HIAS-E-132

 The Trend Effect of Foreign Exchange Intervention
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Rasmus Fatum(a), Yohei Yamamoto(b), Binwei Chen(b)(a) University of Alberta(b) Hitotsubashi University

Aug 2023

ŉŪŵŰŵŴŶţŢŴũŪġŊůŴŵŪŵŶŵŦġŧŰųġłťŷŢůŤŦťġŔŵŶťźĭġŉŪŵŰŵŴŶţŢŴũŪġŖůŪŷŦųŴŪŵźġ
ĳĮĲĭġŏŢŬŢĭġŌŶůŪŵŢŤũŪĭġŕŰŬźŰġĲĹķĮĹķıĲĭġŋŢűŢůġ
ŵŦŭĻĬĹĲġĵĳġĶĹıġĹķķĹġ ũŵŵűĻİİũŪŢŴįũŪŵĮŶįŢŤįūűİġ
ġġ

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The Trend Effect of Foreign Exchange Intervention

This version: 27 August 2023

Rasmus Fatum
School of Business
University of Alberta
Edmonton, Alberta
Canada, T6G 2R6
Email: rasmus.fatum@ualberta.ca

Yohei Yamamoto*Department of Economics
Hitotsubashi University
2-1 Naka, Kunitachi
Tokyo 186-8601, Japan
Email: yohei.yamamoto@r.hit-u.ac.jp

Binwei Chen
Graduate School of Economics
Hitotsubashi University
2-1 Naka, Kunitachi
Tokyo 186-8601, Japan
Email: ea220601@g.hit-u.ac.jp

Abstract:
The 2022 and the 2010-2011 Bank of Japan interventions provide an opportunity
for investigating whether unusually large-scale and infrequent interventions are capable ofgenerating trend effects. To this end, we estimate the counterfactual exchange rate and analyze
structural changes in the level and the trend of the gap sequence between actual and counterfactual
exchange rates. Our results show that the trend of the gap sequence reversed in the desired direction
around the intervention dates, indicating that the intervention policy instrument is potentiallypowerful enough to generate long-term trend effects. This is an important insight not previously
found in the intervention literature.

Key words: Foreign Exchange Intervention; Counterfactual Exchange Rate; Currency Factors;
Synthetic Control Methods; Structural Changes.
JEL Classifications: F31, C38.

* Corresponding author. Fatum is also Research Associate at the Federal Reserve Bank of Dallas
and member of the Economic Policy Research Unit (EPRU) at the University of Copenhagen.
Yamamoto is also Professor at Tokyo Tech Academy of Energy and Informatics, Tokyo Instituteof Technology. We thank Kathryn Dominguez, Lukas Menkhoff, Toshitaka Sekine and participantsat the 4th TWID International Conference for very helpful comments.

1.

Introduction

The vast literature on central bank foreign exchange intervention is primarily focused on
assessing contemporaneous or short-term exchange rate effects of intervention. This isappropriate when intervention operations are small-scale and carried out over several daysin relatively short succession, and thus consistent with a policy-aim of influencing
immediate currency price volatility or immediate relative currency values. Recently, in thefall of 2022, and prior to that in 2010 and 2011, the Bank of Japan (BoJ) on behalf of the
Ministry of Finance carried out interventions that are anything but typical. Rather, theseinterventions are large-scale and occur against a backdrop of no BoJ intervention activity
for more than a decade with respect to the 2022 interventions and for more than half adecade with respect to the 2010-2011 interventions. Due to their scale these interventions
have the potential for generating substantial portfolio-balance effects and due to theirnewsworthiness, in the sense that they occur after years of no intervention activity, havethe potential for generating substantial signaling effects. The 2022 BoJ interventions
alongside the 2010-2011 BoJ interventions, therefore, provide an opportunity forinvestigating whether large and infrequent interventions are associated with longer-lastingexchange rate changes such as trend effects.
The 2022 BoJ interventions, carried out as unannounced purchases of domestic
currency in the JPY/USD market on three days in September and October, are particularly
remarkable for several reasons. First, they mark the first time the BoJ intervenes in morethan a decade. This is important, as years of no central bank intervention instills in themarket a perception that the central bank in question may no longer consider intervention
a viable or necessary policy instrument. By contrast, the sudden reemergence of central

2

bank intervention may signal not only an immediate concern with relative currency values
or market volatility but may also effectively switch the exchange rate regime from one
characterized by no expectation of central bank trading activity, and thus no central banksignaling via intervention of future policy intentions, to one where markets price in not
only realized interventions but also the possibility of future interventions and their effects
on prices and expectations. Second, the 2022 interventions constitute the first time inalmost 25 years that the BoJ intervenes with an aim towards strengthening the JPY, i.e.
until the September 2022 intervention no BoJ intervention purchase of domestic currency
had been carried out since 1998, thereby giving further credence to the suggestion that adramatic policy change occurred that is likely to substantially influence market
expectations of future central bank policy and willingness to actively attempt to manage
exchange rates. Third, the intervention amounts - JPY2,838.2 (USD19.93) billion on
September 22, JPY5,620.2 (USD38.06) billion on October 21, and JPY729.6 (USD4.90)
billion on October 24 - are unusually large-scale to the point that the first two 2022
interventions are, respectively, the largest and second-largest intervention JPY purchases
ever made and, in absolute terms, only surpassed by the massive 2011 intervention JPY
sale.
The effectiveness of foreign exchange interventions has been studied from various
angles. For example, a large body of the intervention literature assesses thecontemporaneous effect of intervention on daily or higher frequency exchange rate returns
in the context of linear event study regression models (e.g. Humpage, 1984, andDominguez and Frankel, 1993). Other studies define short pre- and post-event windows,
typically spanning a few days or at most a few weeks, around intervention episodes across3

which exchange rate movements are compared using various criteria for what constitutes
intervention success or effectiveness (e.g. Fatum and Hutchison, 2003, Fratzscher et al.,2019). A recent exception to the short-term focus is the contribution by Menkhoff et al.,(2021), in which structural vector autoregressions are used to assess the cumulative
response of exchange rates to intervention over a time-horizon of one to four quarters.
Importantly, their analysis does not consider trend shifts as these are intrinsicallyeliminated in the analysis of vector autoregressions.
An inherent concern in the context of intervention studies is that central bankintervention is undertaken in response to exchange rate market fluctuations and conditions.
The self-selection aspect of intervention creates possible endogeneity issues that are moreconcerning the longer the time-horizon that is being considered. To address this concern,
Chen et al. (2012) apply a data augmentation method in the system of simultaneous
equations, including an intervention reaction function, while Fatum and Yamamoto (2014),
Naef and Weber (2022) and Menkhoff et al. (2021) use various instrumental variableapproaches, and Kearns and Rigobon (2005) develop heteroskedasticity-based
identification methods.
Other strands of the intervention literature apply natural experiment methods toobtain stylized causal identifications of the effects of foreign exchange interventions. For
example, Fatum and Hutchison (2010) use a propensity-score matching method,
Kuersteiner et al. (2018) employ the regression discontinuity method to investigate therule-based interventions. Chamon et al. (2017), Esaka and Fujii (2019) and Dominguez(2020) introduce the synthetic control method (SCM) to the intervention literature. Morespecifically, Chamon et al. (2017) study the influence on the level of the exchange rate of4

