Self-selection and treatment effects: Revisiting the effectiveness of foreign exchange intervention

Self-selection and treatment effects: Revisiting the effectiveness of foreign exchange intervention

Journal of Macroeconomics 57 (2018) 299–316 Contents lists available at ScienceDirect Journal of Macroeconomics journal homepage: www.elsevier.com/l...

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Journal of Macroeconomics 57 (2018) 299–316

Contents lists available at ScienceDirect

Journal of Macroeconomics journal homepage: www.elsevier.com/locate/jmacro

Self-selection and treatment effects: Revisiting the effectiveness of foreign exchange intervention

T

Victor Pontinesa,b a b

Research and Training Centre, The South East Asian Central Banks (SEACEN), Kuala Lumpur, Malaysia. Centre for Applied Macroeconomic Analysis (CAMA), Australian National University (ANU), Canberra, Australia

A R T IC LE I N F O

ABS TRA CT

Keywords: Foreign exchange intervention Self-selection JPY/USD exchange rate Censored data Tobit Inverse probability weights Local projections

Along the lines of the treatment effects literature, this paper empirically revisits the issue of the so-called “intervention effect”, i.e., the effectiveness of official foreign exchange intervention on the movement of the exchange rate. We specifically examine the effectiveness of official daily interventions by Japanese monetary authorities in the JPY/USD market over the period from 1 January 1999 to 31 December 2011. To achieve our aim, we extended in a continuous treatment setting the inverse probability weights estimator developed by Jorda and Taylor (2015) and Angrist, Jorda and Kuersteiner (forthcoming) et al. (2018) to control for self-selection bias. In accordance with existing evidence, this paper finds that periods of intervention characterized by large, infrequent and sporadic interventions are effective in moving the changes in the exchange rate in the desired direction for the full-sample period and across two of the three sub-samples. We also find evidence that once the exchange rate moves in the desired direction, the effect is not long-lasting, but, slightly longer, contrary to existing evidence.

JEL codes: C14 C32 E52 E58 F31

1. Introduction This paper evaluates the effectiveness of official foreign exchange intervention on the movement of the exchange rate, i.e., the socalled “intervention effect”. In line with the concept of “success” or effectiveness in the literature, we examine whether official foreign exchange intervention influence or push the changes in the exchange rate (daily exchange rate returns) in the desired direction. Specifically, we assess whether official daily amounts of interventions by Japanese monetary authorities in the JPY/USD market over the period from 1 January 1999 to 31 December 2011 move changes in the JPY/USD exchange rate in the correct or desired direction. In general, the literature has not reached a definite conclusion on the effectiveness of foreign exchange intervention on the changes in the exchange rate, in fact at most times, suggesting the absence of any relation (e.g., Baillie and Humpage, 1992; Baillie and Osterberg, 1997; Hillebrand and Schnabl, 2004; Neely, 2008; Galati and Disyatat, 2005; Sarno and Taylor, 2001). Also, the survey papers of Edison (1993) and Almekinders (1995) conclude the lack of a firm relationship between intervention and exchange rate returns. In contrast, Dominguez and Frankel (1993), Ito (2003), Fatum and Hutchison (2006), Fatum and Hutchison (2010) find evidence that foreign exchange intervention tends to be effective when intervention operations are large and infrequent. Furthermore, based on results of surveys conducted among central banks, intervention is implicitly supported because it is generally believed that it is a useful and effective instrument (Neely, 2008). With respect to Japanese official foreign exchange intervention in the JPY/USD market, ever since Japanese monetary authorities

E-mail addresses: [email protected], [email protected] https://doi.org/10.1016/j.jmacro.2018.06.007 Received 7 March 2018; Received in revised form 11 June 2018; Accepted 20 June 2018 Available online 04 July 2018 0164-0704/ © 2018 Elsevier Inc. All rights reserved.

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released data on their foreign exchange intervention activities in 2001, several studies have examined the effects of Japanese foreign exchange intervention on the daily changes of the JPY/USD exchange rate. Takagi (2014) reviewed 30 such studies that examined intervention data for the period April 1991 to March 2004, and reflective of the above general literature on this issue, finds contrasting evidence on its effectiveness. However, towards the end of his survey, Takagi (2014) suggested that, on average, Japanese official foreign exchange intervention moves the changes in the JPY/USD exchange rate in the desired direction when the scale is large, and intervention is infrequent. Conducting our empirical examination for the full sample period and across three separate sub-samples (i.e., January 1999December 2002; January 2003-March 2004; and, September 2010-December 2011),1 we also find that Japanese official foreign exchange intervention influences the changes in the JPY/USD exchange rate in the desired direction (i.e., sales of JPY against purchases of USD leads to appreciation of the USD vis-à-vis the JPY) when the scale is large, and intervention is infrequent for the fullsample as well as across two of the three sub-samples. Furthermore, this study contributes to the literature in four different ways. First, previous studies that examined the effectiveness of Japanese official foreign exchange intervention have typically covered the period from April 1991 to March 2004. This study is one of the first2 to investigate the issue of the effectiveness of Japanese foreign exchange intervention for the period of September 2010 to December 2011, that is, the period that followed the 6½ years of no intervention by Japanese monetary authorities since March 2004. Second, to the best of our knowledge, the literature, including previous studies that investigated evidence of the effectiveness of Japanese official foreign exchange interventions on the duration of the effectiveness of foreign exchange intervention has been relatively scarce. An exception is the study by Nagayasu (2004) which examined earlier data on Japanese foreign exchange intervention over the period April 1, 1991 to September 28, 2001 and found, using GARCH-like specifications, of an intervention effect on the changes in the JPY/USD exchange rate which lasts only a day when the intervention take place. In contrast to Nagayasu (2004), our study covers a much later period of Japanese foreign exchange intervention. More importantly, while our study also finds that this intervention effect is short-lived, we obtain results over the full-sample period and across two of the three sub-samples, which indicate that the duration of this intervention effect is slightly longer, lasting for two days after the intervention takes place. Third, in line with the findings of Chaboud and Humpage (2005) and Fatum and Hutchison (2005, 2010) we find that for the sub-period of January 2003-March 2004, Japanese official foreign exchange interventions were ineffective in moving the changes in the JPY/USD exchange rate in the desired direction. However, we also obtain results which indicate that Japanese official foreign exchange interventions during this period had some undesired or “perverse” result of moving the exchange rate in an erroneous direction. The battery of robustness tests we conducted in this study tended to validate all these results. Finally, we obtained the above results using a novel econometric method that address a particular source of endogeneity − selfselection bias − the bias that occurs when the decision to officially intervene in the foreign exchange market is not taken at random. Specifically, we employ a modern technique on the treatment effect literature to confront this problem of self-selection bias. The way the technique works is that it creates a pseudo-population that mimics a situation of “as if” the decision to intervene had been taken at random and then performing a weighted linear Local Projections (LP) due to Jorda (2005) to eventually uncover the causal effect of Japanese official foreign exchange interventions on the changes in the JPY/USD exchange rate in various horizons. This technique has been called the “doubly robust” inverse probability weighted (IPW) estimator based on the works of Jorda and Taylor (2015) and Angrist et al. (2018). In this paper, we extend the application of the IPW estimator in a continuous treatment setting.3 At the same time, we also note that careful attempt has been made to follow the method commonly employed in this literature to achieve a clear identification of the causal effect of Japanese foreign exchange intervention on the changes in the JPY/USD exchange rate. This involves adopting a two-stage estimation to control for another particular source of endogeneity (i.e., simultaneity bias or reverse causality) in which the predicted values obtained from a Japanese intervention reaction function estimated in the first-stage is used as an instrumental variable for contemporaneous intervention in the second stage estimation, which then links the changes in the JPY/USD exchange rate to the official Japanese foreign exchange intervention (e.g., Kearns and Rigobon, 2005; Galati and Melick, 2002; Galati et al., 2005; Fatum and Yamamoto, 2014). In addition, because there is a non-negligible proportion of zero values in the intervention data, we also adopted the strategy of modeling the intervention reaction function as a censored variable (e.g., Almekinders and Eijffinger, 1994; Humpage, 1999; Kim and Sheen, 2002; Rogers and Siklos, 2003; Brandner and Grech, 2005; Adler and Tovar, 2014). Also, to the best of our knowledge, the technique we employed in this study to address the problem of self-selection bias is the first such application that investigates the effectiveness of foreign exchange interventions. The only previous study we can find related to ours which also employs the modern technique from the treatment effect literature is by Fatum and Hutchison (2010). However, unlike ours, this study uses propensity score and matching techniques to assess the effectiveness of Japanese foreign exchange intervention. Their method is carried out by also first estimating an intervention reaction function, but instead of using the actual

1 Aside from being established by previous studies, we would see later on in the analysis that these three subsamples were determined based on a careful analysis of the raw intervention data and by formal structural break analysis. 2 Another study that we are aware of which looked at this same period is Fatum and Yamamoto (2014) which used non-temporal threshold analysis to investigate the exchange rate effects of large and small interventions. 3 Following the treatment effects literature, treatment refers to the decision by monetary authorities to intervene in the foreign exchange market. The extension is made in a continuous treatment setting because the actual daily amounts of intervention is used in the construction of the inverse probability weights rather than converting the intervention data as an indicator variable that takes on the value of 1 on days when there is intervention and 0 otherwise. More discussion on this aspect follows in subsequent sections.

