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Modeling the intensity of foreign exchange intervention activity Michael Frenkela,*, Christian Pierdziochb, Georg Stadtmannc a

WHU Koblenz, Otto Beisheim Graduate School of Management, Burgplatz 2, 56179, Vallendar, Germany b Institute of World Economics, Kiel, Germany c WHU Koblenz, Otto Beisheim Graduate School of Management, Germany Received 5 December 2003; accepted 10 March 2004 Available online 25 August 2004

Abstract We suggest a count data model to study the intensity with which central banks conduct foreign exchange market intervention. The application to the Swiss interventions of the 1990s suggests that it yields important insight into the determinants of intervention policy. D 2004 Elsevier B.V. All rights reserved. Keywords: Foreign exchange interventions; Reaction function; Count data model JEL classification: F31; F33

1. Introduction A number of central banks have intervened in the foreign exchange market over the past few decades in order to influence the otherwise floating exchange rate of their currency. Because several central banks have used foreign exchange market intervention, a substantial and rapidly growing literature has emerged studying the determinants and the effects of central bank interventions in the foreign exchange market.1

* Corresponding author. Tel.: +49 261 6509280; fax: +49 261 6509289. E-mail address: [email protected] (M. Frenkel). 1

For a survey of the literature, see Sarno and Taylor (2001).

0165-1765/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2004.03.036

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M. Frenkel et al. / Economics Letters 85 (2004) 347–351

To identify the factors that trigger central bank foreign exchange market intervention, it is common practice in the literature to estimate central bank reaction function models. Among such reaction functions that have recently been used in the empirical literature on foreign exchange market intervention are qualitative dependent variable models of which several variants have been used in different publications.2 We propose a qualitative dependent variable model that is particularly suited for tracing out the factors governing the intensity with which central banks intervene in the foreign exchange market. The intensity of intervention is a crucial aspect of central bank intervention policy. For example, the so-called signaling model implies that the determination of central banks and, thus, the intensity with which they defend their exchange rate target is of key importance for the effectiveness of intervention. In order to study the intensity of intervention, we make use of the stylized fact that interventions tend to occur in clusters, i.e., central banks usually intervene over a string of successive days. While the clustering of intervention has generally been acknowledged in the intervention literature, no attempt has been made so far to use the clustering of intervention as an indicator of the intensity of central bank intervention. We propose that the length of an intervention cluster, i.e., the number of consecutive intervention days, can be used as an indicator of the intensity of central bank intervention. We demonstrate the practical usefulness of our approach by examining the factors that determined the intensity with which the Swiss National Bank (SNB) conducted its interventions in the 1990s.3

2. The central bank reaction function model We use a count data model in order to study whether the length of intervention clusters is linked to the explanatory variables commonly used in the literature on estimating central bank reaction function models.4 In our count data model, the probability to observe an intervention cluster of length y t , ya{0,1,2,. . .} in period t is given by the Poisson distribution ProbðYt ¼ yt Þ ¼

exp ð kt Þkyt t ; yt !

ð1Þ

where y t and k t denote the realization of the random variable Y t and the parameter of the Poisson distribution, respectively. The parameter k t is linked to the explanatory variables of the model in the following way: lnkt ¼ bxt ; 2

ð2Þ

For example, Almekinders and Eijffinger (1994) use a tobit model, Almekinders and Eijffinger (1996) use a friction model, and Baillie and Osterberg (1997) use a probit model. 3 In contrast to the interventions of major central banks, the SNB interventions have so far only been investigated in relatively few studies (see, e.g., Dominguez and Frankel, 1993; Fischer and Zurlinden, 1999). 4 Count data models are described in some detail in, e.g., Greene (2000).

M. Frenkel et al. / Economics Letters 85 (2004) 347–351

349

Fig. 1. SFR/USD exchange rate and interventions of the Swiss National Bank. The left scale measures the SFR/USD exchange rate, the right scale measures the number of consecutive intervention days.

where blnQ denotes the natural logarithm, b denotes the (1m) vector of coefficients, and xt denotes an (1m) vector of explanatory variables. With n denoting the number of observations in the sample, the loglikelihood function, LL, can be written as

LL ¼

n X

ðyt bxt kt lnyt !Þ:

ð3Þ

t¼1

A feature of count data models based on a Poisson distribution is that the conditional mean and conditional variance of y t are identical, i.e. E( y t |xt )=Var ( y t |xt )=exp (bxt ). This is a problematic feature because empirical studies typically find Var ( y t |xt )NE( y t |xt ), a phenomenon called overdispersion. We account for overdispersion by assuming Var (bˆ)=rˆ 2VarLL(bˆ) when computing robust standard errors, where bˆ refers to estimated coefficients.

3. The interventions of the Swiss National Bank During the period 1986–1995, the SNB conducted 101 interventions in the Swiss franc/US (SFR/ USD) market.5 Typically, its interventions occurred in clusters. We have 74 intervention clusters in our sample. We plot the length of the intervention clusters in Fig. 1 together with the exchange rate. The length of the intervention clusters varied between one and four consecutive days. More than 25% of all clusters contain more than one intervention day. Also, the intensity of interventions was higher in the first half of the sample compared with the second half. Intervention intensity was highest in 1988 and 1989 when the Swiss Franc depreciated sharply against the USD. 5

The SNB did not intervene between 1996 and 2003.

