Fatemeh Salimi
email: fatemeh.salimi-namin@univ-amu.fr

Guglielmo Caporale

Yin-Wong Cheung

Christelle Lecourt

Gilles Dufrenot

Kate Phylaktis

Rosnel Sessinou

Zhichao Zhang

Exchange Rates, Stock Prices, and Stock Market Uncertainty 

Keywords: exchange rate determination, implied volatility, UEP, flight to safety, flight to quality JEL classification: F31, F32, G15

While the reference framework for international portfolio choice emphasizes a mean-variance framework, uncovered parity conditions only involve mean stock or bond returns. We propose to augment the empirical specification by using the relative stock market uncertainty of two countries as an extra determinant of their bilateral exchange rate returns. A rise in the relative uncertainty of one stock market will lead capital to flow to the other stock market and generate an appreciation in the currency of the latter. By focusing on the JPY/USD exchange rate returns during the most recent decade (2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019) and relying on a nonlinear framework, we provide evidence that the Japanese-US differential stock market uncertainty affects the JPY/USD returns both contemporaneously and with weekly lags. This finding is robust when we control for the stock returns differential and the differential changes in Japanese and US unconventional monetary policy measures.

Introduction

Modern Portfolio Theory [START_REF] Markowitz | Portfolio selection[END_REF], in its domestic as well as international versions1 has been based on the first two moments of asset prices, i.e., mean returns and variances. But uncovered parity conditions, specifically Uncovered Interest Parity (UIP) and Uncovered Equity Parity (UEP) [START_REF] Cappiello | The uncovered return condition[END_REF]Hau andRey, 2008, 2006) seem to take a step backward from the mean-variance framework. They assume that capital flows and exchange rate movements are only induced by two countries' mean (bond or stock) returns differential.2 The role of the second moment as a measure of uncertainty or risk is thus overlooked in investors' portfolio choice. As a result, despite evidence on the impact of market uncertainty on capital flows [START_REF] Balakrishnan | Financial flows from the United States to latin Amercia: Basic patterns, causes, and implications[END_REF][START_REF] Nier | Gross private capital flows to emerging markets: Can the global financial cycle be tamed? IMF Work[END_REF], the relative uncertainty of two countries' financial markets has not been seriously considered as a driver of exchange rate movements.

In this study, we set three objectives. Our primary goal is to evaluate, for the first time, to what extent the relative uncertainty in two countries' financial markets affects the decision of stock investors to move their investment to the safer/higher-quality market, which in turn appreciates its currency. Consistent with the time-varying effect of uncertainty on financial markets, we pursue this objective in a nonlinear framework. As our second objective, we aim to re-examine the power of relative stock returns in driving exchange rate returns, as suggested by UEP. To do so, we revisit the relationship between the stock returns differential and exchange rate returns in a nonlinear framework. Our third objective is to evaluate the role of the differential between two corresponding countries' monetary policy stances in driving exchange rate movements. This objective is inspired by UIP, which proposes interest rates differential to be a driving force of exchange rate movements. When the zero-lower bound (ZLB) 3 binds in both corresponding countries, and Unconventional Monetary Policies (UMP) are implemented, the interest rate differential cannot be informative. Instead, we shift our attention toward the differential changes in UMP measures and their nonlinear effect on exchange rate movements.

The main focus of our empirical analysis is on the Japanese yen-US dollar exchange rate (JPY/USD), which is the second most traded currency pair in the global foreign exchange market, after the euro-US dollar (Bank for International Settlements, 2019). We choose this currency pair because it serves as a typical example of the failure of standard variables to drive exchange rate movements. For instance, according to previous studies, the movements of this currency pair do not comply with UEP (see [START_REF] Hau | Exchange rates, equity prices, and capital flows[END_REF] and [START_REF] Curcuru | Uncovered equity parity and rebalancing in international portfolios[END_REF]), and the relationship of the movements of this exchange rate with the UMP measures do not have the expected sign (see [START_REF] Ueda | The effectiveness of non-traditional monetary policy measures: The case of the bank of Japan[END_REF]).

We explore the dynamics of the JPY/USD over the most recent period, after the global financial crisis, from 2009 to 2019. During this period, the two countries experienced episodes of (near-) zero interest rates, and both implemented large-scale UMP. 4 Conducting such an analysis for the pre-crisis period would require a comparison between two different measures for monetary policy stances of the countries, such as interest rates for the US and reserves growth for Japan, which would be unusual. However, similar measures of the monetary policies of the two countries since 2009 allow us to use a differential UMP variable, facilitating comparison and interpretation. We refrain from including the crisis period during which extreme outliers and noises caused by high volatility may distort estimation results, and because some UMPs were not yet in place.

In this paper, to proxy for stock market uncertainty, we rely on implied volatility indices, such as the VIX index and its counterparts for other stock markets, among the broad range of financial and economic uncertainty measures. We do not intend to thoroughly review these measures here since it has been done by [START_REF] Caporale | Macro-financial linkages in the high-frequency domain: The effects of uncertainty on realized volatility[END_REF] and [START_REF] Ferrara | Uncertainty fluctuations: Measures, effects and macroeconomic policy challenges[END_REF]. The VIX of the Chicago Board of Exchange is constructed on the basis of the S&P 500 option prices and is a generally accepted proxy for the uncertainty of the US stock market, even being customarily labeled the "fear gauge". This index has received supportive evidence concerning its explanatory power with respect to various financial markets such as emerging stock markets (Sarwar andKhan, 2019, 2017), commodity-related equities [START_REF] Badshah | Contemporaneous spill-over among equity, gold, and exchange rate implied volatility indices[END_REF][START_REF] Boscaljon | Do large shocks in VIX signal a flight-to-safety in the gold market?[END_REF][START_REF] Jubinski | VIX, gold, silver, and oil: How do commodities react to financial market volatility?[END_REF][START_REF] Sari | Do global risk perceptions influence world oil prices?[END_REF], as well as for capital flows [START_REF] Balakrishnan | Financial flows from the United States to latin Amercia: Basic patterns, causes, and implications[END_REF][START_REF] Nier | Gross private capital flows to emerging markets: Can the global financial cycle be tamed? IMF Work[END_REF].

In addition to being reliable uncertainty proxies, we chose implied volatility indices because they suit our purpose in three ways. First, they have a forward-looking nature. Second, they are available at a high frequency. And finally, they represent financial (and not economic) uncertainty. However, such proxies have been criticized in as much as they would not be able to reflect the Knightian uncertainty 5 since they do not exclusively reflect uncertainty but include some forecastable components referred to as risk. Distinguishing between uncertainty and risk components can be essential to establish which one of them is dominantly affected by macroeconomic fundamentals. 6 However, such a decomposition is not necessary for the present study because both components may impact investors' portfolio choice in a similar way, though to different extents. Therefore, in this paper, when using these indices, we follow [START_REF] Bloom | Fluctuations in Uncertainty[END_REF] in referring to the broad definition of uncertainty, which is a mixture of risk and uncertainty.

In contrast to the implied volatility indices, other proxies of financial uncertainty are at least partially constructed based on historical data and do not fully reflect expectations. For example, the realized volatility of stock markets employed by [START_REF] Chauvet | What does financial volatility tell us about macroeconomic fluctuations?[END_REF] is a backward-looking proxy. In turn, the variance risk premium proposed by [START_REF] Bollerslev | Expected stock returns and variance risk premia[END_REF] and employed by [START_REF] Londono | Variance risk premiums and the forward premium puzzle[END_REF] and [START_REF] Aloosh | Global variance risk premium and forex return predictability[END_REF] relies on the difference between the realized and implied variances, creating a combination of forward-looking and backward-looking components.

Economic policy proxies are usually meant to capture economy-, business-or firm-level uncertainties and are not limited to financial uncertainty. For instance, the most popular economic uncertainty proxy, i.e., the news-based Economic Policy Uncertainty (EPU) index of [START_REF] Baker | Measuring economic policy uncertainty[END_REF], reacts more to policy-related events as opposed to the VIX which is highly affected by financial events [START_REF] Baker | Measuring economic policy uncertainty[END_REF]. Similar to VIX, EPU has been used in a diverse range of applications, particularly for predicting business cycles (see [START_REF] Caporale | Macro-financial linkages in the high-frequency domain: The effects of uncertainty on realized volatility[END_REF] Recently, sophisticated econometrically-driven proxies have been proposed-for instance, by [START_REF] Ferrara | Forecasting growth during the Great Recession: Is financial volatility the missing ingredient?[END_REF] with a conditional volatility model, [START_REF] Jo | Macroeconomic uncertainty through the lens of professional forecasters[END_REF] with a factor stochastic volatility model, [START_REF] Gilchrist | Uncertainty, financial frictions, and investment dynamics[END_REF] based on firm-level time-varying equity volatility, and [START_REF] Carriero | Measuring uncertainty and its impact on the economy[END_REF] thanks to the use of a large VAR model with stochastic error volatility depending on aggregate macroeconomic and financial uncertainty, among many others (refer to [START_REF] Ferrara | Uncertainty fluctuations: Measures, effects and macroeconomic policy challenges[END_REF] and [START_REF] Carriero | Measuring uncertainty and its impact on the economy[END_REF] for comprehensive list of previously proposed measures). These econometrically-driven proxies are also backward-looking and indicate economic rather than financial uncertainty. Finally, the recursive estimation of expectations by [START_REF] Jurado | Measuring uncertainty[END_REF] and [START_REF] Joëts | Does the volatility of commodity prices reflect macroeconomic uncertainty?[END_REF] help create a forward-looking measure using a sophisticated stochastic volatility model for the unpredictable component of a large set of macroeconomic and financial variables.