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official amounts of Japanese foreign exchange intervention as the dependent variable, the intervention data were converted into binary variables to reflect intervention or no intervention. From this estimation, logit or propensity scores were obtained from which a particular observation of changes in JPY/USD exchange rate coinciding with intervention (the treatment observation) is matched with another observation of changes in JPY/USD exchange rate that coincides with no intervention (the control or “counterfactual” observation). The matching of pairs of observations were done using a matching mechanism (i.e., nearest-neighbor technique) based on observations that have quite similar propensity scores. The treatment or intervention effect is then obtained by comparing the means of the changes in JPY/USD exchange rate between the treatment and control group. Although, not reported as a problem that was encountered in the Fatum and Hutchison (2010) study, the main issue raised in general with the use of such matching technique, particularly those based on nearest-neighbor technique is that one would typically encounter a dilemma between incomplete matching and inaccurate matching. That is, while trying to maximize exact matches, cases may be excluded due to incomplete matching, or while trying to maximize cases, more inexact matching typically results (Guo and Fraser, 2015). This paper is structured as follows. The next section gives a description of the institutional details of Japanese intervention in the foreign exchange market as well as the Japanese intervention data. The third section discusses the empirical strategies employed in the paper. The fourth section presents the empirical results and the battery of robustness tests. The fifth section concludes. 2. Institutional details and data 2.1. Institutional details Typically, the principal institution that decides on intervention is either the Ministry of Finance (the Treasury) or the Central Bank, or both. In Japan, it is the Ministry of Finance (MOF) that makes the decision on intervention,4 although intervention operations are done in consultation with the Bank of Japan (BoJ), who carries out orders as an agent or broker of the government. It is, therefore, appropriate to refer to the MOF and the BoJ collectively as the Japanese monetary authorities. The decision to intervene at the MOF typically involves four people: Minister, Vice Minister for International Affairs, Director General of the International Bureau, and the Director of the Foreign Exchange and Money Market Division. The Finance Minister has to be notified of the intervention strategy before interventions take place, but day-to-day operations are left to the three bureaucrats (Fatum and Hutchison, 2005; Ito, 2007; Takagi, 2014). When intervention operations are carried out, an account of the government called the Foreign Exchange Fund Special Account (FEFSA) is used. This fund comprises of foreign currency funds and yen funds. For intervention to sell the yen and buy foreign currency, financing bills (short-term government bills with maturity of three months) are issued by the MOF to the market to obtain yen funds for the FEFSA, which in turn, is used to purchase the foreign currency denominated assets. So, in a technical sense, the intervention is automatically sterilized. Foreign exchange interventions are usually carried out in the Tokyo market. When trading shifts to the European markets around 5:00 p.m. JST and then to the New York market, the BoJ requests foreign monetary authorities to conduct interventions on behalf of the Bank. The final decision to use this method is made by the MOF. When a foreign monetary authority conducts the interventions on behalf of the BoJ, it is the foreign monetary authority that shows up as the contracting party in the transactions. However, this is not considered concerted or coordinated intervention as intervention is defined by whose money is used, not who is transacting in the market (Fatum and Hutchison, 2005; Ito, 2003, 2007). 2.2. Data The period of study is from 1 January 1999 to 31 December 2011 during which all official daily amounts of interventions in the JPY/USD market were sales of JPY against purchases of USD. The advantage of examining periods of interventions in one direction rules out the possibility that “negative” interventions are simply observed opposite interventions (i.e., selling instead of buying and vice versa).5 The data are available from the MOF website and the items provided are as follows: (i) the date of intervention; (b) the yen amount and direction (sold/bought) of intervention for the day; and, (iii) currencies that are involved in intervention. The disclosed data, therefore, does not contain information on the following: (i) exact time of the day (hour, minute, second) of all transactions from the intervention order; (ii) the market (Tokyo, London, or New York) where the intervention was carried out, and; (iii) the exact exchange rate that intervention was carried out. With the exception of the 18 March 2011 coordinated intervention by G7 economies to stem the strength of the yen against the US dollar in the wake of the Tohoku earthquake and Fukushima meltdown, the BoJ was strictly the only one active in the JPY/USD market during the period of study. The US Federal Reserve which was also active in the JPY/USD market prior to the period of study, had stopped intervening since June 1998 (Reitz and Taylor, 2012).6 The first column of Table 1 shows that during this period, intervention by Japanese monetary authorities occurred on a total of 167 days. The daily intervention amount ranges from USD 1 The Foreign Exchange and Foreign Trade Law stipulates that the “Minister of Finance shall endeavour to stabilize the external value of the yen through foreign exchange trading and other measures” (Article 7, Section 3). 5 Almekinders and Eijffinger (1994) use a similar argument in selecting daily interventions in one direction to examine the effectiveness of interventions by the German Bundesbank and US Federal Reserve. 6 While there were instances during the period of study in which the European Central Bank and the US Federal Reserve operated on behalf of the BoJ, as discussed in the previous sub-section these transactions were not considered concerted intervention. 4

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Table 1 Official Japanese intervention, 1 January 1999 to December 31, 2011. Source: Author's calculations. Full sample: January 1999 – December 2011 (1)

Sample 1: January 1999 – December 2002 (2)

Sample 2: January 2003 – March 2004 (3)

Sample 3: September 2010 – December 2011 (4)

Total intervention days Average daily amount

167 4134

30 4977

129 2520

8 29,330

Maximum daily amount Minimum daily amount >1000 >500 >250 >0

102,426 1 121 21 5 20

13,211 804 28 2 0 0

15,568 1 85 19 5 20

102,426 2916 8 0 0 0

Notes: (a) Daily Japanese intervention data obtained from the Japanese Ministry of Finance statistics. (b) All amounts are in millions of USD. Average daily amount refers to intervention days only. (c) Daily intervention operations of USD 1000 million or greater: > 1000; daily intervention operations of USD 500 million or greater, but less than USD 1000 million: > 500; daily intervention operations of USD 250 million or greater, but less than USD 500 million: > 250; daily intervention operations of less than USD 250 million: > 0.

million to USD 102 billion, while the average intervention amount is USD 4.1 billion. The extent of intervention on most days of intervention is quite substantial with purchases of USD 1000 million and larger being more prevalent (i.e., 121 days) as compared to 46 days of reported purchases of less than USD 1000 million and only 20 days of reported purchases of less than USD 250 million.7 Columns two to four of Table 1 further provide a description of the official daily amounts of intervention by Japanese monetary authorities in the JPY/USD market across three sub-samples. Column two shows that only 30 days of intervention occurred during the first four years of the period, with the magnitude of intervention being substantial, i.e., all these days of reported intervention were purchases of USD 500 million and larger. Between January 2003 to March 2004, interventions occurred for 129 days, for which during this sub-sample, the extent of intervention on most days of intervention was quite substantial with purchases of USD 1000 million and larger dominated (i.e., 85 days) as compared to 44 days of reported purchases of USD of less than USD 1000 million and only 20 days of reported purchases of less than USD 250 million. One then notes from this description of the intervention data that while the scale of intervention was relatively large in both sub-periods, the frequency of intervention between the two sub-periods was different. In the first sub-sample (January 1999 to December 2002) interventions were infrequent as opposed to the second subsample (January 2003 to March 2004) for which interventions can be described as frequent. This importantly suggests that the two sub-samples represent two contrasting intervention tactics. Panel A of Fig. 1 depicts these two contrasting intervention tactics on the part of Japanese monetary authorities. The figure shows the relatively large amounts of interventions in both sub-samples, averaging USD 5 billion (column 2, Table 1) during the first subsample, and USD 2.5 billion (column 3, Table 1) during the second sub-sample. At the same time, the more pronounced clustered occurrence of daily intervention during the second sub-sample as opposed to the first sub-sample observed in Panel A of Fig. 1, indicates the more frequent intervention on the part of Japanese monetary authorities during the former. Indeed, the observation that these two sub-samples represent contrasting intervention tactics affirms what Ito (2003, 2007), Chaboud and Humpage (2005), Fatum and Hutchison (2005, 2010), Takagi (2014) and others have established for these two subsamples. The first sub-sample belongs to the period when Mr. Sakakibara was the then Vice Minister of MOF until July 1999 when he was succeeded by Mr. Kuroda who served in the same capacity until January 2003. Both shared the same philosophy towards intervention: infrequent, large amount of intervention is most effective. The second sub-sample exactly coincide with the period when Mr. Mizoguchi replaced Mr. Kuroda as Vice Minister. Mr. Mizoguchi had an approach to intervention different from his two predecessors. During his time, interventions were also large-scale but were frequent. After the intervention conducted on 16 March 2004, there was six-and-a-half years of no reported intervention, which then ended in September 2010 when Japanese monetary authorities returned to intervene in the JPY/USD market. Therefore, the start of this period must be considered a separate period in intervention by Japanese monetary authorities in the JPY/USD market. The last column of Table 1 describes the official daily amounts of intervention by Japanese monetary authorities in the JPY/USD market during the last sub-sample, September 2010 to December 2011. Beyond this sub-period, there has been no reported intervention by Japanese monetary authorities. The magnitude and frequency of intervention conducted by Japanese monetary authorities during this last sub-period was dramatic. Intervention was only carried out on 8 days, but for all these days of intervention, there were purchases of USD 1000 million and larger, with the average amount of USD 29 billion, and daily intervention amount that ranged from USD 2.9 billion to an astounding

7

This idea of an intervention frequency follows from Fatum and Hutchison (2010). 302

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Fig. 1. Panel A. Daily Intervention volume (in millions of USD), 1 January 1999 to March 31, 2004 Panel B. Daily Intervention volume (in millions of USD), 1 January 1999 to December 31, 2011 Source: Raw data obtained from the Japanese MOF website.

USD 102 billion.8 Aside from the sporadic incidence of intervention during this sub-sample, the sheer scale of the intervention overshadowed the magnitude of intervention in the first two sub-samples (Panel B, Fig. 1). The empirical analysis conducted in subsequent sections of this paper is for the entire period under study as well as for these three sub-samples.

