Marie Brière
email: marie.briere@amundi.com

Valérie Mignon
email: valerie.mignon@u-paris10.fr

Kim Oosterlinck

Ariane Szafarz
email: aszafarz@ulb.ac.be

Towards Greater Diversification in Central Bank Reserves

Keywords: Foreign exchange reserves, diversification, asset allocation. JEL codes: F31, G11, G15, E58

This paper compares the performance of various diversification strategies regarding foreign exchange reserves. The aim is to provide central banks with guidelines in portfolio allocation. We pay particular attention to the situation of upward pressures on U.S. interest rates by implementing our analysis over both the whole 1986-2015 period and a rising rate subsample. Relying on geometric tests of mean-variance efficiency, we show that introducing currencies weakly correlated to the USD (AUD and CAD) significantly reduces portfolio risk. Expected return is improved through mortgage-backed securities, corporate bonds, and equities.

Introduction

Central banks' foreign exchange (forex) reserves are massively held in U.S. dollars (USD), 1 particularly in the form of short-to medium-run government bonds. According to data released by the International Monetary Fund (IMF), the USD share in global forex reserves represented, on average, 63% of total reserves at the end of 2014. 2 This strategy has proven highly profitable during the last 30 years, a period of declining interest rates. Today, however, U.S. rates are historically low, exposing central banks to a major interest-rate risk. Should the Federal Reserve raise rates, the value in USD of forex reserves could suffer substantial losses.

Therefore, the risk associated with hiking rates should not be underestimated. To address the issue, this paper investigates the asset allocation of central bank reserves in a risk-return perspective, and compares the diversification benefits of competing investment opportunities.

Even if the share of U.S. dollar-denominated Treasury bonds remains predominant in forex reserves, several central banks, such as New Zealand's, have started to diversify their holdings with the twofold aim of earning returns above those of U.S. Treasuries, and reducing exposure to a rise in interest rates (Ramaswamy, 2008; McCauley and Rigaudy, 2011; Jones, 2014). The increase in U.S. current-account and fiscal deficits have also stepped up the pressure on central banks to diversify away from the USD.

Central banks have access to two diversification strategies. First, they can invest in asset classes that are more profitable than U.S. bonds and less sensitive to interest-rate risk. For instance, while its forex reserves are mainly held in U.S. Treasuries, the China State Administration of Foreign Exchange (SAFE) has been reducing its exposure by investing in various asset classes (U.S. agency bonds, corporate bonds and equities) since the mid-2000s.

To achieve this objective the SAFE relies on its New York office, which invests in U.S. assets, real estate, and private equity (Wei and Cui, 2013). Likewise, the Bank of Japan has recently invested in exchange traded funds to boost its equity exposure. As for the Swiss National Bank, equities now represent 16% of its reserves (Plender, 2014). 3 Second, although the USD remains the unchallenged reserve currency,4 non-U.S. central banks implement currency diversification strategies (Chinn, 2014). Investments include government bonds in G4 currencies (USD, EUR, GBP, JPY), or a portfolio of these currencies with various possible weighting schemes such as the long-established Special Drawing Rights (SDR). 5 Some central banks hold other major currencies, such as the Australian (AUD) or the Canadian (CAD) 6 dollars, but also emerging currencies, such as the Korean won (KRW), Brazilian real (BRL), Polish złoty (PLN), and Chinese renminbi (RMB). Diversification strategies are applied by central banks in both developed and developing countries. For example, those of Nigeria, Chile, and South Korea hold RMB reserves.

The objectives of central banks' reserves include: facilitating international trade, ensuring the liquidity of financial markets, easing interventions on the forex market, supporting the domestic currency, and maintaining the market's trust in the country's ability to repay its foreign debt. Plausibly, these objectives explain the composition of the banks' foreign reserves. Beck and Rahbari (2011) consider that the USD may be a safe haven during "sudden stops". 7 This would explain why several countries hold the currency in substantial amounts. Beck and Weber (2011) show that many central banks focus on supposedly risk-free assets, and exhibit a behavior driven by precautionary motives. However, some scholars emphasize the benefits of diversification. Ben-Bassat (1980) determines the optimal forex portfolio in a mean-variance framework.8 Wooldridge (2006) shows that central banks are gradually diversifying their allocations into corporate bonds, equities and non-traditional currencies, such as the CAD and AUD. Borio et al. (2008) point out that central banks are increasingly concerned with profitability, along with traditional objectives related to liquidity and safety; they gradually shift asset allocation to riskier assets exposed to credit and liquidity risks.

Forex reserves are sometimes used to create a separate fund, independent from the central bank's balance sheet, with the aim of making returns through efficient management of part of these holdings.9 Eichengreen and Flandreau (2014) confirm that central banks tend to adopt active forex management practices similar to those of private financial institutions. This paper investigates the potential diversification strategies of a central bank. As a starting point, we consider three "benchmark" investment strategies widely used by central banks for reserve allocation: (i) investment exclusively in U.S. government bonds (1 to 5 years), (ii) investment in G4 government bonds (1 to 5 years) in the following representative proportions: 63% in USD, 22% in EUR, 4% in GBP, and 4% in JPY,10 and (iii) investment in G4 government bonds (1 to 5 years), with proportions corresponding to the weight of each currency in the SDR basket: 47% USD, 34% EUR, 12% GBP and 7% JPY. 11 The last of these approaches echoes the IMF's statement that "an SDR allocation is a low cost way of adding to members' international reserves, allowing members to reduce their reliance on more expensive domestic or external debt for building reserves". 12 We challenge these three benchmark reserve allocations with optimized portfolios in various investment universes. First, we consider the optimal portfolio invested in the G4 currencies only. This allocation meets the liquidity objective of forex reserves. Under current market conditions, however, it has two major drawbacks: low profitability and high sensitivity to the risk of a rise in interest rates. Second, to overcome these drawbacks, we consider three alternative asset allocations in larger universes made up of: G4 currencies plus CAD and AUD (referred to as "G6 currencies"); G4 currencies plus other asset classes that have been included or considered for inclusion by many central banks (McCauley and Fung, 2003; Morahan and Mulder, 2013; Jones, 2014), namely U.S. mortgage-backed securities, corporate bonds (investment grade and high yield), and equities;13 and finally G6 currencies plus all the other asset classes.

To assess the performances of diversification strategies, we compare their mean-variance (MV) efficient frontiers built from monthly returns over the 1986-2015 period. Our empirical design relies on two geometric tests of MV efficiency. The test proposed by Basak et al. (2002) is based on the "horizontal distance" between the portfolio whose MV efficiency is in question and its same-return counterpart on the MV efficient frontier. In contrast, the "vertical test" proposed by Brière et al. (2013) uses the difference between the portfolio's expected return and the expected return of its same-variance counterpart on the MV efficient frontier.

After performing full-sample estimations and tests, we specifically address the current concern of potentially rising U.S. interest rates by restricting the data to the sub-periods of rate hiking only.

As expected, our results confirm that diversification improves asset allocation, in particular in terms of risk exposure. Central banks are no exception to this basic financial principle. Over the long term, the optimal risk-reducing strategy consists in increasing the share of U.S. government bonds, and diversifying the portfolio into currencies weakly correlated with USD, such as GBP, AUD, and CAD. To increase expected returns, the strategy is tilted toward asset classes such as mortgage-backed securities, corporate bonds, and equities. In times of rate hiking, risk can be reduced through a similar currency diversification strategy focused on GBP, JPY, and AUD. Higher expected returns are obtained by introducing either risky asset classes-especially high-yield corporate bonds and equities, which are relatively insensitive to interest-rate risk-or Treasury bonds in foreign currencies -JPY, GBP, AUD and CADthat outperform those in EUR and USD in times of rate hikes. Evidently, the central bank's ability to implement those strategies is subject to the legal constraints it is facing. Some are barred from investing in given asset classes. For instance, parts of the reserves are held to match imports. This is the case of China (Pan and Junbo, 2008). 14 Overall, our results confirm that diversification of forex reserves deserves to be taken seriously, especially-but not only-when the risk of rate hiking is high.

The rest of the paper is organized as follows. Section 2 presents the data and provides descriptive statistics. Section 3 displays our results. Section 4 concludes.