This study draws on three strands of literature. First, we draw on the emerging literature that emphasizes the ability of stock markets' uncertainty to predict exchange rate movements. Intuitively, when high stock market uncertainty or volatility is accompanied by low equity prices, investors fly to safety or quality [START_REF] Baele | Flights to safety[END_REF]. 7 Because capital flows connect stock markets through the foreign exchange market, the movements of capital toward the safer market induce an appreciation of the currency corresponding to the safer market, with more intensity during periods of market stress [START_REF] Vayanos | Flight to quality, flight to liquidity, and the pricing of risk[END_REF]. Among the few studies which investigate this relationship, [START_REF] Londono | Variance risk premiums and the forward premium puzzle[END_REF] show that the US stock variance risk premium can forecast exchange rate movements. They use the US stock variance premium as a measure of unexpected volatility computed as the difference between the option-implied and the expected realized stock variance. They find that a higher stock variance risk premium indicates a rise in uncertainty in the US stock market, which in turn depreciates the USD. 8 In a similar attempt, Aloosh (2014) finds evidence of the predictability of the returns of the euro, yen, and British pound against the USD by a valueweighted average stock variance risk premium at a one-month horizon.9

A shortcoming of this strand of literature stems from the unilateral view underlying the variance risk premium. This view can result in biased conclusions, specifically in cases when both currencies involved are safe-haven currencies such as the JPY/USD. In such cases, an investor needs an evaluation of the relative uncertainty of the two corresponding countries, which can affect exchange rate movements.10 Therefore, we put forward the use of a simple differential measure, consistent with the comparative view of an investor to the uncertainty of two stock markets. We call it "differential fear" or the implied volatility (IV) differential. It is defined as the difference between the CBOE's implied volatility index (VIX) and its Japanese counterpart at the Osaka Securities Exchange, VXJ, calculated based on Nikkei 225 option prices. Besides, we depart from the existing literature by focusing mainly on uncertainty, instead of risk premiums, which involve limitations associated with expected realized variance.

In pursuing the second objective of this study, we draw on the literature on UEP [START_REF] Cappiello | The uncovered return condition[END_REF]Hau andRey, 2008, 2006). This parity condition relies on two underlying mechanisms. The first is that following an outperformance of a foreign over the domestic stock market, investors repatriate their portfolio to reduce their foreign exchange rate risk. Therefore, capital flows toward the domestic stock market. 11 The second mechanism consists of the depreciation of the foreign against the domestic currency in response to the investment repatriation (selling foreign and buying domestic assets).

Despite the logical and intuitive mechanisms underlying UEP, this parity condition has received mixed empirical support. The most extreme case of rejection is reported by [START_REF] Cenedese | What do stock markets tell us about exchange rates?[END_REF], who evaluate UEP using a trading strategy for a sample of 43 countries from 1983 to 2011. In attempts to rationalize the unfavorable evidence on UEP, [START_REF] Kim | The risk adjusted uncovered equity parity[END_REF][START_REF] Fuertes | Uncovered equity "disparity" in emerging markets[END_REF][START_REF] Cho | Flight-to-quality and correlation between currency and stock returns[END_REF] argue that UEP holds when both corresponding countries are among developed countries. They even suggest that for an emerging economy, the relationship between stock returns differential and exchange rate movements can be the opposite of what is indicated by UEP. [START_REF] Cho | Flight-to-quality and correlation between currency and stock returns[END_REF] identified that flight to quality during turmoil can be a major driver of exchange rate movements when at least one of the two economies is an emerging one. Along the same lines, [START_REF] Fuertes | Uncovered equity "disparity" in emerging markets[END_REF], find that the divergence from UEP increases in turmoil due to investors' return-chasing behavior, and suggest that risk pricing is essential in exchange rate determination. While [START_REF] Cenedese | What do stock markets tell us about exchange rates?[END_REF] blame systematic equity market risk and global equity volatility risk for the failure of UEP, [START_REF] Kim | The risk adjusted uncovered equity parity[END_REF] argues that significant market risk and government restrictions on capital outflows in emerging markets contribute to this failure. In general, these studies agree that the relevance of UEP depends on investors' assessment of the relative uncertainty in two markets. Surprisingly, however, neither of these studies considers that relative uncertainty can play a role in the decisions of an international investor, and subsequently affect capital flows and exchange rate movements.

Finally, to investigate the third objective, we draw on the literature on the effects of UMPs (such as forward guidance, large-scale asset purchases, and Quantitative Easing (QE)), implemented by central banks during the (near-)zero interest rate period, on exchange rate dynamics. The existing literature argues that this kind of policy mainly influences asset prices and, subsequently, exchange rates by affecting market expectations through at least four main channels. The first channel is the portfolio-balance channel aimed at boosting demand for riskier assets, following large purchases of specific assets by the central bank, which reduce their supply and lowers the term premium [START_REF] Gagnon | The financial market effects of the federal reserve's large-scale asset purchases[END_REF]. The second channel is the liquidity channel through which asset prices are affected by the presence of the central bank as a consistent and significant buyer in the market [START_REF] Gagnon | The financial market effects of the federal reserve's large-scale asset purchases[END_REF]. The last two channels, which are more informational, are the signaling and the confidence channels. The former can induce demand for (the foreign or domestic) higheryielding assets by informally communicating the commitment of the central bank to keep yields low [START_REF] Bauer | The signaling channel for Federal Reserve bond purchases[END_REF]. The latter can affect asset prices by providing information to investors, through easing announcements, on the current and future good health of the economy [START_REF] Fratzscher | On the international spillovers of US quantitative easing[END_REF].

The existing literature considers that in an open economy framework, the dominant effect of easing policies is a depreciation of the currency of the country implementing it vis-à-vis the high-yielding currencies [START_REF] Glick | Central bank announcements of asset purchases and the impact on global financial and commodity markets[END_REF][START_REF] Kenourgios | On quantitative easing and high frequency exchange rate dynamics[END_REF][START_REF] Neely | Unconventional monetary policy had large international effects[END_REF][START_REF] Rosa | How "unconventional" are large-scale asset purchases?[END_REF][START_REF] Ueda | The effectiveness of non-traditional monetary policy measures: The case of the bank of Japan[END_REF]. This effect is anticipated because yields are expected to be low for an extended period in the country implementing UMP, inducing capital outflows. However, [START_REF] Ueda | The effectiveness of non-traditional monetary policy measures: The case of the bank of Japan[END_REF] documented that the JPY, differently from other currencies, appreciated against the USD in response to some UMP announcements by the Bank of Japan (BoJ) from 1999 to 2011.

Most of the literature focuses either on cases where only one of the two corresponding countries implements UMP or completely neglects the equally-important effect of the monetary policies of the other country on the exchange rate [START_REF] Fratzscher | On the international spillovers of US quantitative easing[END_REF]. Accordingly, inspired by UIP and consistent with our relative view, we consider whether the differential of the changes of the UMP measures can partially explain exchange rate dynamics.

In addition to the sign of the effect of UMP on exchange rate dynamics, its intensity can also vary over time. For instance, [START_REF] Gagnon | The financial market effects of the federal reserve's large-scale asset purchases[END_REF] state that the liquidity channel may be functioning more effectively during the first stages of UMP. [START_REF] Fratzscher | On the international spillovers of US quantitative easing[END_REF] claim that the effectiveness of UMP depends on changes in macro-financial uncertainty, i.e., in periods of low macroeconomic uncertainty, the US capital outflows rise following QE announcements. Therefore, nonlinearity is an essential characteristic of such relationships, which has often been neglected in the literature.

In this study, we use the nonlinear Markov-switching framework of [START_REF] Hamilton | A new approach to the economic analysis of nonstationary time series and the business cycle[END_REF] to fulfill our three objectives. The advantage of this model is that it allows time-varying but recurring relationships between variables where regime changes are endogenously determined (as opposed to the structural break detection of [START_REF] Bai | Computation and analysis of multiple structural change models[END_REF]). We avoid the use of a nonlinear VAR model or a system of equations. 12 In a linear VAR model, the number of parameters grows with the square of the number of variables included in the model, which exhausts the degrees of freedom very quickly, leading to imprecise estimation of parameters [START_REF] Krolzig | General-to-specific model selection procedures for structural vector autoregressions[END_REF]. This problem can be amplified in a Markov-switching framework, in which all model parameters are allowed to switch. Therefore, to avoid the curse of dimensionality, we prefer to consider a single-equation model. 13We reach three main results. First, the IV differential plays a significant role in explaining exchange rate dynamics. The findings follow our intuition that higher uncertainty in the Japanese relative to the US stock market encourages investors to rebalance their portfolio toward the less risky market and leads to a depreciation of the Japanese yen vis-à-vis the US dollar.

Second, we find that the stock returns differential is an important driver of the JPY/USD exchange rate movements at a one-week horizon. Following an outperformance of the Japanese over the US stock market, the Japanese yen depreciates against the USD at a one-week horizon. Previous studies never detected this UEP-consistent finding for the JPY/USD, mostly because they rely on samples chosen regardless of the specificities of the two corresponding countries. This effect does not last more than one week, which is in line with the rapid reflection of market participants to events in financial markets.

