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1
Interest Rates and Prices Causality in the Czech Republic –
Granger Approach
J. Poměnková, S. Kapounek
POMĚNKOVÁ, J., KAPOUNEK, S. (2009), Interest Rates and Prices Causality in the Czech Republic
- Granger Approach. Agricultural economics : Zemědělská ekonomika. Vol. 55, No. 7, pp. 347-356.
ISSN 0139-570X.
Monetary policy analysis concerns itself with both the assumptions of the
transmission mechanism and the direction of causality between the nominal (i.e.
the money) and real economy. The traditional channel of monetary policy
implementation works via interest rate changes and their impact on the
investment activity and the aggregate demand. Altering the relationship between
the aggregate demand and supply then impacts the general price level and hence
inflation. Alternatively, Post-Keynesians postulate money as a residual, In their
approach, banks extend credit in response to movements in investment activities
and demand for money. In this paper authors use the VAR (i.e. the vector
autoregressive) approach applied to the “Taylor rule” concept to identify the
mechanism and impact of the monetary policy in the small open post-
transformation economy of the Czech Republic. The causality (in Granger sense)
between the interest rate and prices in the Czech Republic is then identified. The
two alternative modelling approaches are tested. First is the standard VAR
analysis with lagged values of interest rate, inflation and economic growth as
explanatory variables. This model shows the one way causality (in a Granger
sense) between inflation rate and interest rate (i.e. the inflation rate is (Granger)
caused by lagged interest rate). In second, the lead (instead of lagged) values of
interest rate, inflation rate and real exchange rate are used. This estimate shows
one way causality between inflation rate and interest rate in the sense that interest
rate is caused by the lead (i.e. the expected future) inflation rate. The assumptions
based on the money as a residual of the economic process were rejected in both
models.
Keywords:
exogenous and endogenous money, transmission mechanism, Taylor rule
2
The Constitution of the Czech republic states that: “the primary target of the Czech national
bank is to maintain price stability“ (the Constitution of the Czech republic, head 6, article 98).
The basic law establishing the Czech National Bank (CNB) (law Nr..6/1993, §2) then defines
its basic function as: “the primary target of the Czech national bank is to maintain price
stability. Without the prejudice to this primary target, Czech national bank sustains economic
policy of the government which leads to the sustainable economic growth“.
In fulfillment of its mandate, CNB adopted so called IT (inflation targeting) monetary
policy strategy in December 1997. The key element in this strategy is setting the medium term
target for the inflation rate. This is then compared to the medium term forecast of the same
rate The CNB then determines the changes in monetary policy character according to the
deviations of forecasted inflation rate from its target.
The main operational tools for the CNB are the central bank´s referencing rates. An
increase in those rates is assumed to lead to a decrease of aggregate demand dynamics and
hence to a weakening of inflationary pressures (and, indeed, vice versa). The basic idea
behind this policy is the concept of a monetary transmission mechanism where changes in
monetary policy reference rates directly determine the short interest rate on the interbank
market. This in turn causes commercial banks to raise/lower both their deposit and credit
rates. The result is a contraction/expansion of investment activity and aggregate demand and
ultimately a weakening/strengthening of inflationary pressures.
Common approach for the analysis of the nature and functioning of the monetary
transmission mechanism is the VAR analysis. The general assumptions about the transmission
mechanism are based on the unidirectional causality between the monetary variables and
aggregate demand. The behaviour of commercial banks, non-bank public and the basic
parameters of the demand for money are determined by monetary authorities. As a result,
these authorities control the short-term interest rates on the interbank market. Underlying
these assumptions are historically the monetarists´ ideas which focus on the authorities
behaviour and the stability of the money multiplier. In contrast, post-Keynesians argue that
the stability of monetarist empirical relationships comes about because money is a residual in
the economy without any causal significance. The authorities, from this point of view, have
passively supplied money in response to contemporaneous and prior movements in income
and thus the demand for money.
To determine the nature of monetary transmission mechanism and hence the role of
money in the Czech economy, we use the VAR approach. This approach enables us to
ascertain the direction of causality between monetary and real variables and hence to answer
the question about the role of money in the Czech economy implicitly posted in the previous
paragraph.