Data and Descriptive Statistics

Data

The analysis relies on monthly data covering the period from January 1986 to June 2015. We consider short-term governments bonds (1 to 5 years, Merrill Lynch index) in USD, EUR, GBP, JPY, CAD, and AUD extracted from Bloomberg; mortgage-backed securities (Barclays U.S. indexes); corporate bonds (investment grade and high-yield, Barclays U.S. indexes); and equities (U.S. MSCI index) taken from Datastream.

Due to the current fears of a hike in rates, we pay special attention to periods of rising U.S. interest rates (federal funds rates). To identify these periods, we rely on a smoothing procedure. Specifically, any date framed by two months with rate increases is assumed to be an increase date. Conversely, a month with an "isolated" hike is disregarded. 15 The hiking periods are displayed in Fig. 1, together with the corresponding fed funds rates.

Figure 1. U.S. interest rates and hiking periods, 1986-2015

Source: Authors' calculations. U.S. interest rates are Fed funds rates extracted from Bloomberg.

In line with most of the literature, we consider USD as the numeraire for central banks' reserve allocations (Bernadell et al., 2004). 16

Descriptive Statistics

Table 1 provides the full-sample summary statistics. The short-term government bond investments in G4 currencies provide annual returns ranging from 5.15% for JPY to 7.57% for GBP. The AUD and CAD offer attractive returns, with annual averages of 9.26% and 7.12%, respectively. The average annual returns of the other assets range between 6.70% and 11.28%, with volatilities between 2.41% (for the USD) and 15.25% (for the equities).

Unsurprisingly, most assets exhibit the stigma of non-normal return distributions, as attested by the Jarque-Bera test statistics. In particular, the AUD and CAD government bonds, corporate bonds, and equities are characterized by negative skewness. The kurtosis of all asset classes is above the value of 3 that corresponds to normal distribution. The high yield corporate bond category exhibits the fattest tail, with a kurtosis reaching 11.67.

Table 2 displays the full-sample correlation matrix. The return on short-term government bonds in AUD is weakly correlated with that in USD (3%) but not statistically significant. For CAD and JPY government bonds, the 8% correlation is also statistically insignificant. Both AUD and CAD bonds combine low risk (see Table 1) with promising diversification potential since their correlations with USD bonds are 3% (but not significantly different from zero) and 19%, respectively. Riskier assets, such as high-yield corporate bonds and equities, are negatively correlated with U.S. government bonds (ranging from -5% to -4%). Since none of these correlations is statistically significantly different from zero, these assets are particularly interesting to include. 16 It is worth mentioning that this choice is not benign since numeraires play a key role in asset allocation issues (Borio et al., 2008). Strictly speaking, the numeraire should depend on the use of forex reserves. For example, if the purpose of the reserves is to access imports under stress, then the numeraire could be a basket of imports. By contrast, if the reserves are meant to hedge the country's debt, the numeraire should be linked to the composition of the debt currency, which typically combines USD and domestic currency. Alternatively, the domestic currency could be used as the numeraire. This would meet central banks' concerns about the impact of fluctuations in the value of reserves on profitability and capital (Borio et al., 2008; Ramaswamy, 2008). As argued by Ramaswamy (2008, p. 46), "the reserves could also be viewed as domestic wealth whose value is to be maximized". Tables 3 and4 give the same statistics but over the sub-period of U.S. rate hikes only. Table 3 shows that the short-term government bond investment in USD and EUR performs considerably less well than over the full sample, with average annual returns of 2.33% and 3.12%, respectively. Both GBP and JPY bonds deliver attractive annual returns of around 7% (7.09% and 7.21%, respectively). Interestingly, the annual returns on non-G4 bonds are even more attractive: 9.91% for AUD and 8.29% for CAD. Volatilities exhibit similar levels for all short-term government bond and mortgage-backed security investments. However one may notice a significant decrease in volatility for corporate bonds and equities (from 5.38% to 4.40%, 8.59% to 4.80%, and 15.25% to 12.21% for investment grade and high-yield bonds, and equities respectively). Rising interest rates tend to coincide with a sustainable growth environment, which explains why both corporate bonds (especially high yield, very sensitive to the economic cycle) and equities exhibit attractive returns and lower volatility.

Interestingly, the asset return distributions tend to be closer to normality over the rising rate periods than over the full sample period. Indeed, at the 5% significance level, the Jarque-Bera test statistics reported in Table 3 reject the null hypothesis of normality for two asset classes only, namely the high-yield bonds and the equities.

Table 4 shows that correlations change dramatically during the hiking period. Some wholesample low correlations (Table 2) increase substantially. This is the case for the USD-CAD correlation (35% in the hiking period v. 19% in the full sample) as well as for correlations between corporate bonds and equities. For example, the pairwise correlations of investment grade, high-yield corporate bonds and equities with U.S. short-term government bonds rise from whole-sample figures of 63%, -4% and -5%, respectively to hiking period values of 90%, 49% and 39%, respectively. Conversely, EUR, GBP and JPY, which apparently provide limited diversification benefits in the whole sample (Table 2), are more attractive in a rate hiking environment. AUD stands out as the only currency weakly correlated with USD, no matter the period considered. Let us now investigate in greater detail the risk-return profile associated with each investment strategy by calculating efficient frontiers and applying MV efficiency tests.

Results

Our three benchmark portfolios are: (i) U.S. government bonds only, (ii) G4 governments bonds with central banks' average proportions according to IMF (63% USD, 22% EUR, 4% GBP, and 4% JPY), and (iii) G4 government bonds, with SDR basket proportions (47% USD, 34% EUR, 12% GBP, and 7% JPY). The MV efficiency tests are based on distances between these portfolios and four distinct efficient frontiers. We consider frontiers corresponding to four investment universes: (i) G4 currencies; (ii) G6 currencies; (iii) G4 currencies plus U.S.

mortgage-backed securities, corporate bonds, and equities; (iv) G6 currencies and the other asset classes. The analysis is performed first on the whole 1986-2015 period, and second on the rate hiking sub-period.

The MV approach assumes that the two first moments of the return multivariate distribution are sufficient to make meaningful decisions on asset allocation. On the other hand, our fullperiod descriptive statistics show that most return series exhibit serious non-normality relating to the moments of orders 3 and 4. That financial returns are non-normal is well-known, and constitute a potential cause for concern in any application of the MV approach. Despite this, MV-based studies continue to flourish in the literature for at least two reasons. First, the MV framework offers a two-dimensional representation that is both simple and appealing since it effectively captures the underlying intuition of the risk-return trade-off that investors have to face. Second, and perhaps more importantly, the MV approach is known to be robust against moderate non-normality (Levy and Markowitz, 1979). Therefore, going beyond a twomoment analysis is still a divisive issue.

We apply two MV efficiency tests. The first, developed by Basak, Jagannathan and Sun (2002) (henceforth, BJS), is based on the "horizontal distance" between the portfolio whose MV efficiency is in question and its same-return counterpart on the MV efficient frontier.

Unfortunately, as stressed by Gerard et al. (2012), some portfolios lack such a counterpart, limiting the applicability of the BJS test. The second test, introduced by Brière et al. ( 2013), uses the "vertical distance" proposed by Kandel and Stambaugh (1995), Wang (1998), and Li et al. (2003), namely the difference between the tested portfolio's expected return and the expected return of its same-variance counterpart on the MV efficient frontier. Both tests are complementary, but the vertical test is more intuitive than the BJS one since it is based on a difference in return, which is more easily interpretable than a difference in variance. 17

Full-Sample

Fig. 2 displays the efficient frontiers corresponding to the four investment universes over the whole period, together with the three benchmark portfolios. It shows that all these portfolios, made up of G4 currencies, are located close to the G4 efficient frontier. This means that the imposed proportions do not create inefficient portfolios but fix a level of risk that the central bank can no longer control. The least risky allocation is fully invested in USD, the second is the G4 average allocation, which includes 63% of USD, and the last is the G4 SDR basketbased portfolio, with a 47% share of USD.

For the G6 currencies, which include the core G4 currencies plus the non-core AUD and CAD, we obtain a higher frontier. This highlights the benefits of currency diversification: for a same level of volatility, returns are always higher when investing in a broader sample of currencies is allowed. Adding other asset classes to the G4 currencies is even more interesting, since the corresponding efficient frontier is distinctly above the G6-only frontier.

12 However, the full diversification strategy combining the G6 currencies and other asset classes delivers a frontier very close to the previous one. This suggests that including AUD and CAD provides no additional benefits once other assets are present in the investment universe. To sum up, for the representative central banks the most relevant strategy seems to be holding reserves in G4 currencies and in U.S. mortgages, investment grade and high-yield corporate bonds, and equities.