8 Nevertheless, because this sub-sample spans only 8 intervention days, we note that any results pertaining to this sub-sample should be treated with caution. Furthermore, we must also note at this point that since overall turnover in the JPY/USD market has increased over the entire duration of the study, a USD 1 million intervention undertaken in 1999 is relative to market size larger than USD 1 million intervention undertaken in 2011. We thank an anonymous referee for bringing out these two important points.

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3. Estimation strategy Addressing the problem of endogeneity to clearly isolate the causal effect of foreign exchange intervention is a recognized challenge in the literature. Specifically, there are two reasons why foreign exchange intervention can be endogenous, and as such render any estimate of the effect of Japanese foreign exchange intervention on the changes in the JPY/USD exchange rate inconsistent. These two threats to a clear identification of the causal effect are simultaneity (reverse causality) and self-selection bias. With regards to the former, the two-way causation between Japanese foreign exchange intervention and the changes in the JPY/USD exchange rate complicates causal inference because while our main aim is to uncover the effect of Japanese foreign exchange intervention on the changes in the JPY/USD exchange rate, Japanese monetary authorities may also be prompted to intervene when the changes in the JPY/USD exchange rate moves in the contrary direction. With regards to the latter, the decision to intervene by Japanese monetary authorities is not a random occurrence. The bias occurs because when authorities choose the amounts of their official foreign intervention, the decision is influenced by various observed variables (also known as “confounding factors”), rather than having the amounts of their official interventions determined upon them as would be the case in a randomly-controlled experiment, which is, obviously, impossible or impractical to do when dealing with observed data. In this sense, self-selection bias is similar to omitted variable bias as there are excluded variables (i.e., confounders) that correlate with the amounts of official foreign exchange intervention and the changes in JPY/USD exchange rate. Because of this, it then necessitates the need to first model the selection decision by the Japanese authorities as a function of observed confounders, which in our case, is achieved by the estimation of the intervention reaction function by the Japanese monetary authorities. To control for simultaneity, this paper follows the literature by taking a two-stage estimation procedure. In the first stage, a Japanese official intervention reaction function is estimated and the predicted values from this estimation are used as an instrument for Japanese contemporaneous official intervention in the second stage. In addition, because a non-negligible proportion of the observations for the dependent variable in the reaction function (i.e., amount of intervention by Japanese authorities) is zero, the reaction function is modeled as a censored variable with the estimation conducted using a Tobit model. The second stage entails estimating an outcome equation that links the daily changes in the JPY/USD exchange rate to Japanese official interventions. The contribution of this paper is from the aspect of controlling the second source of the endogeneity problem, i.e., self-selection bias. To confront this problem, we rely on the recently developed IPW estimator advocated by Jorda and Taylor (2015) and Angrist et al. (2018). Specifically, inverse probability weights are constructed from the first stage estimation of the Japanese official intervention reaction function, then the linear LP of Jorda (2005) are employed in the second stage estimation of the outcome equation with weights obtained from the inverse probability weights. Treating intervention as a “treatment” and using the actual official amounts of Japanese foreign exchange intervention (rather than converting the official amounts to a binary variable to reflect intervention or no intervention) we then extend the construction of the inverse probability weights in a continuous treatment setting. The self-selection bias in Japanese official foreign exchange intervention is addressed because the observations in the second stage estimation of the outcome equation are rebalanced using the inverse probability weights by effectively creating a pseudo-population in which the explanatory variables (our confounders) from the first-stage intervention reaction function and the official intervention or “treatment” variable are independent of each other. This then implies that we mimic a situation of “as if” the decision to intervene by Japanese intervention authorities had been taken at random. Finally, by projecting the daily changes of the JPY/USD exchange rate through the linear LP, the effect of Japanese official exchange rate intervention on the JPY/ USD exchange rate is assessed at each horizon. This summary of the approaches employed in this paper is elaborated below. 3.1. Intervention reaction function As earlier mentioned, to extract the predicted values of Japanese official intervention to be used as instruments for the second stage estimation of the outcome equation as well as to facilitate the construction of the inverse probability weights, an intervention reaction function is estimated in the first stage. The reaction function is modeled as a censored variable, given that all the official intervention operations over the sample period are sales of Japanese yen against US dollar purchases and a non-trivial proportion of zero intervention operation by Japanese monetary authorities during the same period:

INTt=max {0,α 0 + β0 EXR , t − 1 + β1 MA21EXR , t − 1 + β2 YEAREXR , t − 1 3

+ β3 125EXR , t − 1 + ∑ j = 1 β4 INT, t − 1 + ɛt

(1)

where INT is the actual intervention amount in billions of USD, EXR is the first-difference of the logarithm of the JPY/USD exchange rate, MA21EXR is the 21-day moving average of the logarithm of the JPY/USD exchange rate, YEAREXR is the 1-year moving average of the logarithm of the JPY/USD exchange rate, 125EXR is the first difference of the logarithm of the JPY/USD exchange rate deviation from an exchange rate target of 125 JPY/USD, and ε is the error term. The above reaction function is estimated over the full sample period and separately across the three sub-samples using a Tobit model with heteroscedasticity and autocorrelation (HAC) consistent standard errors. The choice of the explanatory variables to include in the above reaction function, which effectively are our observed confounders follows Ito (2003), Ito and Yabu (2007), Fatum and Hutchison (2010) and Fatum and Yamamoto (2014).9 9 For instance, Ito (2003), Ito and Yabu (2007) conjecture that apart from the previous day's JPY/USD exchange rate, the past trends, i.e., the 21 business days (one-month) and the 260 business days (one-year) in the JPY/USD exchange rate play an important role in prompting Japanese authorities to intervene.

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3.2. Inverse probability weights This sub-section discusses the extension of the construction of the inverse probability weights in a continuous treatment setting. The first-stage estimation of the intervention reaction function provides an appropriate set-up to construct the inverse probability weights designed to simulate a setting in which the decision to intervene is random. If, in the simple case that the dependent variable, INT, in Eq. (1) is an indicator variable that takes on the value of 1 on days when there is intervention and 0 otherwise, the inverse probability weights are constructed by estimating in the first-stage, the propensity scores or predicted probabilities of Japanese official intervention, and then obtaining the inverse of these propensity scores to weight the observations.10 Constructing the inverse probability weights in this fashion have been carried out in a few recent studies that examine various other issues in macroeconomics and finance.11 However, we avoid carrying out the analysis in the above manner as this implies a loss of information with our Japanese official intervention data. Nonetheless, the weights can still be straightforwardly constructed in a non-discrete treatment such as the case on hand. In this case, conditional densities from the first stage Tobit estimation of the Japanese intervention reaction functions are used to construct the inverse probability weights. Robins et al., (2000) recommended that inverse probability weights in a continuous treatment setting be constructed as follows: 12

Inverse Probability Weights=

f (INT) f (INT X)

(2)

where the denominator, also referred to in the treatment-effects literature as the generalized propensity score (GPS), is the conditional density derived from the estimation of the Japanese official intervention reaction function from Eq. (1) above.13 The numerator is the marginal density of INT which is simply obtained from a Tobit estimation of the Japanese official intervention reaction function that only includes the intercept term and without the explanatory variables from Eq. (1). Hence, the extent to which the official intervention or treatment variable is confounded can be assessed by a comparison of these two densities in the numerator and denominator of Eq. (2). That is, the closer the ratio is to 1, the less is the confounding. Finally, noting that we modeled the Japanese official intervention reaction function as a censored variable, its density function would be given as follows:

INT − μ ⎫d ⎧ μ 1−d 1 ⎞ · 1 − Φ⎛ ⎞⎫ f (INT) = ⎧ ϕ ⎛ ⎨ σ ⎝ σ ⎠⎬ ⎠⎬ ⎩ ⎭ ⎭ ⎨ ⎩σ ⎝

(3)

letting d = 1 denote the censoring indicator that a particular observation of INT is not censored, while d = 0 indicate a censored INT observation, Eq. (3) then suggests that this density function has two components. The first term corresponds to the contribution of the uncensored observations of INT to the likelihood, while the second term reflects the contribution to the likelihood of the censored observations of INT. 3.3. Outcome equation – linear local projections (LPs) with inverse probability weights Once the inverse probability weights are constructed, the final step is to bring everything together through the estimation of the outcome equation that links the daily returns in the JPY/USD exchange rate to Japanese official foreign exchange intervention. The estimation of the outcome equation then serves as the second plank of the IPW estimator. Based on the so-called selection-onobservable assumption (or conditional independence assumption (CIA)) expressed as follows:

EXR ⊥ INT Z,

(4)

for all INT

The IPW estimator then provides a convenient empirical strategy that automatically converts Eq. (4) into a causal effect. Introduced by Jorda (2005), the linear LP involves estimating the following set of h-step ahead predictive regressions of the changes in JPY/USD exchange rate:

t + EXR t + h = α h + β h INT

p

∑i =1 γih Zit +

ϵth+ h

(5)

 is the intervention substituted by the predicted values of Japanese official intervention from the where EXR is defined as before, INT  and we set the lag first-stage estimation of the intervention reaction as the instrument,14 Z include lagged values of EXR and INT 10 Typically, the weights are so called “stabilized” to counter large weights where a few observations drive the results of the analysis. Instead of taking a simple inverse of the propensity scores, stabilized weights are constructed by replacing the numerator (which is 1) by the proportion of the treated observations (for the treatment observations) and the proportion of the control observations (for the control observations). Stabilized weights tend to produce estimates that have smaller variance. 11 For instance, Kuvshinov and Zimmermann (2016) on the estimation of the cost of sovereign default; Bordon et al. (2016) on the role of the business cycle and macroeconomic policies in the impact of structural reforms; Jorda, et al. (2016) on the long-run financial stability risks of real estate lending booms; Diniz (2016) on the effects of fiscal austerity measures. 12 This is the formula for stabilized weights referred to in footnote 10. 13 This also follows from the work of Hirano and Imbens (2004) for continuous treatments. 14 Adler and Tovar (2014) refer to these predicted values as the shadow intervention values.