Third, the differential of the changes in the Japanese and the US UMP measures (reserves growth differential) partially explains the JPY/USD exchange rate movements at one-and two-week horizons. The effect has opposite signs in the two regimes of our model from 2009 to 2019. During the high-volatility regimes of the foreign exchange market, the relationship between the reserves growth differential and the JPY/USD is positive (depreciation of the JPY) in one-and two-week horizons. The depreciation effect is expected inasmuch as more UMP in a country with low-yields finances investments in high-yields countries. However, in the low-volatility regime of the foreign exchange market, the relationship is negative (appreciation of the JPY) at a one-week horizon and changes sign after a week. We conclude that the ultimate effect of a relatively higher increase in the Japanese relative to the US reserves is the depreciation of the JPY against the USD. However, the transitory impact can be affected by the instruments used to implement UMPs.

Our paper contributes to the related strands of literature in several ways. First, the most important contribution of our paper is to put forward a new differential variable as a candidate for the determination of exchange rate dynamics. We underline that not only stock returns differential, but also the differential of stock markets' uncertainty or the "differential fear" can impact exchange rate returns. Second, we provide evidence of the nonlinearity and time-variability of the relationship between the stock returns differential and exchange rate returns. This nonlinear characteristic is highlighted by the fact that while we provide UEP-consistent evidence for JPY/USD over a recent sample, previous studies never found it over earlier samples. And finally, we stress the importance of having a relative view of the monetary stances, stock returns, or uncertainty levels of the two sides of a currency pair when assessing the movement of an exchange rate. An exclusively unilateral view, forgetting the bilateral nature of an exchange rate, may lead to a misleading conclusion.

The rest of the paper is organized as follows: In section2, we present the data and the modeling strategy we use. In section 3, we provide the results of our empirical investigation concerning the three objectives of this study. Section 4 provides concluding remarks.

Data and Methodology

Data

with l being currency pair and 𝑃 , its spot price at time t.

We investigate the power of three differential variables in explaining exchange rate movements.

The first is the differential of uncertainty measures of the two countries, which is computed using logarithms of the VXJ and VIX indices. Data on both indices are obtained from Datastream. The IV differential is shown in the lower panel of Figure 1. It is worth mentioning that although the VIX is taken by many as a global uncertainty index, it is, in fact, a composition of both global and US factors [START_REF] Balakrishnan | Financial flows from the United States to latin Amercia: Basic patterns, causes, and implications[END_REF]. By taking the differential of the VXJ and VIX, we aim for our differential variable to be mostly free from the global factor.

The second variable is the stock returns differential, as suggested by the UEP literature. We compute weekly averages of the differential of the Nikkei 225 and the S&P 500 daily returns as Diff_SRt = RNIK, t -RS&p500,t with RNIK, t, and RS&p500,t being calculated following Equation (1) (see the upper panel of Figure 2 for a graph of this variable). We use these two indices as the representatives of the Japanese and the US stock markets, respectively.

The last variable, as suggested by UIP, should be the interest rate differential. However, as shown in the upper panel of Figure 2, interest rates of both Japan and the US have been almost zero since the beginning of our sample in 2009. While the Japanese short-term interest rate continues to linger around zero, the US short-term interest rate has been rising gradually since late 2015. Therefore, for the whole sample, interest rate differential (as suggested by UIP) cannot be informative in explaining exchange rate movements. Instead, we focus our attention on UMP measures, which can be used as indicators of monetary policy stances of the two countries.

The quantitative easing policy started in late 2008 in the US in the aftermath of the global financial crisis to stimulate the economy. The policy resulted in financial institutions holding excess reserves with the Federal Reserve. The Federal Reserve started tapering policies in 2013, which led to the decrease of these reserves from early 2014 (lower panel of Figure 1). In contrast to the US, the quantitative easing started much earlier in Japan, in March 2001, to trigger the sluggish economy. The BoJ stopped implementing this policy in 2006, but it was resurged after the global financial crisis in late 2008 at a low pace. In October 2010, the Comprehensive Monetary Easing (CME) policy was launched. Later in April 2013, the Japanese UMP was reinforced in the form of a Quantitative and Qualitative Easing policy (QQE), which was followed by a negative interest rate policy in early 2016. All the policies implemented after December 2010 allowed the BoJ to purchase ETFs in addition to government bonds. These policies contributed to an ever-growing expansion of the reserves held at the BoJ and its current account outstanding balance. 14We use the growth rate of the commercial banks' reserves held with the BoJ and the growth of the excess reserves maintained with the Federal Reserve, which are calculated as (Rl,t ) using Equation (1) with l being the reserves held with the BoJ or the Federal Reserve and 𝑃 , their values at time t. The differential of growth in reserves is computed as Diff_ΔLRES = RRES(JP) -RRES(US). The Japanese and the US data are obtained from CEIC and the Board of Governors of the Federal Reserve System at weekly and fortnightly frequencies, respectively. We conduct our analysis at the weekly frequency to be consistent with the rapid responses of financial variables to changes and events. To match the frequency of the US reserves, we use the Litterman method (1983)15 of temporal disaggregation using money supply (money zero maturity) as the indicator variable. economic growth at the global level, and Brexit. 16 Table 1 shows the descriptive statistics and stationarity results of the exchange rate returns, stock returns differentials, the IV differential, and the reserves growth differential. All variables have non-normal distributions. Besides, the IV differential and the differential of reserves growth suffer from serial autocorrelation. According to the unit-root, ADF (1979), and stationarity, KPSS (1992), tests all variables are stationary.

The use of returns or differenced data may cause a concern, that is, possible long-run relationships between the exchange rate and the levels of explanatory variables are overlooked. Among the three differential variables, the IV differential is computed using the levels of the IV indices and is already stationary. Therefore, a long-run relationship between this variable and the level of the JPY/USD exchange rate is ruled out. The stock returns differential, and the reserves growth differential are computed using first differences of the variables because this approach is intuitively acceptable and theoretically supported. However, to ensure that we do not overlook the long-run aspect of the analysis, we try computing these two differential variables using levels of their constituent components (i.e., logarithms of the stock prices and logarithms of the level of reserves).

The results of stationarity and cointegration tests show that the differential of reserves computed using log levels of reserves is stationary and the differential of log stock prices is non-stationary. However, even the latter does not form any long-run relationship with the exchange rate (as reported in Table A 1 in the Appendix). 16 for more details see [START_REF] Arbatli | Policy uncertainty in Japan[END_REF]), Le Moign et al. (2018).  ΔLJPY/USD: returns of the Japanese yen vis-à-vis the US dollar, Diff_SR: the differential between the Japanese and the US stock returns (Diff_SRt = RNIK, t -RS&p500,t), diff-IV: the differential between the logarithms of the VXJ and the VIX (LVXJ-LVIX), diff_ΔLRES: differential of the changes in the reserves held with the BOJ and the Federal Reserve (Diff_ΔLRES = RRES(JP) -RRES(US)).

Methodology

The determinants of exchange rates can vary depending on the economic situation and implemented economic policies, investors' behavior, and investing technologies, among other factors. For instance, when the interest rates differential is zero or very close to zero, it may not play an essential role in determining the dynamics of exchange rates, leaving room for a temporary effect of other variables. Therefore, it is advisable to use a nonlinear model to capture this timevarying exchange rate dynamics. Accordingly, we use the Markov-switching model of [START_REF] Hamilton | A new approach to the economic analysis of nonstationary time series and the business cycle[END_REF], which, in contrast to structural break tests, benefits from the possibility of regime recurrence (Hamilton, 2016).

To analyze the determinants of the JPY/USD exchange rate returns, we use the following general specification:

Δ𝑒 𝛼 𝑠 Δ𝑒 𝛽 , 𝑠 𝑑𝑖𝑓𝑓 , 𝜎 𝑠 𝜀 (2)
where Δ𝑒 , the JPY/USD exchange rate return, is regressed on its 1 to p lagged values (Δ𝑒 ). The matrix 𝑑𝑖𝑓𝑓 , contains the contemporaneous and lagged values of the three differential variables with j indicating stock returns (SR), implied volatility (IV) or reserves growth (ΔLRES), and k the number of lags varying from 1 to q. The error term 𝜀 follows a Gaussian white noise process with covariance matrix Σ.

In this equation, 𝑠 is an unobservable variable that specifies the state at each time. We allow all the parameters in this model to switch state. Therefore, 𝛼 𝑠 s are the state-dependent coefficients of the p autoregressive lags of exchange rate returns. Similarly, 𝛽 , 𝑠 s are the state-dependent coefficients of the stock returns differential, IV differential, and the reserves growth differential. 𝜎 𝑠 𝑡 is the state-dependent variance.

The state variable (𝑠 ) follows a first-order Markov chain, implying the dependence of the current value of 𝑠 only on its immediately preceding value. According to our model specification, each observation is designated to a specific state, allowing us to obtain smoothed transition probabilities from one state to the other and the probability of persistence of each state. Estimation of the model parameters is done using the sequential quadratic programming algorithm of Lawrence and Tits (2001) along with a pre-estimation with the Expected Maximization (EM) algorithm of [START_REF] Dempster | Maximum likelihood from incomplete data via the EM algorithm[END_REF].

In this empirical analysis, we choose the number of regimes based on statistical tests. To determine the best number of regimes and the best number of lags for the dependent and independent variables, we follow a two-step approach. The first step consists of determining the number of lags to include in Equation (2). To do that, we estimate a vector autoregressive model in a linear framework as follows:

𝑌 Π 𝑌 𝜉 (3)
in which Y is a vector of all our four variables [diff_IV, diff_ΔLRES, diff_SR, ΔLJPY/USD] with l=1 to 12. We compare the estimated models with 1 to 12 lags using different information criteria, e.g., the Schwarz (SC), Akaike (AIC), and Hannan and Quinn (HQ) information criteria and we choose the model which yields the lowest value for the information criteria. We use the Granger causality test to ensure the one-way causality from the independent variables to the JPY/USD returns. In the case of a two way-causality, the time t value of the independent variable can be neglected to avoid a simultaneity issue.

