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
Academy of Economic Studies
Doctoral School of Finance and Banking
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
Basic features:
- the Markov property for the unobservable variable St
- the transition matrix for k states
- main equation :
- Log-likelihood :
Observation: A permanent switches/structural break – absorbing state
3.1 A Simple Markov Switching Model
))(,0( )( t ttttt SNxSy
PkkkPkP
PkPP
PkPP
P
21
22212
12111
T
t
K
i
K
jttttt jSyfiSPijYL
1 1 1111 ),,|(*),|Pr(*log)|(
Piji)S|jP(S.)k,Si,S|jP(S 1-tt2-t1-tt
3.2 Application to the Exchange rate ROL/USD
1997 1998 1999 2000 2001
The first difference of the daily
(log) exchange rate ROL/USD
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 EstimatesAR(p) representation of the daily exchange rate ROL/USDSelection Criteria:-Akaike and Schwartz-significance of each parameter
Best specification :
Log-likelihood = 3483.77 Akaike = -5.96018 Schwartz = -5.93416 Standard errors were computed from the inverse of the negative Hessian
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***
2 regimefor ),0(
1 regimefor ),0( )(2
1
N
NSCy
t
tttt
-0.5
0.0
0.5
1.0
1.5
1997 1998 1999 2000 2001
Estimated smoothed probability of being in regime 1 (high volatility)
0
100
200
300
400
500
600
-0.25 0.00 0.25 0.50 0.75 1.00
0
100
200
300
400
500
600
700
800
900
-0.25 0.00 0.25 0.50 0.75 1.00
Statistics Regime 1 Regime 2=============================================Standard deviation 0.245428 0.016161Skewness 1.235997 0.135784Kurtosis 15.200675 3.994950Informal Jarque – Bera test 1884.105 38.788
1997 1998 1999 2000 2001
Histogram of errors in Histogram of errors in
Regime 1 Regime 2
Exchange rate ROL/USD
Hamilton (1996) LM test for omitted ARCH effects and AutocorrelationStatistics Value Probability===================================================================Test for ARCH across regimes 1 and 2 123.13993 0.0000Test for Autocorrelation across regimes 0.0433623 0.9997Asym. distribution - Chi-square(4) Test for ARCH in regime 1 1.6652259 0.1969Test for Autocorrelation in regime 1 0.0269802 0.8695Asym. Distribution - Chi-square(1) Test for ARCH in regime 2 0.3690371 0.5435Test for Autocorrelation in regime 2 0.0052255 0.9425Asym. Distribution - Chi-square(1)
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
Hamilton (1996) LM test for omitted ARCH effects and Autocorrelation
Hansen nonstandard Likelihood Ratio testNull : C1 = C2 Alternative: there are switches in regimes
1 = 2
Grid search over the nuisance parameters spaceGrid 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 incrementsDifference in drift - 6 points: from 0.003 to 0.020 in 0.034 incrementsDifference in standard deviations - 6 points: from 0.01 to 0.11 in 0.02 increments
Newey-West Band width: 5 6 7 P-value 0.00 0.00 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 positionIt follow that -high volatility on FX market-appreciation of the real ROL/USD exchangeare not desirableCentral 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
In the logistic specification we use first a discrete variable
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
p
ktttktkttt ISySScy
11*)(*)()(
The variable It use in the main equation : Net purchases of foreign currency made by NBR
)*exp(1
)*exp(),|(
1
111
tJJ
tJJ
ttt DI
DIDIjSjSp
Estimates of the model with discrete intervention variable
Parameters h=1 h=2 h=3 h=4 h=5 h=6
State 1 (high volatility) -1.340246 -1.1885870* -1.4444623** -1.5940234*** -1.7356188*** -1.9135868**