pre-announced interventions in the BRL/USD market, while Esaka and Fujii (2019)consider short-run effects of the 2011 BoJ interventions on JPY/USD exchange rate returns.
Dominguez (2020) provides a comprehensive study of foreign exchange stabilizing
intervention policies of emerging market countries in which she considers a quasiexperiment of stabilizing interventions in reaction to the second US quantitative easing(QE2) and the Taper Tantrum announcements.
As noted earlier, the majority of intervention studies focus on the short-term effects
of intervention on exchange rate returns or on the persistence of the effect of intervention
on exchange rate levels and, to the best of our knowledge, no previous study considers
whether intervention is associated with long-term trend effects of the exchange rate.
From a policy perspective, intervening after no intervention activity for more thana decade, in massive amounts, and in the form of the first JPY purchases in 25 years,
constitutes a policy shift that surely is implemented with the intention of generating shortterm or transient JPY/USD rate effects; rather, this is consistent with a policy goal aimed
at generating long-term or lasting effects. Consequently, the appropriate research questionin this context, and from a policy stand-point the relevant issue, is not whether theseinterventions are associated with contemporaneous or short-lived exchange rate effects but
whether they are associated with longer lasting effects and, specifically, if they are able tobreak the persistent downward trend of the relative value of the domestic currency thatpreceded the interventions.1

1

Coinciding with a widening interest rate gap between the US and Japan, due to the rapidly changing US
monetary policy stance, from January to October 2022 the JPY/USD went from 115 to 150, constituting a
JPY depreciation against the USD of more than 30%. Ito (2022) highlights the increase in global uncertainty
stemming from the Russia-Ukraine war as a contributing factor to the depreciation of the JPY.

5

Our analytical approach is based on the synthetic control method (SCM) originallyproposed by Abadie et al. (2010, 2015), which in our context translates to using a control
pool of no-intervention currencies for estimating a counterfactual currency that has notbeen treated by intervention even though the intervention was implemented to the actual
currency.2 The causal effect of intervention is then identified as the gap between the actualand the counterfactual rates. As we use the cross-sectional information of the control
currencies, the level, the trend, and the time dependence of the treated currency are fully
unrestricted.
The conventional SCM is based on a weighted average of the control units includedin the analysis. In our context, where exchange rates form a system and there are several
factors which determine the exchange rates, there is no theoretical justification for why aparticular exchange rate, in our case the JPY/USD rate, would be determined as a weighted
average of other rates. To address this concern, we use the so-called generalized version of
the standard SCM in which a linear panel data model is applied to compute the synthetic
treated unit. Our linear panel data model includes major determinants of exchange rates
and does not rely on one statistical criterion for weighting the control currencies, thereby
resulting in a more theoretically justified estimated counterfactual rate. Specifically, we
follow the framework of the generalized SCM proposed by Xu (2017), who considers alinear panel data model with unobserved common factors. In particular, our setting
incorporates interest rate differentials, as suggested by the uncovered interest rate parity(UIP), global uncertainty, as suggested by the literature on safe haven currencies (Ranald
and Söderlind, 2010, Habib and Stracca, 2012, and Fatum and Yamamoto, 2016), and2

See Neely (2005) for a survey of the earlier intervention literature.

6

unobserved common factors in global foreign exchange markets, as suggested by thecurrency factor literature (Lustig et al., 2011, Greenaway-McGrevy et al., 2018, andAloosh and Bekaert, 2022). The unobserved common factors are intended to capture global
fluctuations that are otherwise unaccounted for. Importantly, since interventions are notrandom assignments but typically conducted when the gap between the actual and thecounterfactual rates is large and expanding in an unwanted direction, we augment thegeneralized SCM with a time-series analysis of structural changes in the level and trend of
the gap sequence that allows us to investigate if any changes occur around the intervention
dates.
Our main findings are as follows. We provide significant evidence that the trend of
the gap sequence reversed around the 2022 BoJ intervention dates. This is a new andimportant finding for a number of reasons. First, it suggests that foreign exchangeintervention when carried out in a certain manner – large-scale and after an extended lullof no intervention operations – is not only associated with contemporaneous or short-term
exchange rate effects, as evidenced by numerous earlier studies, but also capable ofgenerating a longer lasting trend effect in the intended direction. Second, while previous
studies such as Fatum and Pedersen (2009) suggest that the direction of intervention must
be consistent with the underlying monetary policy stance in order for intervention to beeffective, our findings suggest that this need not be the case. The 2022 interventions are
JPY purchases aimed at strengthening the JPY while the coinciding monetary policy stanceis characterized by an increasing US-Japan interest rate differential which in and of itself
is consistent with a weakening of the JPY. This is an interesting finding that may indicatethat intervention can be a potentially more powerful policy instrument than previously

7thought. Importantly, this finding adds credence to the suggestion that intervention when
carried out during certain circumstances and in a particular manner, such as large-scale andinfrequently and against a persistent exchange rate trend, can be considered an independent
policy instrument.
The rest of this paper is organized as follows. Section 2 describes the data. Section
3 discusses the econometric methodology. Section 4 presents the results and Section 5extends the analysis to consider the 2010-2011 BoJ interventions. Section 6 concludes.

2.

Data

Our data set consists of official Bank of Japan intervention data, daily frequency spot
exchange rates, short-term interest rates, and a global uncertainty measure. Our main dataspans the January 1, 2021 to December 31, 2022 period, encompassing the 2022
intervention period and a one year training sample period spanning January 1 to December
31, 2021.
Figure 1 shows the BoJ intervention amounts juxtaposed against the JPY/USD
exchange rate. To provide historical context we show daily intervention and exchange rate
data spanning from 1998 to the end of our sample period. As can be seen in the figure, the2022 interventions are the first since 2011 and, as noted earlier, the 2022 intervention
amounts in absolute terms are similar to those of the 2010-2011 interventions. Moreover,the 2022 interventions constitute the first JPY intervention purchases since 1998, and are
the largest JPY intervention purchases in history.
There are no official statements available regarding whether the 2022 interventions
under study are sterilized or unsterilized. However, whether or not the interventions under8

study are sterilized or unsterilized is an important issue in terms of possible policy
implications of our analysis, since only sterilized intervention can be considered an
independent policy instrument, as well as for the possible transmission mechanisms
through which intervention might work. In essence, unsterilized intervention changes themonetary base in which case any effects of intervention on exchange rates may occur not
only via transmission channels such as the signaling or the portfolio balance channel, butalso via a likely stronger monetary channel stemming from the intervention induced change
in relative money supplies. To address the issue we plot the 2022 interventions against
daily changes in the Japanese monetary base. As Figure 2 shows, there is no indication thatany of these interventions are associated with discernible changes in the monetary base,
thereby implying that the interventions under study are sterilized and that any associatedexchange rate effects occur via traditional transmission channels rather than via a monetarychannel.3
We follow Aloosh and Bekaert (2022) and Engel and Wu (2023) in selecting seriesof relative currency values vis-à-vis the USD for all the non-US G10 countries, thereby
incorporating the most liquid currencies that account for almost 90% of total currency
market trading volume.4 Figure 3 displays separately the evolution of each of the ninecurrency pairs over the sample period. As the first sub-figure shows, the JPY exhibits a
depreciating trend relative to the USD.
Figure 4 shows separately for each non-US G10 country the short-term interest rate
differential vis-à-vis the US. 5 The interest rate differentials are quite similar across all

3

For a conceptual discussion of sterilized versus unsterilized intervention see Dominguez and Frankel (1993).
See BIS (2022) for trading volume statistics.
5
In their recent UIP study, Ismailov and Rossi (2018) use three-month Euro LIBOR rates to capture countryspecific interest rate differentials relative to the US rate. However, due to the 2021 benchmark rate reform
49

countries considered, i.e. unchanged at the beginning and decreasing toward the end of thesample period when the pace of the US interest rate hike increases. As the figure shows,the magnitude of the change in the interest rate differential is largest for Japan.
Figure 5 displays the global uncertainty measure, the VIX. The VIX, provided by
the Chicago Board Options Exchange, is a forward-looking, model-free measure of thenear-term (30-day) implied volatility of S&P 500 index options.