Figure 2. Benchmark portfolios and efficient frontiers, whole sample, 1986-2015

Source: Authors' calculations.

Table 5. Results of BJS and vertical tests, whole sample, 1986-2015

Note: Panel A presents the results of the BJS and vertical tests. Horizontal distance is the result of the BJS test, i.e. the difference in variance between the tested portfolio and the optimal portfolio with the same return on the efficient frontier multiplied by 10E5. Vertical distance is the result of the vertical test, i.e. the difference in return between the tested portfolio and the optimal portfolio of same variance on the efficient frontier multiplied by 12 to provide an annualized return. Panel B (resp. Panel C) displays the horizontal (resp. vertical) optimal shares of each currency and asset class. *** (resp. **, *): significant at the 1% (resp. 5%, 10%) statistical level.

Fig. 2 provides visual evidence of diversification benefits. However, only proper tests can confirm the empirical relevance of this observation. Panel A in Table 5 displays the results of the BJS and vertical tests, and gives the compositions of optimal portfolios. As mentioned previously, it is not always possible to run the horizontal test due to the possible lack of the efficient same-return counterpart of the considered portfolio, hence the missing values for this test. In particular, when the tested portfolio is invested in USD only, the risk is very low-and there is no less-risky efficient portfolio. This limitation emphasizes the relevance of the vertical test, which does not suffer from the same technical limitation.

Considering first the full USD allocation (Columns (1)-( 4)), our findings show that portfolio volatility cannot be reduced. However, higher returns can be obtained by extending the investment universe. The optimal asset allocation in G6 currencies contains only small proportions of AUD and CAD bonds (6% and 2%, respectively). Thus, currency respective shares of 13% and 3% (Column (10)). Extending the investment universe to broad asset classes (8% mortgages, 11% high yield and 3% equities) leads to better performances than the currency diversification strategy, since volatility decreases from 5.52% to 2.44% for a similar return (Column ( 11)). In addition, allowing for investment in AUD and CAD does not strongly modify these findings (a modest share of 2% AUD government bonds is added to the previous portfolio, obtained by slightly reducing exposure to mortgages, high yield and equities), since volatility amounts to 2.42% (Column ( 12)). Considering returns, the performance is significantly improved (from 6.04% to 8.32%) only with the full diversification strategy. This is achieved through a wholly diversified portfolio including 25% mortgages, 18% investment grade and high-yield bonds, 16% equities, 12% GBP and 11%

AUD short-term government bonds, ruling out USD government bonds from the asset allocation.

To sum up, the central banks' average allocation and the SDR basket-based allocation strategies are shown to be clearly inefficient and can be easily improved. It is easier to reduce volatility than to increase return, the former being achieved by augmenting the shares of USD and GBP, the latter by extending investment opportunities to non-core currencies and/or riskier asset classes. In particular, adding mortgage-backed securities, high-yield corporate bonds and equities is a useful strategy in terms of return improvement. Unless a central bank is obligated to invest in USD government bonds, our results show that there is room for improvement in a risk-return framework.

Hiking Period

We now conduct the same analysis but restrict the sample to the hiking period. Fig. 3 illustrates that our three benchmark portfolios are dominated by better-diversified portfolios lying on efficient frontiers. Currency and asset class diversifications provide little additional return for low-risk portfolios. By contrast, including G6 currencies in high-risk portfolios leads to a notable increase in expected returns. Overall, the most effective strategy combines both types of diversification. Table 6 shows that, even in the hiking period, improving a portfolio's return is easier than reducing its risk. Risk can indeed be dampened by allowing for greater flexibility in the shares of the core currencies and extending the investment opportunities. In all the cases presented in Table 6, the horizontal distance is significant at the 1% statistical level, whereas the vertical distance is significant, at best, at the 10% level (Columns (7), (8), and (12) in Panel A) and entails a considerable enlargement of the set of investment opportunities.

Table 6. Results of BJS and vertical tests, hiking period, 1986-2015

Note: Panel A presents the results of the BJS and vertical tests. Horizontal distance is the result of the BJS test, i.e. the difference in variance between the tested portfolio and the optimal portfolio of same return on the efficient frontier multiplied by 10E5. Vertical distance is the result of the vertical test, i.e. the difference in return between the tested portfolio and the optimal portfolio of same variance on the efficient frontier multiplied by 12 to provide an annualized return. Panel B (resp. Panel C) displays the horizontal (resp. vertical) optimal portfolios, with the optimal shares of each currency and asset class. *** (resp. **, *): significant at the 1% (resp. 5%, 10%) statistical level.

With reasonable levels of risk (2.01%) and return (2.33%), pure U.S. bond investing (Columns (1)-( 4)) does not reduce volatility in times of rising rates. Nor does it improve return, regardless of the diversification strategy followed.

The two other benchmark portfolios perform well in hiking periods, but they can still be significantly improved. For the portfolio based on the central banks' average allocation (Columns (5)-( 8)), the risk goes from 3.07% to 2.06% by using the G4 currencies only. The corresponding currency shares are: from 63% to 87% for USD, from 4% to 10% for GBPwhich is less correlated with USD than with EUR when interest rates are rising -and from 4% to 3% for JPY. Extending the investment universe to the two non-G4 currencies (Column (6)), other asset classes (Column (7)), or both (Column (8)) reduces the risk only marginally.

Optimal allocations involve marginal exposures to alternative currencies (5% AUD in Columns ( 6) and ( 8)), and other assets (2% high-yield corporate bonds, and 1% equities in Column ( 7)). Boosting the return value is hard: the improvement is significant at the 10% statistical level when the investment universe includes alternative asset classes. Specifically, to reach the highest accessible return value of 5.07% (Column ( 8)), central banks should invest in high-yield corporate bonds (5%) and equities (7%) as well as GBP (4%), JPY (6%), AUD (10%) and CAD (12%). 18 Let us turn to our third benchmark, the SDR-based portfolio (Columns ( 9)-( 12)). Its risk can be significantly reduced by augmenting the share of USD government bonds in a range lying between 75% and 81%, and introducing a slight proportion of U.S. high-yield corporate bonds (between 0% and 4%) and equities (between 1% and 5%) or Treasury bonds in AUD (7%) or CAD (between 3% and 5%). Improving the corresponding return-only at the 10% significance level-requires the inclusion of both additional currencies and asset classes, namely a portfolio invested in 30% U.S. government bonds, 25% CAD, 16% equities, 13%

JPY and AUD and 1% high yield (Column ( 12)).

Conclusion

Forex reserves are key assets that central banks can mobilize in troubled times. The inability to manage reserves optimally can have far-reaching consequences. Nevertheless, some central banks are constrained by legislation forbidding them to invest in given assets or forcing them to limit specific exposures. For example, the foreign exchange reserves of the Central Bank of Chile can be invested only in "foreign currency, gold, negotiable instruments and securities or commercial paper issued or guaranteed by foreign states, central banks or foreign or international banks or financial institutions" (Banco Centrale de Chile, 2012, p. 7). On the other hand, many central banks seek to increase returns by diversifying their investments.

This paper investigates the performance of various diversification strategies with the aim of providing central banks with guidelines for optimal portfolio allocation. To this end, we determine the efficient frontier corresponding to each strategy, and compare them using two tests of portfolio mean-variance (MV) efficiency. Some strategies are accessible to most

Figure 3 .

 3 Figure 3. Central bank reserve benchmark portfolios and efficient frontiers, hiking period, 1986-2015

Table 1 . Descriptive statistics of monthly returns, whole sample 1986-2015

 1 Note: USD: U.S. dollar, EUR: euro, GBP: British pound, JPY: Japanese yen, AUD: Australian dollar, CAD: Canadian dollar, MBS: mortgage-backed securities, CORP IG: investment grade corporate bonds, CORP HY: high-yield corporate bonds, EQUITIES: U.S. equities.

Table 2 . Correlation matrix of monthly returns, whole sample 1986-2015

 2

	Note: USD: U.S. dollar, EUR: euro, GBP: British pound, JPY: Japanese yen, AUD: Australian dollar, CAD:
	Canadian dollar, MBS: mortgage-backed securities, CORP IG: investment grade corporate bonds, CORP HY:
	high-yield corporate bonds, EQUITIES: U.S. equities. *** (resp. **, *): significant at the 1% (resp. 5%, 10%)
	statistical level.

