Construction of China’s Monetary Condition Index Based on the STR Model
De-cai Zhou, Wen-ping Qi, Zheng-yi Jiang
School of Economics & Management, Nanchang University, Nanchang, China. P. R.
（decaizhou@163.com）
Abstract - Based on China’s monthly data ranging
from January 1996 to January2012, using smooth
transition regression model (STR), construct China’s
nonlinear monetary condition index. The conclusion
shows that the constructed nonlinear MCI is highly in
consistent with the tendency of inflation, thus it could be
the indictor of the implement of China’s monetary policy.
Keywords - MCI, STR Model, Monetary policy, China
I.
INTRODUCTION
Since Charles. Freedman (1994) puts forward the
concept of Monetary Condition Index (MCI) [1], scholars
from worldwide have been constructing different country
and region’s monetary condition index by various
methods[2]. Many scholars also have constructed similarly
China’s monetary condition index (CMCI) [3].Such as
Chen Yulu and Bian Weihong (2003) initially introduced
and commented MCI in China [4]. Bu Yongxiang and
Zhou Qing (2004), Peng Wensheng and Liang Weiyao
(2005), Bian Zhicun (2008) estimated the CMCI by using
single equation estimate methods [5-7]. Chen Jianbin and
Long Cuihong (2006), Zhao Yongqing and Fan Conglai
(2009), Xu Changsheng, Zhang Shuai and Zhuang
Jiaqiang (2010) constructed the CMCI by using VAR
TABLE Ⅰ
UNIT ROOT TEST
ADF test
Variable
(C, t, n)
T-stat
Prob
stationary
(C, t)
LCPIH
(0,0,1)
-11.1787
0.0000
stationary
(0,0)
LM1H
(0,0,1)
-2.5732
0.0100
stationary
(0,0)
LNEERH
(0,0,1)
-3.3340
0.0009
stationary
(0,0)
LCRH
(0,0,1)
-4.8026
0.0000
stationary
(0,0)
model [8] [9] [10]. To sum up, the majority of current papers
are based on linear method to construct MCI. Considering
the nonlinear relationship between currency price,
currency supply and demand and some economic
variables, it is advisable to construct China’s nonlinear
monetary condition index by using STR model.
II.
STR MODEL
The following is general format of STR model [11]:
(1)
Y𝑡 = 𝛷 ′ 𝑧𝑡 + 𝜃 ′ 𝑧𝑡 𝐺(𝛾, 𝑐, 𝑠𝑡 ) + 𝑢𝑡
Amongst z𝑡 = (𝑤𝑡′ , 𝑥𝑡′ )′ is explanatory variable
vector, w𝑡′ = (1, 𝑦1 , ⋯ , 𝑦𝑝 ) and x𝑡′ = (1, 𝑥1𝑡 , ⋯ , 𝑥𝑘𝑡 )
are exogenesis explanatory variable’s vectors; Φt =
(𝛷0 , 𝛷1 , ⋯ , 𝛷𝑚 )′
and
θt = (𝜃0 , 𝜃1 , ⋯ , 𝜃𝑚 )′
are
respective parameter vectors of (m + 1) × 1’s linear and
nonlinear parts; u𝑡 ~i. i. d. N(0, σ2 ) is random error term;
𝐺(𝛾, 𝑐, 𝑠𝑡 ) is the transition function, the bounded
function about continuous transition variable s𝑡 ; 𝛾 is the
smoothing parameter; s𝑡 is the state variable (transition
variable); 𝑐 = (𝑐1 , ⋯ , 𝑐𝑘 ) is location parameter; if the
transition function’s formation is as following:
-1
G(γ, c, st )=(1+exp{-γ ∏K
k=1 (st -ck ) }) , γ>0 (2)
The model is general Exponential Smooth Transition
Regression (LSTR) model, in which when K=1 it is
called LSTR1 model and when K=2 it is called LSTR2
model. There are generally 3 steps to estimate STR model:
selection of model’s format, estimation of parameters and
diagnosis.