Indeed, one of the major issues in VAR modelling is the nature of lags and leads in the
model. It stems from two areas. Some authors argue that the major disadvantage of the VAR
model is an inadequate description of the central bank reaction function. And, indeed, the
length of lags (and leads) in any monetary analysis remains always a major issue. In the view
of the existence of lags and leads in the practice of monetary policy it is always necessary to
work with current as well as past and future values.
This is even more important under the inflation targeting regime where monetary policy
decisions generally arise from expected future value of inflation rate. Inflation targeting
generally (and in this paper as well) means setting of monetary policy according to
discrepancy between the expected and desired inflation rate.
Because the monetary policy implementation is based on this fact, the monetary policy
operational target represented by short-term interest rate on the inter-banking market is
affected not only by actual trends in the economy but also by predictions of the main
macroeconomic variables included in the inflation specification models.
3
The discussion in this paper is based on the analysis of the relationship between the
short-term interest rate, inflation and economic growth as represented by the Taylor rule. For
small open economies this was expanded by including the exchange rate movements (Romer,
2001). Under these assumptions the variable vector considered includes the inflation rate, the
short term interest rate, an economic growth and the real exchange rate.
The aim of this paper is to identify causality in the monetary policy reaction function,
modelled by Taylor rule. In the first step, the VAR approach is applied empoying
alternatively both lags and leads. Secondly, Granger causality is applied to identify type of
causality (bilateral or unilateral) between the variables.
The results reported in this paper are outcomes of the research grant n. MSM
6215648904 with the title “The Czech Economy in the Process of Integration and
Globalisation, and the Development of Agricultural Sector and the Sector of Services under
the New Conditions of the Integrated European Market”, thematic area “Macroeconomic and
microeconomic performance of the Czech economy, and the Czech government’s econo-
political measures in the context of the integrated European market.” The holder of the
research grant is Mendel University of Agriculture and Forestry Brno, Faculty of Business
and Economics.
VAR MODELLING AND GRANGER CAUSALITY
The price stability, an increase in economic growth, the full employment and a quality of life
are often mentioned as general goals of central banks. In this context, the impact of the
monetary policy on the price stability and exchange rate movement in the open economy is
generally agreed upon. But there is no theoretical or empirical consensus whether the central
banks are able to exert an influence over the economic growth.
According to classical economics (and its supply oriented models) the real output is in
the long run determined by a production capacity of the economy, which can not be directly
influenced by central banks monetary policy. However, the monetary policy can be used to
affect accumulation of capital, i.e. value of investments, and consequently the level of
technological advance. On the other hand Keynesian economics admits that the real output
could be influenced by the monetary policy to the extent to which it is able to influence the
aggregate demand. Especially, interest rates directly affect the investment decision-making
process in the most companies. Živělová (2004) describes the long-term financial planning
which is based on the expected cash flows and calculated interest rates. “The basic function of
calculated interest rate is to express the expected profitability of an investment. The
calculated interest rate also enables to express the level of expected risk. Regarding the fact
that the future revenues will be attained not only by means of owned capital but also by
foreign funds...” (Živělová, 2004). If the calculated return on the investments is less than the
interest rate on the outside funds (credit), the company management rejects the investment
project financed by borrowed funds.
From this argument it could be assumed that in the demand-side economics the
monetary policy is an effective tool to influence the economic growth. According to supply-
side economics, however, a monetary expansion exerts influence over the real output only in
the short-run, in the long-run the rise in the real output is offset by price increase.
In the supply-side economic theory the monetary policy is an effective tool for
influencing the real output under the conditions that it is also able to maintain price stability
effectively. Price stability increases transparency of the price mechanism and so helps to
improve the allocation of resources. Moreover, it reduces inflation risks and inflation premia
in interest rates. Lower real interest rates have positive impact on investments, which then
lead to innovations and technological advance, which determines the log-run real output of
the economy. Furthermore, price stability reduces distortions caused by inflation or deflation
4
and creates conditions essential for the formation of a stable rational expectation. Many
economists (e.g. Angeloni, 2002) therefore assume that the price stability is the important tool
to maintain the economic growth. The impact of central bank’s monetary policy on the real
output is therefore indirect, but significant.
On the assumption that there is a dichotomy between the real and monetary sectors,
the real activity is determined only by real factors such as the capacity of capital, marginal
labour and capital productivities, natural resources, a technology development and other real
factors which determine the aggregate supply and demand of labour. On the other hand,
nominal wages and prices are determined by monetary factors only. Therefore, an increase in
the money supply leads only to increases in nominal wages and prices, leaving the real
variables unchanged. (This is the phenomenon called the neutrality of money.).
