Download the efficiency of central bank intervention on the exchange

Academy of Economic Studies
Doctoral School of Finance and Banking
THE EFFICIENCY OF CENTRAL BANK
INTERVENTION ON THE FOREIGN EXCHANGE
MARKET IN ROMANIA.
A MARKOV SWITCHIG APPROACH
MSc Student: Catalin Gaina
Supervisor: Professor Moisa Altar
CONTENTS
1. Theoretical framework
2. Introduction to the Romanian context
3. Is a Markov Switching Model valid for the
exchange rate ROL/USD ?
4. How were the official intervention efficient ?
5. Concluding remarks
1. Theoretical framework
Central Bank intervention:
- Nonsterilized
- Sterilized
Sterilized intervention affect exchange rate through:
- portfolio balance channel (Isard, 1983; Dominguez
and Frankel, 1993)
- signaling channel (Mussa, 1983)
2. Introduction to the Romanian context
NBR adopted a managed float regime since the 1997
liberalization
- there is no explicit commitment to a specific
exchange rate
The disinflation objective and the need to maintain
external competitiveness seems contradictory
- Inflation pressure through sterilization operations
Sterilization began in June 1997
- deposit-taking
- sales of Treasury bonds
3.1 A Simple Markov Switching Model
Goldfeld and Quandt (1973)
Hamilton (1989, 1990, 1994)
Characteristics:
- A very popular nonlinear time series model
- Time varying parameters
- A discrete Kalman filter
- Most of the economic time series exhibit different behaviors
or have different structures and causality relations with
other time series in different periods
- The realizations of the unobservable discrete variable
generate the states/regimes
3.1 A Simple Markov Switching Model
Basic features:
- the Markov property for the unobservable variable St
P(St  j | St -1  i, St -2  k,.)  P(St  j | St -1  i)  Pij
- the transition matrix for k states
 P11 P 21 Pk1
P   P12 P 22 Pk 2
 P1k P 2k Pkk 
main equation :
- Log-likelihood :
-
yt   (St ) xt   t
 t  N (0,  (St ))
K K

L( | Y )   log  Pij * Pr( S t 1  i |  t 1 , ) * f ( yt | St  j,  t 1 , )
t 1
 i 1 j 1

T
Observation:
 A permanent switches/structural break – absorbing state
3.2 Application to the Exchange rate ROL/USD
The first difference of the daily
(log) exchange rate ROL/USD
1997