3.

Econometric Methodology

We first estimate the following panel data exchange rate model:

𝑆𝑖,𝑡 = 𝜇 + 𝜙𝑖,𝑡 + 𝛽𝑅𝑖,𝑡 + 𝛾𝑖 𝑉𝐼𝑋𝑡 + 𝜆′𝑖 𝐹𝑡 + 𝑢𝑖,𝑡(1)

where 𝑆𝑖,𝑡 is the log of the value of the currency of country 𝑖 relative to the USD at time 𝑡
for 𝑖 = 1, … , 𝑁 and 𝑡 = 1, … , 𝑇 , with 𝑁 and 𝑇 denoting the number of cross-sectional
units and time observations, respectively. Equation (1) considers the bilateral exchange
rate as determined by two observed covariates, namely the interest rate differential 𝑅𝑖,𝑡 (thedifference between short-term interest rates of country 𝑖 and that of the US, in basis points)
and the volatility index 𝑉𝐼𝑋𝑡 . We assume that UIP holds thus the coefficient estimate 𝛽these rates are now unavailable for several countries. We therefore use instead the following interest ratemeasures (Bloomberg mnemonics listed in parentheses). The swap OIS rate for the US (USSOC), the TIBOR
fixing for Japan (TI0003M), the ESTR rate for the Euro area (EESWEC), the SARON rate for Switzerland(SFSNTC), the USSONIA swap rate for the UK (BPSWSC), the OIS rate for Australia (ADSOC), Canada(CDSOC), Sweden (SKSOC), and New Zealand (NDSOC), and the NIBOR for Norway (NIBOR3M). As arobustness check, we use instead three-month interbank deposit rates for all countries (USDRC for US,
JYDRC for Japan, EUDRC for Euro area, SFDRC for Switzerland, BPDRC for the UK, CDDRC for Canada,
SKDRC for Sweden, NKDRC for Norway, ADDRC for Australia, and NDDRC for New Zealand) as wellas, subsequently, ten-year government bond yields computed using Bloomberg Generic (BGN) methodology.
Our findings are qualitatively unchanged regardless of which interest rate series we use.

10

associated with 𝑅𝑖,𝑡 is the same across all currencies whereas the influence of global
uncertainty is assumed to be country-specific. Moreover, we include the term 𝜆′𝑖 𝐹𝑡 tocapture time-varying unobserved heterogeneity, where 𝐹𝑡 is an 𝑟 × 1 vector of common
factors and 𝜆𝑖 is an 𝑟 × 1 vector of factor loadings. This term is included to capture global
co-movements not accounted for by the interest rate differentials and the global uncertainty
index. The model also includes a common intercept 𝜇 and an error term 𝑢𝑖,𝑡 .
Most importantly, and the focal point of our analysis, the model contains theunknown nonrandom parameter 𝜙𝑖,𝑡 . This is the key parameter of interest as it captures theeffects of intervention. By contrast, a model without 𝜙𝑖,𝑡 forms the counterfactual𝑐𝑐exchange rate (𝑆𝑖,𝑡), where super-script 𝑐 indicates counterfactual. Accordingly, 𝑆𝑖,𝑡is theuntreated exchange rate if no interventions are implemented:

𝑐𝑆𝑖,𝑡 = 𝑆𝑖,𝑡
+ 𝜙𝑖,𝑡 ,

(2)

𝑐
𝑆𝑖,𝑡
= 𝜇 + 𝛽𝑅𝑖,𝑡 + 𝛾𝑖 𝑉𝐼𝑋𝑡 + 𝜆′𝑖 𝐹𝑡 + 𝑢𝑖,𝑡 .

(3)

where

To identify the causal effects, we divide the cross-sectional units into two by, in ourcontext, setting the JPY/USD rate as the treated unit and the exchange rates of the othereight countries as the control group. For convenience, we reorder the data such that thetreated unit is located at the end of the reordered series, i.e. 𝑖 = 𝑁, and the units 𝑖 =1, … , 𝑁 − 1 are all control units. We also divide the entire time dimension into two by
setting the training sample as 𝑡 = 1, … , 𝑇0 and the testing sample as 𝑡 = 𝑇0 + 1, … , 𝑇. The
gap sequence 𝜙𝑖,𝑡 is by construction assumed to be zero for the control units over the entire

11

sample period. It is also assumed to be zero for the treated unit in the training sample but
not in the testing sample.
The standard SCM procedure would set 𝑇0 at the intervention date, and label thetwo samples the pre- and the post-intervention samples. However, doing so would beconcerning for two reasons. First, since it is well-known that empirical exchange rate
models are inherently associated with a poor fit of actual data, the gap between the actualand the counterfactual rates is likely substantial and may include various confounding
factors for inference. Second, and more importantly, as illustrated in Figure 6, interventions
are not random occurrences but typically conducted when the gap is large and expandingin an unwanted direction.6 To address these concerns, we introduce a model of the gap 𝜙𝑖,𝑡
as a linear trend with multiple endogenously determined structural breaks:

𝜙𝑖,𝑡 = 𝐷𝑖,𝑡 𝜋𝑖 ,

(4)

𝑚
𝑚
𝑙
𝑙
1
1
where 𝐷𝑖,𝑡 = [1, 𝑐𝑖,𝑡
, … , 𝑐𝑖,𝑡
, 𝑡, 𝑑𝑖,𝑡, … , 𝑑𝑖,𝑡] with 𝑐𝑖,𝑡
= 𝐼(𝑡 > 𝑇𝑖,𝑙 ) and 𝑑𝑖,𝑡
= 𝐼(𝑡 >

𝑇𝑖,𝑙 )(𝑡 − 𝑇𝑖,𝑙 ) for 𝑙 = 1, … , 𝑚 with coefficient vector 𝜋𝑖 .7

3.1.

Estimation

The expression described in Equation (1) is a linear panel data model with a common factor
structure in the error term and it is estimated using the following standard econometric

6

Chamon et al. (2017) account for the first concern by adjusting the counterfactual values to match the actual
value at the date of intervention. Doing so, however, does not take into account the second concern, i.e. thatthe distance between the actual and the counterfactual exchange rates is determined endogenously.
𝑙7
Note that 𝑐𝑖,𝑡accounts for the change in the intercept such that 𝜙𝑖,𝑡 can be associated with jumps or level𝑙shifts while 𝑑𝑖,𝑡 captures shifts in the linear trends.