Although the central banks accept the neutrality of money assumption and their
monetary policy objectives therefore have monetarist character, the transmission mechanism
includes many alternate elements. On the one side, the Czech national bank´s monetary policy
assumes that money supply in the middle and long-run periods affects the aggregate demand
and prices. On the other side, the relationship between the interest rates and saving and
investment decisions is typical for the Keynesian transmission mechanism. The Keynesians
assume that lower interest rates stimulate investments demand and autonomous consumption
along with the aggregate demand and output. Of course, in the extreme textbook case of
liquidity trap, monetary expansion has no impact on the aggregate demand and output even in
the Keynesian thinking. It happens in the situation of high sensitivity money demand to
interest rates which causes a high speculation demand for money as well the changes in the
interest rates. The change in the money supply is then absorbed by change in the velocity of
money. (Mach, 2002)
In this analysis the authors accept the Keynesians assumptions that the lower interest
rates stimulate investments demand and autonomous consumption along with the aggregate
demand and output. This process will be understood as a Keynesian transmission mechanism.
The complexity of the transmission mechanism and the existence of lags between the external
shocks, main referencing interest rates of the central bank, financial market´s reactions and
final effects on the macroeconomic indicators, especially on the inflation and economic
growth complicate monetary policy implementation in the real economy. Max. 16 months
lags will be applied in the analysis.
Secondly, with the exogenous money assumption, the interest rate changes allowed to
proceed with different behaviour. Although central banks may have certain control of the
money supply, they cannot fix the stock of money in a country. The money supply is not an
exogenously set policy variable but is the result of the portfolio decisions of the bank and
non-bank private sector. “Thus, even if a central bank can directly set the value of its own
liabilities, the money supply is endogenously determined as a residual of the economic
process.” (Fontana, Palacio-Vera, 2003) If the money is a residual of the economic process,
the rate of change in monetary aggregates is in fact a function of the aggregate demand and
economy fluctuations. The implied direction of causation would then be from changes in
nominal income to changes in the stock of the money which, in turn impact the short interest
rates on the interbank market.
For the empirical part of this article we start with the simple specification based on the
quantity theory of the money:
YPVM
×
=
×, (1)
where M represents money stock, V velocity of the money in the economy, P aggregate price
level and Y is real output of the economy. Assume that money stock is fixed or grows in the
predetermined constant rate If the velocity of the money is dependent on the interest rate r and
real output of the economy, from the formula (1) it follows:
5
),( YPfIR =, (2)
This is the formula used by Taylor (2001) and defines linear causality between the
interest rates, price level and real output:
f
IRPPhgyPIR +−++= *)(, (3)
where IR represents short-term interest rates, P inflation and y real output of the economy
(percentage change). The variable IRf represents long-term safe interest rate and variable P* is
inflation target.
Romer (2006) reformulated the Taylor rule in the following form:
)ln(ln*)( ttttt YYcPPbRIPIR −+−+=− , (4)
where variable t
Y represents potential economy growth and IRt nominal short-term interest
rate,
R
I
long-term safe interest rate. For the case of the Czech Republic, small open
economy is the formula (4) expanded on the exchange rate movements et:
tttttt dERYYcPPbRIPIR +−+−+=− )ln(ln*)(. (5)
The authors assume that central banks have direct impact on the short-term interest
rates which represented the operational target of the monetary policy and that money has an
exogenous character in the empirical analysis.
The money endogeneity assumption could be accepted only if the causality between
the interest rate movements and other variables is rejected. Concurrently, the interest rates are
determined on the interbank money market which is caused by the money demand and supply.
Thus, endogenous money is directly followed by the supply and demand movements on the
interbank market and, in turn, by short term-interest rate. The key decision to be made by the
central bank relates to the discount rate, with the general structure of the short-term interest
rates resting on the stock of money endogenously determined outside the control of the
monetary authority. The central bank´s reaction function, in this paper represented by Taylor
rule, is not significant in the context of endogenous money.