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length to nine,15 and ϵth+ h is a prediction error term. The linear LP involves the estimation of separate linear regressions of the changes in JPY/USD exchange rate for each period or horizon (i.e., h + 1). For the first horizon, for instance, the changes in the JPY/USD in time t is regressed on the contemporaneous term of the predicted values of Japanese official intervention and up to nine lags selected for this same variable of the predicted values of official intervention as well as the changes in the JPY/USD exchange rate. For the second horizon, the changes in the JPY/USD in time t + 1 is regressed on the same (not re-dated) set of explanatory variables. One advantage that the linear LP brings forth and perhaps account for its rising usage in empirical applications is that it is less vulnerable to mis-specification. This is due to the estimation in each horizon involving its own regression as opposed, for instance, to relying on the iteration of previously, possibly mis-specified expectations as one may have in VAR impulse responses. We estimate Eq. (5) with weighted least squares (WLS) up to horizon h = 10 (i.e., ten days) using weights defined by the inverse probability weights in Eq. (2). In doing so, the weights simulate a situation of “as if” the decision to intervene by Japanese monetary authorities had been taken at random by rebalancing the observations so that the official intervention variable is unconfounded. Performing a weighted regression on the rebalanced data is conceptually identical to performing an unweighted, ordinary regression in the created pseudo-population in which the confounders and the official intervention or treatment variable are independent of each other. Because we are interested in the estimation of the impact on EXRt+h with respect to a change in the predicted values of  for h ranging from 1 to 10, keeping all other variables constant, the estimate of the regression coefficient βh at each intervention, INT, horizon is then the causal effect of interest, as this denotes the effect of Japanese official foreign exchange intervention on the changes of the JPY/USD exchange rate. The technique just laid out above and implemented in the empirical analysis that follows is considered doubly-robust to misspecification.16 The reason being that consistent estimates are still produced even if one of the regression in stages one and two is incorrectly specified. In other words, only one of the two stages of estimation needs to be correctly specified to produce consistent estimates. 4. Results 4.1. Baseline estimates We begin by first reporting our baseline estimates of the first-stage intervention reaction function (Eq. (1)) and the second-stage outcome equation (Eq. (5)). Ordinary least squares (OLS) were used in the baseline estimations. As mentioned, we conduct all estimations over the full sample period and separately across the three sub-samples. We estimate the first-stage intervention reaction function by first including all explanatory variables in Eq. (1). The insignificant explanatory variables are then excluded, and a reduced reaction function is re-estimated across all samples. These reduced reaction functions estimated using OLS are presented in Table A1. The significant variables differ across the full sample (column 1) and three sub-samples (columns two to four). The significant variables in the reduced estimates suggest that intervention reacts to the previous day changes in the JPY/USD exchange rate (except in the third sub-sample), and intervention conducted on a given day is affected by the intervention carried out in the previous day (across all samples) as well as two (except in the first sub-sample) and three days ago (except in the first and second subsample). These latter results across different sub-samples suggest that the conduct of interventions is clustered.17 We next report our baseline estimates of Eq. (5), the second-stage outcome equation. We estimate this model using the linear LP advocated by Jorda (2005), but without the inverse probability weights. Given that in each horizon, we are interested in the estimated coefficient of the contemporaneous term for intervention, we show the causal effect of intervention on the changes in the JPY/ USD exchange rate from the sequence of estimates for this coefficient, i.e., the intervention effects.18 Table 2 displays the results. For the full sample and three sub-samples, we do not find any significant influence of intervention across all horizons, with the exception of a significantly negative effect of intervention in period five (January 1999 to December 2002 sub-sample). However, this effect is of the “wrong” sign. 4.2. Linear LP with inverse probability weights Before we present the analysis of the second-stage outcome equation using linear LP with inverse probability weights, we first discuss the results of the estimation of the first-stage intervention reaction function. One of the challenges in specifying these intervention reaction functions is that on most days, intervention takes a value of zero because the central bank does not intervene in the foreign exchange market. This implies that the OLS estimates of these reaction functions, such as the baseline estimates we presented earlier, are inconsistent. Modelling the reaction function as a censored variable and estimating using a Tobit model across the four samples overcomes this problem. We again estimate the first-stage intervention reaction function by first including all explanatory variables in Eq. (1), then 15

Based on the Akaike information criterion. See Lunceford and Davidian (2004) and Glynn and Quinn (2010) in the case of binary treatments, while Zhang et al. (2016) in the case of continuous treatments. 17 Fatum and Hutchison (2010) make a similar point. 18 Both variables, the changes in JPY/USD exchange rate and the predicted values of intervention were found to be stationary according to standard ADF unit-root tests. 16

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Table 2 Causal effects of intervention on changes in yen-US dollar rate estimated using Local Projections: Baseline estimates. Source: Author's calculations. Horizon

Full sample: January 1999 – December 2011 Sub-sample 1: January 1999 – December 2002 Sub-sample 2: January 2003 – March 2004 Sub-sample 3: September 2010 – December 2011

1

2

3

4

5

6

7

8

9

10

−1.17 (0.722) −0.464 (0.370) 0.012 (0.488) 2.02 (1.29)

−0.216 (0.724) 0.149 (0.370) −0.271 (0.491) −0.705 (1.31)

−0.151 (0.724) 0.271 (0.370) 0.477 (0.491) −1.52 (1.31)

−0.161 (0.724) 0.005 (0.037) 0.607 (0.492) −1.16 (1.31)

0.022 (0.724) −1.13*** (0.370) −0.426 (0.492) −0.868 (1.31)

−0.649 (0.724) 0.143 (0.373) −0.053 (0.495) 0.210 (1.31)

0.094 (0.724) −0.365 (0.372) −0.951* (0.495) 0.435 (1.32)

−0.597 (0.723) −0.010 (0.373) 0.281 (0.500) 0.203 (1.32)

−0.645 (0.723) −0.059 (0.372) −0.232 (0.496) −0.090 (1.32)

−0.400 (0.723) −0.465 (0.372) −0.368 (0.494) −0.981 (1.33)

Notes: (a) For each horizon, the dynamic causal effect of intervention on changes in yen-US dollar rate is the estimated coefficient of βh in Eq. (5) in the main text using Local Projections, but without inverse probability weights. The estimate of this coefficient is the impact on EXRt+h with respect  , keeping all other variables constant. The predicted values of intervention, INT  , are obtained to a change in the predicted values of intervention, INT from an OLS estimation of Eq. (1) in the main text. (b) Estimation by Local Projection uses 9 lags of Zit in Eq. (5) in the main text. (c) Values in parentheses are the estimated standard errors. (d) *, **, ***: Significant at 10%, 5% and 1% levels, respectively.

Table 3 Intervention reaction functions: Tobit estimates. Source: Author's calculations. Full sample: January 1999 – December 2011 (1)

Sample 1: January 1999 – December 2002 (2)

Sample 2: January 2003 – March 2004 (3)

Sample 3: September 2010 – December 2011 (4)

n.a.

INT,

t-1

INT,

t-2

INT,

t-3

0.805*** (0.123) 0.642*** (0.116) n.a.

−144.74** (62.18) 238.74* (136.48) 0.700** (0.348) 0.709** (0.349) n.a.

−208.71*** (78.89) −64.83* (39.09) n.a.

YEAREXR,t-1

−98.26 (74.80) −3.53** (1.62) −63.05* (34.42) 79.38* (40.78) 1.21** (0.548) 1.77*** (0.525) n.a.

−445.16 (440.68) n.a.

MA21EXR,t-1

−24.33*** (1.94) −2.60*** (0.805) n.a.

−1030.69 3193

−160.18 986

−73.56 307

Constant EXR,

t-1

Log L Observations

n.a. 4.49** (2.18) 1.07* (0.585) 1.75* (1.02) −55.60 327

Notes: (a) Heteroscedasticity and autocorrelation consistent standard errors in parentheses. (b) The estimated intervention reaction functions are defined in equation (X) in the text. (c) The dependent variable, INT, is the official intervention amount in millions of USD. (d) The independent variables are defined as: EXR is the first-difference of the log of the JPY per USD exchange rate; MA21EXR is the 21-day moving average of the log of the JPY per USD exchange rate; YEAREXR is the 1-year moving average of the log of the JPY per USD exchange rate; and lagged amounts of INT. (e) n.a. indicates that the variable is omitted due to lack of significance. * significant at 10% level; ** significant at 5% level; *** significant at 1% level.

excluding the insignificant explanatory variables, and re-estimating the reduced reaction function across all samples. This time, the common results across all samples is the insignificance of the lone variable, lagged YEAREXR. The Tobit estimates of the reduced reaction functions are presented in Table 3. The significant variables for the full sample (column 1) are lagged EXR and the one and two period lags of INT, and, similar to baseline estimates, the significant variables differ across the three sub-samples (columns to four). The significant variables in the reduced estimates suggest that intervention reacts to the previous day's changes in the JPY/USD exchange rate (except in the second sub-sample), the 21-day moving average of the exchange rate (MA21EXR) and 1-year moving

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Table 4 Tests of structural change. Source: Author's calculations.

