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.