A prerequisite to the MS estimation of Equation ( 2) is to test the outperformance of a Markovswitching model over a linear model. We benefit from the optimal test of Markov-switching by [START_REF] Carrasco | Optimal test for Markov switching parameters[END_REF], which only requires the estimation of the Markov-switching model under the null hypothesis of constant parameters. We compute the critical values from 500 iterations for a model that allows switching intercept and variance. Conditional on the rejection of the linear model by this test, we proceed to the second step using the optimal lag suggested by the information criteria from the preceding step.

We allow all the parameters to be regime-dependent and estimate five models with 1 (linear model) to 4 regimes. We compute the Markov-Switching Criterion (MSC), developed by [START_REF] Smith | Markov-switching model selection using Kullback-Leibler divergence[END_REF]. This criterion is based on the Kullback-Leibler (KL) divergence. As opposed to AIC, SC and HQ, which mislead users to choose an inaccurate number of regimes [START_REF] Psaradakis | On the determination of the number of regimes in Markovswitching autoregressive models[END_REF][START_REF] Smith | Markov-switching model selection using Kullback-Leibler divergence[END_REF], MSC is shown to be efficient across different sample sizes and with noisy data [START_REF] Smith | Markov-switching model selection using Kullback-Leibler divergence[END_REF]. This criterion uses full-sample smoothed probabilities in order to balance the fit of the model with its parsimony. The criterion is computed as:

𝑀𝑆𝐶 2𝐿 𝜏̂ 𝜏̂ 𝑆𝜂 𝜏̂ 𝑆𝜂 2 (4)
where L is the log-likelihood of the estimated model, S is the number of regimes, and η is the number of regressors. 𝜏̂ is defined as the sum of smoothed probabilities of being in r th regime computed using full-sample smoothed probabilities. The model which yields the minimum MSC is chosen as the optimal number of Markov-switching regimes. After selecting the optimal number of lags and regimes, we test whether the linearity of each of the parameters can help improve the fit of the model according to SC.

Determinants of the JPY/USD Movements

Markov-switching Model Estimation

Following the first step of our approach, we choose a model with two lags for the dependent and independent variables. According to our systematic model comparison using SC, we choose a model in which only four parameters are regime-dependent (Table 3). In this model, the constant term is not significant. Therefore, none of the regimes can be designated to a specific direction of either appreciation or depreciation of the JPY vis-a-vis the USD. The first regime is the dominant and the most persistent (see Table A 6). The variance of the error terms is the parameter that usually governs the regime changes. Therefore, the first and second regimes are the low-and high-volatility regimes, respectively. Apart from the variance of the error terms, only the second autoregressive lag, the second lag of the IV differential, and the first lag of the reserves growth differential are regimedependent, according to SC. 18 The coefficients of the first and second autoregressive lags are significant with opposite signs, therefore contributing to the JPY/USD appreciation at a one-week horizon and its depreciation at a two-week horizon, respectively.

In accordance with our conjecture, we find a non-switching, positive, and significant relationship between the JPY/USD exchange rate returns and the contemporaneous value of the IV differential during the whole sample. This shows that when volatility is higher in the Japanese stock market in comparison with the US stock market, investors move a part of their portfolio to the safer market (the US market) and induce a depreciation of the Japanese yen vis-à-vis the US dollar and vice versa. This is in line with the findings of [START_REF] Londono | Variance risk premiums and the forward premium puzzle[END_REF] and [START_REF] Aloosh | Global variance risk premium and forex return predictability[END_REF]. However, it is obtained in a much less complicated framework and taking a two-country relative perspective.

This relationship reverses sign in a two-week horizon. In other words, the coefficient of the second 17 For the sake of comparison between the linear and nonlinear estimations (although the models are not identical), we provide the generalized impulse responses of the VAR estimation in the Appendix (see Figure A 1). The impulse responses show that the exchange rates only react to a shock to the stock returns differential and are not influenced by the shocks to the IV differential and reserves growth differential. 18 The AIC also suggests a model with minor differences.

lag of the IV differential is significant and negative in both regimes, with a stronger appreciating effect on the exchange rate during the high-volatility (second) regime. This may be a sign that investors move their capital to the market that has already passed an uncertain period, hoping that they can benefit from a "buy the dips" strategy.

The JPY/USD returns have a significantly positive and non-switching relationship with the stock returns differential at a one-week horizon. The positive sign of this coefficient is consistent with UEP, meaning that relatively higher stock returns in Japan lead to a depreciation of the JPY vis-àvis the USD at a one-week horizon. The coefficient of the second lag is, however, not significant. Therefore, as expected from the fast reactions of investors, the effect of the stock returns differential is short-lived. The UEP-consistent finding at a one-week horizon is unique to this study. The key to this finding is the choice of the sample with regard to the specificities of the two corresponding countries, which was neglected by previous studies.

Finally, the reserves growth differential and the JPY/USD exchange rate returns are not contemporaneously related; however, with one and two weeks of lag, their relationship is significant. The effect with a one-week lag is regime-dependent. During the low-volatility (highvolatility) regime, relatively higher (lower) Japanese reserves growth leads to a stronger (weaker) JPY against the USD. Regardless of how the reserves growth differential affects the exchange rate returns in a one-week horizon, the effect with a 2-week lag contributes completely to a depreciation of the JPY vis-à-vis the USD. The depreciation effect is much more expected in the literature. The appreciation of the JPY against the USD following reinforcement of UMP in Japan has been a source of ambiguity in previous studies such as [START_REF] Ueda | The effectiveness of non-traditional monetary policy measures: The case of the bank of Japan[END_REF] (for a sample from 1999 to 2011). 19 One piece of conjecture about the channel through which the reserves growth differential occasionally leads to an appreciation of JPY against the USD is that the Japanese UMP relatively succeeded in guiding investments toward more risky assets inside Japan at a one-week horizon. This could have taken place either by incentivizing investors to rebalance their portfolio toward more risky Japanese assets or by the BoJ's direct purchases of ETFs since December 2011 under 19 In contrast to the results of the linear VAR model (presented in the Appendix, Figure A 1), the Markov-switching model shows that the movements of the JPY/USD are also influenced by the IV differential and the reserves growth differential.  SupTS shows a sup-type test statistic used by [START_REF] Davies | Hypothesis testing when a nuisance parameter is present only under the alternative[END_REF], and expTS shows an exponential-type test statistic suggested by [START_REF] Andrews | Optimal tests when a nuisance parameter is present only under the alternative[END_REF].

the CME policy. 20 In contrast, the literature enlightens us more about the channel through which the reserves growth differential leads to a depreciation of the JPY vis-à-vis the USD. During the high-volatility periods, reinforced Japanese UMP contributes to the relatively higher reserves growth in Japan, which as a result of low yields of investment in Japan, leads to more carry-induced capital outflows compared to the US. Thus, the JPY depreciates against the USD at a one-week horizon. The same channel functions in a two-week horizon. Nevertheless, the ultimate effect of the reserves growth differential on the exchange rate is the depreciation of the currency of the country with higher reserves growth. This is consistent with the literature but in a two-country relative framework.

To ensure about the explanatory power of our differential variables and the outperformance of our selected model, we ran a comparison between constrained models by sequentially omitting one of the explanatory variables. The results in Table A 6 show that AIC always favors our selected model. Also, all three likelihood ratio tests reject the exclusion of our differential variables. So, our selected model outperforms each of the constrained models, and the inclusion of the IV differential statistically significantly improves the explanatory power of the model.

Portfolio Rebalancing through Capital Flows

Ideally, the channel through which the differential variables affect the exchange rate movements, namely capital flows, should be analyzed in a similar Markov-switching framework. However, such analysis is not possible in this study. On the one hand, it is because of the lack of freely 20 A more-than-two-country framework can be helpful to shed light on the direction of outflows from the US and Japan and to show which country has been serving more as the funding carry trade currency. available capital flows data at a high-frequency. 21 On the other hand, it is because analysis at a low-frequency requires averaging the high-frequency data, leading to the disappearance of some of the rapid market reactions to the differential variables. Against this limitation, we try to have a close look at the events causing high volatility over the sample and noting the direction of capital flows inducing changes in the JPY/USD exchange rate. To do so, we rely on monthly bilateral data on the Japanese-US capital flows provided by the Treasury International Capital (TIC) system disaggregated based on the type of the capital flows (such as stocks, bonds) and also quarterly international portfolio investment flows data provided by the IMF (See Figure 4).

One of the periods of excessive foreign exchange market volatility prevails from the beginning of the sample in 2009 until mid-2010, during which financial markets were still turbulent after the global financial crisis (see Figure 4 and the regime classifications in Table A 5). The upper panel of Figure 4 shows that during this period, an increasing (decreasing) net-net equity flows (defined as the net equity inflows into Japan minus the net equity inflows into the US) are associated with an appreciation (depreciation) of the JPY against the USD.

The short period of high volatility from March to May 2011 was caused by the earthquake and the heightened worries of the nuclear crisis in Japan. Instability in the Japanese stock market soared, and the JPY depreciated vis-à-vis major currencies. The disorderly foreign exchange market was very soon stabilized thanks to the concerted foreign exchange market intervention by G7 countries. The same negative relationship exists between the net-net equity flows and the exchange rate returns (Figure 4).