III
EMPIRICAL RESULTS OF STR MODEL
A. Variables’ selection and data’s disposal
We select China’s consumer price index (CPI),
narrow money supply (M1),
nominal effective exchange
PP test
rate of Renminbi (NEER) and
interbank interest rate (CR) to
T-stat
Prob
stationary
represent inflation, money
-11.5520
0.0000
stationary
supply, nominal exchange rate
-3.0036
0.0028
stationary
and short-term interest rate
respectively. All are monthly
-3.3798
0.0008
stationary
data ranging from January
-4.4705
0.0000
stationary
1996 to February 2012 which
come from the national bureau of statistics of China, the
people's bank of China, bank for international settlements
web site and CEInet data. All the time series are seasonal
adjusted and then taken natural logarithm to eliminate
potential heteroscedasticity. Respectively, they are
recorded as LCPI, LM1, LNEER, and LCR. Then we take
the balance the above variables value minus the trend
values of their HP filters as the gap values of them. They
are recorded as LCPIH, LM1H, LNEERH and LCRH.
TABLE Ⅱ
THE TEST OF LAG ORDERS
the basis of the framework
model
put
forward
by
[11]
Lag
0
1
2
3
4
5
6
7
8
Lütkepohl H，Krä tzig(2004) ,
Log L
743.8
748.5
757.7*
754.9
753.2
752.2
750.2
747.0
744.6
Luukkonen R ， Saikkonen P
AIC
-7.6771 -7.7234 -7.8188* -7.7882 -7.7693 -7.7578 -7.7349 -7.6987 -7.6711
and Terasvirta (1994) [12]
determine the concrete forms
SC
-7.6263 -7.6047 -7.6315* -7.5318 -7.4435 -7.3618 -7.2684 -7.1611 -7.0619
of it, namely the form of either
*
HQ
-7.6565 -7.6753 -7.7430
-7.6843 -7.6373 -7.5973 -7.5459 -7.4808 -7.4242
LSTR1(K=1)
or
TABLE Ⅲ
LSTR2(K=2).According to STR model’s test methods,
OUTCOME OF NONLINEAR TEST
we make linear and nonlinear tests for the relationship
Transition
between inflation and MCI’s several variables. The
F
F4
F3
F2
F1
LCPIH(-1)*
1.90E-04 2.20E-01 1.75E-05 2.36E-01 LSTR2 outcomes show in Table Ⅲ. According to table Ⅲ, we
Variable
can find that when transition variable is LCPIH (-1), the P
LCPIH(-2)
3.21E-02 2.41E-01 1.59E-01 3.71E-02 LSTR1
value corresponding to F3 is the minimum. Therefore the
LM1H
1.83E-02 5.07E-01 6.67E-01 2.42E-04 LSTR1 LSTR2 model is exogenous optimal form.
LNEERH
1.79E-06
1.97E-03
1.08E-03
1.10E-02
LSTR2
LCRH
1.04E-03
6.87E-02
2.28E-03
1.38E-01
LSTR2
LM1H(-1)
3.07E-03
3.07E-02
6.72E-02
5.11E-02
LSTR1
LNEERH(-1)
1.28E-06
2.53E-05
3.42E-03
1.48E-01
LSTR1
D. Estimation Outcome of LSTR2 and Its Analysis
After have determined the form of STR model’s
transition variable and transition function, we need to
LCRH(-1)
8.05E-02 2.73E-01 2.16E-01 9.11E-02
Linear estimate the parameters of LSTR2 model. Firstly, we use
LM1H(-2)
8.05E-02 2.73E-01 2.16E-01 9.11E-02
Linear the grid search to determine the initial value of smooth
velocity and location function. At last we get the initial
LNEERH(-2)
2.10E-05 8.10E-03 2.32E-03 1.81E-02 LSTR2
values 1.4048, -1.1376 and 1.9895 of the smooth velocity
LCRH(-2)
2.02E-03 1.94E-01 2.75E-03 7.37E-02 LSTR2 γ and location parameters c1, c2. Basing on the initial
values of above grid search, we have estimated the
equation (1) at first. Then according to the principle of
B. Stability test
generality to particularity, we have removed the
insignificant variables step by step. Lastly, we get the
This paper uses unit root test to examine sequence
estimated values of the parameters Φ, θ, γ, c in equation
stability. The outcome shows in table Ⅰ. From it, we can
(1) [13].All results show in table Ⅳ. Table Ⅳ indicates
find that LCPIH, LM1H, LNEERH and LCRH are
that there are strong significances of estimated parameters
stationary time series at the significance level of 1%
and better fit. The 1 order lag of inflation, namely, LCPI
according to the ADF test and PP test.