State 2 (calm state)
0.0207033*** 0.0205464*** 0.0204798*** 0.0203533*** 0.0202304*** 0.0202036***
0.7947433* 0.7281051 0.4421180 0.0730117 -0.1817141 -0.2648565
Log 2508.1781 2507.3957 2507.0924 2506.5456 2506.4483 2506.4914
AIC -4.2745126 -4.2731718 -4.2726520 -4.2717149 -4.2715482 -4.2716220
BIC -4.2137837 -4.2124429 -4.2119231 -4.2109860 -4.2108192 -4.2108931
1
2
2
The coefficients of the third lag and for the intervention in the main equation were insignificant, so they were restricted to zero ( )01
31
Introducing the absolute value of interventions in the logistic specification of the probabilities
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
MODEL 2
))(*exp(1
))(*exp())(,|(
1
111
tJJ
tJJ
ttt Iabs
IabsIabsjSjSp
Estimates of the model with absolute intervention variable
Parameters h=1 h=2 h=3 h=4 h=5 h=6
State 1 (high volatility) -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)
0.0203094*** 0.0206823*** 0.0206909*** 0.0206973*** 0.0206520*** 0.0205716***
11.8781973** 4.5347188** 3.4012453** 2.6910080* 1.9312174 1.3701604
3.6068717*** 3.1075410*** 3.0820758*** 3.0433684*** 3.0110835*** 2.9886004***
Log 2511.9266 2508.2045 2507.9778 2507.6832 2507.1040 2506.9194
AIC -4.2809369 -4.2745579 -4.2741694 -4.2736646 -4.2726719 -4.2723555
BIC -4.2202080 -4.2138289 -4.2134404 -4.2129356 -4.2119429 -4.2116266
1
22
The coefficients of the third lag and for the intervention in the main equation were insignificant, so they were restricted to zero ( ) 01
31
1
2
MODEL 3
Combining Model 1 and Model 2
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)
)*ons)Interventi(*exp(1
)*ons)Interventi(*exp(
11-t
11-t
tJJJ
tJJJJJ DIabs
DIabsP
Estimates Model 3 h x h combinations
Parameters 5 x 1 5 x 1 (restricted)
State 1 (high volatility)
: DI -2.0087014*** -2.0908710***
: abs(I) -0.4747301 restricted
1.7933197*** 1.7809765***
restricted restricted
State 2 (calm state): DI -1.2684510** -1.2825677**
: abs(I) 15.9210006*** 15.9872159***
3.9007792*** 3.9040398***
0.0199909*** 0.0200149***
Log 2516.5079 2516.4649
AIC -4.2853606 -4.2870007
BIC -4.2159561 -4.2219340
11
22
1
22
1
-0.5
0.0
0.5
1.0
1.5
1997 1998 1999 2000 2001
-0.5
0.0
0.5
1.0
1.5
1997 1998 1999 2000 2001
-8.E+07
-6.E+07
-4.E+07
-2.E+07
0.E+00
2.E+07
4.E+07
6.E+07
8.E+07
1997 1998 1999 2000 2001
Smoothed probability of being in state 1. A simple Markov switching Model
Filtered probability of being in state 1. Model 5x1
Official intervention on FX market. Net purchases
)*exp(1
)*exp(
1
111
t
JJt
JJ
DI
DIP
For the logistic specification of the probability in regime 1, because the amounts hardly counts, we have:
Inflexion point
z* = 0.85
-2 -1 0 1 2 3 Intervention variable
P11
Using the estimates of alpha and beta from model 5 x 1
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
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 increasing the depreciation rate ( > 0) . In the high volatility state they do not ( was 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)
1 2
References:Ang, A. and Bekaert G. (1998), “Regime Switches In Interest Rates”, Research
Paper1486, Standford University.Antohi, D, Udrea I. And Braun H. (2002), “Mecanismul de Transmitere a Politicii
Monetare in Romania”, Paper presented at the seminar Monetary Policy Transmission in the Euro Area and in Accesion Countries, organized by ECB at Frankfurt.
Beine M., Laurent, S. and Lecourt, C. (2001), “Official Central Bank Intervention and Exchange Rate Volatility: Evidence From A Regime Switching Analysis”, Working Paper 2001-W01.202.