The next period of excess foreign exchange market volatility, which started in March 2013 and continued for around five months, was provoked by the implementation of a very intense monetary stimulus in Japan. The purpose of the stimulus was to defeat Japan's continued deflation and to achieve a targeted inflation rate of two percent in the next two years. Subsequently, the BoJ's balance sheet experienced a rapid expansion, the Japanese stock market rallied, and the yen depreciated. This monetary policy change was followed by a massive quantitative easing program in April 2013, in response to which financial market uncertainty increased, the JPY experienced further depreciation, and the stock market surged. However, skepticism about Abe's expansionary policies coupled with some international news on the US tapering in May and June 2013 and China's slowing growth caused an escalation of uncertainty in stock markets. Stock markets were hit both in Japan and the US, with a more striking effect in the former. The sudden drop of the netnet equity flows into Japan during this period (the third shaded area in Figure 4) is associated with higher uncertainty in the Japanese market and depreciation of this country's currency, consistent with our hypothesis.

The next series of events giving rise to heightened volatility in the JPY/USD exchange rate and uncertainty in different countries started in late 2015. On the one hand, in December 2015, US interest rates began to increase, accompanied by signals of further gradual increases during the following years. One the other hand, the BoJ adopted a negative interest rate policy in late January 2016 to stimulate investment and borrowing as well as boosting inflation and weakening the currency. In both cases, uncertainty around the consequences of the moves caused plunges in major, and sometimes in emerging markets. As a result, flight to safety by international investors and repatriation of Japanese overseas investments caused reinforcement of the safe-haven status of the JPY, and the Japanese yen appreciated accordingly. Similarly, later events such as the news on China's slowdown signals in February, and the Brexit referendum in June both contributed to a strong JPY vis-à-vis the USD. The presidential election in the US in November and an increase in the US target rate in December both led to surges in the value of the USD after long periods of high financial market instability and the JPY depreciation.

In this period of high volatility, in contrast to the previous three periods, a positive relationship exists between the net-net equity flows and the exchange rate returns. Therefore, at the first look, it might seem that relatively higher volatility in Japan does not lead to the depreciation of the JPY. But, given the specific status of the Japanese yen and the US dollar as safe-haven currencies, it may not be enough to only take into account the Japanese-US bilateral equity flows. As shown in the lower panel of Figure 4, during this period, gross inflows to Japan increased until mid-2016 and decreased afterward, while the opposite happens to the gross inflows to the US. Therefore, the JPY appreciates until midway in the period and then depreciates against the USD.

Conclusion

In this study, we explored for the first time the relationship between relative uncertainties in two countries' stock markets and their corresponding exchange rate returns. We also examined the explanatory power of some of the previously-proposed determinants of the exchange rate dynamics, namely the stock returns differential and the differential of the growth of unconventional monetary policy measures.

Using a Markov-switching model and focusing on the JPY/USD exchange rate from 2009 to 2019, we show that our proposed determinant, the IV differential has a significant relationship with the exchange rate dynamics in our sample. Moreover, we document that the stock returns differential is an essential non-switching determinant of the JPY/USD exchange rate returns as consistent with UEP [START_REF] Cappiello | Explaining exchange rate dynamics: The uncovered equity return parity condition[END_REF][START_REF] Hau | Exchange rates, equity prices, and capital flows[END_REF]. The differential of the relative increase in UMP of the two corresponding countries also plays a crucial nonlinear role in explaining the JPY/USD dynamics with one and two weeks of lag. Our unique findings emphasize the importance of the choice of sample based on corresponding countries' monetary stances.

A serious examination of the role of capital flows, as the transmission mechanism of the effects of the IV differential, stock returns differential, and reserves growth differential on exchange rate remains as a future extension of this study. Also, a comparison of findings using alternative uncertainty measures such as the EPU index can be very informative. -ΔLJPY/USD: returns of the Japanese yen vis-à-vis the US dollar, Diff_SR: the differential between the Japanese and the US stock market returns, Diff_IV: the differential between the log transformations of VXJ and VIX, Diff_ΔLRES: the differential of the Japanese and the US reserves growth.

  Figure 2 One-week interest rates and reserves Notes: one-week interest rates of Japan and the US in the upper panel and commercial banks' reserves held with the Japanese and the US central banks in the lower panel (in billions of JPY and millions of USD, respectively).



  ΔLJPY/USD: returns of the Japanese yen vis-à-vis the US dollar, diff_SR: the differential between the Japanese and the US stock market returns, diff_IV: the differential between the log transformations of VXJ and VIX, diff_ΔLRES: the differential of the Japanese and the US reserves growth. Robust standard errors are shown in parenthesis and p-values in squared brackets.  Numbers centrally aligned between the regimes show the constancy (nonlinearity) of the respective coefficients.

Figure 3

 3 Figure 3 Smoothed regime probabilities (2009-2019)

Figure 4

 4 Figure 4 Capital flows and exchange rate Notes: upper panel shows the JPY/USD exchange rate in black on the left axis, and monthly net-net Japan-US bilateral equity flows in blue, net-net Japan-US bilateral bond flows in red, on the right axis. Lower panel shows quarterly net international investment inflows to Japan in red and net international investment inflows to the US in blue. Shaded areas are classified in the second regime by our selected model (the shaded area in March 2011 disappears in the lower panel due to its short duration and a lower frequency of the data).

  To test our hypotheses on the determinants of exchange rate movements, we use weekly averages of the JPY/USD exchange rate returns from January 2009 to July 2019 obtained from the Pacific Exchange Rate Service. Exchange rate returns computed as:

	𝑅 ,	ln	𝑃 , 𝑃 ,

Table 1

 1 Descriptive statistics (sample: January 2009 to July of 2019)

		ΔLJPY/USD	diff_ΔLRES	Diff_SR	Diff_IV
	Mean	0.00007	0.00547	-0.00009	0.01067
	Standard deviation	0.00272	0.07069	0.00460	0.18860
	Skewness	-0.01475	1.39790	-0.26056	0.45153
	Excess kurtosis	0.74451	7.69450	1.42010	0.40342
	Minimum	-0.00996	-0.30477	-0.02190	-0.48909
	Maximum	0.00921	0.48708	0.01708	0.74229
	Jarque-Bera Normality	12.676***	22.337***	52.251***	1530.3***
	autocorrelation	30.826	782.51***	40.565	2688.1***
	ADF (1979)	-14.0205***	-4.64369***	-15.1215***	-16.9121***
	KPSS (1992)	0.128653	1.10976	0.0721538	0.014626
	*** Significant at the 1% level.

  Table A 2 in the Appendix shows that all the three criteria choose a model with two lags for the sample from 2009 to 2019. 17 According to the Granger causality test results in Table A 3 in the Appendix, the only variables between which a two-way causality is possible are the exchange rate movements and the stock returns differential. The exchange rate movements can influence the stock returns differential. Therefore, in our nonlinear estimation of Equation (2), we omit the time t value of the stock returns differential and only allow its lagged values in the model as explanatory variables. In the second step, MSC suggests a model with two regimes (Table A 5 in the Appendix). As shown in Table 2, Carrasco et al. (2014)'s test of Markov-switching versus a linear model rejects the null of linearity. Carrasco et al. (2014)'s test results are also confirmed by the MSC, which shows that the outperformance of a linear model is rejected.

Table 2

 2 Linearity vs. Markov-switching test of Carrasco et al. (2014) (sample: 2009/09/26-2019/07/08) Numbers in squared brackets are p-values.  Critical values are computed from 500 iterations for a model with switching mean and variance.

	Dependent variable	supTS	expTS
	ΔLJPY/USD	12.689 [0.000]	127.181 [0.000]
	

Table 3

 3 Estimated Markov-switching model (sample: 26/09/2009-08/07/2019)

		Regime 1	Regime 2
	Constant	0.0001
		(0.0001)
	ΔLJPY/USD (-1)	-0.1191**
		(0.0480)
	ΔLJPY/USD (-2)	0.1543**	-0.1037
		(0.0621)	(0.0768)
	Diff_SR (-1)	0.0948***
		(0.0273)
	Diff_SR (-2)	-0.0278
		(0.0264)
	Diff_IV	0.0048***
		(0.0012)
	Diff_IV (-1)	-0.0019
		(0.0015)
	Diff_IV (-2)	-0.0024*	-0.0037**
		(0.0013)	(0.0017)
	Diff_ΔLRES	0.0012
		(0.0017)
	Diff_ΔLRES (-1)	-0.0060***	0.0084***
		(0.0022)	(0.0029)
	Diff_ΔLRES (-2)	0.0036**
		(0.0017)
	Variance	0.0020***	0.0034***
		(0.0001)	(0.0002)
	Prob. of per.	0.9865	0.9706
	Normality test	0.64646
		[0.7238]
	ARCH 1-1 test	2.3781
		[0.1236]
	Portmanteau (23)	11.427
		[0.9681]
	*** Significant at the 1% level, ** Significant at the 5% level, * Significant at
	the 10% level

Table A 2

 A Information criteria obtained based on linear VAR estimation of Equation (2) for the lag selection (sample: 2009/01/26-2019/07/08)

	Lag	AIC	SC	HQ
	0	-19.77207	-19.74010	-19.75956
	1	-21.78944	-21.62959	-21.72691
	2	-21.95583* -21.66809* -21.84326*
	3	-21.92047	-21.50484	-21.75787
	4	-21.89069	-21.34718	-21.67806
	5	-21.85484	-21.18344	-21.59217
	6	-21.85688	-21.05760	-21.54418
	7	-21.83477	-20.90760	-21.47204
	8	-21.80237	-20.74733	-21.38961
	9	-21.80607	-20.62314	-21.34328
	10	-21.84517	-20.53435	-21.33234
	11	-21.87965	-20.44095	-21.31680
	12	-21.87757	-20.31098	-21.26468
	* indicates the optimal number of lags suggested by
	each criterion.