(-1) in it appears the relation of significant smooth
transition and the parameters of other variables are
C. Determine the Lag Orders and Concrete Forms of
relative large and significant. It indicates that there isn’t
STR Model
only stable linear relationship between China’s money
supply, nominal effective
TABLE Ⅳ
exchange
rate
of
OUTCOME OF LSTR2 MODEL’S ESTIMATION
Renminbi
(NEER),
Linear part
LCPIH(-1) LM1H LCRH LM1H LNEERH(-1)LNEERH(-2)LCRH(-2)
interest rate and inflation.
Initial value
0.0989
0.0751 0.1799 0.0975
0.0729
0.0765
0.1731
Estimated value 0.1985
0.0604 0.1463 0.0879
0.0810
0.0753
0.1540
There have structural
t-statistics
1.9521
2.1984 1.6900 3.0612
2.7753
2.6727
1.9429
changes and nonlinear
P-value
0.0525
0.0292 0.0928 0.0026
0.0061
0.0082
0.0536
relationship. Figure 1
Nonlinear part Constant termLCPIH(-1)LM1HLNEERH LCRH
LCRH(-1) LM1H(-2) γ
c1
c2
shows that the dynamic
Initial value
1.9583
1.4657 0.6481 0.6084
7.9711
5.8933
0.3552 1.4048 1.1376 1.9859
of
Estimated value 0.5971
0.7250 0.5004 0.4512
4.0661
2.1428
0.4852 1.0426 0.9637 1.5761 characteristics
t-statistics
1.8026
2.9135 4.2711 3.6511
5.6026
2.5491
2.6696 1.918013.64873.6427 estimated Statistics of
P-value
0.0732
0.0040 0.0000 0.0003
0.0000
0.0117
0.0083 0.0568 0.0000 0.0004 LSTR2
model
are
1) Determine the Lag Order of STR Model. Firstly
similar with those of raw statistics. This means that
we test the length of lag. Though the standard test of lag
nonlinear model can better explain China’s inflation.
length based on regression model, we determine the
optimal lag orders of STR model. In order to determine
the suitable orders, we choose the maximum lag orders 8
to test them. The test results are in table Ⅱ. Seeing from
table Ⅱ, we find that according to the criteria of LOGL,
AIC, SC and HQ, they all indicate that the optimal lag
orders of the variables of STR model are 2 orders.
2) Determine the Concrete Forms of STR Model. On
constructing the monetary condition index, set October
1998 as the base period in which the exogenous variables
2
are relative balanced. We have calculated China’s
monthly nominal nonlinear monetary condition index
1
ranging from March 1996 to January 2012 according to
0
the linear and nonlinear parts’ weights above. Its
-1
reference indicator is monthly Year-on-year CPI of China.
The overall outcome is shown in Figure 2, indicating that
-2
integrating factors of money supply, interest rate and
-3
exchange rate, MCI roundly reflects and measures the
relationship between China’s monetary policy and
fitted time series
original time series
inflation. MCI has a resemble tendency with inflation rate,
indicating the inherent consistency between MCI and
Fig.1. the fitted and original time series
inflation. MCI goes head of inflation, and what is more
noticeable is the fact that the former’s turning point leads
the latter’s 1-3 months.