12techniques. First, we standardize 𝑆𝑖,𝑡 by subtracting the sample mean and dividing by the
sample standard deviation for each 𝑖. We then use ordinary least squares (OLS) to estimate
the regression model with the standardized 𝑆𝑖,𝑡 as the dependent variable and 𝑅𝑖,𝑡 and 𝑉𝐼𝑋𝑡
as the independent variables to obtain the residuals 𝑧𝑖,𝑡 . Next, let 𝑍 denote a 𝑇 × 𝑁 matrixof the residuals with the (𝑡, 𝑖)th element being 𝑧𝑖,𝑡 . Then, the 𝑟 principal components, i.e.
the eigenvectors corresponding to the 𝑟 largest eigenvalues of 𝑍𝑍 ′ /(𝑁𝑇) denoted by 𝐹̂𝑡with normalization 𝑇 −1 ∑𝑇𝑡=1 𝐹̂𝑡 𝐹̂ ′𝑡 = 𝐼𝑟 , are our estimates of the unobserved common
factors. The factor loadings 𝜆𝑖 are subsequently estimated by the least squares of 𝑧𝑖,𝑡 on 𝐹̂𝑡such that 𝜆̂𝑖 = 𝑇 −1 ∑𝑇𝑡=1 𝐹̂𝑡 𝑧𝑖,𝑡 .
The efficiency of the OLS coefficient estimators for 𝜃 ≡ {𝜇, 𝛽, 𝛾𝑖 } can be improvedby accounting for the unobserved factor structure in the errors. To this end, we apply theinteractive fixed effects estimation procedure proposed by Bai (2009). This procedure is
implemented by rather than using the dependent variable 𝑆𝑖,𝑡 and the regressors 𝑅𝑖,𝑡 and
𝑉𝐼𝑋𝑡 , we use the complementary projections of these variables on the space spanned by
the estimated factors. Doing so yields new coefficient estimates 𝜃̃ ≡ {𝜇̂ , 𝛽̃, 𝛾̃𝑖 } andassociated residuals 𝑧̃𝑖 ,𝑡 . Subsequently, the common factors and the factor loadings are thenre-estimated using the principal components of the updated residuals 𝑧̃𝑖,𝑡 , denoted by 𝐹̃𝑡and 𝜆̃𝑖 .
Importantly, if the residuals 𝑧𝑖,𝑡 do not include the gap 𝜙𝑖,𝑡 , the unobserved common
factors can be consistently estimated. However, since the residuals do include 𝜙𝑖,𝑡 for thetreated units in the testing sample, estimating the unobserved common factors would leadto inconsistent estimates of the factors and the factor loadings. To circumvent this problem
we exclude the sample for 𝑖 = 𝑁 and 𝑡 = 𝑇0 + 1, … , 𝑇 by employing the tall-wide (TW)13

algorithm proposed by Bai and Ng (2021) in the context of matrix completion algorithm.
Their method uses 𝑧𝑖,𝑡 (or 𝑧̃𝑖,𝑡 ) for 𝑖 = 1, … , 𝑁 − 1 and all 𝑡 to estimate 𝐹𝑡 for 𝑡 = 1, … , 𝑇.
We thus follow the Bai and Ng (2021) procedure to obtain 𝐹̂𝑡𝑇𝑊 (or 𝐹̃𝑡𝑇𝑊 ) and, in turn, thefactor loading estimates 𝜆̂𝑇𝑊(or 𝜆̃𝑇𝑊) for 𝑖 = 1, … , 𝑁 are obtained from the OLS𝑖𝑖coefficients of regressing 𝑧𝑖,𝑡 (or 𝑧̃𝑖,𝑡 ) on 𝐹̂𝑡𝑇𝑊 (or 𝐹̃𝑡𝑇𝑊 ) using 𝑡 = 1, … , 𝑇0 and 𝑖 = 1, … , 𝑁.
Once we obtain the estimates for the coefficients, common factors, and factor
loadings, the counterfactual rate is constructed as the fitted value of the model describedby Equation (5):

′ 𝑇𝑊
𝑐
𝑆̃𝑖,𝑡
= 𝜇̃ + 𝛽̃𝑅𝑖,𝑡 + 𝛾̃𝑖 𝑉𝐼𝑋𝑡 + 𝜆̃𝑇𝑊
𝐹̃𝑡
𝑖

(5)

Subsequently, the gap between the actual and the counterfactual rates is obtainedby subtracting the latter from the former:𝑐
𝜙̃𝑖,𝑡 = 𝑆𝑖,𝑡 − 𝑆̃𝑖,𝑡(6)

for 𝑖 = 𝑁 and 𝑡 = 𝑇0 + 1, … , 𝑇. At this stage, we retrieve the original scales of theexchange rates by multiplying the sample standard deviation and by adding the sample
mean of the original data for each country 𝑖.
Once we have estimated the gap 𝜙𝑖,𝑡 , our strategy for estimating the trend break isthe following. We first fit an intercept and a linear trend with possible structural breaks to
𝜙̃𝑖,𝑡 using generalized least squares, and then we apply the multiple structural change test

14

proposed by Kejriwal and Perron (2010). 8 This test considers multiple breaks at 𝑡 =𝑇1 , … , 𝑇𝑚 in the trend and/or the intercept where the estimation errors are accounted for by
the noise component. The noise component can either be stationary or integrated such that:

𝜙̃𝑖,𝑡 = 𝐷𝑖,𝑡 𝜋𝑖 + 𝑣𝑖,𝑡(7)

𝑣𝑖,𝑡 = 𝜌𝑣𝑖,𝑡 + 𝜀𝑖,𝑡(8)

for 𝑡 = 𝑇0 + 1, … , 𝑇 , where 𝑣𝑖,𝑡 captures estimation errors, 𝜌 (|𝜌| ≤ 1) is a persistence
parameter in the noise component, and 𝜀𝑖,𝑡 is assumed to be an i.i.d. sequence.
The procedure first determines the number of structural breaks in the trend and/orintercept by using the sequential tests for no break in the null hypothesis 𝐻0 against one
break in the alternative hypothesis 𝐻1 . If the test rejects 𝐻0 , it proceeds to a test for one
break in 𝐻0 against two breaks in 𝐻1 , and so on. We denote the test statistic for 𝑙 breaks
against 𝑙 + 1 breaks by 𝐹𝑇 (𝑙 + 1|𝑙). The number of breaks in 𝐻0 when the test stops
rejecting is considered as the number of breaks present. We follow Bai and Perron (1998)
and set the required data points between the two adjacent breaks to 10% of the entire sample
size. The critical values of the 𝐹𝑇 (𝑙 + 1|𝑙) test are provided by Kejriwal and Perron (2010).

3.2.

Confidence Intervals

We construct the confidence intervals of 𝜙𝑖,𝑡 and other coefficient estimates included in
Equation (1) by employing the residual-based bootstrap method proposed by Xu (2017).

8

Kejriwal and Perron (2010) extends the single break model developed by Perron and Yabu (2009) toconsider multiple breaks.

15

The key objective here is to generate the bootstrap samples “as if no 𝜙𝑖,𝑡 is present”. Thisis detailed in Step 2 of the bootstrap algorithm described below.