Sub-sample 1 Sub-sample 2

Sub-sample 2 Sub-sample 3

LR-statistic

p-value

955.38 2666.77

0.00*** 0.00***

Notes: (a) The Andrews (1993) test is used to formally test for structural change. The test relies on a general set of assumptions that remain valid for a broad class of estimators including maximum likelihood. The test is then conducted on the Tobit estimates of the intervention reaction functions reported in Table 2 which were obtained using maximum likelihood. (b) The null hypothesis of this likelihood ratio test is that the two sub-samples in the first two columns of the table are the same (no structural change) as opposed to the alternative hypothesis that the two are different (with structural change). (c) The likelihood ratio test statistic is defined as: LR = 2 [l1 (β )1 + l2 (β )2 − l (β )] where l1 (⋅) and l2 (⋅) are the loglikelihood before and after the break, respectively, while, l (⋅) is the log-likelihood for the entire sample that encompasses the before and after break periods. (d) Because the periods for subsample 2 and 3 are not contiguous, l (⋅) is evaluated in the second row of the table that includes the intervening period between sub-sample 2 and 3. (e) * significant at 10% level; ** significant at 5% level; *** significant at 1% level.

average of the exchange rate (YEAREXR) (except in the third sub-sample for both variables).19 Intervention conducted on a given day reacts to intervention carried out in the previous day; intervention effected two days ago; and, to intervention made three days ago (except in the first and second sub-samples). Similar to the baseline estimates, interventions are found to be carried out in clusters. The Tobit estimates reported in Table 3 exhibit structural breaks across the sub-samples, consistent with the observed changes in intervention intensity as well as with the shifts in intervention episodes or regimes established by several previous studies. Given the application of maximum likelihood to obtain the Tobit estimates, we use a likelihood ratio test to formally assess whether the estimated coefficients are unchanged between sub-samples. Table 4 presents the results. Overall, the likelihood ratio test indicates that the estimated coefficients intervention reaction functions are non-constant between regimes, which indicates the existence of three separate regimes. From the first-stage estimation of the Japanese official intervention reaction functions, the inverse propensity weights were then computed using Eq. (2) above. The weights ranged from 0.76 to 1.03 across the four sub-samples which suggests that sufficient unconfounding of the official intervention variable was achieved from the first-stage estimation of the intervention reaction functions.20 We now turn to the linear LP estimates using inverse probability weights, and the results are presented in Table 5. The results indicate a significant positive response in the changes in the exchange rate to interventions in earlier periods, but this positive effect of intervention disappears in subsequent horizons. For the full-sample, intervention, on average, leads to a 0.26% increase in the JPY/ USD exchange rate in the first period, but becomes significantly negative in the second period. For the first sub-sample (January 1999 to December 2002), we also find a significant impact of intervention on the changes in the JPY/USD exchange rate in the first and third periods,21 and, this effect is of the correct sign (appreciation of the USD vis-à-vis the JPY). Specifically, we find a 1.04% and 1.18% increase in the JPY/USD exchange rate for the first and third periods, respectively. The intervention, however, does not have a significant effect in later horizons. Turning to the second sub-sample (January 2003 to March 2004), the results indicate that interventions may have a perverse effect in earlier periods for this sub-sample on the JPY/USD exchange rate in view of the significant but negative effects in the second and third periods. Subsequent horizons, however, indicate that interventions do not have a significant effect on the JPY/USD exchange rate. Finally, focusing on the third and final sub-sample (September 2010 to December 2011), intervention causes a significant increase in the JPY/USD exchange rate by 0.25% and 0.44% only in the first and second periods, respectively.22 4.3. Robustness tests To test the robustness of our main results, we carry out a number of sensitivity tests that validate our earlier main results where we find positive and significant causal effects of intervention on the changes in the JPY/USD exchange rate only in earlier horizons for three of the four samples, and where these positive intervention effects vanish in subsequent horizons. First, we estimate the 19 Again, refer to Section 3.1, particularly, footnote 9 for the choice of the length of the moving average terms to define the past trends in the JPY/ USD exchange rate. While the choice of the length is arbitrary, we also conducted estimates of our Tobit intervention reaction functions in the first and two sub-samples (as these were the periods that these terms were found to be significant) by including 63 (3 months) and 126 (6 months) business days in the estimation. These two moving average terms were found to be insignificant. For the sake of brevity, we do not report these results, but are available upon request. 20 These results are available upon request. 21 The intervention effect, however, comes out insignificant for the second period. 22 Again, as mentioned in footnote 8, we reiterate that given that this sub-sample spans only 8 intervention days, the results pertaining to this subsample should be treated with caution.

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Table 5 Causal effects of intervention on changes in yen-US dollar rate estimated using Local Projections with inverse probability weights (9 lags). Source: Author's calculations. Horizon

Full sample: January 1999 – December 2011 Sub-sample 1: January 1999 – December 2002 Sub-sample 2: January 2003 – March 2004 Sub-sample 3: September 2010 – December 2011

1

2

3

4

5

6

7

8

9

10

0.264** (0.127) 1.04** (0.533) 0.392 (0.471) 0.252* (0.135)

−0.044*** (0.338) 0.168 (0.534) −0.978** (0.472) 0.442*** (0.139)

−0.215 (0.131) 1.180** (0.535) −0.965** (0.482) −0.007 (0.015)

−0.011 (0.131) −0.800 (0.536) −0.030 (0.489) −0.068 (0.137)

−0.084 (0.133) −0.484 (0.538) 0.111 (0.485) −0.056 (0.137)

0.010 (0.127) −0.272 (0.537) 0.044 (0.491) −0.139 (0.137)

−0.047 (0.127) 0.561 (0.540) −0.758 (0.497) −0.003 (0.136)

−0.089 (0.127) 0.033 (0.537) 0.300 (0.502) −0.103 (0.136)

0.022 (0.127) −0.162 (0.537) −0.615 (0.501) −0.045 (0.137)

−0.079 (0.127) −0.661 (0.536) 0.848 (0.595) 0.008 (0.137)

Notes: (a) For each horizon, the dynamic causal effect of intervention on changes in yen-US dollar rate is the estimated coefficient of βh in Eq. (5) in the main text using Local Projections. The estimate of this coefficient is the impact on EXRt+h with respect to a change in the predicted values of  , keeping all other variables constant. The predicted values of intervention, intervention, INT  , are obtained from a Tobit estimation of Eq. (1) in the main text. INT (b) Estimation by Local Projection uses 9 lags of Zit in Eq. (5) in the main text. (c) Values in parentheses are the estimated standard errors. (d) *, **, ***: Significant at 10%, 5% and 1% levels, respectively. Table A1 Intervention reaction functions: OLS estimates. Source: Author's calculations.

Constant EXR,

t-1

INT,

t-1

INT,

t-2

INT,

t-3

R-squared Observations

Full sample: January 1999 – December 2011 (1)

Sample 1: January 1999 – December 2002 (2)

Sample 2: January 2003 – March 2004 (3)

Sample 3: September 2010 – December 2011 (4)

0.167*** (0.049) −0.099*** (0.032) 0.069** (0.029) 0.055** (0.026) 0.062*** (0.016) 0.014 3193

0.143*** (0.035) −0.146*** (0.047) 0.058* (0.034) n.a.

0.504*** (0.110) n.a.

0.566 (0.037) −0.554* (0.297) 0.045*** (0.015) 0.005* (0.003) 0.036** (0.017) 0.004 327

n.a.

0.332*** (0.062) 0.180*** (0.040) n.a.

0.012 986

0.191 307

Notes: (a) Heteroscedasticity and autocorrelation consistent standard errors in parentheses. (b) The estimated intervention reaction functions are defined in equation (X) in the text. (c) The dependent variable, INT, is the official intervention amount in millions of USD. (d) The independent variables are defined as: EXR is the first-difference of the log of the JPY per USD exchange rate; MA21EXR is the 21-day moving average of the log of the JPY per USD exchange rate; YEAREXR is the 1-year moving average of the log of the JPY per USD exchange rate; and lagged amounts of INT. (e) n.a. indicates that the variable is omitted due to lack of significance. * significant at 10% level; ** significant at 5% level; *** significant at 1% level.

second-stage linear LP with inverse probability weights across the four samples using shorter lags, i.e., four lags instead of nine.23 The estimates of the causal effects are shown in Table A2. We find the results of this sensitivity test to be very similar to the main results across the four samples, except that the significant but “incorrect” negative effect found in the second sub-sample only appears in the second period. Second, because the treatment variable, the amount of intervention, has a skewed distribution in which a substantial proportion of the observations are zero. In order to make a more reasonable assumption that this treatment variable is normally distributed, we transform this variable using a Box-Cox transformation. Though far from perfect, the Box-Cox searches for a transformation of the amount of intervention for which the marginal distribution is the closest to the standard normal. Once the transformation is undertaken, we then again estimate the second-stage linear LP with inverse probability weights across the four samples. The results of this robustness test are presented in Table A3. The results of this sensitivity test are qualitatively identical to the main results although

23

Based on the Schwartz information criterion. 309

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Table A2 Causal effects of intervention on changes in yen-US dollar rate estimated using Local Projections with inverse probability weights (4 lags). Source: Author's calculations. Horizon

Full sample: January 1999 – December 2011 Sub-sample 1: January 1999 – December 2002 Sub-sample 2: January 2003 – March 2004 Sub-sample 3: September 2010 – December 2011

1

2

3

4

5

6

7

8

9

10

0.194* (0.108) 0.971* (0.536) 0.092 (0.413) 0.245* (0.133)

−3.0*** (0.272) 0.211 (0.537) −0.889* (0.412) 0.461*** (0.137)

−0.020 (0.013) 1.06** (0.536) −0.684 (0.430) −0.074 (0.149)

−0.012 (0.125) −0.776 (0.535) −0.145 (0.431) −0.062 (0.138)