1998
1999
2000
2001
Identifying without ex-ante knowledge the periods of high
volatility and/or high depreciation tendency from the “calm”
periods
Characteristics of the exchange rate in each regime
Is a two state Markov switching representation better than a
one state (linear) representation ?
Applying the EM algorithm to obtain parameters estimates
Parameters Estimates
AR(p) representation of the daily exchange rate ROL/USD
Selection Criteria:
-Akaike and Schwartz
-significance of each parameter
Best specification : y  C ( S )  
  N (0,  1 )
t
t
t
t
for regime 1
 t  N (0,  2 ) for regime 2
Parameters
Estimates and Significance
State 1 (high volatility)
Constant1
0.0370114***
Var1(e)
0.0160235***
P11
0.905137***
State 2 (calm regime)
Constant2
0.0163847***
Var2(e)
0.0002611***
P22
0.967872***
Log-likelihood = 3483.77
Akaike = -5.96018
Schwartz = -5.93416
Standard errors were computed from the inverse of the negative Hessian
1.5
900
600
800
500
700
1.0
600
400
500
0.5
300
400
300
200
0.0
200
100
100
0
0
-0.5
1997
1998
1999
2000
2001
Estimated smoothed probability of
being in regime 1 (high volatility)
-0.25
0.00
0.25
0.50
0.75
Histogram of errors in
Regime 1
1.00
-0.25
0.00
0.25
0.50
0.75
1.00
Histogram of errors in
Regime 2
Statistics
Regime 1
Regime 2
=============================================
Standard deviation
0.245428
0.016161
Skewness
1.235997
0.135784
Kurtosis
15.200675
3.994950
Informal
Jarque – Bera test
1884.105
38.788
1997
1998
1999
2000
Exchange rate ROL/USD
2001
Hamilton (1996) LM test for omitted ARCH effects and Autocorrelation
Hamilton (1996) LM test for omitted ARCH effects and Autocorrelation
Statistics
Value
Probability
===================================================================
Test for ARCH across regimes 1 and 2
123.13993
0.0000
Test for Autocorrelation across regimes
0.0433623
0.9997
Asym. distribution - Chi-square(4)
Test for ARCH in regime 1
Test for Autocorrelation in regime 1
Asym. Distribution - Chi-square(1)
1.6652259
0.0269802
0.1969
0.8695
Test for ARCH in regime 2
Test for Autocorrelation in regime 2
Asym. Distribution - Chi-square(1)
0.3690371
0.0052255
0.5435
0.9425
LM for ARCH*
10.58549
0.0011
Breusch-Godfrey test for autocorrelation*0.070629
0.7904
===================================================================
(Restricted Sample: June 1, 1998 – May 31, 1999. Observations : 256)
(*) They were conducted for the linear specification AR(2) and are having the usual NR2 form
Hansen nonstandard Likelihood Ratio test
Null :
C1 = C2
Alternative: there are switches in regimes
1 = 2
Grid search over the nuisance parameters space
Grid for P - 12 points: from 0.10 to 0.925 in 0.075 increments
Grid for Q - 12 points: from 0.10 to 0.925 in 0.075 increments
Difference in drift - 6 points: from 0.003 to 0.020 in 0.034 increments
Difference in standard deviations - 6 points: from 0.01 to 0.11 in 0.02 increments
Newey-West Band width:
P-value
5
0.00
6
0.00
7
0.00
CONCLUSION:
We reject the null at a level of confidence lower than the above p-values
Note: A program in GAUSS to calculate this test is available at:
http://www.ssc.wisc.edu/~bhansen/
4. Estimating the efficiency of intervention.
Time varying transition probabilities
Given the objectives of NBR in the period June 1997 – December 2001,
-reducing inflation by stabilizing exchange rates
-a safe external position
It follow that
-high volatility on FX market
-appreciation of the real ROL/USD exchange
are not desirable
Central Bank intervention should have different motivation and goals
depending on the state that exchange rate actually follow
Introduced by Diebold, Lee and Weinbach (1994)
and Filardo (1994, 1998)
- Logistic specification
- The transition probabilities loose the Markov property
MODEL 1
The variable It use in the main equation : Net purchases of foreign
currency made by NBR
p
yt  c(St )   (St ) k * yt k   (St ) * I t 1   t
k 1
In the logistic specification we use first a discrete variable
exp( J   J * DI t 1 )
p( St  j | St 1  j, DI t 1 ) 
1  exp( J   J * DI t 1 )
DIt =
0, if no intervention at time t
1, if intervention were conducted at time t
2, if intervention were conducted in the same direction at time t and t-1
………………..
h, if interventions were conducted in the same direction for h days
Estimates of the model with discrete
intervention variable
Parameters h=1
h=2
State 1 (high volatility)

1
-1.340246
-1.1885870*
h=3
-1.4444623**
h=4
-1.5940234***
h=5
h=6
-1.7356188***
-1.9135868**
0.0202304***
0.0202036***
-0.1817141
-0.2648565
State 2 (calm state)
2