Cai, J. (1994), “A Markov Model Of Uncoditional Variance in ARCH”, Journal of Business and Economic Statistics, 12, 309-316.
Campbell, S. D. (2001), “Specification Testing and Semi-Parametric Estimation of Regime Switching Models: An Examination of the US Short Term Interest Rate”, University of Pennsylvania, Discussion Paper 2001-W1.
Cosslett, M. P. and Lee, L.F (1985), “Serial Correlation in Latent Discrete Variable Models”, Journal of Econometrics, 27, 79-97.
Clarida, R. H., Sarno, L, Taylor M.P and Valente, G. (2001), “The Out-of-Sample Sccess Of term Structure Models As Exchange Rate Predictors: A Step Beyond”, NBER Working Paper Series, No. 8601, Cmbridge, Massachusetts.
Dahl, C. and Hansen, N. (2002), “The Formation Of Inflation Expectations Under Changing Regimes”, Working Paper 1602-1193, Danmarks Nationalbank.
Dempster, A.P., Laird N.M. and Rubin D.B. (1977), “Maximum Likelihood From Incomplete Data via the EM Algorithm”, Journal of Royal Statistical Society B, 39, 1-38.
Diebold F. X., Lee J. H., Weinbach G. (1994), “Regime Switching with Time Varying Transition Probabilities”, in C.Hargreaves (ed.) Nonstationary Time Series Analysis and Cointegration, 283-302, New York:Oxford University Press.
Dominguez, K. and Frankel, J. (1993) Does Foreign Exchange Intervention Work ?”, Institute for Economics, Washington, DC.
Filardo, A. (1998), “Choosing Information Variables for Transition Probabilities in a Time Varying Transition Probability Markov Switching Model”, Federal Reserve Bank of Kansas City, RWP 98-09.
Hamilton, J. D. (1989), “A new Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle”, Econometrica, 57, 357-84.
Hamilton, J. D. (1990), “Analysis of Time Series Subject to Change in Regime”, Journal of Econometrics, 45, 39-70.
Hamilton, J. D. (1994), “Time Series Analysis”, Princeton, NJ: Princeton University Press.
Hamilton, J. D. and Susmel, R. (1994), “Autoregressive Conditional Heteroschedasticity and Changes in Regime”, Journal of Econometrics, 64, 307-333.
Hamilton, J. D. and Perez-Quiros G. (1996), “What Do Leading Indicators Lead ?”, The Journal of Business Volume 69, Issue 1, 27-49.
Hansen, B. E. (1992), “The Likelihood Ratio Test Under Nonstandard Conditions: Testing The Markov Switching Model of GNP”, Journal of Applied Econometrics, 7, S61-S82.
Hansen, B. E. (1996), “Erratum: The Likelihood Ratio Test Under Nonstandard Conditions: Testing The Markov Switching Model of GNP”, Journal of Applied Econometrics, 11, 195-198.
Isard, P. (1995), “Exchange Rate Economics”, Cambridge University Press.
Krolzing, H. M. (2002), “Regime Switching Models”, University of Oxford, Review Paper, 2002-W1.
Martinez-Peria, M. S. (1999), “A Regime Switching Approach to Studying Speculative Attack: A Focus on The European Monetary System Crisis”, Working Paper WPS 2132, World Bank.
Mussa, M. (1981), “The Role Of Official Intervention”, Group of Thirty Occasional Paper, no.6.
Sims, and Zha (2002), “Macroeconomic Switching”, Research Paper, W2002-1
Stix, H. (2002), “Does Central Bank Intervention Influence The Probability Of a Speculative Attack ? Evidence From the EMS”, Discussion Paper, Oesterreichische Nationalbank.
Taylor, M. P. and Sarno, L.(2001), “Official Intervention In The Foreign Exchange Market. It Is Effective And If So, How Does It Work ?”Journal of Economic Literature XXXIX, 839-868.
Tillmann, P. (2001), “Information Disparities And The Probability Of Currency Crisis”, University of Bonn, Working Paper W01-2000.