Table A 6

 A Comparison of the fit of the linear, selected MS and constrained models (sample: 26/01/2009-08/07/2019) Standard errors are shown in parenthesis and p-values in squared brackets.

		Selected model				Constrained models
	Excluded variable			Diff_IV		Diff_ΔLRES	Diff_SR (-1)
		Regime 1	Regime 2	Regime 1	Regime 2	Regime 1	Regime 2	Regime 1	Regime 2
	Constant	0.0001		0.0001		-		0.0000
		(0.0001)		(0.0001)				(0.0001)
	ΔLJPY/USD (-1)	-0.1191**	-0.1292***	-0.1054**	-0.1687*	-0.0185
		(0.0480)		(0.0487)		(0.0482)		(0.0976)	(0.0580)
	ΔLJPY/USD (-2)	0.1543**	-0.1037	0.0379		0.1738***	-0.1310*	-0.0097
		(0.0621)	(0.0768)	(0.0490)		(0.0623)	(0.0708)	(0.0451)
	Diff_SR (-1)	0.0948***	0.0809***	0.0856***	-
		(0.0273)		(0.0269)		(0.0273)
	Diff_SR (-2)	-0.0278		-0.0267		-0.0314		-
		(0.0264)		(0.0269)		(0.0263)
	Diff_IV	0.0048***	-		0.0049***	0.0053***
		(0.0012)				(0.0011)		(0.0012)
	Diff_IV (-1)	-0.0019		-		-0.0015		-0.0033**
		(0.0015)				(0.0015)		(0.0015)
	Diff_IV (-2)	-0.0024*	-0.0037**	-		-0.0028		-0.0019
		(0.0013)	(0.0017)			(0.0012)		(0.0012)
	Diff_ΔLRES	0.0012		0.0009		-		0.0013
		(0.0017)		(0.0018)				(0.0018)
	Diff_ΔLRES (-1)	-0.0060***	0.0084***	-0.0064***	0.0094***	-		-0.0044	0.0059**
		(0.0022)	(0.0029)	(0.0023)	(0.0028)			(0.0033)	(0.0025)
	Diff_ΔLRES (-2)	0.0036**	0.0024		-		0.0034*
		(0.0017)		(0.0017)				(0.0019)
	Variance	0.0020***	0.0034***	0.0019***	0.0034***	0.0019***	0.0034***	0.0014***	0.0032***
		(0.0001)	(0.0002)	(0.0001)	(0.0002)	(0.0001)	(0.0002)	(0.0002)	(0.0002)
	prob. of per.	0.99%	0.97%	98%	97%	99%	98%	85%	93%
	Log likelihood	2502.63005	2491.37935	2496.0271	2491.9201
	SC	-8.95936438	-8.97586932	-8.98135078	-8.93512639
	AIC	-9.10120896	-9.07831263	-9.09167435	-9.06930439
	Likelihood ratio test			22.50*** [0.0001]	13.206 *** [0.0042]	21.42 *** [0.0001]
	*** Significant at 1% level, ** Significant at 5% level, *	Significant at 10% level
	-

Japan has started much earlier in 2001 but reinforced its policies after the global financial crisis.

[START_REF] Knight | Risk, uncertainty and profit[END_REF] differentiates uncertainty from risk by defining the former as a situation in which the likelihood of events happening is not forecastable while the latter relates to a situation in which the probability distribution of events is known.

[START_REF] Bekaert | Risk, uncertainty and monetary policy[END_REF] propose an approach to decompose the VIX index into uncertainty and time-varying risk components.

Rebalancing portfolios toward safer assets which are less volatile and more liquid such as government bonds, gold, or safe haven currencies such as the Japanese yen, Swiss franc or the US dollar, following heightened uncertainty and low returns in the market, is known as flight to safety or quality. For theoretical background on flight to safety refer to[START_REF] Vayanos | Flight to quality, flight to liquidity, and the pricing of risk[END_REF],[START_REF] Caballero | Collective risk management in a flight to quality episode[END_REF] and[START_REF] Brunnermeier | Market liquidity and funding liquidity[END_REF] among others.

In a different approach, Della[START_REF] Della Corte | Volatility risk premia and exchange rate predictability[END_REF] and[START_REF] Londono | Variance risk premiums and the forward premium puzzle[END_REF] investigate the role of currency risk premium in explaining exchange rates. Della[START_REF] Della Corte | Volatility risk premia and exchange rate predictability[END_REF] introduce currency volatility risk premium ("the difference between expected future realized volatility and a model-free measure of implied volatility derived from currency option"). They argue that currencies with low implied volatility relative to historical realized volatility have cheap volatility insurance and vice versa. Therefore, investors rebalance their portfolio toward the currencies with cheaper volatility insurance and predictably induce their appreciation. Similarly[START_REF] Londono | Variance risk premiums and the forward premium puzzle[END_REF] use global currency variance risk premium (the average of the differences between option-implied and the realized variance of returns of several currencies against the USD) and find that a higher currency variance risk premium signifies a heightened level of global uncertainty and induces an appreciation of the USD as this currency acts as a safe-haven currency.

[START_REF] Balakrishnan | U.S. dollar dynamics: How important are policy divergence and FX risk premiums? IMF Work[END_REF] blame the lack of attention to the time-varying risk pricing for the failure of traditional models. Using foreign exchange risk premium (constructed based on interest rate different and Consensus exchange rate forecasts), they show that shocks to the global risk sentiment induce dollar appreciation against major currencies complying with the safe-haven status of the USD and flight-to-safety phenomenon.

Looking from a different angle, capital flows, which link different stock markets to the foreign exchange market, are also influenced by the uncertainty in stock markets. In this regard,[START_REF] Nier | Gross private capital flows to emerging markets: Can the global financial cycle be tamed? IMF Work[END_REF] document that during volatile periods, the CBOE's implied volatility index (VIX) is a major determinant of gross capital flows whereas economic fundamentals prevail during low-volatility periods. Fratzscher (2012) also shows that capital flows are influenced by global shock such as crisis and global liquidity and risk.

Although, the true incentive behind capital movements following such an outperformance of the foreign over the domestic market is still open to further research and[START_REF] Curcuru | Uncovered equity parity and rebalancing in international portfolios[END_REF], introduce carry trade or return chasing behaviour of investors as the underlying reason.

For the sake of comparison, a linear VAR model is also estimated and the results are available in Appendix.

Using Granger causality tests, we ensure about the lack of a two way causality between the independent variables of the single-equation model.

for more details about the Japanese QE, CME and QQE refer to[START_REF] Ueda | The effectiveness of non-traditional monetary policy measures: The case of the bank of Japan[END_REF],[START_REF] Harada | The BOJ's ETF purchases and its effects on Nikkei 225 stocks[END_REF] among others.

Litterman's method of temporal disaggregation for deriving high-frequency from low-frequency time series. This method is a variant of[START_REF] Chow | Best linear unbiased interpolation, distribution, and extrapolation of time series by related series[END_REF] method which interpolates low-frequency series by relating it to a reference high-frequency series based on a regression.Figure1The Japanese and the US stock returns differential (upper panel) and the implied volatility differential of the Japanese and the US stock markets (lower panel)

There are at least two sources of high-frequency data on capital flows, none of which is accessible freely. EPFR dataset contains weekly portfolio investment flows at mutual funds level. IIF also provides net private capital inflows at a daily frequency.

comments and suggestions. I also thank Melissa Horn for her help in proofreading. This work was supported by the French National Research Agency Grant ANR-17-EURE-0020.

Appendix

 ΔLJPY/USD: returns of the Japanese yen vis-à-vis the US dollar, Diff_SR: the differential between the Japanese and the US stock market returns, Diff_IV: the differential between the log transformations of VXJ and VIX, Diff_ΔLRES: the differential of the Japanese and the US reserves growth. 29


Romain David

Audrey Richard

Laurence Mabile

Diana Stepanyan

Krista Versteeg

Jonathan Mineau-Cesari

Michel-Yves Mistou

Hervé Raoul

Issues and obstacles to the sharing of sensitive data in Europe, who are the stakeholders and what are their responsibilities ?

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

DURC data typically falls into one or more of these categories:

❖ Demonstrates how to render a vaccine ineffective ❖ Enhances the harmful consequences of a pathogen or toxin or renders a non-pathogen virulent ❖ Increases the transmissibility of a pathogen ❖ Alters the host range of a pathogen or toxin ❖ Enables evasion of diagnostic or detection modalities ❖ Enhances the susceptibility of a host population to a pathogen or toxin ❖ Generates or reconstitutes certain eradicated or extinct pathogens or toxins ❖ Enables weaponization of a biological agent or toxin.

Dual use metadata must be machine readable (like Metadata for machine -M4M implemented in Go-FAIR) to be reused at large scale. They can contain sensitive content, therefore an authentication and authorization mechanism must be implemented by an authorized infrastructure (AAIs are part of the 6 European recommendations for FAIR data).