IV. CONSTRUCT NONLINEAR MONETARY
Using the methods of the time-varying cross
CONDITION INDEX OF CHINA
correlation coefficient, we
TABLE Ⅵ
have calculated the time
Time varying Cross correlation Coefficient of MCI and CPI
varying
cross-correlation
L
0
1
2
3
4
5
6
7
8
coefficient
of
China’s
nonlinear monetary condition
CPI,MCI(-L) 0.254 0.3833 0.1437 0.0336 -0.0416 -0.1337
-0.134
0.0135
0.165
index with inflation, which is
CPI,MCI(+L) 0.254 0.1892 0.1317 0.1119
0.2014
0.0221
-0.2153 -0.1921 -0.0887
shown in Table Ⅳ. Table Ⅳ
shows
that
the
correlation
coefficient of MCI of lag 1
A. Determining weight
order with inflation is max, indicating that the former
runs one month ahead of the latter.
Refer to Hataiseree(1998)[14], substitute the linear
96M03
97M03
98M03
99M03
00M03
01M03
02M03
03M03
04M03
05M03
06M03
07M03
08M03
09M03
10M03
11M03
3
B. Calculation of Index
Based on the definition of MCI and each variables’
estimated weights in previous words, referring to
Goodhart and Hofmann (2001)’s method [15], divide MCI
into parts of linear and nonlinear and multiply the
nonlinear part with transition function value. The formula
is as follow:
𝑀𝐶𝐼 = 100 + [∑𝑛𝑖=1 𝑊𝛷𝑖 (𝑋𝐺𝐴𝑃𝑖𝑡 − 𝑋𝐺𝐴𝑃𝑖0 ) +
∑𝑛𝑖=1 𝑊𝜃𝑖 (𝑋𝐺𝐴𝑃𝑖𝑡 − 𝑋𝐺𝐴𝑃𝑖0 )𝐺]
(4)
Among 0 and t represent base period and report
period respectively, X is optional variable in con
-structing MCI, GAP is the corresponding gap value, G
is the transition function value of nonlinear part.
Then according to formula (4), we construct China’s
nonlinear MCI We choose China’s narrow money supply,
nominal effective exchange rate of Renminbi and
interbank interest rate as the exogenous variables of
105.0
100.0
95.0
90.0
96M02
97M04
98M06
99M08
00M10
01M12
03M02
04M04
05M06
06M08
07M10
08M12
10M02
11M04
and nonlinear coefficients of LM1H, LNEERH, LCRH
and their lag terms estimated by LSTR2 model into the
following formulas to do their weights W𝛷 and W𝜃 :
∑𝑛𝑡=0 𝛷𝑖𝑡
𝑊𝛷𝑖 =
;
𝑛
∑𝑖 (|∑𝑡=0 𝛷𝑖𝑡 | + 𝑀|∑𝑛𝑡=0 𝜃𝑖𝑡) |)
∑𝑛𝑡=0 𝜃𝑖𝑡
𝑊𝜃𝑡 =
; 𝑖 = 1,2,3 (3)
∑𝑖(|∑𝑛𝑡=0 𝛷𝑖𝑡 | + 𝑀|∑𝑛𝑡=0 𝜃𝑖𝑡) |)
Amongst Φit and θit represent the coefficients of
the variable 𝑖 ’s linear and nonlinear parts at time t
respectively, 𝑀 represents the mean of transition
function’s value.
MCI
CPI
Fig.2. China’s nonlinear MCI and CPI
VI. CONCLUSION
This paper conducts nonlinear test to three variables:
interest rate, exchange rate and money supply chosen to
construct China’s monetary condition index, and then
finds significant nonlinear relationships between their
effects to inflation. Accordingly, based on STR model,
this paper estimates China’s nonlinear monetary condition
index. Through comparing its relation to inflation, we
find that it can well reflect changes in inflation. And
further research shows that MCI leads roughly 1 month
ahead of inflation. Therefore, it is predictable to inflation
and can be the indictor of monetary policy.
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