Table 3 . Descriptive statistics of monthly returns, hiking period 1986-2015

 3 Canadian dollar, MBS: mortgage-backed securities, CORP IG: investment grade corporate bonds, CORP HY: high-yield corporate bonds, EQUITIES: U.S. equities.

		USD	EUR	GBP	JPY	AUD	CAD	MBS	CORP IG CORP HY EQUITIES
	Mean	0.19%	0.26%	0.59%	0.60%	0.83%	0.69%	0.22%	0.10%	0.35%	1.03%
	Ann. Mean	2.33%	3.12%	7.09%	7.21%	9.91%	8.29%	2.62%	1.22%	4.23%	12.30%
	Median	0.14%	0.16%	0.18%	0.63%	0.83%	0.77%	0.11%	-0.17%	0.56%	1.01%
	Maximum	1.69%	6.28%	8.17%	7.82%	8.17%	5.21%	2.85%	2.88%	4.14%	13.28%
	Minimum	-1.05%	-5.98%	-8.24% -6.60% -10.18% -4.38% -2.83%	-3.29%	-3.78%	-5.35%
	Std. Dev.	0.58%	2.55%	2.75%	3.13%	3.11%	2.03%	1.10%	1.30%	1.39%	3.53%
	Volatility	2.02%	8.85%	9.52%	10.83% 10.78% 7.03%	3.82%	4.50%	4.80%	12.21%
	Skewness	0.22	-0.10	0.16	0.17	-0.25	-0.15	0.00	-0.20	-0.63	0.71
	Kurtosis	3.12	2.79	3.82	2.43	3.94	2.64	3.55	3.12	4.59	3.86
	Jarque-Bera	0.63	0.26	2.33	1.31	3.38	0.65	0.90	0.54	12.44	8.31
	Probability	0.73	0.88	0.31	0.52	0.18	0.72	0.64	0.76	0.00	0.02
	Observations	72	72	72	72	72	72	72	72	72	72

Note: USD: U.S. dollar, EUR: euro, GBP: British pound, JPY: Japanese yen, AUD: Australian dollar, CAD:

Table 4 . Correlation matrix of monthly returns, hiking period 1986-2015

 4

	Note: USD: U.S. dollar, EUR: euro, GBP: British pound, JPY: Japanese yen, AUD: Australian dollar, CAD:
	Canadian dollar, MBS: mortgage-backed securities, CORP IG: investment grade corporate bonds, CORP HY:
	high-yield corporate bonds, EQUITIES: U.S. equities. *** (resp. **, *): significant at the 1% (resp. 5%, 10%)
	statistical level.

This is the case for most worldwide central banks, with the notable (and evident) exception of the U.S. Federal

Other examples include the Bank of Israel and the Czech National Bank, which have also raised their equity exposures to more than 10% of reserves.

See the so-called "exorbitant privilege"[START_REF] Eichengreen | Exorbitant Privilege: The Rise and Fall of the Dollar and the Future of the International Monetary System[END_REF][START_REF] Cova | Foreign Exchange Reserve Diversification and the 'Exorbitant Privilege[END_REF].

The SDR is an interest-bearing international reserve asset created by the IMF in 1969 to supplement other reserve assets of member countries. The SDR is based on a basket of international currencies comprising the U.S. dollar, Japanese yen, euro and pound sterling. https://www.imf.org/external/np/exr/faq/sdrallocfaqs.htm

Many central banks are planning to increase their holdings of advanced country currencies, which are not part of the SDR basket[START_REF] Morahan | Survey of Reserve Managers: Lessons from the Crisis[END_REF].

A "sudden stop" is an abrupt reduction in private capital inflows.

According to[START_REF] Ben-Bassat | The Optimal Composition of Foreign Exchange Reserves[END_REF], the composition of developed countries' reserves is mainly influenced by the stability of the international monetary system, whereas developing countries care mainly about the profitability and liquidity of their reserves.

Some examples are Korea Investment Corporation and China Investment Corporation, respectively launched in 2005 or 2007.

These shares correspond to the IMF average allocation of central banks in the G4 currencies (data collected in 2014, see footnote 2). These four currencies serve as the reference for the SDR and are now mostly used by central banks to diversify their foreign exchange reserves[START_REF] Morahan | Survey of Reserve Managers: Lessons from the Crisis[END_REF].

See https://www.imf.org/external/np/fin/data/rms_sdrv.aspx. These figures are those of June 2015.

https://www.imf.org/external/np/exr/faq/sdrallocfaqs.htm. Moreover,[START_REF] Medeiros | The Potential Role of the SDR in Diversified Currency Portfolios of Central Banks[END_REF] show that the SDR plays a key role in central banks' reserve allocation.

We consider diversification in the U.S. assets only. The mortgage-backed securities market is much less developed in non-US countries, and the high yield Japanese market is almost inexistent. Moreover, corporate bond markets and equity markets have a relatively high correlation across the different geographical zones[START_REF] Brière | No Contagion, only Globalization and Flight to Quality[END_REF]. US corporate bonds and stock returns may be a good proxy for international returns.

[START_REF] Goldberg | Do Industrialized Countries Hold the Right Foreign Exchange Reserves?[END_REF] describe the strategies of other central banks.

In fact, our sample comprises only two dates with isolated rises in interest rates, namely May 1986 and March 1997. Moreover, Fig.A1in Appendix A shows that in times of U.S. rate hikes, non-U.S. central banks tend to increase their rates as well, especially in Canada and in the Eurozone.

A slightly lower return (4.62%, see Column (7)) can be achieved without alternative currencies: 58% U.S. short term government bonds, 11% high-yield corporate bonds, 12% equities, 14% GBP and 4% JPY.

estimate that more than 15% of central banks invest part of their reserves in equity.

Introducing AUD and/or CAD in addition to other assets is not particularly useful, since the performance is only very slightly changed (Column (4)). Optimal asset allocations including both G6 currencies and diversifying asset classes have a very low proportion of non-G4 currency bonds (2% AUD and 0% CAD).

Let us now turn to the central banks' average allocation in G4 currencies (Columns ( 5)-( 8)).

Portfolio volatility can be significantly reduced by two different moves: increasing the share of U.S government bonds, and enlarging the investment possibilities. For instance, when the share of U.S. government bonds is raised from 79% to 86%, while simultaneously introducing 10% AUD and 2% CAD, the portfolio's volatility drops from 4% to 2.58% (Column ( 6)).

Volatility is even lower (2.33%) if the central bank extends its reserves to high-yield corporate bonds (10%) and equities (2%) (Column ( 7)). The results confirm the intuition gained from Fig. 2 Our third benchmark portfolio, based on the SDR basket (Columns ( 9)-( 12)), can also be improved significantly. Risk can be easily reduced, from 5.52 to 3.83%, by modifying the weights of the four core currencies (Column (9)), i.e. by increasing the share of USD (from 47% to 70%) and GBP (12% to 30%). Risk reduction based on currency diversification can be even larger, from 5.52% to 2.87%, if AUD and CAD are included in the portfolio, with central banks; others require investment restrictions to be lifted. This is why we explore the consequences of investing in four asset universes and starting from three benchmark portfolios. Moreover, we run the estimations over two samples: the full 1986-2015 period, and the rate-hiking periods.

By relying on the MV approach, our study inevitably faces the consequences of ignoring nonlinear risk. MV efficiency uses volatility as a risk measure and ignores extreme risks. This might restrict the interpretation of our full-sample results since many asset classes have nonnormal returns over the period. Alternative approaches include the three-moment and fourmoment strategies proposed by Jondeau and Rockinger (2006) and asset management techniques based on Values-at-Risk (VaR), which are commonly used in risk management (Jorion, 2007). However, each strategy relies on specific assumptions regarding the way the risk-return trade-off is to be addressed. In this regard, the traditional MV approach can reasonably be considered as a simple, middle-of-the-road option.

