استفاده از مدل رگراسیون بازگشت برای مداخله بازار ارز خارجی

In this empirical study, we apply the Tobit-GARCH model to investigate the intervention function of the Bank of Japan (BoJ) in the JPY/USD exchange market. The proposed model has the advantage of handling intervention data with both a majority of zero observations and conditional heteroscedasticity. Thus, the model provides better estimates of the intervention function than such conventional models as the standard Tobit, OLS, Probit, and traditional GARCH models. Results show that the intervention behavior of the BoJ is affected more by its half-year long-term target than its previous-day short-term target, and the BoJ generally follows the policy of “leaning against the wind”. The US-JP interest rate spread was never a trigger of BoJ's interventions during the sample period. The BoJ did not respond to the domestic stock index by the sales-intervention of the JPY, even when the economy was sluggish during the lost decade (1992–2004). However, its intervention behavior was significantly affected by U.S. interventions and was significantly persistent across some of the periods.

To identify what triggers interventions of a central bank in the foreign exchange market, many studies have focused on estimating the intervention (or reaction) functions of central banks (see, e.g., Alkeminders and Eijffinger, 1994, Almekinders and Eijffinger, 1996, Baillie and Osterberg, 1997, Kim and Sheen, 2002, Frenkel et al., 2005, Ito and Yabu, 2007 and Jun, 2008). In this paper, we propose an alternative method to estimate the reaction function of a central bank: the Tobit regression with GARCH errors (Tobit-GARCH hereafter). The model has not yet been applied in related studies. One of the main challenges in specifying these central bank reaction functions is that most interventions take a value of zero, which implies that the response of the dependent variable to the explanatory variables is nonlinear in the regression of the intervention function. This clearly implies that OLS estimates of the central bank intervention function (see, e.g., Eijffinger and Gruijters, 1991, Ito, 2003 and Rogers and Siklos, 2003) will be inconsistent. By separating the bank's reactions to purchases and sales and by treating them as censored from the bottom, Tobit models overcome the problem that the dependent variable takes a value of zero most of the time (see, e.g., Alkeminders and Eijffinger, 1994, Humpage, 1999, Kim and Sheen, 2002, Rogers and Siklos, 2003 and Brandner and Grech, 2005). However, if one ignores the conditional heteroscedasticity in standard Tobit models, the estimates of the coefficients will be inconsistent (see, e.g., Hurd, 1979, Arabmazar and Schmidt, 1981 and Arabmazar and Schmidt, 1982). This problem motivated us to develop a Tobit model that takes into account conditional heteroscedasticity. On the other hand, Kim and Sheen (2002) adopt a friction model (as in Almekinders and Eijffinger, 1996) to describe purchase, sale, and no interventions in a unique regression function. They specify three separate distributional assumptions for these three intervention variables.1Ozlu and Prokhorov (2008) use a threshold regression, which allows for direct modeling of the relationship between the interventions and their determinants. However, all of these studies overlooked conditional heteroscedasticity. The problem of a majority of zeros for the dependent variable can also be circumvented by using a quality dummy variable for the intervention. Probit approaches (see, e.g., Baillie and Osterberg, 1997 and Dominguez, 1998) and ordered Probit approaches (see, e.g., Frenkel et al., 2003 and Ito and Yabu, 2007) identify determinants that affect the probability of a central bank intervention.2 The ordered Probit model described by Ito and Yabu (2007) assumes that the intervention dummy takes values of 1, −1, and 0 for purchases, sales, and no intervention respectively.3 The infrequency of central bank interventions in foreign exchange markets explains the conditional heteroscedasticity in the intervention data.4 We confirm this heteroscedasticity in the present study by performing a Lagrange multiplier test of the statistical significance of the ARCH errors.5 Recognizing the prevalence of zero values for the dependent variable and the importance of conditional heteroscedasticity, we empirically apply Calzolari and Fiorentini's (1998) theoretical extension of the standard Tobit model to estimate the central bank intervention function in a way that allows for the possibility of conditional heteroscedastic error processes of the GARCH type. Because the exact likelihood function is not feasible with such a specification, Calzolari and Fiorentini (1998) propose an approximation of the likelihood function by treating the model as conditionally Gaussian. They then use Monte Carlo simulations to prove that the Tobit-GARCH model outperforms the standard Tobit model when the error terms follow a GARCH process. In the present study, we apply the Tobit-GARCH model to test six primary determinants of the Bank of Japan's (hereafter BoJ) intervention in the Japanese Yen/U.S. Dollar (JPY/USD) foreign exchange market:6 (a) daily deviations from a representative trend of the exchange rate, (b) the Fed's intervention in the New York JPY/USD exchange market, (c) the interest rate differentials between Japan and the U.S., (d) the first-business-day effect, (e) the Nikkei 500 stock index, and (f) lagged interventions. Due to the different philosophies underlying BoJ interventions, structural breaks (which really exist) are taken into account in the model.7 Central banks generally consider the trend of the exchange rate to be a potential target rate. In this paper, we find that the BoJ has significantly applied a “leaning against the wind” policy to bring the exchange rate closer (a) to its half-year long-term target from April 1, 1991 to July 2, 2004, (b) to its previous-day short-term target from June 21, 1995 to July 2, 2004, and (c) to its previous-month medium-term target from April 1, 1991 to June 20, 1995. The significance of the half-year long-term potential target for the entire sample period (April 1, 1991 to July 2, 2004) confirms the claim of LeBaron (1999) that 150-day terms are commonly used by market traders. The policy of “leaning with the wind” insignificantly occurred in some periods based on the BoJ's previous-day (short-term) potential target and its previous-month (medium-term) potential target. In other words, the leaning-with-the-wind policy was not significantly adopted by the BoJ, even when Japan suffered economic contraction during the lost decade (1992–2004) after the bubble burst. In contrast to the findings of Baillie and Osterberg (2000) and Kim and Sheen (2002), our results show that the JP-U.S. interest rate spread was never a triggering factor for BoJ intervention. The BoJ sales intervention of the JPY did not respond to changes in the domestic stock index, even when the economy was sluggish during the lost decade. Besides, the first-business-day effect never affected BoJ interventions. However, in contrast to the conclusion of Frenkel et al. (2005), the BoJ interventions were significantly affected by U.S. interventions. In addition, interventions by the BoJ were significantly persistent from April 1, 1991 to June 20, 1995 and from January 14, 2003 to July 2, 2004, but not in the period from June 21, 1995 to January 13, 2003. This result is inconsistent with that of Ito and Yabu (2007), who find persistence in the period from June 21, 1995 to January 13, 2003. This paper is organized as follows: Section 2 describes the data source, explanatory variables, and some of the basic statistics. Section 3 specifies the model both theoretically and empirically. Section 4 reports the estimates derived from the Tobit-GARCH model and compares them to estimates from the standard Tobit, OLS, traditional GARCH, and Probit models. Finally, Section 5 presents a discussion of the findings.