fiscal policy (govt - taxt)=0 and trade (ext -
imt - trt)=0, then the equilibrium (19) is again a second-order
difference equation which can lead the economy into oscillation.
As we have shown
mathematically, the behavioral difference of the equation in interest rates of
the deposit and loan sources, create fluctuations in the money and capital
markets. This phenomenon can easily fluctuate the aggregate supply and demand
in the real sector through investment demand and saving supply functions as
shown emphatically. Bidabad (1990) argues that if the time behavior of yt
obeys a second order difference equation, type of roots (being real or
complex or double), their absolute values (being larger or smaller than one),
are critical for the shape of fluctuations.
In order to show the oscillatory natures
of the interest rates, we need to conduct an empirical test to see whether the
equations (11) and (15) are true in nature or not. Using the sample of USA data[1]
for the period of 1948-2009, we test weather equations (11) and (15) are oscillatory
or not. If it is true, then the oscillation will be transferred to equations
(18) and (19) which are the macroeconomic equilibrium condition. Our empirical
results show that the source of oscillation is emanated from interest rates to the
real sector. Ten types of short, medium, and long terms interest rates have
been selected. We fit a second order linear non-homogenous difference equation
to all 10 selected interest rates.
Table 1.
Estimation results and characteristic roots of ten estimated equations
|
Dependent
Variable |
Yt=�0
+ �1.Yt-1 + �2 .Yt-2 |
|
|
|||||||||
|
Yt |
Sample |
obs. |
�0 |
�1 |
�2 |
R2 |
roots |
Characteristic
roots |
||||
|
Certificates of Deposit Rate (secondary market-3 month) |
1967-2009 |
43 |
1.412 |
1.173 |
-0.405 |
0.714 |
complex |
0.586�0.865i |
|
|||
|
� |
|
(2.124) |
(7.828) |
(-2.675) |
|
� |
|
|
||||
|
Commercial Paper Rate |
1974-2009 |
36 |
1.092 |
1.208 |
-0.406 |
0.761 |
complex |
0.603�0.877i |
|
|||
|
� |
|
(1.609) |
(7.807) |
(-2.564) |
|
� |
|
|
||||
|
Discount Rate (End of Period) |
1950-2009 |
60 |
0.877 |
1.168 |
-0.349 |
0.774 |
complex |
0.584�0.830i |
|
|||
|
� |
|
(2.387) |
(9.376) |
(-2.786) |
|
� |
|
|
||||
|
Federal Funds Rate |
1957-2009 |
53 |
1.159 |
1.121 |
-0.332 |
0.721 |
complex |
0.560�0.803i |
|
|||
|
� |
|
(2.241) |
(8.255) |
(-2.445) |
|
|
|
|
||||
|
Lending Rate (Prime Rate) |
1950-2009 |
60 |
1.193 |
1.195 |
-0.364 |
0.799 |
complex |
0.597�0.849i |
|
|||
|
� |
|
(2.553) |
(9.559) |
(-2.962) |
|
|
|
|
||||
|
Treasury Bill Rate(Bond Equivalent-3 month ) |
1977-2009 |
33 |
0.920 |
1.212 |
-0.384 |
0.768 |
complex |
0.606�0.866i |
|
|||
|
� |
|
(1.412) |
(7.048) |
(-2.153) |
|
|
|
|
||||
|
Mortgage Rate |
1974-2009 |
36 |
0.713 |
1.301 |
-0.386 |
0.874 |
real |
0.843, 0.458 |
|
|||
|
� |
|
(1.140) |
(7.983) |
(-2.339) |
|
|
|
|
||||
|
Treasury Bill Rate |
1950-2009 |
60 |
0.738 |
1.173 |
-0.330 |
0.792 |
real |
0.705, 0.469 |
|
|||
|
� |
|
(2.126) |
(9.257) |
(-2.614) |
|
|
|
|
||||
|
Govt. Bond Yield: Long Term (10 year) |
1956-2009 |
54 |
0.511 |
1.103 |
-0.180 |
0.880 |
real |
0.903, 0.200 |
|
|||
|
� |
|
(1.491) |
(7.973) |
(-1.319) |
|
|
|
|
||||
|
Govt. Bond Yield: Medium Term (3 year) |
1950-2009 |
60 |
0.539 |
1.127 |
-0.222 |
0.856 |
real |
0.872, 0.255 |
|
|||
|
� |
|
(1.656) |
(8.668) |
(-1.718) |
|
|
|
|
||||
T-statistics are in parentheses.
4. Conclusion
This study shows
that business cycles occur because of the dynamic structure of different
interest rates. The results demonstrate that there is an inherent lag structure
between deposit and loan interest rates. The observed lag structure actually
forms a second-order difference equation behavior in the banking sector as a source
of oscillations, which start from the money market and expands to the real
economy. Using the sample of the United States interest rates data for the
period of 1948-2009, the results show the short-term interest rates is one of
the main causes of fluctuations. The estimated dynamic equations for short-term
interest rates had complex characteristic roots that let the equations be
oscillatory. The long-term and medium-term interest rates equations had real
characteristic roots and were not oscillatory.
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