Our main findings can be summarized as follows. Diversification can improve the typical allocation of a central bank, particularly in terms of risk exposure. Specifically, over the whole period, the optimal risk-reducing strategy consists in increasing the share of USD, and diversifying into currencies that are weakly correlated with USD, such as GBP, AUD, and

CAD. An efficient investment strategy for increasing portfolio return is based on diversified asset classes such as mortgage-backed securities, corporate bonds, and even equities. In times of rising rates, risk can be reduced through the same strategy, i.e. currency diversification notably into GBP, JPY, and AUD. In this case, however, the improvement in terms of portfolio return is harder to achieve, because it requires introducing either high-yield corporate bonds and equities, or specific currencies (JPY, GBP, AUD, and CAD) that outperform both EUR and USD when interest rates are rising.


Benjamin David

Professor Valérie Mignon

Ryo Kambayashi

Computer technology and probable job destructions in Japan: an evaluation *

Keywords: JEL Classification: C53, J21, O33 Computer technology, Japanese labor market, Automation, Random Forest

This paper evaluates the risk of job destructions induced by computer technology in Japan. Relying on recent methodology, we find evidence that approximatively 55% of jobs are susceptible to be carried by computer capital in the next years. We also show that there is no significant difference on the basis of gender. On the contrary, non-regular jobs (those that concern temporary and part-time workers) are more vulnerable to computer technology diffusion than the others.

Introduction

In recent years, an important dissemination of computer and communication technologies has been observed in Japan and in other industrialized countries. This diffusion in economic activities is a broad and international movement with country specific timeline. According to [START_REF] Murata | Lessons from the history of information system development and use in japan[END_REF], this process begins in Japan in the 1950s via the acquisition of a US computer (Bendix G-15) by the Railway Technical Research Institute (1957) and continued through the 1960s by the introduction of second and third generation of computers. 1 These machines which were both imported and produced locally, were progressively dedicated to special purpose terminals in manufacturing, distributions and financial industries in the 1970s. During the 1980s, Japan undergone a massive development of office automation benefiting from the invention of Personal Computer (PC) and other specific programs such spreadsheets or work processors. 2 The spread of computers has continued until now and they are used every day in a large range of economic activities. In parallel, technical advance and deregulation policies have caused the emergence of networks supported by computer infrastructure. This concerns the use of the fax machine in the 1980s and above all the development of the Internet and mobile phone in the 1990s and 2000s. Networks have hugely modified the modalities of communication and reduced their costs. The actual situation is characterized by a massive access to these networks: 90% of Japanese people have an access to Internet and the ownership rate of mobile phone is equal to 120% (International Telecommunication Union, 2015).

Another aspect of the actual technological diffusion is the massive development of robotics that can be viewed as a component of the computer revolution [START_REF] Spong | Robot Modeling and Control[END_REF]. 3 In this field, Japan is a key country both in terms of production and use to the point that it was labelled as robot kingdom [START_REF] Schodt | Inside the Robot Kingdom: Japan, Mechatronics and the Coming Robotopia[END_REF]. Indeed, Japan has a long and fruitful history in this matter which began in the 1960s by the introduction of industrial robots dedicated to welding, assembling or painting, followed by the first mobile robots used in inspection, transport or spatial tasks in the 1980s [START_REF] Kumaresan | An integrated network approach to systems of innovation -the case of robotics in japan[END_REF]. Production and use of robots continue at a large scale and were extented through the development of micro-robots and services robots. 1 The second generation of computers is characterized by the introduction of transistors and the third by the use of integrated circuits.

2 The first PC produced in Japan was the NEC PC 8001 (1979).

3 They argue that The key element in the above definition is the reprogrammability of robots. It is the computer brain that gives the robot its utility and adaptability. The so-called robotics revolution is, in fact, part of the larger computer revolution .

Illustrations of this trend are the actual efforts in the humanoid robotic field initiated by researchers of Waseda University who created Wabot 1 (1973) as well as other famous examples as ASIMO (Honda), Wakamaru (Mitsubishi), or Pepper (Aldebaran Robotics and Softbank). Data also show the importance of robotics diffusion in Japan. In 2013, this country has the second highest robot density in the world (323 units per 10000 workers) behind the Republic of Korea and has the most important robot density in the automotive industry with 1520 industrial robots per 10000 employees (International Federation of Robotics, 2014). 4All these digital devices share a common theoretical and technical background based on binary logic and basic electronic components such as transistor or microprocessor. 5 Many scholars suggest that this set is not a simple group of incremental innovations but constitute a Technological Revolution or a technological-discontinuity [START_REF] Brynjolfsson | Race Against the Machine[END_REF] able to transform profoundly the rest of the economy and produce a new economic paradigm [START_REF] Perez | Technological revolutions and techno-economic paradigms[END_REF]. Indeed, efforts of characterization of technologies in the literature suggest that innovations or interrelated cluster of innovations are not comparable in their scale and their degree. In this perspective, ICT can be viewed as a major technological set susceptible to produce large-scale impacts. In support of this vision, the literature on General Purpose Technology (GPT) [START_REF] Bresnahan | General purpose technologies-engines of growth[END_REF][START_REF] Rosenberg | A general-purpose technology at work: The corliss steam engine in the late-nineteenth-century united states[END_REF] supposes that the most important technologies share the feature of generality. This crucial point was anticipated by [START_REF] Simon | The steam engine and the computer: What makes technology revolutionary[END_REF] which stress that the higher is the level of generality of a technology, the higher is its potential because there is a very important number of possible applications. In the case of computer technology, the degree of generality is very high because all economic activities include information processing tasks. This view is reinforced by the actual process of digitization of human activities which makes the amount of information available more and more important ( Big Data ). Furthermore, digitization is coupled with an impressive improvement of ICT capacities in information processing as well as in terms of transmission, storage and transformation of information [START_REF] Nordhaus | Two centuries of productivity growth in computing[END_REF][START_REF] Nagy | Superexponential long-term trends in information technology[END_REF][START_REF] Koomey | Implications of historical trends in the electrical efficiency of computing[END_REF]. Thus, it supposes that the field of application of computer technology is growing, a characteristic that could have notable effects on many economic matters. Among the possible consequences of ICT adoption, an important aspect is its potential destabilising impact on employment. Indeed, labour activities do not escape this trend of digitization: in production activities, there are many tasks consisting of manipulation of information but also that some other tasks can be modeled as information flows. For example, accounting calculations is a task which consists of transferring, stocking and transforming information. On the other hand, some physical activities such as assembly, construction, transport can also be represented as information. Material elements, the space in which they are situated, and movements can be defined as mathematical objects. From this perspective, these tasks are susceptible of being carried out by robots within computer programs representing physical objects, environment and motions in information way. With this in mind, it could be expected that a large number of tasks in a wide variety of fields could be given over to computers now and in the near future. This perspective constitutes a biggest challenge for modern economies. Acknowledging the importance of this topic, our aim in this paper is to investigate the impact of ICT on job destructions in Japan.

The perspective from which a growing share of tasks will be performed by computer capital has strong implications for several Japanese specific economic questions especially those pertaining to the labor market. Among these issues, we can mention the ageing process sustained by gains in longevity, while life expectancy is already one the highest in the world, and low immigration flows. Even if this process concerns several countries in Europe (Germany, France) or in Asia (Korea, China), it is important to stress that Japan has the most rapidly aging population in the world (IMF, 2013). On the supply side of the labor market, significant consequences of this evolution are the massive reduction of the overall labor-force, or a dependency ratio reduction in the coming years and decades. A possible response face to this scenario is to call to the technological solution. Growth of ICT capital stock could contribute to maintain the level of production and to help in the care of elderly people. On the demand side, we note that the Japanese labor market has experienced the introduction of more flexibility from the 1980s. This situation originates in the labor law reform in a context of assetinflated bubble economy collapse [START_REF] Asao | Overview of non-regular employment in japan[END_REF]. The system characterized by job rigidity and wage flexibility (shūshinkoyō) has progressively left space for a growing number of non-regular jobs which represent roughly twenty millions people (Statistics Bureau, 2015). It is important to underline that if computer technology will replace workforce, it could do it differently according to the type of employment. Indeed, it is possible that computer technology destroys more easily non-regular employment either because dismissals are facilitated by legal disposition or because computer technology realizes rather tasks typically carried by non-regular workers. Inversely, if computer and communication tools threaten regular jobs, we can expect that the share of non-regular workers in overall active population increases significantly, thus profoundly affecting the structure of Japanese workforce. We also note that the computer revolution could have notable effects on other questions such as the participation of women in the workplace or could significantly modify the return to education .