Vector autoregressive model of the order k, or VAR(k), can be written as follows:
,vYAδvYA...YAδYt
k
1j
jtjtkk11t ++=++++= ∑
=
− (6)
where
.,,, 2
1
,,2,1
,2,21,21
,1,12,11
0
20
10
2
1
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
=
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎣
⎡
=
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
=
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
=
mt
t
t
jmmjmjm
jmjj
jmjj
mmt
t
t
v
v
v
Y
Y
Y
M
L
MMMM
L
L
MM tjt vAδY
ααα
ααα
ααα
α
α
α
(7)
indicates that all variables in this model have the same lag length of order k. The assumptions
that usually follow VAR model are the assumptions of a reduced form simultaneous equations
model, i.e.
()
iiit wNv ,0~ , for all t, and i=1,...,m, where
(
)
itii vw var
=
,
()
0=
isit vvE , for t
≠
s, and i=1,...,m,
()
ijisit wvvE =, for all t, and i=1,...,m, where
(
)
jtitii vvw ,cov
=
.
Due to its structure, VAR obviates a decision as to what contemporaneous variables are
exogenous. It has only lagged variables on the right-hand side, and all variables are
endogenous. However, in most cases the VAR order is not known and therefore it has to be
selected. For selecting the VAR order the likelihood ratio (LR) test, Akaike information
criterion (AIC) and Schwartz criterion (SC) (Enders, 2004) are commonly used.
6
Once set up and identified, VAR model can be estimated and the results of estimation
can be used to test various hypothesis inherent in the data. One of the testable hypothesis is
the concept of Granger causality..
Causality in the sense by Granger (1969) and Sims (1972) is inferred when the lagged
values of a variable, say Xt, have explanatory power in a regression of a variable Yt on lagged
values Yt and Xt. Test of the restrictions can be based on simple F test in the single equations
of the VAR model. That the unrestricted equations have identical regressors means that these
tests can be based on the results of the OLS estimates. If lagged values of a variable Xt have
no explanatory power of any of the variables in a system, that we would view X as weakly
exogenous to the system. With respect to the direction of causality we can distinguish the
following cases:
- unidirectional causality: the case when Xt caused Yt but Yt does not cause Xt
- bilateral causality: the case when variables Xt and Yt are jointly determined
This causality can be identified using Granger test (1969) based on the premise that the future
cannot cause the present or the past, utilising the concept of the VAR approach. Let us
consider the two variable VAR(k) (Xt and Yt ) model
t
k
j
jtj
k
j
jtjt
t
k
j
jtj
k
j
jtjt
YXX
YXY
2
1
2
1
220
1
1
1
1
110
εβαα
εβαα
∑∑
∑∑
=
−
=
−
=
−
=
−
+++=
+++=
(8)
With respect to this model following cases can be distinguished:
{}
k11211 ,...,,
α
α
α
{}
k22221 ,...,,
β
β
β
the type of causality
≠ 0 = 0 Unidirectional causality, X →Y
= 0
≠
0 Unidirectional causality, Y → X
≠ 0
≠
0 Bilateral causality, X ↔ Y
For the testing causality hypotheses referring to the significance of the VAR model described
above, the Wald FW-statistic can be used
()
()
()
12,~
12/
/−−
−−
−
=knkF
knRSS
kRSSRSS
FW
u
ur , (9)
where
RSSu- sum of squared residuals from the unrestricted equation,
RSSr- sum of squared residuals from the equation under the assumption that a set of variables
is redundant (restricted).
Thus, hypotheses in this test can be formed as follows
H0: X does not Granger cause Y, i.e.
{
}
0,...,, 11211
=
k
α
α
α
, inconclusive, FW < F,
H1: X does Granger cause Y, i.e.
{
}
0,...,, 11211
≠
k
α
α
α
, conclusive, F
≥
FW,
and
H0: Y does not Granger cause X, i.e.
{
}
0,...,, 22221
=
k
β
β
β
, inconclusive, FW < F,
H1: Y does Granger cause X, i.e.
{
}
0,...,, 22221
≠
k
β
β
β
, conclusive, FW
≥
F,
7
EMPIRICAL RESULTS AND DISCUSSION
For the empirical analysis the Taylor rule the small open economy was reformulated as:
tttt dERcYdPaIR
+
+
+
=
.
where (P) stand for inflation (price index percentage change compared to corresponding
period of previous year, based on 1995=100 and national currency), IR is the nominal interest
rate, Y stands for economic growth (GDP in constant prices, percentage change compared to
corresponding period of the previous year) and ER indicates the real effective exchange rate
(industrial countries' real effective exchange rates excluding NMS). For empirical analysis
quarterly data 1997:1 – 2007:1 used. All data were obtained from the Eurostat database.