AAI services, FAIR Data Points, and Fair Implementation Profile for DURC

Reducing the risk of misuse of data is particularly crucial in the context of research on highly pathogenic agents. But as demonstrated during the COVID19 crisis, sharing data of high quality is a sine qua non condition to compare research results at a large scale.

Our actual challenge is to ensure compliance with the FAIR principles while taking into account the dangers and pitfalls concerning dual use type data / samples (because there are often some good reasons to not share).

Identifying stakeholders and organising their interaction is strategic to ensure that data will be accessible easily while observing in a highly secure environment the essential rules with regards to the rights of access and reuse of sensitive data (as open as possible, as closed as necessary). To that aim, preparing all stakeholders and improving their FAIRness literacy must be prioritized by all institutions (David et al., 2020).

❖❖

  How can we take these aspects into account so that in the meantime FAIR principles and legislations are applied ? ❖ How to increase the possibilities of sharing dual use data to reduce overlap of services? and to encourage collaboration on DURC while securing their uses? ❖ How to reward and credit back good practices? What data should be prohibited to share? ❖ Who should be prohibited from sharing or accessing data which may be classified as DURC? Dual Use Research Concern (DURC) Dual Use Research of Concern (DURC) is defined by the United States Government Policy for Oversight of Life Sciences as "Life sciences research that, based on current understanding, can be reasonably anticipated to provide knowledge, information, products, or technologies that could be directly misapplied to pose a significant threat, with broad potential consequences, to public health and safety, agricultural crops and other plants, animals, the environment, materiel, or national security." Many countries or regions have adopted laws to regulate exchanges concerning DURC. As an example, in the European Union, dual use biological materials are listed in "Council Regulation (EC) No 428/2009".

We recommend: ❖ the setting of pre-approved data sharing agreements for highly secured repositories. ❖ that considering DURC in actual Data stewardship should be developed. ❖ to be cautious while being too careful and classifying all data in dual uses; it would be another pitfall, and would prevent re-use despite public health issues. ❖ to identify actors at least inside a country or inside a community of countries (e.g. Europe) and organize their interactions as reducing duplication of effort and improving trial design concerning Dual Use research is a challenge, ❖ that, to enable dual use data sharing information, an authorized metadata should be available centrally on an intergovernmental web page with explicit authority contact and / or be applied considering officials sharing conventions.

Take home messages


Hugo Bouteiller

Mathieu Pasturel

Pierric Lemoine
email: pierric.lemoine@univ-rennes1.fr

On the crystal structures of the polymorphs of manganese(II) chloride tetrahydrate: -MnCl24H2O and -MnCl24H2O

Keywords: Manganese chloride, Single-crystal X-ray diffraction, Crystal structure, Hydrogen bond

The manganese(II) chloride tetrahydrate MnCl24H2O (-form) crystallizes in the space group P21/n with a = 6.1918(4) Å, b = 9.5230(6) Å, c = 11.1918(6) Å,  = 99.757(3) °, and V = 650.37(7) Å 3 (Z = 4). A second polymorph of MnCl24H2O (-form) is mentioned in the literature to be isomorphous with FeCl24H2O but its crystal structure was never confirmed. In this study, we report for the first time on the crystal structure of this second polymorph of manganese(II) chloride tetrahydrate, -MnCl24H2O, using room temperature single-crystal X-ray diffraction. The -form crystallizes in space group P21/c with a = 5.9893(5) Å, b = 7.2877(6) Å, c = 8.5838(7) Å,  = 110.952(4) °, and V = 349.89(5) Å 3 (Z = 2), confirming that -MnCl24H2O is isotype to Fe(II)Cl24H2O. To the best of our knowledge this is the first compound reported to crystallize in both MnCl24H2O-type (-form) and FeCl24H2O-type (-form) structures. The crystal structure of both -form and form of MnCl24H2O consists of discrete octahedra complexes [MnCl2(H2O)4] linked by O-HCl -hydrogen bonds. However, chlorine atoms are in trans-configuration in the -form (trans-[MnCl2(H2O)4] complexes) and in cisconfiguration in the -form (cis-[MnCl2(H2O)4] complexes). Moreover, the coordination polyhedra of the manganese(II) atoms are less distorted in the -form. This leads to two different hydrogen bond networks and to a slightly more compact [MnCl2(H2O)4] complexes arrangement in the -form.

INTRODUCTION

MnCl24H2O has been widely studied in biology and medicine for its impact on biological activity [1][2][3][4][5][6], as a neuronal contrast agent for enhanced magnetic resonance imaging [7,8], and in materials and coordination chemistry as a precursor for the solvothermal synthesis of cathode materials [9,10], manganese titanite and ferrite [11,12], nanoparticles [13,14], polyoxometallates [15], metal-organic frameworks [16], single-molecule magnets [17], magnetic coordination polymers [18][19][20], magnetic coordination clusters [21,22], and other magnetic Mn(II) complexes [23]. Historically, this compound has been studied extensively for its magnetic properties [24][25][26][27][28][29][30][31][START_REF] Giauque | e d M a n u s c r i p t[END_REF][START_REF] Altamn | [END_REF][34][35][36][37] as a good example of simple uniaxial Heisenberg antiferromagnet.

-MnCl24H2O is reported to crystallize in the space group P21/n with a = 11.186 Å, b = 9.513 Å, c = 6.186 Å, and  = 99.74 ° [38]. This structure was reported as the stable room temperature form of the manganese(II) chloride tetrahydrate [39]. Indeed, a second polymorph described as a metastable room temperature form, -MnCl24H2O, is reported in the literature to be isomorphous with FeCl24H2O [38][39][40]. Crystals of the -form have been obtained from the slow evaporation, between 0°C and 6°C, of a supersaturated solution [40]. However, the crystals rapidly change in appearance when removed from their mother-liquor [39,40]. Consequently, the crystallographic structure of this second polymorph was never confirmed.

In this article, we report on the crystal structures of the two polymorphs of manganese(II) chloride tetrahydrate, -MnCl24H2O and -MnCl24H2O, both determined from single-crystal X-ray diffraction at room temperature. Crystals of -MnCl24H2O were obtained from the slow evaporation of a concentrated ethanol solution in presence of K2S. Herein, we confirm that -MnCl24H2O is isostructural with FeCl24H2O and crystallizes in the space group P21/c with a = 5.9893(5) Å, b = 7.2877(6) Å, c = 8.5838(7) Å, and  = 110.952(4) °.

EXPERIMENTAL

Synthesis method

A c c e p t e d M a n u s c r i p t Single crystals of both structural and -forms were obtained by solvent evaporation techniques. Two solutions were prepared from MnCl2•4H2O precursor: (i) 100 mg was solubilized in ethanol (3g) and (ii) 200 mg was solubilized in a 50% diluted ethanol solution (3g). Finally, 1g of K2S saturated ethanol solution was added to both solutions prior to be heated under reflux at 110°C under argon flow for 2h and cooled to room temperature. Single crystals of and -forms of MnCl24H2O were obtained from the slow recrystallization in ambient atmosphere of the solutions (i) and (ii), respectively.

Single-crystal X-ray diffraction

Single-crystal X-ray data were acquired under ambient atmosphere at room temperature (T = 293 K) on an APEX II Bruker AXS diffractometer using Mo-K wavelength ( = 0.71073 Å) at the Centre de Diffractométrie X of the Institut des Sciences Chimiques de Rennes. Crystals of MnCl24H2O were picked up from the mother liquor and immediately submerged in PARATONE® oil in order to limit the exposure to air and avoid degradation, mainly caused by dehydration. Despite the weak stability of the -form under ambient atmosphere, no degradation of the crystal was observed during the measurement. Measurements were processed with the APEX 2 program suite [41]. Frame integration and data reduction were carried out with the SAINT program [START_REF] Sheldrick | SAINT version 8.37A[END_REF]. The SADABS program [START_REF] Sheldrick | SADABS version[END_REF] was employed for multiscan-type absorption corrections. The structures were solved by direct methods using the SIR97 program [START_REF] Altomare | [END_REF] and then refined with full-matrix least-square methods based on F 2 (SHELXL-2014) [45] through the WinGX platform [46]. All non-hydrogen atoms were refined with anisotropic atomic displacement parameters. Hydrogen atoms were introduced in the structural model through Fourier difference maps analysis. The atomic coordinates for hydrogen atoms were refined and the equivalent isotropic displacement parameters were constrained to be equal to 1.2 times that of their parent atom. The weak residual electronic density peaks, obtained in the final refinements, indicate that no extra atoms were missing in the structural models. The conditions for the data collections and structure refinements are summarized in Table 1.

RESULTS AND DISCUSSION

Analysis of the single-crystal X-ray diffraction data recorded at room temperature (Table 1) confirms that the second polymorph of the manganese(II) chloride tetrahydrate, -MnCl24H2O, crystallizes in the FeCl24H2O-type structure [47][48][49]. Its structure consists of discrete octahedral complexes [MnCl2(H2O)4] (Figure 1), where each manganese(II) atom is coordinated by 4 H2O molecules in quasi-square configuration (Mn-O distances of 2.160 Å and 2.163 Å, Table 2) and 2 chlorine atoms in trans-configuration (Mn-Cl distances of 2.549 Å, Table 2). Manganese atoms are located on the special 2a position (i.e. on an inversion center) leading to trans-[MnCl2(H2O)4] complexes (Figure 1). The crystal packing of these trans-[MnCl2(H2O)4] complexes is ensured by O-HCl hydrogen bonds (Figure 2). Each hydrogen atom (i.e. H1A, H1B, H2A, and H2B) is involved in a single hydrogen bond (Figure 3) and each chlorine is a fourfold hydrogen-bond acceptor. Hence, each trans-[MnCl2(H2O)4] complex forms 16 hydrogen bonds with its surrounding complexes: 8 from acceptive chlorine atoms and 8 from dative oxygen atoms. However, due to the localization of Mn atom on the inversion center, only 4 different hydrogen bonds occur in the -form (Table 3). The determined hydrogen bond geometries of -MnCl24H2O are in reasonable agreement with those reported by Verbist et al. for FeCl24H2O [49]. The only difference resides in the O-H distances, and consequently the HCl distances, which are shorter and longer, respectively, in our structural model. x,½ + y,(b) x,½ + z ;½ + y,.