Bootstrap Algorithm𝑐Step 1. We first estimate the model described in Equation (1) in order to obtain 𝑆̃𝑖,𝑡and

𝜙̃𝑖,𝑡 and, in turn, the coefficient estimate 𝜃̃ = {𝜇̃, 𝛽̃, 𝛾̃𝑖 } and the residuals 𝑢̃ =[𝑢̃1 , 𝑢̃2 , … , 𝑢̃𝑁 ], where 𝑢̃𝑖 = [𝑢̃𝑖,1 , 𝑢̃𝑖,2 , … , 𝑢̃𝑖,𝑇 ]′.
Step 2. Next, we generate the bootstrap residuals for the treated unit (JPY/USD; 𝑖 = 𝑁).
To ensure that the treated unit is free of 𝜙𝑖,𝑡 we do as follows. We first randomly select one
control unit from 𝑖 = 1, … , 𝑁 − 1 , and consider this a “fake treated unit”. We thenrandomly select the rest of the control units with replacement 𝑁 − 1 times to form a set of“fake control units”. Subsequently, we combine the fake control units and the fake treatedunit to produce new residuals with 𝑁 − 1 control units and one treated unit. Finally, we reestimate Equation (1) using the new and modified data and obtain the associated residuals∗∗∗∗
for 𝑖 = 𝑁 , denoted by 𝑢𝑁= [𝑢𝑁,1, 𝑢𝑁,2, … , 𝑢𝑁,𝑇]′ . We repeat this 𝐵 times and store∗ (1), ∗ (2),∗ (𝐵)].
[𝑢𝑁𝑢𝑁… , 𝑢𝑁∗
Step 3. We generate the bootstrap residuals for the control units 𝑢𝑖,𝑡for 𝑖 = 1, … , 𝑁 − 1

by resampling the residual vectors of size 𝑇 × 1 from the pool of (𝑁 − 1) units withreplacement. This way the bootstrap retains time dependence in the residuals. We also use
the bootstrap residuals for the treated unit 𝑖 = 𝑁 from Step 2.
Step 4. We generate the bootstrap sample free of 𝜙𝑖,𝑡 by estimating the following
expression:∗∗𝑆𝑖,𝑡= 𝜇̃ + 𝛽̃𝑅𝑖,𝑡 + 𝛾̃𝑖 𝑉𝐼𝑋𝑡 + 𝜆̃𝑇𝑊′
𝐹̃𝑡𝑇𝑊 + 𝑢𝑖,𝑡
𝑖

16

(9)

for 𝑖 = 1, … , 𝑁 and 𝑡 = 1, … , 𝑇. We then implement the same estimation method described∗in Step 1 using the bootstrapped sample 𝑆𝑖,𝑡
. We obtain the bootstrap counterfactual rate∗
for the treated unit 𝑆̃𝑁,𝑡
for 𝑡 = 𝑇0 + 1, … , 𝑇 , and the bootstrap estimate for the gap∗
sequence 𝜙̃𝑁,𝑡
for 𝑡 = 𝑇0 + 1, … , 𝑇. We also obtain the bootstrap coefficient estimate 𝜃̃ ∗ ≡{𝜇̃∗ , 𝛽̃∗ , 𝛾̃𝑖∗ }.
∗Step 5. We repeat Steps 3-4 𝐵 times and store the counterfactual rates {𝑆̃𝑁,𝑡(𝑗)}𝑇𝑡=𝑇0+1 and∗the gap sequence {𝜙̃𝑁,𝑡(𝑗)}𝑇𝑡=𝑇0+1 for 𝑗 = 1, … , 𝐵 . The 100 × (1 − 𝛼)% confidence

interval is then constructed using the percentile method, i.e. for every 𝑡, let the 100 × 𝛼𝜙,𝛼∗percentile of {𝜙̃𝑁,𝑡(𝑗)}𝐵𝑗=1 be 𝐶𝑡 . The confidence interval of the counterfactual rate is𝜙,1−𝑐then described by [𝑆̃𝑁,𝑡
− 𝐶𝑡

𝛼
2

𝜙,𝛼/2

𝑐
, 𝑆̃𝑁,𝑡− 𝐶𝑡
𝜙,1−sequence is described by [𝜙̃𝑁,𝑡 − 𝐶𝑡𝛼2] and the confidence interval of the gap

𝜙,𝛼/2, 𝜙̃𝑁,𝑡 − 𝐶𝑡
] . Finally, to construct theconfidence interval of the coefficient estimates we set the 100 × 𝛼/2 and the 100 × (1 −𝛼2) percentiles for each element of (𝜃̃ ∗ − 𝜃̃) to 𝐶 𝜃,𝛼/2 and 𝐶 𝜃,1−𝛼/2 . The confidence𝛼interval of each coefficient in 𝜃 is then described by [𝜃̃ − 𝐶 𝜃,1− 2 , 𝜃̃ − 𝐶 𝜃,𝛼/2 ].9

4.

Results

Table 1 reports the results of estimating Equation (1). As the table shows, the interest rate
differentials coefficient estimate is negative, as expected, as well as statistically significant,9

While the confidence intervals of the trend break dates in 𝜙𝑖𝑡 would also be of interest, to the best of ourknowledge a method for calculating such confidence intervals has not been developed, and it is beyond thescope of this study for us to attempt to do so.

17

at the 5% level. The coefficient estimates associated with the global uncertainty measureare heterogeneous across the currencies considered. Of particular interest is that only for
the JPY do we find that the global uncertainty coefficient estimate is negative andstatistically significant at the 5% level. This is in line with Fatum and Yamamoto (2016)
and other studies of safe haven currencies that typically identify the JPY as a currency thatexhibits a particularly strong safe haven behavior.
Figure 7 displays the estimated currency factors 𝐹̃𝑡𝑇𝑊 . The number of factors is set
to 3 following Aloosh and Bekaert (2022).10 It is known that the estimated factors are
orthogonal by assumption and their signs are indeterminant, hence rigorous interpretationsof individual factor estimates are not applicable. Nonetheless, the figures show that the first
factor captures the depreciation trends of the JPY, the CHF, the SEK, and the NOK. The
second factor captures co-movements of the EUR and the GBP. The third factor represents
features of the AUD, the NZD and the CAD, consistent with the presence of a “commodity
factor”, as suggested by Greenaway-McGrevy et al. (2018) and Aloosh and Bekaert (2022).
Figure 8 shows the actual and the counterfactual JPY/USD rates. The upper panel𝑐presents the actual rate (𝑆𝑁,𝑡 ) in a solid thin line and the counterfactual rate (𝑆̃𝑁,𝑡) in a solid

thick line along with the associated 95% confidence intervals. The lower panel plots theestimate of the gap sequence (𝜙̃𝑁,𝑡 ). The intervention dates are indicated by dotted verticallines. The upper panel shows that starting in April, the actual rate moves upward while thecounterfactual rate stays largely unchanged. As a result, the gap expands considerably, as

10While several statistical methods are proposed for determining the number of factors present in the data,
e.g. Bai and Ng (2002), Onatski (2010) and Ahn and Horenstein (2013), none is suitable in our context of
only 9 currency pairs. We therefore set the number of currency factors to 3 and subsequently change that
number to 1, 2 and 4. Doing so yields qualitatively identical results as well as points to the first factor being
particularly important.