The inflation targeting regime of the central banks requires the predictions of the
various macro and microeconomic indicators. The authors of this article approximate these
the predictions in the estimations by using the actual observed values (the approach justifiable
by the rational expectations hypothesis) as leads in the actual VAR model construction. Jílek
(2004) argues that it takes approximately one year for the monetary policy changes to impact
the demand and inflation rate. Standard procedures of VAR analysis are then used for
identification of statistically significant dependent variables and their lags (leads). Forward
VARs is based on the central bank reaction function. The Granger causality for the
identification of a type of relationship in both cases is subsequently identified.
Transmission mechanism of monetary policy is a chain of economic connections
through which changes in short-term interest rate lead to changes in prices (inflation). The lag
among monetary aggregates and inflation is commonly estimated between 6 and 12 month
(Jílek, 2004). In our VAR analyses the AC, SC and LL identification criteria were applied to
determine the lag length. For leads (where applicable) the optimum length p=4 was identified
using LR criteria (Seddighi, 2000). (Other criteria values (AIC, SC; Seddidghi 2000) showed
as optimum lag length p=19. VAR application for leads showed same problem, optimum
length was identified as p=15.) Given the data set character and sample size large lags (leads)
values can caused reduction of test power and model parsimony. Thus, using the economic
theory combined with the “second best” results, the length p=3 was chosen.
In the case of the lagged variables results for the interest rate are given in Table I and
for the inflation rate in the Table II below.
Tab. I: Results of lagged VAR(4), IR dependent
variable in period 1997/Q1 – 2008/Q1
Variable lag Coefficient t-statistic t-probability Significance
IR 1 1,2419 5,8814 0,0000 ***
2 -0,3361 -1,5680 0,1300
3 0,0655 1,7258 0,0972 *
4 -0,0072 -0,2415 0,8113
P 1 -0,0031 -0,0291 0,9771
2 -0,0966 -0,8876 0,3836
3 -0,0339 -0,3190 0,7525
4 0,0260 0,0340 0,7370
Y 1 0,3648 1,1148 0,2760
2 -1,0894 -1,7577 0,0916 *
3 0,3046 0,4870 0,6307
4 0,4090 1,0218 0,3171
ER 1 -3,0618 -0,8330 0,4131
2 -3,3713 -0,8338 0,4126
3 2,8430 0,7373 0,4681
4 -3,1289 -1,1717 0,2528
const 0,8137 1,4736 0,1536
n = 41 Rad
j
2 = 0,9861 Q = 2,6153
Note: Statistical significance at the 1% (***),10% (*)
Source: Own calculation
From estimated model for interest rate (IR) in Table I can be seen that interest rate
(IR) and economic growth (Y) are statistically significant. Real exchange rate (ER) as well as
8
the inflation rate (P) are statistically insignificant, i.e. they don’t have impact on interest rate
in the analysed period.
Tab. II: Results of “lagged” VAR(4), P dependent
variable in period 1997/Q1 – 2008/Q1
Variable Lag Coefficient t-statistic t-probability Significance
IR 1 0,2369 0,6432 0,5262
2 -0,0403 -0,1079 0,9150
3 0,0392 0,5924 0,5591
4 0,0622 1,1893 0,2460
P 1 0,4273 2,2904 0,0311 **
2 0,0325 0,1712 0,8655
3 0,3733 2,0141 0,0553 *
4 -0,6035 -4,5203 0,0001 ***
Y 1 -1,3148 -2,3033 0,0302 **
2 0,4001 0,3701 0,7146
3 0,6546 0,6001 0,5541
4 0,0536 0,0768 0,9394
ER 1 -9,1509 -1,4272 0,1664
2 -6,8991 -0,9782 0,3377
3 8,4057 1,2497 0,2234
4 -2,2073 -0,4739 0,6399
const 2,5560 2,6535 0,0139 **
n = 41 Rad
j
2 = 0,9514 Q = 1,0017
Note: Statistical significance at the 1% (***), 5%(**), 10% (*)
Source: Own calculation
From estimated model for inflation rate (P) in the table II can be seen the statistical
significance of inflation rate and economic growth. Effective real exchange rate (ER) as well
as the interest rate (IR) appear to be statistically insignificant, i.e. they don’t have impact on
inflation rate in analysed period.