Turning to methodological issues, in order to assess the potential risk for Japanese workers associated with the diffusion of computer technology, we use Career matrix data from the Japan Institute for Labour Policy and Training (JILPT) and we build a training sample containing occupations without doubt automatable and other occupations that could be considered as nonautomatable. With this sample, we estimate a model explaining the probability of computerisation by the differential dotation in non-automatable skills. Estimation is achieved by using the Random Forest algorithm, which builds several uncorrelated decision trees from bootstrap samples from the training set and averages the results to obtain the final estimation. Then, by using our estimates and data from the Population Census (2010), we evaluate the number of jobs threatened by technology and we study the distribution of the probabilities by gender and type of employment. Our results suggest that a large share of jobs could be performed by computer system in the coming years. More precisely, according to our estimates, one half of Japanese jobs are susceptible to be destroyed by computer technology. However, this global result masks differential effects according to the kind of workers since non-regular workers seem to be more exposed. On the contrary, we don't find results differentiated by gender. The rest of this paper is organized as follows. Section 2 briefly reviews the literature. Section 3 presents the methodology. Section 4 presents the results and section 5 concludes.

Literature review: employment and computer

A vast literature exists on the link between technology and employment, dating at least from classical economists such as [START_REF] Ricardo | On the Principles of Political Economy and Taxation[END_REF] or Marx (1867).

In this field, a recurrent question concerns the capacity of technology to re-place workers in economic activities. The possibility of the realization of this capital/labor substitution may be interpreted from the economic perspective by the following alternative: compensation theory or technological unemployment [START_REF] Keynes | Economic possibilities for our grandchildren[END_REF].

The first approach refers to the fact that there are compensation mechanisms that are triggered by technical change itself and which can counterbalance the initial labor saving impact of process innovation [START_REF] Vivarelli | Innovation, employment and skills in advanced and developing countries: A survey of the literature[END_REF]. 6 In this perspective, technology is not a serious threat to employment level but it could produce a qualitative shift in jobs. Under technological pressure, some tasks are no longer carried out by workers whilst other appear because of new activities. The second view is more pessimistic because it supposes that even if there are some compensation mechanisms, a part of the workforce replaced by technology doesn't find new jobs and contributes to technological unemployment . In this perspective, there is an inequality between the number of jobs destroyed and the number of jobs created.

Recently, this recurrent question has been raised again due to the diffusion of IT which seems capable of performing an ever-increasing share of tasks traditionally carried out by workers. In the recent literature, a major theoretical and empirical contribution in the understanding of the relationship between computer technology and the evolution of the distribution of occupations was made by [START_REF] Autor | The skill content of recent technological change an empirical exploration[END_REF]. They have developed an equilibrium model ( task model ) in which producers use two types of inputs: routine and non-routine labors.7 They suppose that the first kind of labor input is perfectly substitutable by computer capital while the second constitutes a complement. The driving force of the model is the fall in prices of computer capital which produces differential evolution of each type of labor. [START_REF] Autor | The skill content of recent technological change an empirical exploration[END_REF] provide econometrical evidences to support their model. A very similar study was written by [START_REF] Maurin | Changes in the functional structure of firms and the demand for skill[END_REF] who bring empirical arguments in favor of this hypothesis in France. [START_REF] Goos | Lousy and lovely jobs: The rising polarization of work in britain[END_REF] have extended this approach by showing that the non-routine tasks are mainly located in the top and the low level of wage distribution which can explain the polarization of the labor market observed in the UK. Many other works confirm the task-based polarization hypothesis for several economies such as [START_REF] Goos | Job polarization in europe[END_REF] or [START_REF] Autor | The growth of low-skill service jobs and the polarization of the us labor market[END_REF].

With regard to the Japanese economy, [START_REF] Ikenaga | Polarization of the japanese labor market: The adoption of it and changes in tasks contents[END_REF] uses the same frame-work as [START_REF] Autor | The skill content of recent technological change an empirical exploration[END_REF] and shows that since the 1990s, labor input of knowledge-intensive non-routine analytic tasks and low-skill non-routine manual tasks is growing, whereas, at the same time labor input of routine manual tasks has declined. In addition, Ikenaga identifies a complementary relationship between ICT capital and workers who carry out non-routine analytic tasks and a substitution trend with workers engaged in routine tasks. [START_REF] Ikenaga | Long-term trends in the polarization of the japanese labor market: The increase of non-routine task input and its valuation in the labor market[END_REF] also pay interest to the evolution of the input share of each type of tasks on the basis of a specific measure of task intensity in each occupation. Their analysis suggests that there is a longterm increase in non-routine task input and a long-term decrease in routine tasks between 1960 until 2005. In addition, they found a positive correlation between the average wage in an occupation and the routine cognitive task input, and a negative correlation with routine manual task input.

Recently, [START_REF] Frey | The future of employment: How susceptible are jobs to computerization?[END_REF] have renewed the analysis of the exposure of workers faced with recent technological diffusion. A starting point of their approach is that the identification between non-routine tasks and low susceptibility to automation is called into question by the improvements of computer tools in the fields of machine learning and mobile robots. Indeed, non-routine tasks can also be carried out by computer capital. A famous example is the autonomous driverless cars, now in development (but operational), and nonetheless considered as a good example of non-automatable tasks by [START_REF] Autor | The skill content of recent technological change an empirical exploration[END_REF] (cited by [START_REF] Brynjolfsson | Race Against the Machine[END_REF]). On the basis of expert opinions and relying on the computer science literature, Frey and Osborne (2013) go beyond the distinction routine tasks/non-routine tasks and propose that computerisation 8 has strong limitations in perception and manipulation tasks, creative intelligence tasks, and social intelligence tasks. By using O*NET and SOC databases (from the US department of labor), the authors, helped by a panel of computer scientists, consider 70 occupations which are without doubt automatable or not in the next years. For example they consider that the cashier occupation is automatable, while childcare worker occupation is non-automatable. Then, they construct a probabilistic classification model with this training sample. The dependent variable is the probability of computerisation and the explicative variables are nine variables that representing the three bottlenecks . They use this estimated model to predict the probabilities of automatization of the 702 occupations of their database. Then, they evaluate the number and the distribution of jobs by sector now threatened by computer capital. Their results suggest that 47 percent of total US employment is at risk (by considering a threshold of probability equal to 0.7).

In the present paper, we aim at implementing a similar analysis about Japanese labor market by assessing the share of jobs which could be threatened by computer technology over the next few years. This approach is justified by the fact that the results obtained by [START_REF] Frey | The future of employment: How susceptible are jobs to computerization?[END_REF] for the United States are not fully transposable to the case of the Japanese labor market. Indeed, there are some differences in industry and occupational structures between these two countries. Industries have not the same weight in each economy and occupations are partially different (follows that US and Japanese classificatiosn are not the same). We note, for instance, the existence of Japanese specific occupations such as kimono dressing instructor, sushi chef, pachinko employee, Juku teacher, administrative scrivener and some differences in occupations which have not the same valuations of skills [START_REF] Ikenaga | Long-term trends in the polarization of the japanese labor market: The increase of non-routine task input and its valuation in the labor market[END_REF]. On the other hand, Japan is a country where the technological issue is particularly interesting. Even if the spread of computer devices is an international dynamic, there are country specific characteristics. As discussed above, Japan has a high level of technology diffusion and it is a major producer of innovations. If computer technology has a significant impact on the structure or on the level of employment, we can expect that it will be particularly important in this country, in particular due to the development and the dissemination of robots.

Methodology

Data

The first step of our analysis is to constitute a training sample with which we build our prediction model. The purpose is to select occupations, which can be undoubtedly, in the current state, performed or not by computer capital. We also need some information about the levels of skills required to perform each occupation.

For that purpose, we use data from Career matrix, a database created by the JILPT containing 499 occupations based on the Classification of Oc-cupations for Employment Services (ESCO). It contains 35 variables that describe the level of different skills necessary for each occupation. These values are defined on the basis of surveys and range between 0 and 5, 0 being the lowest value and 5 the maximum value. Firstly, we select 61 occupations similar or very close to Frey and Osborne ( 2013) selection (which is itself based on computer science expert opinions). In order to expand our sample and ensure robust estimation, we add other automatable occupations identified on an empirical basis. This means that they are now subject to automation process or that a technology in an advanced development stage is susceptible to replace workers in these occupations. For example, we include in this sample the occupation Train Driver because there are already automatic trains in running in Japan. Finally, the training sample considered in this study contains 69 occupations representing roughly 14% of those of Career Matrix (tables 3, 4).