−0.098 (0.128) −0.486 (0.536) 0.358 (0.434) −0.028 (0.138)

0.013 (0.122) −0.293 (0.534) −0.255 (0.439) −0.141 (0.138)

−0.054 (0.122) 0.613 (0.537) −0.620 (0.441) −0.011 (0.137)

−0.072 (0.122) −0.026 (0.535) 0.096 (0.447) −0.095 (0.133)

0.016 (0.122) −0.157 (0.534) −0.298 (0.448) −0.037 (0.134)

−0.078 (0.122) −0.714 (0.534) 0.720 (0.445) 0.014 (0.134)

Notes: (a) For each horizon, the dynamic causal effect of intervention on changes in yen-US dollar rate is the estimated coefficient of βh in Eq. (5) in the main text using Local Projections. The estimate of this coefficient is the impact on EXRt+h with respect to  , keeping all other variables constant. The predicted values of intervention, a change in the predicted values of intervention, INT  , are obtained from a Tobit estimation of Eq. (1) in the main text. INT (b) Estimation by Local Projection uses 4 lags of Zit in Eq. (5) in the main text. (c) Values in parentheses are the estimated standard errors. (d) *, **, ***: Significant at 10%, 5% and 1% levels, respectively. Table A3 Causal effects of intervention on changes in yen-US dollar rate estimated using Local Projections with inverse probability weights (with Box-Cox transformation). Source: Author's calculations. Horizon

Full sample: January 1999 – December 2011 Sub-sample 1: January 1999 – December 2002 Sub-sample 2: January 2003 – March 2004 Sub-sample 3: September 2010 – December 2011

1

2

3

4

5

6

7

8

9

10

0.172* (0.100) 0.368** (0.165) 0.522 (0.661) 0.207* (0.115)

−5.80*** (0.315) 0.142 (0.165) −1.161* (0.660) 0.377*** (0.119)

−0.164 (0.111) 0.243 (0.165) −1.43** (0.666) −0.067 (0.126)

0.003 (0.110) −0.159 (0.166) −0.015 (0.675) −0.058 (0.116)

−0.062 (0.113) −0.178 (0.166) 0.118 (0.669) −0.046 (0.116)

0.015 (0.107) −0.039 (0.166) 0.092 (0.678) −0.116 (0.116)

−0.035 (0.107) 0.112 (0.166) −1.06 (0.688) −0.001 (0.115)

−0.078 (0.107) 0.072 (0.166) 0.422 (0.701) −0.088 (0.115)

0.017 (0.107) −0.011 (0.017) −0.739 (0.695) −0.039 (0.116)

−0.064 (0.107) −0.134 (0.165) 1.147 (0.700) 0.008 (0.116)

Notes: (a) For each horizon, the dynamic causal effect of intervention on changes in yen-US dollar rate is the estimated coefficient of βh in Eq. (5) in the main text using Local Projections. The estimate of this coefficient is the impact on EXRt+h with respect to a change in the predicted values of  , keeping all other variables constant. The predicted values of intervention, intervention, INT  , are obtained from a Tobit estimation of Eq. (1) in the main text. INT (b) Box-Cox transformation of the actual amount of intervention is undertaken prior to the estimations of Eqs. (1) and (5) in the main text. (c) Estimation by Local Projection uses 9 lags of Zit in Eq. (5) in the main text. (d) Values in parentheses are the estimated standard errors. (e) *, **, ***: Significant at 10%, 5% and 1% levels, respectively.

now, only the first period in the first sub-sample is significantly positive. Third, if the underlying data generating process is nonlinear, then LPs can be easily extended to polynomial expansion that is used to approximate nonlinearity (Jorda, 2005). To account for this possibility, we then include a quadratic term of the contemporaneous intervention in the outcome equation to approximate this likely nonlinearity and estimate accordingly the LP with inverse probability weights across the four samples. The results are presented in Table A4. In this robustness test, we find significant and positive effects in the first period of the full sample, in the second period of the first sub-sample and in the second and third periods of the third subsample. These positive effects are now slightly higher in magnitude compared to the main results. Also, the significant but negative effect found in the second sub-sample only shows up in the third period. Fourth, it is possible that findings of positive intervention effects may be illusory if foreign exchange interventions are accompanied by further policy measures, in particular, monetary policy. Coinciding with our period of study, Japan began in January 1999, the zerointerest rate policy (ZIRP) which saw money market rates effectively hit the lower bound. Apart from our earlier explanation that given the institutional nature of Japanese foreign exchange interventions in which they are in a technical sense, automatically sterilized (i.e., independent of monetary policy), a number of studies have also argued that during this period when Japanese monetary policy was constrained, foreign exchange interventions by the Japanese monetary authorities were indeed sterilized (e.g., Spiegel, 2003; Fatum and Hutchison, 2005; Ito, 2005; Christiano, 2000). Nonetheless, we test whether our findings of positive intervention effects in earlier horizons still hold once we control for Japanese interest rate changes. To do this, we include nine lags of the daily changes in the 310

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Table A4 Causal effects of intervention on changes in yen-US dollar rate estimated using Local Projections with inverse probability weights (with squared contemporaneous term of the predicted values of intervention). Source: Author's calculations. Horizon

Full sample: January 1999 – December 2011 Sub-sample 1: January 1999 – December 2002 Sub-sample 2: January 2003 – March 2004 Sub-sample 3: September 2010 – December 2011

1

2

3

4

5

6

7

8

9

10

2.99*** (0.496) 0.223 (1.25) 1.08 (0.874) 0.496 (0.444)

−8.90*** (0.472) 3.24*** (1.25) −0.009 (0.875) 1.51*** (0.455)

−0.528 (0.431) 1.51 (1.26) −1.78** (0.890) −5.0*** (0.326)

−0.490 (0.432) 1.38 (1.26) −0.832 (0.897) 0.637 (0.443)

−0.646 (0.431) −0.432 (1.26) −0.071 (0.894) −0.549 (0.442)

−0.262 (0.431) 0.378 (1.26) 0.416 (0.906) −0.591 (0.443)

−0.038 (0.430) 0.033 (1.26) −1.26 (0.908) 0.014 (0.445)

−0.033 (0.430) 1.69 (1.26) −0.256 (0.921) −0.074 (0.445)

−0.133 (0.430) 1.60 (1.26) −0.422 (0.920) 0.633 (0.446)

−0.328 (0.430) −3.60 (1.25) 0.247 (0.909) 0.050 (0.449)

Notes: (a) For each horizon, the dynamic causal effect of intervention on changes in yen-US dollar rate is the estimated coefficient of βh in Eq. (5) in the main text using Local Projections. The estimate of this coefficient is the impact on EXRt+h with respect to a change in the predicted values of  , keeping all other variables constant. The predicted values of intervention, intervention, INT  , are obtained from a Tobit estimation of Eq. (1) in the main text. INT (b) Estimation by Local Projection uses 9 lags of Zit in Eq. (5) in the main text as well as including a squared contemporaneous . term of the predicted values of intervention, INT, (c) Values in parentheses are the estimated standard errors. (d) *, **, ***: Significant at 10%, 5% and 1% levels, respectively.

Japanese uncollateralized overnight call rate in the outcome equation and estimate accordingly the LP with inverse probability weights across the four samples. The results shown in Table A5 suggest that our main results still hold. The only difference in this case is that the significant but negative effect found in the second sub-sample again only shows up in the third period. Fifth, in view that the literature has also examined whether the second moment of the changes in the exchange rate (i.e, exchange rate volatility) matter for intervention authorities to intervene, we include a measure of conditional volatility of the changes in the JPY/USD exchange rate obtained from a GARCH(1,1) in the intervention reaction function. We again test whether our main findings remain intact once we control for a measure of conditional exchange rate volatility in the reaction function. To do this, we estimate the reaction function using the Tobit model across the four samples, and the outcome equations that correspond to the instrumented contemporaneous intervention coming from these reaction functions. The results of the Tobit estimates are presented in Panel A of Table A6, while the results of the estimated outcome equation are shown in Panel B of Table A6. The conditional volatility measure came out to be significant only in the full sample, however (column 1, Panel A). On the other hand, the results of the estimated outcome equation indicate that with the inclusion of a measure of conditional volatility in the first-stage estimation, our main findings still stand. Again, the only exception in this case is the significant but negative effect found in the second sub-sample, which only appear in the third period. Table A5 Causal effects of intervention on changes in yen-US dollar rate estimated using Local Projections with inverse probability weights (with 9 lags of the changes in the Japanese uncollateralised overnight call rate). Source: Author's calculations. Horizon

Full sample: January 1999 – December 2011 Sub-sample 1: January 1999 – December 2002 Sub-sample 2: January 2003 – March 2004 Sub-sample 3: September 2010 – December 2011

1

2

3

4

5

6

7

8

9

10

0.264** (0.127) 0.924* (0.537) 0.451 (0.489) 0.251* (0.139)

−4.37*** (0.338) 0.222 (0.538) −1.00 (0.491) 0.459*** (0.142)

−0.215 (0.131) 1.18** (0.539) – 0.858* (0.500) −0.072 (0.152)

−0.013 (0.131) −0.827 (0.541) −0.194 (0.505) −0.102 (0.140)

−0.082 (0.134) −0.552 (0.542) 0.073 (0.496) −0.036 (0.139)

0.010 (0.127) −0.390 (0.541) 0.242 (0.508) −0.133 (0.140)

−0.049 (0.127) 0.582 (0.544) – 0.910* (0.517) 0.033 (0.140)

−0.090 (0.127) −0.033 (0.542) 0.498 (0.521) −0.103 (0.140)

0.025 (0.127) −0.160 (0.542) −0.830 (0.517) −0.006 (0.140)

−0.079 (0.127) −0.715 (0.540) 0.649 (0.513) 0.066 (0.140)

Notes: (a) For each horizon, the dynamic causal effect of intervention on changes in yen-US dollar rate is the estimated coefficient of βh in Eq. (5) in the main text using Local Projections. The estimate of this coefficient is the impact on EXRt+h with respect toa change in the predicted values of  , keeping all other variables constant. The predicted values of intervention, intervention, INT  , are obtained from a Tobit estimation of Eq. (1) in the main text. INT (b) Estimation by Local Projection uses 9 lags of Zit in Eq. (5) in the main text, and with 9 lags of the changes in the overnight interest rate also included in Zit. . (c) Values in parentheses are the estimated standard errors. (d) *, **, ***: Significant at 10%, 5% and 1% levels, respectively. 311

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Table A6 Panel A Intervention reaction functions: Tobit estimates (with conditional volatility obtained from a GARCH(1,1)). Full sample: January 1999 – December 2011 (1)

Sample 1: January 1999 – December 2002 (2)

Sample 2: January 2003 – March 2004 (3)

Sample 3: September 2010 – December 2011 (4)

n.a.