18

shown in the lower panel of Figure 8. Most importantly, the gap is large and expanding up
until around the time when interventions are undertaken and subsequently, after theinterventions are carried out, the gap sequence reverses, consistent with the suggestion thatthe 2022 interventions are associated with a trend effect.
Turning to the formal analysis of the trend break in the gap sequence, we report theresults of the structural change tests in Table 2. As the table shows, accounting for two
breaks is optimal as the 𝐹𝑇 (1|0) and the 𝐹𝑇 (2|1) tests reject their null hypotheses at the
1% and the 10% significance level, respectively, and the 𝐹𝑇 (3|2) test does not reject thenull hypothesis. The break dates are identified as April 22 and October 17. Figure 9
illustrates the estimated gap sequence (dotted line) and the conditional mean or fitted value(solid line). The amounts of interventions are also shown as (scaled) bars on the rightvertical axis. The figure shows that the depreciating trend continued since the beginning of2022 and reversed right around when the interventions are carried out. As the interventions
under study are all JPY purchases, and thus consistent with a policy objective aimed atpreventing further JPY depreciation, our results are consistent with the notion that the 2022
BoJ interventions were instrumental in breaking the trend of the JPY depreciation.11
Dominguez (2020) finds that intervention operations in the form of accumulationof reserves in response to the US QE2 were successful as the actual exchange rate
depreciated more than its counterfactual rate. Moreover, she finds that the selling ofreserves in some countries following the Taper Tantrum were also successful as these
operations were associated with the actual exchange rate appreciating more than its

11

The first break is associated with a small level shift that is unrelated to intervention as no intervention
occurred around the first break date. Since the gap sequence takes into account the possibility of currencyspecific confounding factors, this finding is unsurprising.

19

counterfactual rate. Her results also show persistence in the effects of intervention on the
gap between the actual and counterfactual rates. Although our context is very different, as
the large-scale BoJ interventions are conducted in response to domestic currency market
conditions rather than in response to exogenous US monetary policy shocks, our results
also document long-term effects of interventions and are thus in that sense consistent withthe findings of Dominguez (2020).
To ensure robustness of our findings, we first consider if the observed covariates(interest rate differentials and VIX) drive our main results. Replacing our short-term
interest rates with long-term interest rate measures as discussed in Section 2 and using amodel without the VIX does not affect our results. Next, we consider if our findings are
sensitive to the number of common factors included. In the baseline analysis we follow the
recent literature on currency factors (e.g. Aloosh and Bekaert, 2022) and use three factors(r=3). As it turns out, estimating the gap between the actual and counterfactual JPY/USD
rates with instead 𝑟 = 1, 2, or 4 does not qualitatively change our results. Additional
details and associated figures of the gap sequences are available upon request.

5.

The 2010-2011 Intervention Period

We extend our analysis to consider if the 2010-2011 BoJ interventions are also associatedwith a trend effect.12 As shown in Figure 1, during the 2010-2011 intervention period the
BoJ carried out intervention operations on eight days (September 15, 2010; March 18,

12

Similar to the 2022 interventions, no official statements are available regarding whether the 2010-2011
interventions are sterilized or not. When we plot the 2010-2011 interventions against changes in the Japanesemonetary base we again find no indication that the interventions are associated with discernible changes in
the monetary base.

20

August 4; October 31 to November 4, 2011).13 All of these interventions are sales of JPY
against the USD, consistent with a policy aim towards preventing further JPY appreciation
following the Global Financial Crisis. The 2010-2011 interventions are large-scale,including JPY4,512.9 (USD57.2) billion on August 4 and JPY9,091.7 (USD116.30) billion
over the October 31-November 4 5-day period. To carry out the trend effect analysis we
use daily observations spanning the October 1, 2009 to December 31, 2011 period, and we
set the training sample from the beginning of the sample period to July 31, 2010 and thetesting sample from August 1, 2010 to the end of the sample period.
Table 3 reports the results of re-estimating the counterfactual model over the 20092011 sample. As before, the interest rate differential coefficient estimate is negative andhighly significant, as expected, and the coefficient estimate associated with the VIX is once
again also negative and highly significant for the JPY and the CHF, as well as for the EUR
and the NZD.
Figure 10 presents the estimated currency factors. The first factor captures theappreciation trends of the JPY, the CHF, the SEK and the NOK while the second and thethird factors show features similar to what we found for the 2022 period.
Figure 11 plots the actual and the counterfactual JPY/USD rates as well as the gap
sequence for the 2010-2011 intervention period. The actual and the counterfactual rates do
not show significant differences when the first two interventions are conducted, on
September 15, 2010, and on March18, 2011, but move in opposite directions starting inMay 2011, i.e. the actual rate appreciated (moved downward) while the counterfactual rate

13

The March 18, 2011 intervention differs from the other interventions considered in this study due to it
being carried as part of a concerted G7 intervention effort to stem the the sudden JPY appreciation following
the March 16, 2011 Fukushima earthquake.

21

depreciated (moved upward). Then, following August 2011, the former stays stable
whereas the counterfactual rate moves further downward. As a result, the gap sequence
takes the form of a V-Shape, decreasing until August 2011 and recovering afterwards.
It is interesting to notice that the four intervention episodes were carried out during
different exchange rate conditions and associated with different outcomes. The September
15, 2010 and the March 18, 2011 interventions occurred when both the actual and thecounterfactual JPY rate appreciated and, consequently, the gap was insignificant and not
expanding. By contrast, while the August 4, 2011 intervention was also conducted against
an appreciating trend of the actual rate, the counterfactual rate at this time was moving in
the opposite direction. Finally, the October 31- November 4, 2011 interventions took placewhen the actual rate was appreciating but the counterfactual rate was constant.
Turning to the structural change tests, Table 4 displays the results. As the tableshows, we find that two breaks are present as the 𝐹𝑇 (1|0) and the 𝐹𝑇 (2|1) tests reject thenull hypothesis at the 1% and at the 10% levels, respectively, while the 𝐹𝑇 (3|2) test doesnot. The optimal break dates are estimated at February 18, 2011 and September 2, 2011,
thus very close to the March 18, 2011 and the August 4, 2011 intervention dates. Figure 12
shows the estimated gap sequence and the conditional mean function for the 2010-2011
period. There is a mild JPY appreciation trend occurring early in 2010 followed by asteepening of the trend subsequent to the first break date. Since all 2010-2011 interventions
are JPY sales, including the September 15, 2010 and the March 18, 2011 interventions,these interventions are deemed ineffective in terms of having a trend effect. Subsequently,
the trend of the gap sequence reversed in the intended direction, and the reversal occurred22

not far from the August 4 intervention with the second break date estimated at September
2, 2011, suggesting that these latter interventions are associated with trend effects.
To check the robustness of the previous findings we impose the same number ofbreaks as the number of intervention episodes, namely four. As shown in the lower panelof Figure 12, the four breaks are estimated at November 3, 2010, March 1, July 27, andOctober 11, 2011. The first break is quite far from the September 15, 2010, intervention,
while the remaining three breaks are very close to subsequent intervention episodes. In
particular, the July 27, 2011 break date is very close to the August 4, 2011 intervention
date and associated with a steep shift in desired direction of the trend of the exchange rate,
and the fourth and final break date, October 11, 2011 is close to the October 31-November
4, 2011 interventions and is thus also consistent with an intervention related correction ofan unwanted local trend. It is not surprising to observe that the most effective intervention
episodes in regards to trend effects are also the ones associated with the largest intervention
amounts.
Overall, our results of the analysis of the 2010-2011 interventions further indicatethat interventions have the potential to induce a trend effect. At the same time, the 20102011 results also show that not all interventions have trend effects. In particular, thesefindings suggest that in order for a trend effect to materialize interventions have to be
implemented when the gap is large, when the gap is expanding in an unwanted direction,i.e. interventions occur as leaning against the wind, and when interventions are carried out
in very large amounts.

6.