Single-crystal X-ray diffraction data acquisition was also carried out on the well-known polymorph (-form) of manganese(II) chloride tetrahydrate (Table 1). Our results are in agreement with the crystal structure previously determined from both single-crystal neutron diffraction [50] and single-crystal X-ray diffraction data [51]. Similarly to -MnCl24H2O, the -form is built on discrete octahedra complexes [MnCl2(H2O)4] linked to one another by O-HCl hydrogen bonds (Figures 2 and3). Nevertheless, in the -form, chlorine atoms are in cisconfiguration as opposed to the trans-configuration observed in the -form (Figure 1). Moreover, in the -form the cis-[MnCl2(H2O)4] complexes are highly distorted (Table 4) in comparison to the almost regular trans-[MnCl2(H2O)4] complexes encountered in the -form (Figure 1). The average interatomic distances <Mn-O> and <Mn-Cl> are slightly longer and shorter, respectively, in the -form (Table 4) compared to the -form (Table 2). Due to its different chlorine atoms configuration and more distorted octahedra [MnCl2(H2O)4] complexes, the form possess a more complex O-HCl hydrogen bonds network (Figure 3 and Table 5) and a slightly more compact crystal packing (i.e. 162.6 Å 3 per formula unit) in comparison to the -form (i.e. 174.9 Å 3 per formula unit). From a crystal chemistry point of view, MnCl24H2O stands out as being the only divalent metal tetrahydrate halogenide to crystallize in both and -form (Table 6). However, it is worth noting that other crystal structures can be found among MX24H2O compounds, as recently reported by Falkowski et al. on the orthorhombic form of MnBr24H2O (Cmcm space group) [61]. Finally, as the -form of MnCl24H2O was extensively studied for its magnetic properties, -MnCl24H2O undoubtedly offers some similarly interesting prospects. In such coordination complexes materials, the magnetic ordering is related to strong indirect exchange coupling occurring between the nearest-neighbor metal atoms through Mn-O-HCl-Mn and Mn-ClCl-Mn interactions. Hence, by considering (i) that the arrangements of discrete octahedra complexes [MnCl2(H2O)4] are different, with the -form having two short MnMn distances of 5.637(1) Å while the -form has four short MnMn distances of 5.630(1) Å, and (ii) that the isotype compound FeCl24H2O exhibits antiferromagnetic ordering around 1 K [62-67], we can expect magnetic ordering to occur in -MnCl24H2O, which should be different from the -form.

A c c e p t e d M a n u s c r i p t

Figure 1 .Table 2 .

 12 Figure 1. Representation of the trans-and cis-[MnCl2(H2O)4] complexes in the -form (left) and -form (right) of MnCl24H2O, respectively. Displacement ellipsoids are shown at the 50% probability level. H atoms are represented as spheres of arbitrary radius.

Figure 2 .

 2 Figure 2. Representation of the O-HCl hydrogen bonds network encountered in the -form (left) and in the form (right) of MnCl24H2O. Displacement ellipsoids are shown at the 50% probability level. H atoms are represented as spheres of arbitrary radius.

Figure 3 .Table 3 .

 33 Figure 3. Representation of the hydrogen bonds between H2O molecules and chlorine atoms in the -form (left) and -form (right) of MnCl24H2O. Displacement ellipsoids are shown at the 50% probability level. H atoms are represented as spheres of arbitrary radius.

  A c c e p t e d M a n u s c r i p t

  ) Symmetry codes: (a) -½ + x, ½ -y, -½ + z ; (b) -1 + x, y, z ; (c) ½ -x, -½ + y, 3 2 ⁄ -z ; (d) 3 2 ⁄ -x, -½ + y, 3 2 ⁄z ; (e) ½ + x, ½ -y, ½ + z ; (f) -½ + x, ½ -y, ½ + z.

A c c e p t e d M a n u s c r i p t

Table 1 .

 1 Summary of single crystal data collection and structure refinement conditions at room temperature for and -MnCl24H2O.

	Structural Formula	-MnCl24H2O	-MnCl24H2O
	Space group	P21/c	P21/n
	Temperature (K)	293(2)	293(2)
	Formula weight	197.90	197.90
	Wavelength (Å)	0.71073	0.71073
	Crystal system	Monoclinic	Monoclinic
	a (Å)	5.9893(5)	6.1918(4)
	b (Å)	7.2877(6)	9.5230(6)
	c (Å)	8.5838(7)	11.1918(6)
	β (°)	110.952(4)	99.757(3)
	V (Å 3 )	349.89(5)	650.37(7)
	Z	2	4
	Calculated density (g.cm -3 )	1.878	2.021
	Absorption coefficient (mm -1 )	2.578	2.774
	F(000)	198	396
	Crystal size (mm)	0.07 x 0.06 x 0.05 0.52 x 0.26 x 0.08
	Crystal color	Colorless	Colorless
	Theta range (°)	3.643 / 27.516	2.826 / 27.454
	h_min, h_max	-7, 6	-7, 7
	k_min, k_max	-9, 9	-12, 12
	l_min, l_max	-10, 11	-14, 9
	R(int)	0.0560	0.0296
	Collected reflections	3900	5956
	Unique reflections [I>2σ]	606	1269
	Completeness	0.999	0.998
	Data/restraints/parameters	805/0/47	1483/0/89
	Goodness-of-fit	1.006	1.069
	Final R1 [I>2σ]	0.0339	0.0213
	Final wR2 [I>2σ]	0.0539	0.0384
	Largest difference (e -.Å -3 )	0.399 and -0.360	0.238 and -0.300

Table 4 .

 4 Selected bond lengths (Å) and angles (°) of -MnCl24H2O.

	Mn1-O1 2.211(2) O1-Mn1-O2	91.7(1)
	Mn1-O2 2.180(2) O1-Mn1-O4	89.9(1)
	Mn1-O3 2.216(2) O1-Mn1-Cl1 94.2 (1)
	Mn1-O4 2.190(2) O1-Mn1-Cl2 86.5(1)
	<Mn-O>	2.199	O2-Mn1-O3	87.0(1)
	Mn1-Cl1 2.478(1) O2-Mn1-O4	81.7(1)
	Mn1-Cl2 2.501(1) O2-Mn1-Cl2 93.3(1)
	<Mn-Cl>	2.489	O3-Mn1-O4	92.1(1)
	O1-H1A 0.76(2)	O3-Mn1-Cl1 87.5(1)
	O1-H1B	0.77(2)	O3-Mn1-Cl2 91.4(1)
	O2-H2A 0.73(2)	O4-Mn1-Cl1 89.0(1)
	O2-H2B	0.73(2) Cl1-Mn1-Cl2 96.3(2)
	O3-H3A 0.79(2) H1A-O1-H1B 104(1)
	O3-H3B	0.70(2) H2A-O2-H2B 116(1)
	O4-H4A 0.68(2) H3A-O3-H3B 106(1)
	O4-H4B	0.75(2) H4A-O4-H4B 106(1)

Table 5 .

 5 Hydrogen bond geometries of -MnCl24H2O.

	D-HA	DA (Å) D-H (Å) HA (Å) D-HA (°)
	O1-H1ACl1 a 3.175(1)	0.76(2)	2.43(2)	173(2)
	O1-H1BO3 b 2.930(2)	0.77(2)	2.17(2)	173(2)
	O2-H2ACl1 c 3.209(2)	0.73(2)	2.50(2)	164(2)
	O2-H2BCl1 d 3.322(2)	0.73(2)	2.65(2)	154(2)
	O3-H3ACl2 e 3.180(1)	0.79(2)	2.41(2)	163(2)
	O3-H3BCl1 d 3.301(1)	0.70(2)	2.77(2)	134(2)
	O3-H3BCl2 d 3.294(1)	0.70(2)	2.72(2)	141(2)
	O4-H4ACl2 f 3.303(2)	0.68(2)	2.64(2)	166(2)
	O4-H4BO1 c 2.969(2)	0.75(2)	2.22(2)	172

Table 6 .

 6 Compilation of the divalent metal tetrahydrate halogenides MX24H2O reported to crystallize in either MnCl24H2O-type (-form) or FeCl24H2O-type (-form) structures.

		Cl	Br I References
	Be			 [52]
	Ca		  [53,54]
	Cr			 [55]
	Mn    [38,49,50,56,57], this work
	Fe		  [47-49,58]
	Co		  [58,59]
	Ni			 [58,60]

SUPPLEMENTARY MATERIAL

The crystallographic data were deposited with the Cambridge Crystallographic Data Centre (CCDC-1941799 and CCDC-1941800 for MnCl24H2O in its -form and -form, respectively).

ACKNOWLEDGEMENT

The authors thank G. Guélou for his technical proofreading.