Vol,t-1

−47.97*** (7.62) 1.02*** (0.135) 0.776*** (0.119) n.a.

−90.50 (90.89) 176.8 (189.5) 3.84 (4.74) 0.566 (0.376) 0.570 (0.377) n.a.

−229.17* (136.72) −58.32 (45.75) n.a.

YEAREXR,t-1

−112.80 (79.13) −3.22** (1.62) −59.65* (34.27) 77.88* (40.34) 8.80 (12.03) 1.19** (0.549) 1.75*** (0.525) n.a.

−2.86 (3.48) n.a.

MA21EXR,t-1

5.81 (4.12) −4.37*** (1.07) n.a.

−995.14 3193

−159.93 986

−73.24 307

Constant EXR,

t-1

INT,

t-1

INT,

t-2

INT,

t-3

Log L Observations

n.a. 37.72 (194.94) 3.80 (3.93) 1.02 (1.06) 1.75* (1.02) −55.59 327

Notes: (a) Heteroscedasticity and autocorrelation consistent standard errors in parentheses. (b) The estimated intervention reaction functions are defined in Eq. (1) in the text. (c) The dependent variable, INT, is the official intervention amount in millions of USD. (d) The independent variables are defined as: EXR is the first-difference of the log of the JPY per USD exchange rate; MA21EXR is the 21-day moving average of the log of the JPY per USD exchange rate; YEAREXR is the 1-year moving average of the log of the JPY per USD exchange rate; Vol is the conditional volatility obtained from a GARCH(1,1) of EXR; and lagged amounts of INT. (e) n.a. indicates that the variable is omitted due to lack of significance. *significant at 10% level; ** significant at 5% level; *** significant at 1% level. Table A6 Panel B Dynamic causal effect of intervention on changes in yen-US dollar rate estimated using Local Projections with inverse probability weights (with conditional volatility included in the intervention reaction function). Source: Author's calculations. Horizon

Full sample: January 1999 – December 2011 Sub-sample 1: January 1999 – December 2002 Sub-sample 2: January 2003 – March 2004 Sub-sample 3: September 2010 – December 2011

1

2

3

4

5

6

7

8

9

10

0.327** (0.146) 1.10** (0.542) 0.729 (0.575) 0.246* (0.133)

−2.93*** (0.299) 0.144 (0.543) −1.11 (0.580) 0.448*** (0.137)

−0.211 (0.145) 1.21** (0.544) −1.16** (0.588) −0.112 (0.145)

0.032 (0.144) −0.841 (0.546) −0.099 (0.596) −0.044 (0.135)

−0.086 (0.147) −0.473 (0.547) 0.041 (0.591) −0.062 (0.134)

0.079 (0.140) −0.223 (0.547) 0.123 (0.600) −0.147 (0.135)

−0.068 (0.140) 0.591 (0.549) −1.06* (0.607) −0.008 (0.134)

−0.092 (0.140) 0.006 (0.547) 0.398 (0.614) −0.100 (0.134)

0.043 (0.140) −0.125 (0.546) −0.857 (0.613) −0.036 (0.135)

−0.120 (0.140) −0.740 (0.545) 0.105 (0.607) 0.005 (0.135)

Notes: (a) For each horizon, the dynamic causal effect of intervention on changes in yen-US dollar rate is the estimated coefficient of βh in Eq. (5) in the main text using Local Projections. The estimate of this coefficient is the impact on EXRt+h with respect to a change in the predicted values of  , keeping all other variables constant. The predicted values of intervention, intervention, INT  , are obtained from a Tobit estimation of Eq. (1) in the main text. INT (b) Estimation by Local Projection uses 9 lags of Zit in Eq. (5) in the main text.  (c) With conditional volatility included in the intervention reaction function to obtain INT. (d) Values in parentheses are the estimated standard errors. (e) *, **, ***: Significant at 10%, 5% and 1% levels, respectively.

Sixth, the third sub-sample (September 2010 to December 2011) includes the 18 March 2011 coordinated intervention by G7 economies to stem the strength of the yen against the US dollar in the wake of the Tohoku earthquake and Fukushima meltdown.24 We examine the sensitivity of the results obtained for this sub-sample once we control for this coordinated intervention. To do this,

24 As also mentioned in Section 2.2, and repeated here, the US Federal Reserve which was also active in the JPY/USD market prior to the period of study had stopped intervening since June 1998 (Reitz and Taylor, 2012).

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Table A7 Dynamic causal effect of intervention on changes in yen-US dollar rate estimated using Local Projections with inverse probability weights (accounting for the 18 March 2011 coordinated intervention). Source: Author's calculations. Horizon

 Predicted values of intervention, INT Dummy for coordinated intervention

1

2

3

4

5

6

7

8

9

10

0.236* (0.129) 3.34*** (0.611)

0.446*** (0.139) −0.673 (0.640)

−0.069 (0.148) −0.260 (0.632)

−0.069 (0.137) 0.087 (0.633)

−0.058 (0.137) 0.257 (0.633)

−0.143 (0.137) 0.623 (0.632)

−0.003 (0.136) 0.013 (0.636)

−0.112 (0.135) 0.058 (0.629)

−0.043 (0.137) −0.328 (0.639)

0.002 (0.137) 0.121 (0.638)

Notes: (a) For each horizon, the dynamic causal effect of intervention on changes in yen-US dollar rate is the estimated coefficient of βh in Eq. (5) in the main text using Local Projections. The estimate of this coefficient is the impact on EXRt+h with respect to a change in the predicted values of  , keeping all other variables constant. The predicted values of intervention, intervention, INT  , are obtained from a Tobit estimation of Eq. (1) in the main text. INT (b) Dummy for coordinated coordination takes a value of 1 on 18 March 2011, and 0 for all other dates during the sub-sample of September 2010 to December 2011. (c) Estimation by Local Projection uses 9 lags of Zit in Eq. (5) in the main text. (d) Values in parentheses are the estimated standard errors. (e) *, **, ***: Significant at 10%, 5% and 1% levels, respectively.

given the flexibility of the LP method to various specifications in each separate linear regression, we include a dummy variable equal to 1 on the 18th of March 2011 and re-estimate the outcome equation for this sub-sample. The results are presented in Table A7. The results indicate that while the coordinated intervention dummy variable is significant in period 1, the main results of a positive intervention effect in earlier horizons for this sub-sample remain intact, i.e., the effect in periods 1 and 2 remains positive and significant but becomes insignificant in later periods. Seventh, the intervention frequency was unusually high during the first quarter of 2004.25 We tested whether our finding for the second sub-sample holds by conducting our estimations only for this short period of the first quarter of 2004. The results are presented in Table A8. The results indicate that the significant but negative effects found in the second and third periods of this subsample have now disappeared. But, again, the lack of a significant positive effect of intervention obtained for this sub-sample also remain intact. Finally, one way that self-selection bias arises and presents a major challenge to any study that assess the effectiveness of foreign exchange intervention is that an intervention authority can select and intervene in periods for which they believe will have a higher likelihood of success.26 In this instance, it can then show up in the results as an apparent intervention effect. While the empirical technique that we employ to examine the issue of the effectiveness of intervention already controls for self-selection bias, it would be interesting to have this source of self-selection bias further tested and to ascertain how our main results stand up to this kind of analysis. Admittedly, our lack of access to Japanese intra-daily intervention data makes it less straightforward on how we can formally conduct our test.27 Nonetheless, a simplistic attempt to test this source of bias uses the argument that intervention authorities are more likely to intervene on days when there is an observed strong deviation in the changes of the JPY/USD exchange rate from its fundamental value.28 That is, one can argue that it is relatively easy for monetary authorities to move the exchange in the desired direction when the exchange rate veers severely away from whatever is its fundamental value. Based on this, we then specify our earlier intervention reaction function by including this time, a measure of the absolute deviation of the changes in the JPY/USD exchange from its one month and one-year moving averages. The results of the Tobit estimates of the reaction functions are presented in Panel A of Table A9, while the results of the corresponding outcome equation are shown in Panel B of Table A9. The results in Panel A indicate that Japanese monetary authorities intervene when there are longer term deviations or misalignments as opposed to shorter-term deviations. This result fits nicely to the finding by Neely (2008) that monetary authorities target longer-term deviations of the exchange rate but are less likely to intervene in case of shorter-term deviations. Turning to the estimated results of the corresponding outcome equations in Panel B indicate that again our main results hold, except that the observed positive effect of intervention appears in the third period of the full sample, and the significant but negative effect in the second sub-sample only appears in the second period.