Log
AIC
BIC
2
0.0207033***
0.0205464***
0.0204798***
0.0203533***
0.7947433*
0.7281051
0.4421180
0.0730117
2508.1781
2507.3957
2507.0924
2506.5456
2506.4483
2506.4914
-4.2745126
-4.2731718
-4.2726520
-4.2717149
-4.2715482
-4.2716220
-4.2137837
-4.2124429
-4.2119231
-4.2109860
-4.2108192
-4.2108931
The coefficients of the third lag and for the intervention in the main equation were
insignificant, so they were restricted to zero (
)
 13   1  0
MODEL 2
Introducing the absolute value of interventions in the logistic
specification of the probabilities
exp( J   J * abs( I t 1 ))
p( St  j | St 1  j, abs( I t 1 )) 
1  exp( J   J * abs( I t 1 ))
Abs(It) = 0, if no intervention
abs(It) , if intervention were conducted at time t
abs(It + It-1) , if intervention were conducted in the same
direction at time t and t-1
……………………………..
abs(It + It-1 + … + It-h-1) , if intervention were conducted in
the same direction last h days
Estimates of the model with absolute
intervention variable
Parameters h=1
h=2
State 1 (high volatility)
1
1
h=3
h=4
h=5
h=6
-1.4911202
-1.5267045
-1.9000435
-2.2058554*
-2.3340316*
-2.960437**
1.8236649***
1.7766214***
1.7832594***
1.7685076***
1.7468065***
1.7349040***
State 2 (calm state)
2
0.0203094***
0.0206823***
0.0206909***
0.0206973***
0.0206520***
0.0205716***
2
11.8781973**
4.5347188**
3.4012453**
2.6910080*
1.9312174
1.3701604
3.6068717***
3.1075410***
3.0820758***
3.0433684***
3.0110835***
2.9886004***
2511.9266
2508.2045
2507.9778
2507.6832
2507.1040
2506.9194
-4.2809369
-4.2745579
-4.2741694
-4.2736646
-4.2726719
-4.2723555
-4.2202080
-4.2138289
-4.2134404
-4.2129356
-4.2119429
-4.2116266
2
Log
AIC
BIC
The coefficients of the third lag and for the intervention in the main equation were insignificant,
so they were restricted to zero (
)
 13   1  0
MODEL 3
Combining Model 1 and Model 2
PJJ 
exp( J   J * abs(Interventi ons) t -1   J * DI t 1 )
1  exp( J   J * abs(Interventi ons) t -1   J * DI t 1 )
There could be any combination of h for the two variables
Note h1 x h2 the pair with: h1 the maximum number for DIt
h2 the maximum number for abs(It)
Estimates Model 3
Parameters
State 1 (high volatility)
 1 : DI
 1 : abs(I)
1
1
5x1
h x h combinations
5 x 1 (restricted)
-2.0087014***
-2.0908710***
-0.4747301
restricted
1.7933197***
1.7809765***
restricted
restricted
-1.2684510**
-1.2825677**
15.9210006***
15.9872159***
3.9007792***
3.9040398***
0.0199909***
0.0200149***
2516.5079
2516.4649
-4.2853606
-4.2870007
-4.2159561
-4.2219340
State 2 (calm state)
 2 : DI
2
2
2
Log
AIC
BIC
: abs(I)
1.5
Smoothed probability of
being in state 1. A simple
Markov switching Model
1.0
0.5
0.0
-0.5
1997
1998
1999
2000
2001
1.5
1.0
Filtered probability of being
in state 1. Model 5x1
0.5
0.0
-0.5
1997
1998
1999
2000
2001
8.E+07
6.E+07
4.E+07
Official intervention on FX
market. Net purchases
2.E+07
0.E+00
-2.E+07
-4.E+07
-6.E+07
-8.E+07
1997
1998
1999
2000
2001
For the logistic specification of the probability in regime 1, because the
amounts hardly counts, we have:
exp( J   J * DI t 1 )
P11 
1  exp( J   J * DI t 1 )
Using the estimates of alpha and beta from model 5 x 1
P11
1.2
1.0
Inflexion point
0.8
z* = 0.85
0.6
0.4
0.2
0.0
-0.2
-2
-1
0
1
2
3
Intervention variable
5. Concluding remarks





Even if the intervention were consistent, the amounts do
not seems to count. Only the previous day count.
NBR had to reverse the direction of intervention according
to the direction of market pressure (the net purchases were
not significant when considered in levels)
In the high volatility state (1) the best effect on the
persisting probability was find to be when h = 5 (approx. a
week)
In the calm state (2) net purchases were significant in
2
increasing the depreciation rate (  > 0) . In the high
volatility state they do not (  1was restricted to zero)
The obstinacy of keep intervening is efficient in state 1 in
decreasing the probability P11, but it turn to be “perverse”
in state 2 (calm regime)
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