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Table 1 Estimation results Specification

Constant (z-statistic)

Long-term target (z-statistic)

Medium-term target (z-statistic)

Short-term target (z-statistic)

LL

AIC

LRI

VWF

CT1

CT2

I

2.95*** (6.30) 2.88*** (6.10) 4.07*** (14.96) 3.98*** (14.15)

2.31*** (3.03) 2.26*** (2.98) 2.20* (1.73) 2.15* (1.71)

25.6*** (5.29) 26.72*** (5.40) 33.83*** (6.18) 35.43*** (6.28)

–

411.28

0.33

0.08

1.52

2.20**

1.52

0.22 (0.91) –

410.65

0.33

0.08

1.46

2.28**

1.65*

415.36

0.34

0.07

1.83

2.01**

1.13

0.26 (1.01)

414.39

0.34

0.08

1.78

2.20**

1.06

II III IV

The model was estimated by maximum likelihood. Robust standard errors were used to compute the z-statistics and a constant variance-weighting factor was applied. Because VWFN1, we use the test developed by Cameron and Trivendi pﬃﬃﬃ (1990) to test ˆ t Þ2 yt Þ=ðkˆ t 2Þ on a constant formally for overdispersion. This test is based on the t-statistic of a regression of z ¼ ððy k t t ˆ (CT1) or on k t = exp(bˆxt ) (CT2). For details on this test, see Greene (2000, pp. 884–885). *** (**, *) denotes significance at the 1 (5, 10) percent level. LL denotes the value of the maximized loglikelihood function, AIC denotes the Akaike information criterion, AICu2LL/n+2m/n, LVI denotes the likelihood ratio index LVI=1LLc/LLc, where LLc is the value of the maximized loglikelihood function containing only a constant in the vector of regressors. In models I and II, we use the deviation from PPP as a long-term target. In models III and IV, we use the deviation from 1.50 SFR/USD as a long-term exchange-rate target.

We consider three variables as potential determinants of the SNB interventions: (1) The difference between the actual SFR/USD exchange rate and a long-term exchange rate target. As the long-term exchange rate target, s t *long, we use the exchange rate implied by purchasing 6 long |, the higher is the incentive power parity: s t *long=sPPP t . The larger is the absolute wedge |s t s t * of the central bank to intervene in the foreign exchange market in order to reduce this wedge. (2) The difference between the SFR/USD and a medium-term exchange rate target. We derive a ¼ medium-term exchange rate target from the moving average of the SFR/USD, i.e., smedium t Pn ð1=nÞ i¼0 sti where n reflects the number of days used to compute the moving average. We set n=25 and use |s t s t *medium| in order to assess whether the SNB used its interventions to smooth exchange rate dynamics. (3) For a central bank seeking to calm bdisorderlyQ markets, a short-term target with respect to the foreign exchange market could be seen in low exchange rate volatility. In empirical work, this can be taken into account by using the absolute exchange rate returns preceding the intervention.7 We summarize the estimation results in Table 1. The coefficient of the medium-term exchange rate target has the expected positive sign and is significantly different from zero. The coefficient of the shortterm target is not significantly different from zero. The coefficient of the long-term target is significantly different from zero, but has an unexpected negative sign. This result and the fact that the SNB intervened in both directions, although the exchange rate was overvalued according to PPP over the entire sample 6

According to the Penn World Tables (Heston et al., 2001), the nominal SFR/USD exchange rate was in line with PPP in the beginning of 1986. We used CPI data (IFS) to compute the PPP exchange rate. 7 Alternatively, the volatility could be estimated by means of a GARCH model.

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period, indicates that the SNB did not target PPP. Therefore, as an alternative long-term target, we use 1.50 SFR/USD. This is the exchange rate level, above (below) which a maximum of interventions to strengthen (weaken) the SFR occurred. Estimation results (specifications III and IV) do not support the hypothesis that the SNB used the absolute difference of the actual exchange rate from the 1.50 SFR/USD level as a kind of an implicit long-term exchange rate target when deciding on the intensity of its interventions. The reason for this is that, as illustrated by Fig. 1, at the beginning and the end of the sample period, the deviation of the exchange rate from 1.50 SFR/USD was particularly strong. Although the central bank intervened during these periods, the intervention intensity was relatively low. We conclude that the intensity of the interventions of the SNB was mainly governed by considerations concerning the medium-run exchange rate target.

4. Conclusions In this paper, we suggest a count data model that allows studying the determinants of the intensity with which central banks conduct foreign exchange market interventions. We propose the use of the length of intervention clusters as an indicator of intervention intensity. The application to the Swiss intervention data demonstrates the usefulness of our model. The generality of the model implies that it can be used in future empirical analyses as a modeling device that yields interesting insights into the determinants of central bank interventions not revealed by the type of qualitative dependent variable models that have traditionally been used in the intervention literature.

References Almekinders, G.J., Eijffinger, S.C.W., 1994. Daily Bundesbank and Federal Reserve interventions: are they a reaction to changes in the level and volatility of the DM/$-Rate? Empirical Economics 19, 111 – 130. Almekinders, G.J., Eijffinger, S.C.W., 1996. A friction model of daily Bundesbank and Federal Reserve intervention. Journal of Banking and Finance 20, 1365 – 1380. Baillie, R.T., Osterberg, W.P., 1997. Why do central banks intervene? Journal of International Money and Finance 16 (6), 909 – 919. Dominguez, K.M., Frankel, J.A., 1993. Does foreign exchange intervention matter? The Portfolio Effect. American Economic Review 83 (5), 1356 – 1369. Fischer, A.M., Zurlinden, M., 1999. Exchange rate effects of central bank interventions: an analysis of transaction prices. Economic Journal 109, 662 – 676. Greene, W.H., 2000. Econometric Analysis, fourth ed. Prentice Hall, New Jersey. Heston, A., Summers, R., Aten, B., 2001 (December). Penn World Table Version 6.0. Center for International Comparisons at the University of Pennsylvania (CICUP). Sarno, L., Taylor, M.P., 2001. Official intervention in the foreign exchange market: is it effective and, if so, how does it work? Journal of Economic Literature 39, 839 – 868.