Conclusion

23

We investigate the trend effect of the 2022 BoJ intervention episode by employing acounterfactual estimate of the JPY which incorporates major exchange rate determinants
such as interest rate differentials, global uncertainty, and unobserved currency factors. We
address the issue of inherently poor performance of empirical exchange rate models as wellas the endogeneity concern stemming from leaning-against-the-wind characteristics of theinterventions and consider structural changes in the level and the trend of the gap sequence
between actual and counterfactual exchange rates.
Our results show that the trend of the gap sequence reversed in the desired direction
around the 2022 intervention dates, indicating that the intervention policy instrument ispotentially powerful enough to generate not only immediate and short-term exchange rate
effects, as shown by earlier intervention studies, but also long-term effects in the form of
trend reversals. This is an in important insight not previously found in the intervention
literature.
We also analyze the 2010-2011 intervention period and in this context provide
further evidence to suggest that interventions have the potential to induce a trend effect. At
the same time, the 2010-2011 results show that not all interventions have trend effects. The
latter is not surprising but nevertheless important as it adds more than just nuance to theinterpretation of our findings. In particular, while our main result is that intervention iscapable of influencing the long-term path of the exchange rate, our findings also show that
this is not always the case. Since our 2022 and 2010-2011 samples encompass three andeight intervention days, respectively, we are unable to provide insights based on rigorous
analysis in regards to why some intervention episodes are associated with trend effects andwhy others are not. However, anecdotal evidence based on the data at hand suggests that24

for a trend effect to materialize interventions have to be implemented when the gap is large,
when the gap is expanding in an unwanted direction, i.e. interventions occur as leaning
against the wind, and when interventions are carried out in very large amounts.
While it is beyond the scope of this study to investigate the transmission channels
driving the trend effect of intervention we observe that our findings are consistent withintervention being effective via the portfolio balance channel as well as through thesignaling channel. Moreover, the sterilized nature of the 2022 interventions under study is
consistent with the suggestion that an important policy implication of our analysis is thatinterventions when carried out during certain circumstances and in a particular manner,such as large-scale and infrequently and against a persistent exchange rate trend, can serveas an independent policy instrument.

25

References
Abadie, A., Diamond, A., Hainmueller, J., 2010. Synthetic control methods forcomparative case studies: Estimating the effect of California's tobacco control program.
Journal of the American Statistical Association 105, 493-505.
Abadie, A., Diamond, A., Hainmueller, J., 2015. Comparative politics and the synthetic
control method. American Journal of Political Science 59, 495-510.
Ahn, S.C., Horenstein, A.R., 2013. Eigenvalue ratio test for the number of factors.
Econometrica 81, 1203-1227.
Aloosh, A., Bekaert, G., 2022. Currency factors. Management Science 68, 4042-4064.
Bai, J., 2009. Panel data models with interactive fixed effects. Econometrica 77, 12291279.
Bai, J., Ng, S., 2002. Determining the number of factors in approximate factor models.
Econometrica 70, 191-221.
Bai, J., Ng, S., 2021. Matrix completion, counterfactuals, and factor analysis of missing
data. Journal of American Statistical Association 116, 1746-1763.
Bai, J., Perron, P., 1998. Estimating and testing linear models with multiple structuralchanges. Econometrica 66, 47-78.
Bank for International Settlements (BIS), 2022. Triennial central bank survey: OTC foreignexchange turnover in April 2022.
Chamon, M., Garcia, M., Souza, L., 2017. FX interventions in Brazil: A synthetic control
approach. Journal of International Economics 108, 157-168.
Chen, C.-N., Watanabe, T., Yabu, T., 2012. A new method for identifying the effects offoreign exchange interventions. Journal of Money, Credit and Banking 44, 1507-1533.
Dominguez, K., 2020, Revisiting exchange rate rules. IMF Economic Review 68, 693-719.
Dominguez, K., Frankel, J., 1993. Does foreign exchange intervention work?. Washington
DC: Institute for International Economics.
Engel, C., Wu, S.P.Y., 2023. Forecasting the U.S. Dollar in the 21st century. Journal ofInternational Economics 141.
Esaka, T., Fujii, T., 2019. Evaluating the effectiveness of foreign exchange intervention
using counterfactual analysis: Evidence from Japanese intervention episodes, 2010-2011.
Working Paper.

26

Fatum, R., Hutchison, M.M., 2003. Is sterilised foreign exchange intervention effective
after all? An event study approach. Economic Journal 113, 390-411.
Fatum, R., Hutchison, M.M., 2010. Evaluating foreign exchange market intervention: Selfselection, counterfactuals and average treatment effects. Journal of International Moneyand Finance 29(3), 570-584.
Fatum, R., Pedersen, J., 2009. Real-time effects of central bank intervention in the Euro
market. Journal of International Economics 78, 11-20.
Fatum, R., Yamamoto, Y., 2014. Large versus small foreign exchange interventions.
Journal of Banking and Finance 43, 114-123.
Fatum, R., Yamamoto, Y., 2016. Intra-safe haven currency behavior during the global
financial crisis. Journal of International Money and Finance 66, 49-64.
Fratzscher, M., Gloede, O., Menkhoff, L., Sarno, L., Stohr, T., 2019. When is foreignexchange intervention effective? Evidence from 33 countries. American Economic
Review: Macroeconomics 11, 132-156.
Greenaway-McGrevy, N., Mark, Sul, D., Wu, J.-L., 2018. Identifying exchange ratecommon factors. International Economic Review 59, 2193-2218.
Habib, M.M., Stracca, L., 2012. Getting beyond carry trade: What makes a safe havencurrency?. Journal of International Economics 87, 50-64.
Humpage, O.F., 1984. Dollar intervention and the Deutschemark-Dollar exchange rate: A
daily time-series model. Federal Reserve Bank of Cleveland working paper 8404.
Ismailov, A., Rossi, B., 2018. Uncertainty and deviations from uncovered interest rate
parity. Journal of International Money and Finance, 88, 242-259.
Ito, T., 2022. Down Goes the Yen. Project Syndicate, October 20, 2022.
Kearns, J., Rigobon, R., 2005. Identifying the efficacy of central bank interventions: The
Australian case. Journal of International Economics 66, 31-48.
Kejriwal, M., Perron, P., 2010. A sequential procedure to determine the number of breaks
in trend with an integrated or stationary noise component. Journal of Time Series Analysis
31, 305-328.
Kuersteiner, G.M., Phillips, D.C., Villamizar-Villegas, M., 2018. Effective sterilized
foreign exchange intervention? Evidence from a rule-based policy. Journal of International
Economics 113, 118-138.

27

Lustig, H., Roussanov, N., Verdelhan, A. 2011. Common risk factors in currency markets.
Review of Financial Studies 24, 3731-3777.
Naef, A., Weber, J.P., 2022. How powerful is unannounced, sterilized foreign exchangeintervention?. Journal of Money, Credit and Banking (forthcoming).
Menkhoff, L., Rieth, M., Stohr, T., 2021. The dynamic impact of FX interventions offinancial markets. Review of Economics and Statistics 103, 939-953.
Neely, C.J., 2005. An analysis of recent studies of the effect of foreign exchangeintervention. Federal Reserve Bank of St. Louis Review 87, 685-717.
Onatski, A., 2010. Determining the number of factors from empirical distribution of
eigenvalues. Review of Economics and Statistics 92, 1004-1016.
Perron, P., Yabu, T., 2009. Estimating deterministic trends with an integrated or stationary
noise component. Journal of Business and Economic Statistics 27, 369-396.
Ranaldo, A., Söderlind, P., 2010. Safe haven currencies. Review of Finance 14, 385-407.
Xu, Y., 2017. Generalized synthetic control method: Causal inference with interactive
fixed effects models. Political Analysis 25, 57-76.