The second step in the constitution of our training sample is to select explanatory variables that determine the probability of automation. The baseline model supposes there are three limitations to automation: perception and manipulation tasks, creative intelligence tasks, and social intelligence tasks. Unfortunately, Career matrix doesn't contain variables for representing perception and manipulation tasks and creative intelligence tasks. In order to overcome this problem, we create appropriate dummy variables for the two categories without data. Precisely, we define a dummy variable manual dexterity to reflect perception and manipulation tasks and two other to represent creative intelligence tasks: Fine Arts and Originality . We prefer to create dummies and only three variables to reduce the risk to assign subjectively values between 0 and 5 for the other variables. For example, the occupation of surgeon takes a value of 1 to signify that it requires high level of manual dexterity, while the occupation of lawyer takes a value of 0 to signify the inverse. We consider that this approach is a convenient tradeoff between the accounting of important variables and the risk of subjective assignation. To represent social intelligence tasks, we select, in Career Matrix, the following five variables:

Coordination , Persuasion , Negotiation , Instructing and Service orientation . Lastly, by examining variables contained in Career Matrix, we select another variable that seems impossible for the moment to automatize: Judgment and decision making . We call this task: Appreciation tasks. We present all data in table 5.

Random Forest

We aim to compute the probability of automation of occupations on the basis of the different dotations in non-computerisable tasks inputs by using the methodology of Frey and Osborne ( 2013): (i) considering a training sample of occupations which could be considered as clearly automatable or not, (ii) we build a model with this subsample, (iii) and we finally predict the probability of automation of all occupations. In this perspective, we have constituted a training sample as described in section 3-1. For the estimation, we rely on the Random Forest (RF) algorithm9 , a very useful method from machine learning framework.

The use of RF instead of a standard method requires explanation. In these kind of situation, when we consider a binary dependent variable, it is usual in applied economics to use logistic regression. However, in this case, for technical reasons, this seems impossible. Indeed, as suggested by [START_REF] Peduzzi | A simulation study of the number of events per variable in logistic regression analysis[END_REF], it is necessary to have at least 10 Events Per explanatory Variables (EPV) in order to perform logistic regression. Below this threshold, there are important risks of non-convergence, loss in terms of accuracy, or no normality of regression coefficients. In our case, we have 69 observations in the learning sample including 33 events (i.e. when the probability of automation is equal to one) and 10 explanatory variables (EPV = 3.3). Another potential difficulty is the correlation between several explanatory variables. For example, the persuasion and negotiation variables are highly correlated (r=0.8). In front of these problems, it seems difficult to expand the size of the learning sample or to remove some variables just on a subjective basis.

Initially, for simplicity and to circumvent these technical problems, we have been interested in using regression trees 10 , specifically CART algorithm [START_REF] Breiman | Classification and Regression Trees[END_REF], a simple nonparametric method consisting in splitting the subspace of predictors in different regions and model the response of the dependent variable as a constant in each region. 11 The main advantages of this approach are that no assumption on the functional form to linking the variables is required (that allows taking into account non-linearity), it produces easily readable results and it can avoid the multicolinearity problem between the variables in Career Matrix.

However, regression trees, although being a very compelling method, suffer from a major drawback: instability [START_REF] Breiman | Bagging predictors[END_REF]. If there is a small modification of the dataset, results will be altered substantially, constituting a key issue in terms of results'robustness. To overcome this major drawback, we rely here on another approach. Specifically, in order to stabilize trees and improve the accuracy of estimation, various methods have been developed, such as bagging12 [START_REF] Breiman | Bagging predictors[END_REF] and Random Forest [START_REF] Breiman | Random forests[END_REF]. We use the latter approach because this is a simple method that has interesting theoretical properties.

RF has three main components: tree 1 , randomization 2 and bagging 3 . The first step is to consider a bootstrap sample b of the training data (one third of the sample is left out) and construct a tree 1 . The difference with CART is that at each node p, we select randomly several variables for each node 2 and we split the node in two child nodes, by considering the variable k and the split point s, that produce the best binary partition in terms of minimization of the residual sum of squares. Formally, the aim is to minimize the sum of squared errors from the two regions (R1 and R2):

min k,s   min c1 x i ∈R 1 (p,k,s) (y i -c 1 ) 2 + min c2 x i ∈R 2 (p,k,s) (y i -c 2 ) 2   (1)
The best response in each m region (ĉ m ) is equal to the average value of the dependent variable. Since it is a regression tree, it is recommended that the number of k randomly selected variables is equal to the following floor function K 3 [START_REF] Hastie | The Elements of Statistical Learning: Prediction, Inference and Data Mining[END_REF] where K denotes the number of explanatory variables. The third step is to repeat this procedure on B bootstrap samples 3 and average the results of prediction to obtain the final estimation. It is important to stress that unlike CART, there is not pruning of the estimated tree.13 At each step, the tree is constructed until it reaches its maximum size defined in advance. This procedure is summarized in figure 1.

RF has several advantages, in addition to those generally associated with CART. First, using this method, we lose the possibility to summarize the estimation in a simple tree because with each bootstrap sample we estimate a new tree, but we eliminate the main problem of the instability of the results. Second, RF benefits from the randomization process because it allows to construct de-correlated trees which in turn lead to reduce the variance of the estimated model. Third, RF is a powerful method which performs well when the sample has limited size and even if the number of observations is lesser than the number of predictor variables 14 . Lastly, RF permits also to compute a value which provides information on the importance of the variables in the estimation by using the Mean Decrease in Accuracy(MDA) criteria. For that purpose, we consider the Out-Of-Bag (OBB) sample, ie data that are not used for constructing the b tree, and proceed as follows:

• Compute the error of a b tree on its OBB sample.

• Permute randomly the value of the variable k from the training sample and compute new OBB error.

• Average all the OBB errors to obtain the MDA (the value is normalized by standard deviation).

The underlying idea of this algorithm is to detect if the permutation involves a decrease in the accuracy of the model. If a variable is not important the decrease will be weak while it will be significant if a variable is important.

Results

General results: classification of occupations

Before commenting and studying the probabilities of computerisation and their economic implications, it is necessary to evaluate the accuracy of our model. A simple approach is to check how many predictions of the adjusted model are correct by looking at the confusion matrix (not reported here). If we consider a standard threshold of 0.5 for assigning a class to each occupation, the estimated model achieves accurate prediction in approximately

14 See examples in [START_REF] Verikas | Mining data with random forests: A survey and results of new tests[END_REF].

88% of cases.

A more efficient measure of accuracy in classification problems is the Area Under Curve (AUC) that corresponds to the evaluation of the area situated under the Receiving Operating Curve (ROC). This tool enables to situate the quality of a classifier over two references, a perfect and a random classifier which have respectively an AUC value of 1 and 0.5. The model considered in our analysis has a value of AUC equal to 0.955, suggesting that it has a very good level of performance that allows us to have a relative confidence in the probabilities computed. 15Application of the RF algorithm permits to obtain a probability of automation for all occupations considered (see tables 7 to 21 in appendix). Given that there are 499 occupations, we cannot comment precisely all the results, but we could give an overview of the findings by selecting the top ten, bottom ten and some intermediate occupations (table 1). As shown, in the top 10 occupations, there are only occupations that require high level of creativity, manual dexterity or social intelligence. This is reflected in the variable importance measure that highlights the significant weight of the variables originality and manual dexterity , instructing and negotiation in the estimation (table 6 in appendix). Logically, occupations in the bottom ten are poorly endowed in non computerisable skills. A part of results is plausible with, for example, the probable disappearance of mail deliverer or cashier occupations. On the contrary, some occupations such as model or truck driver is difficult to appear as risky because no replacement process has now began.