Tab. III: Granger causality results for lags VAR
Granger Causality Test
Model with IR as dependent variable
Variable FW-statistic Probability
IR 94,1896 0,0000
P 1,0885 0,3845
Model with P as dependent variable
IR 4,0326 0,0122
P 9,4205 0,0001
Source: Own calculation
From the Granger causality test for the above specified and estimated models (Table
III) we can conclude:
a) in case of model for interest rate (tab. I), Granger causality test for interest rate shows
statistical insignificance for variable inflation rate (Probability = 0,3845)
b) in case of model for inflation rate (tab. II), Granger causality test for inflation rate shows
statistical significance for variable interest rate (Probability = 0,0122)
If statistical Granger causality test with respect to estimated model for lagged VAR is
used, we can see unilateral causality between inflation rate and interest rate in accordance
with I → P, i.e. inflation rate is caused by the lagged interest rate. Comparison economic
theory and Taylor rule (describing the relationship between the interest rate and inflation), the
causality test confirm (in a Granger sense) our expectations about the transmission
mechanism and money exogenity. Thus, these results can be thought of as confirming the idea
of the transmission mechanism of monetary policy and the direction of causation from the
changes of interest rate to changes in inflation rate. Indeed, this appears to validate the
effectiveness of the Czech national bank´s monetary policy.
Under inflation targeting regime, the monetary policy generally focuses on the
expected (predicted) value of inflation rate. Hence, in the context of this paper, the inflation
targeting means setting of monetary policy according to expected inflation rate value, which
9
in turn influences the values of the main operational tool of the monetary policy, the short-
term interest rate. To model this phenomenon, the VAR approach was modified to incorporate
the lead values of the relevant economic variables.
In the “lead” VAR analysis the classic VAR algorithm was used, albeit modified.
During this modification process the data file was reordered and the same criteria used for lag
identification were used to identify leads. Subsequently, three quarters of “leads” were
chosen. Value of dependent variable was expressed in dependence on other lead values. The
aim of this procedure was to estimate relationships for the interest rate and inflation rate.
Granger causality test were applied to identify the interrelationships and then compare these
with expectations. In the case of the „forward“ lag results for interest rate is given in Table IV
and for inflation rate in Table V.
Tab. IV: Results of “lead” VAR(3), IR dependent variable
in time 1997/Q1 – 2008/Q1
Variable Lead Coefficient t-statistic t-probability significance
IR 1 -0,3321 -1,6885 0,1020
2 -2,8140 -2,7450 0,0128 **
3 4,7563 5,0133 0,0000 ***
P 1 0,8971 1,8779 0,0705 *
2 0,1727 0,2475 0,8063
3 -1,4424 -2,3590 0,0253 **
Y 1 3,7687 1,5953 0,1215
2 -2,4388 -0,6607 0,5140
3 -2,2321 -1,1943 0,2421
ER 1 -9,7072 -0,5839 0,5638
2 53,6995 2,1830 0,0373 **
3 -83,9501 -4,5501 0,0001 ***
const 6,5320 2,1702 0,0383 **
n = 42 Rad
j
2 = 0,8233 Q = 1,7154
Note: Statistical significance at the 1% (***), 5%(**), 10% (*)
Source: Own calculation
From estimated model for interest rate (IR) in Table IV can be seen statistical
significance of interest rate (IR), inflation rate (P) and real exchange rate. In case of interest
rate, as well as real exchange rate, lead 3 is significant on 1 % significance level, in case of
inflation rate lead 3 significance is on 5 % significance level. Economic growth (Y) is
statistically insignificant and does not have impact on interest rate in analysed period.