25

We thank an anonymous referee for raising this point. It must be mentioned that the intervention reaction function was estimated by OLS because of the not so substantial number of zeros or non-intervention days for this short period. 26 For instance, Dominguez (2003) cite the example of good knowledge of intra-daily market circumstances that can raise the likelihood of success of intervention. 27 As noted in footnote 26, Dominguez (2003) tested this source of self-selection bias using intra-daily data for the case of the US Federal Reserve. 28 A similar argument was made by Fratzscher et al. (2015) in order to examine this case. 313

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Table A8 Causal effects of intervention on changes in yen-US dollar rate estimated using Local Projections with inverse probability weights (9 lags). Source: Author's calculations. Horizon

Sub-sample period: January 2004 – March 2004

1

2

3

4

5

6

7

8

9

10

1.75 (1.07)

−0.731 (1.10)

0.884 (1.02)

−0.358 (0.993)

0.210 (0.966)

−0.856 (0.973)

−1.73* (0.930)

−2.56 (0.923)

−1.27 (0.993)

−0.629 (0.976)

Notes: (a) For each horizon, the dynamic causal effect of intervention on changes in yen-US dollar rate is the estimated coefficient of βh in Eq. (5) in the main text using Local Projections. The estimate of this coefficient is the impact on EXRt+h with respect to a change in the predicted values of  , keeping all other variables constant. The predicted values of intervention, intervention, INT  , are obtained from an OLS estimation of Eq. (1) in the main text. INT (b) Estimation by Local Projection uses 9 lags of Zit in Eq. (5) in the main text. (c) Values in parentheses are the estimated standard errors. (d) *, **, ***: Significant at 10%, 5% and 1% levels, respectively. Table A9 Panel A Intervention reaction functions: Tobit estimates (with deviation of EXR from its moving average/trend).

Constant EXR,

t-1

Deviation from MA21EXR,t-1 Deviation from YEAREXR,t-1 INT, t-1 INT,

t-2

Log L Observations

Full sample: January 1999 – December 2011 (1)

Sample 1: January 1999 – December 2002 (2)

Sample 2: January 2003 – March 2004 (3)

−12.11*** (1.04) −1.37*** (0.402) −31.01 (51.00) 14.93 (14.17) 1.34*** (0.146) 1.23*** (0.143) −805.23 3193

−24.95 (4.81) −3.21** (1.58) 225.14 (184.40) 102.96** (51.01) 1.19** (0.543) 1.75*** (0.519) −158.79 986

1.56 (2.56) n.a. 18.49 (158.42) −185.13** (82.36) 0.715** (0.361) 0.753** (0.363) −73.39 307

Notes: (a) Heteroscedasticity and autocorrelation consistent standard errors in parentheses. (b) The estimated intervention reaction functions are defined in Eq. (1) in the text. (c) The dependent variable, INT, is the official intervention amount in millions of USD. (d) The independent variables are defined as: EXR is the first-difference of the log of the JPY per USD exchange rate; Deviation from MA21EXR is the absolute deviation of EXR from its 21-day moving average; Deviation from YEAREXR is the absolute deviation of EXR from its 1-year moving average; and lagged amounts of INT. (e) n.a. indicates that the variable is omitted due to lack of significance. (f) No results are reported for sub-sample 3 as convergence was not achieved with the Tobit estimation. * significant at 10% level; ** significant at 5% level; *** significant at 1% level.

5. Conclusion The decision to intervene in the foreign exchange market is not a random decision. Deteriorating market conditions can cause an authority's intervention to work against the success of the said intervention, which can then masquerade in the results as an apparent lack of intervention effect. On the other hand, an intervention authority can select and intervene in periods for which they believe will have a higher likelihood of success. The key then for controlling for this problem of self-selection bias is to purge the correlation between those variables or confounders that influence the decision to intervene and with the level of official foreign exchange intervention. Borrowing from the broad treatment effects literature that view the changes in the JPY/USD exchange rate as the outcome variable, with the daily amounts of official interventions by Japanese monetary authorities in the JPY/USD market as the treatment variable, we build and extend in a continuous treatment setting, the inverse probability weights estimator advocated by Jorda and Taylor (2015) and Angrist et al. (2018) to control for self-selection bias. With this method, the bias is controlled by effectively creating a pseudo-population in which the explanatory variables that models the selection or intervention decision by Japanese

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Table A9 Panel B Causal effects of intervention on changes in yen-US dollar rate estimated using Local Projections with inverse probability weights (with deviation of EXR from its moving average/trend in the intervention reaction function). Source: Author's calculations. Horizon

Full sample: January 1999 – December 2011 Sub-sample 1: January 1999 – December 2002 Sub-sample 2: January 2003 – March 2004

1

2

3

4

5

6

7

8

9

10

0.023 (0.210) 0.956** (0.471) 0.568 (0.495)

0.108 (0.211) 0.075 (0.472) −1.54*** (0.499)

0.383* (0.211) 0.802* (0.473) −0.616 (0.518)

0.155 (0.210) −0.575 (0.474) −0.160 (0.519)

−0.117 (0.211) −0.625 (0.475) 0.513 (0.518)

−0.040 (0.211) −0.190 (0.475) −0.561 (0.521)

0.240 (0.211) 0.446 (0.479) −0.283 (0.526)

0.099 (0.211) 0.026 (0.475) 0.017 (0.528)

0.087 (0.211) −0.452 (0.475) −0.010 (0.530)

0.190 (0.211) −0.380 (0.474) 0.615 (0.526)

Notes: (a) For each horizon, the dynamic causal effect of intervention on changes in yen-US dollar rate is the estimated coefficient of βh in Eq. (5) in the main text using Local Projections. The estimate of this coefficient is the impact on EXRt+h with respect to a change in the predicted values of  , keeping all other variables constant. The predicted values of intervention, intervention, INT  , are obtained from a Tobit estimation of Eq. (1) in the main text. INT (b) Estimation by Local Projection uses 9 lags of Zit in Eq. (5) in the main text. (c) With the absolute deviation of EXR from its 21-day moving average and the absolute deviation of EXR from its 1-year moving average included in  the intervention reaction function to obtain INT. (d) Values in parentheses are the estimated standard errors. (e) No results are reported for sub-sample 3 as convergence was not achieved with the first-stage Tobit estimation of the intervention reaction function. (f) *, **, ***: Significant at 10%, 5% and 1% levels, respectively.

monetary authorities and the treatment variable are independent of each other. The causal effect of Japanese official foreign exchange intervention on the changes in the JPY/USD exchange rate is then obtained by conceptually performing a standard regression in the pseudo-population. Looking at the January 1999 to December 2002 sub-sample, we find that intervention had significant effects on the changes in the JPY/USD exchange rate on the same day of the intervention as well as two days after the intervention took place. These effects are in the right direction. In contrast, we find that for the January 2003 to March 2004 sub-sample, interventions may have had an undesired effect on the changes in the JPY/USD exchange rate in earlier periods. Finally, turning to the September 2010 to December 2011 sub-sample, we again find significant effects of intervention that occur for one and two days from the time the intervention took place. These significant effects are also in the correct direction. All these results are robust to various sensitivity tests. We also note that this study is one of the first to provide evidence for this period given that previous studies that assess the effectiveness of Japanese foreign exchange intervention have typically covered the period from April 1991 to March 2004. Nonetheless, the finding for this period should be treated with some caution in view of the limited number of days of intervention. Noting that Japanese intervention activities in the JPY/USD market were described as large and infrequent during the subsamples January 1999 to December 2002 and September 2010 to December 2011, the finding of significant effects of intervention during these two periods is consistent with evidence in this literature which suggests that only large, infrequent and sporadic interventions are effective in moving the changes in the exchange rate in the desired direction. Furthermore, our study also offers verification on the duration of this intervention effect, an interesting sub-issue for which, to the best of our knowledge, evidence has been relatively scant. Similar to the finding of Nagayasu (2004) which covers an earlier period of Japanese foreign exchange intervention, we also find evidence that the effect of intervention on the changes in the JPY/USD exchange rate is not long-lasting. However, in contrast to Nagayasu (2004), we find that this effect is slightly longer, which lasts more than a day after the intervention takes place. The results imply that while intervention is an effective tool, it cannot be regarded as a panacea that can move exchange rates at will and at all times. It can affect the exchange rate only in certain circumstances. The circumstances that surround its capability to affect the exchange rate relates to the size and frequency of foreign exchange intervention. Only large and infrequent interventions can move exchange rates, which then signifies that small and frequent interventions should be avoided. That being said, we then find robust evidence that once the exchange rate moves in the desired direction, the “success” of large and infrequent interventions are not long-lasting, but nonetheless, slightly longer, in contrast to existing evidence. References Adler, G., Tovar, C., 2014. Foreign exchange interventions and their impact on exchange rate levels. Monetaria 1–48. Andrews, D., 1993. Test for parameter instability and structural change with unknown change point. Econometrica 821–856. Angrist, J., Jorda, O., Kuersteiner, G, 2018Angrist et al.,. Semiparametric estimates of monetary policy effects: string theory revisited. J. Bus. Econ. Stat. Almekinders, G., Eijffinger, S., 1994. Daily Bundesbank and Federal Reserve Interventions: are they a reaction to changes in the level and volatility of the DM/$-Rate? Emp. Econ. 19, 111–130. Almekinders, G., 1995. Foreign Exchange Intervention: Theory and Evidence. Elgar, Brookfield, VT. Baillie, R.T., Humpage, O.F., 1992. Post-Louvre Intervention: Did Target Zones Stabilize the Dollar? Federal Reserve Bank of Cleveland Working Paper 9203. Baillie, R.T., Osterberg, W.P., 1997. Central bank intervention and risk in the forward premium. J. Int. Econ. 43, 483–497.

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