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Figure 1. Foreign Exchange Interventions in JPY/USD Market
1000

180

(billion yen per day)

(JPY/USD)

800

160
600

140
400
200

120

0

100

-200

80
-400

60
-600
-800
1998

40
2000

02

04

06

08

10

12

14

16

18

20

22

Note: The bar chart indicates the intervention amounts in the left axis, whereas a positive amountcorresponds to yen selling intervention and a negative amount is yen purchasing intervention.
Source. Ministry of Finance Japan and Bloomberg.

29

Figure 2. Daily Amount of Monetary Base and Intervention Amount in 2022
75000

600

(billion yen)(billion yen)
500

70000

400
65000

300

monetary base(left axis)

200

60000

intervention amount(right axis)
55000

100
0

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
2022

30

Figure 3. Bilateral Exchange Rates Against the USD

160

JPY
0.9

AUD

CAD
1.5

150
140

0.8

1.4

0.7

1.3

0.6

1.2

130
120
110
100

90
2021

1.1

2022

0.5
2021

2022

1.1
2021

EUR

CHF
1.3

1.5

2022

GBP

1.4

1.2
1

1.3

1.1
1.2
0.9
1

0.8
2021

2022

NOK
12

0.9
2021

0.8

1.1

2022

NZD

11

1
2021

12

2022

SEK

11

0.7

10

10

9
9
0.6

8

8

7
6
2021

2022

0.5
2021

2022

Source: Bloomberg

31

7
2021

2022

Figure 4. Interest Rate Differentials relative to the US
Japan
1

0

Australia

Canada
0.5

(%)
0
-0.5

-1
-2

-1

0

-3

-1.5
-4
-5
2021

0

2022

Switzerland

-2
2021

2022

-0.5
2021

Euro area
0

1

-0.5

2022

UK

0.5

-1
-1
0

-1.5

-2

-0.5

-2
-3

-1

-2.5
-4
2021

1.5

2022

Norway

-3
2021

1

2022

New Zealand

1

-1.5
2021

0

2022

Sweden

-0.5

0.5

0.5
-1

0

-0.5

-1.5
0

-1
-2
-1.5

-2
2021

2022

-0.5
2021

2022

Source: Bloomberg

32

-2.5
2021

2022

Figure 5. VIX Index
40

35

30

25

20

15

10
2021

2022

Source: Chicago Board Options Exchange

33

Figure 6. Randomly Assigned and Lean Against the Wind Interventions(a) Randomly Assigned Intervention

counterfactual

actualtime

intervention(b) Lean Against the Wind Intervention

actualcounterfactualintervention

34

time

Figure 7. Estimated Currency Factors
First Factor

Second Factor

Third Factor′

Note: The series are normalized such that 𝐹̃ 𝑇𝑊 𝐹̃ 𝑇𝑊 /𝑇 = 𝐼𝑟 .

35

Figure 8. The Counterfactual Rate and the Gap Sequence
Actual and Counterfactual Rates
160
150

actualcounterfactual

140
130
120
110
100

90
2022 Feb Mar
Jan

Apr May Jun

Jul

Aug Sep Oct Nov Dec

Gap Sequence
40
30
20
10

0
-10
-20
2022 Feb Mar
Jan

Apr May Jun

Jul

36

Aug Sep

Oct

Nov Dec

Figure 9. Trend Breaks in the Gap Sequence
35
30

600

(gap)

(intervention; billion yen per day)
500

25
20

400

15
10

300

5
200

0
-5

100

-10
-15
2022
Jan

0
Feb

Mar

Apr

May

Jun

Jul

37

Aug

Sep

Oct

Nov

Dec

Figure 10. Estimated Currency Factors
The 2010-2011 Intervention Period
First Factor

Second Factor

Third Factor′
Note: The series are normalized such that 𝐹̃ 𝑇𝑊 𝐹̃ 𝑇𝑊 /𝑇 = 𝐼𝑟 .

38

Figure 11. The Counterfactual Rate and the Gap Sequence
The 2010-2011 Intervention Period
Actual and Counterfactual Rates
100
actual95

counterfactual

90

85

80

75

70
2010 Sep Oct Nov Dec 2011 Feb Mar Apr May Jun

Jul Aug Sep Oct Nov Dec

Gap Sequence
10
5
0
-5
-10
-15
-20
-25
2010 Sep Oct Nov Dec 2011 Feb Mar Apr May Jun

39

Jul Aug Sep Oct Nov Dec

Figure 12. Trend Breaks in the Gap Sequence
The 2010-2011 Intervention Period
Two Breaks
4

900

(gap)

(intervention; billion yen per day)

2

800

0

700

-2

600

-4

500

-6

400

-8

300

-10

200

-12

100

-14
2010 Sep Oct Nov Dec 2011 Feb Mar

0
Apr May Jun

Jul

Aug Sep

Oct Nov Dec

Four Breaks
4900(intervention; billion yen per day)

(gap)
2

800

0

700

-2

600

-4

500

-6

400

-8

300

-10

200

-12

100

-14
2010 Sep Oct Nov Dec 2011 Feb Mar

0

Apr May Jun

40

Jul

Aug Sep Oct Nov Dec

Table 1. Coefficient Estimates of the Counterfactual Model
Coefficient

95% Confidence Interval-20.05**[-27.54, -3.22]

JPY-1.35**[-1.73, -0.26]

AUD

0.16

[-0.35, 0.59]

CAD

0.24*

[-0.01, 0.92]

CHF-0.34*[-0.64, 0.06]

EUR

-0.56

[-1.04, 0.72]

GBP

0.93***[0.56, 1.30]

NOK-0.45*[-0.70, 0.02]

NZD

-0.26

[-0.60, 0.73]

SEK

0.92***[0.56, 1.29]-7.95*[-16.89, 0.18]

𝑅𝑖,𝑡
𝑉𝐼𝑋𝑡

Const.

Note: ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively.

41

Table 2. Structural Change Tests for the Trend of the Gap Sequence
Tests

Break Dates

𝐹𝑇 (1|0)

𝐹𝑇 (2|1)

𝐹𝑇 (3|2)

6.36***

3.69*

3.09

April 22 ; October 17

Note: Same as Table 1.

42

Table 3. Coefficient Estimates of the Counterfactual Model
The 2010-2011 Intervention Period
Coefficient

95% Confidence Interval-18.28***[-32.37, -5.63]

JPY-1.46***[-2.07, -0.61]

AUD

0.37

[-0.69, 1.49]

CAD

-0.39

[-0.98, 0.35]

CHF-1.50***[-2.14, -0.65]

EUR-1.78***[-2.66, -0.71]

GBP-1.40*[-1.23, 0.12]

NOK

1.40

[-0.40, 3.40]

NZD-1.62***[-2.28, -0.74]

SEK

0.55

[-0.49, 1.66]

37.45***[13.03, 56.19]

𝑅𝑖,𝑡
𝑉𝐼𝑋𝑡

Const.
Note: Same as Table 1.

43

Table 4. Structural Change Tests for the Trend of the Gap Sequence
The 2010-2011 Intervention Period
Tests

Break Dates

𝐹𝑇 (1|0)

𝐹𝑇 (2|1)

𝐹𝑇 (3|2)

31.06***

27.92*

1.65

February 18; September 2

Note: Same as Table 1.

44