Tab. V: Results of forward VAR(3), P dependent
variable in time 1997/Q1 – 2008/Q1
Variable Lag Coefficient t-statistic t-probability significance
IR 1 -0,0549 -0,7145 0,4807
2 0,3856 0,9629 0,3435
3 -0,1045 -0,2820 0,7800
P 1 1,0296 5,5118 0,0000 ***
2 -0,0583 -0,2140 0,8320
3 -0,4025 -1,6853 0,1027
Y 1 0,2702 0,2928 0,7718
2 -0,3060 -0,2123 0,8334
3 -0,0777 -0,1065 0,9159
ER 1 10,8147 1,6655 0,1066
2 -5,5988 -0,5827 0,5646
3 -6,2632 -0,8691 0,3919
const 0,9832 0,8363 0,4098
n = 42 Rad
j
2 = 0,9070 Q = 3,3313
Note: Statistical significance at the 1% (***)
Source: Own calculation
From estimated model for inflation rate (P) in Table V can be seen statistical
significance of lead inflation rate (P, lead 4) on 1% significance level. Any other independent
lead variable is not significant. Therefore inflation rate depends on inflation rate in the future
period (i.e. on the expected inflation).
10
Tab. VI: Granger causality results for leads VAR
Granger Causality Test
Model with IR as dependent variable
Variable FW-statistic Probability
IR 14,0498 0,0000
P 3,8831 0,0190
Model with P as dependent variable
IR 1,0920 0,3682
P 20,2563 0,0000
Source: Own calculation
Comparing results of Granger causality test for models describing interest rate and
inflation from forward point of view (Table VI), we can conclude:
• in case of the model for interest rate (tab. IV), Granger causality test for interest rate
shows the statistical significance for variable inflation rate (Probability = 0,0189)
• in case of the model for inflation rate (tab. V), Granger causality test for interest rate
shows statistical insignificance for variable interest rate (Probability = 0,3682)
If statistical Granger causality test with respect to estimated model for the “lead” VAR is
used, we can see unilateral causality between inflation rate and interest rate in accordance
with P → I, i.e. interest rate is caused by „lead“, i.e. the expected, inflation rate. Indeed, it
confirms that the current interest rate depends on a future (predicted) value of inflation.
Central bank which applies inflation targeting regime uses interest rate as the
operational target aimed ultimately to achieve the desired inflation rate. The level of interest
rate is defined on the basis of predicted (future) inflation values. In this sense, result of the
Granger causality tests applied on “leads” VAR estimates can be taken as a confirmation of
this targeting process.
Hence we conclude, that in the case of the lags empirical analysis confirms our
expectations of central bank´s monetary policy transmission mechanism, especially, monetary
policy effectiveness of its price level stabilization function. In the second part of the Granger
causality analysis, the “leads” estimates confirm the Czech national bank´s monetary policy
decision-making process. Moreover, the Granger causality results confirm the unilateral
causalities of the both variables (interest rate and inflation) based on the exogenous money
assumptions.
CONCLUSION
The aim of this paper is to identify causality between the interest rate and prices in a small
open economy of the Czech Republic. Empirical analysis is based on the Taylor rule, defined
as the relationship between the short term interest rate on the interbank market, price index,
economic growth and exchange rate movements. Applied VAR methodology is used with the
unilateral and bilateral causality identification in the Granger sense.
VAR modelling was used in the two steps. The first step is the classical VAR with
lags, the second step then utilized leads. The empirical analysis results are argued in the
context of the exogenous/endogenous money assumptions.
In the first step the standard VAR analysis was utilized to identify the relationship
between the interest rate and inflation. It concluded that:
• interest rate depends on lagged values of interest rate and economic growth
• inflation rate depends on lagged variables of inflation rate and economic growth
The real exchange rate was not found statistically significant in either case. These models
facilitated the evaluation of Granger causality between the involved variables. The unilateral
causality between inflation rate and interest rate (i.e.) could not be rejected.
In the second step the “lead” VAR analysis was used and models for interest rate and
inflation were specified, with the following results:
11
• interest rate depends on the “lead” values of the interest rate, inflation rate and real
exchange rate
• inflation rate depends on the “lead” value of the inflation rate
In neither case the economic growth appeared significant. The Granger causality tests here
indicate the unilateral causality between the future (i.e. the expected) inflation rate and
interest rate (i.e. E(P) → I). I.e. the current. interest rate is caused by the expected inflation
rate.
The assumptions based on the money as a residual of the economic process were
rejected in the analysed period and Czech Republic interbank market.
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Contact details:
Doc. RNDr. Jitka Poměnková, Ph.D., Doc. Ing. Svatopluk Kapounek, Ph.D., Department of
Finance, Faculty of Business and Economics, Mendel University of Agriculture and Forestry
Brno, Zemědělská 1, 613 00 Brno, Czech Republic
e-mail: pomenka@mendelu.cz, skapounek@mendelu.cz