Detailed results

Beyond the results by occupation, it is very interesting to draw lessons at different economic levels. Our aim is to study the number, the distribution and the properties of the jobs which could be destroyed by computer devices in the next years. The drawback is that Career matrix contains data on skills by occupation but no information on the number and the characteristics of workers who perform each occupation. To alleviate this problem, we rely on the data of the last population census ( 2010) that provides detailed information on the number, the type of employment and the gender of people which perform each job. Our strategy is to construct a new data set combining interesting information from these two sources. Since Population Census considers only 232 occupations, we include all Career Matrix occupations in population cen- sus categories and average the values of all variables. In some cases, this approach is quite simple because occupations are similar (pharmacist, architectural engineers, childcare workers...) which led no loss of information. However, in other cases, we must insert several occupations from Career Matrix in Population census categories. For example, in the category Motor vehicle drivers , we include taxi drivers, truck drivers, tourist bus drivers and bus drivers. For few cases, we have not any Career matrix occupation to introduce. Our solution is to compute the mean of all variables from the occupations included in the same occupation group. For example, for house cleaning workers , we average the values of the variables of building cleaning workers, waste treatment workers and other cleaning workers. Lastly, when there is no possible correspondence, we drop the corresponding occupation. We also put aside the category Workers not classifiable by occupation because it contains too heterogeneous components. 16 Finally, our new dataset contains 88% of employed population. By predicting probabilities of automation with this new sample, we get (i) the total number of jobs which are threatened by actual technological advance, and (ii) a detailed view by type of employment and by gender. [START_REF] Frey | The future of employment: How susceptible are jobs to computerization?[END_REF] present their results by decomposing the total of jobs in three categories: high, middle and low risk of automation. These groups are delimited by two thresholds equal to 0.7 and 0.3 and serve as the basis for the determination of the number of jobs currently threatened by computer technology (they evaluate that 47% of US employment is at risk). If we consider the same thresholds, our results suggest that approximatively 55% of employment in Japan has a highly susceptibility to be replaced by technological equipment, namely 8 points higher than in the US (see table 2). Our predictions also state that roughly 25% of jobs are in the intermediate category and 19% can be considered as non-automatable in the next years. These estimates are consistent with the US results but the share of at risk jobs is higher. The difference of the estimated share of automatable occupations can be explained by several factors. Firstly, it is a possible that this result comes from methodological issues. Indeed, the aggregation procedure for combining Career Matrix and data from population census could lead to loss of information causing an underestimation of the number of jobs susceptible to be computerised. For example, some Population census categories contain a large number of workers such as Other general clerical workers or Comprehensive clerical workers . If we had data at a more detailed level, it would have been possible that a share of occupations in- cluded in this group could be considered as non-computerisable which may lower the share of employment threatened. A second type of explanation is linked to the specificities of the Japanese labor market, such as the presence of differences in skills for some occupations and differences in occupational structures. Lastly, we can notice, dealing also with US data, the estimations by [START_REF] Pajarinen | Computerization threatens one third of finnish employment[END_REF] give a value of 49.2% thus reducing the difference observed between the two coutries.

Beyond the determination of the share of jobs threatened by computer technology, we can also draw lessons at a more detailed level (table 2, figure 2). As shown, the vulnerability face to technological pressure is roughly similar between men and women since their respective curves are both quite close to the total curve. However, we identify a significant difference according to the type of employment. Indeed, we find evidence that the type of employment determines the exposure to ICT capital. The non-regular jobs (temporary and part-time employment) appear to be more vulnerable to computer technology at any level of probability (figure 2). This situation concerns part-time workers and is even more pronounced for temporary workers.

Comments

Althought this study has some methodological limitations mainly related to the lack of some variables and to the aggregation procedure17 , we can draw several interesting conclusions. Our findings suggest that the diffusion of computer technology will have an important effect on employment in the next years and decades. This is caused by the fact that a growing number of economic tasks could be technically and economically performed by computer devices (they become feasible at admissible costs). From this point of view, it is expected that some occupations and jobs in Japan (and in other industrialized countries) will disappear in short or medium term. Although, the assessment of the exact share of jobs concerned is difficult to evaluate, our analysis shows that this share is around one half of the total employment.

These estimates are based on a technological background, and the effective realization of these predictions will finally depend on many factors technological, economic and cultural factors. A first determinant is the technological advance in terms of capacities, quality and cost offered by the future technology which will create the opportunities of investment for producers. This is indeed on this technological basis and its cost that their choices will be made. Furthermore, an important element will be the institutional and social response face to this technological wave. In this respect, the attitude of public authorities will play a key-role by promoting or not the technological diffusion. The observation of the part and recent situation suggest that they will act in favor of development and adoption of ICT. Indeed, historically, the Japanese government has supported the development of computer and robotic technologies since its beginning through the Ministry of Internal Affairs and Communication (MIC), the Ministry of Economy, Trade, and Industry (METI) or The New Energy and Industrial Technology Organization (NEDO) and continues to promote actively innovation in these fields [START_REF] Kitano | Roboethics -a comparative analysis of social acceptance of robots between the west and japan[END_REF][START_REF] Lechevalier | The effect of participation in government consortia on the r&d productivity of firms: a case study of robot technology in japan[END_REF][START_REF] Murata | Lessons from the history of information system development and use in japan[END_REF]. One example of this continuity is the call, in May 2015, for a robot revolution by the Prime Minister Abe. These efforts are also made by firms and universities and likely to be continued due to ageing and because ICT constitute a challenge for competitiveness in a context of regional competition with China and the Republic of Korea.

On the other hand, the availability of a technology is obviously not a sufficient condition for its adoption. It is important to emphasize that a crucial determinant of the future automation is the social acceptation of technology by producers and consumers. For instance, it must be noted that a large share of jobs which could be probably automated in the future will be through robots with an important share of humanoid robots. We further observe that there are already experimentations with the introduction of these machines in shops such as Pepper robot in Omotesando Softbank shop or the Toshiba robot (Chihira Aico) in Mitsukoshi department store. A key determinant of this kind of computerisation will be the public reception. Some scholars suggest that Japanese people are more willing to accept these new technologies than western people that might encourage automation. For example, [START_REF] Kaplan | Who is afraid of the humanoid? investigating cultural differences in the acceptance of robots[END_REF] 18 suggests that this better acceptance is due to the fact that from a western point of view, there is a clear distinction between the natural and the artificial which generates a feeling of strangeness or aversion about this kind of robot. Conversly, in the Japanese culture, there is not such distinction but rather a representation which emphasises a network of beings. This type of analysis suggests that Japanese producers and consumers may display a more positive attitude about robots, and more broadly, toward information technologies that may foster job destructions.

Another very important clarification to do about these results is that these possible destructions of jobs are not equal to future unemployment. Indeed, as pointed in section 2, the development of new technologies also supports the creation of jobs by several compensation mechanisms. Existence or importance of technological unemployment will depend on the extent of these unpredictable dynamics. One possibility is that this technological diffusion produces no unemployment, but a deep restructuring of the production apparatus. Another positive point is specific to the Japanese situation and is linked to the decline in the population and its consequence in terms of reduction of labor participation. This dynamics might offset the potential negative impact of computer technology because it is possible that computer capital will replace the individuals who enter retirement instead of the available workers. The convergence of these two phenomena might create a historical opportunity susceptible to avoid the risk of technological unemployment. On the contrary, a more pessimistic view could be supported by the fact that ICT tools seem able to perform a very large kind of tasks. The range of application seems to be unprecedented and it appears that technological limits are continually broken the barriers to capital labor/substitution. This advance could cause serious problems by putting forward a clear risk of technological unemployment in the short run during a transition period, but also in the long run if the compensation mechanisms are insufficient.

Conclusion

The aim of this paper is to assess the number of jobs which could be replaced by computer technology in Japan in the near future. Relying on a recent methodology, our findings suggest that 55% of actual jobs in Japan could be destroyed by computer technology diffusion and that non regular workers are more subject to this risk. The decline in the working population, the support in ICT development by public authorities, firms and universities, and the possible positive attitude about technology by Japanese people, suggest that this capital/labor substitution process could play a key role in Japan.

Figure 1 :

 1 Figure 1: RF Algorithm a-Consider a b bootstrap sample from the original data. b-At each node, select randomly several splitting variables c-Split current node into two child nodes

Figure 2 :

 2 Figure 2: Detailed results

Table 1 :

 1 Overview of results

	Top 10 occupations	Probability
	Speech therapist	0.014
	Lawyer	0.019
	Stylist	0.021
	Classical Musician	0.025
	Theatre Decorator	0.025
	Stage director	0.031
	High school teacher	0.033
	Vocational school teacher	0.033
	Make-up artist	0.035
	Radio director	0.038
	Some intermediate occupations	Probability
	Dentist	0.118
	Tourist guide	0.200
	Programmer	0.365
	Radiology technologist	0.424
	Nutritionist	0.510
	Cargo handler	0.628
	Car Assembler	0.694
	Postal clerk	0.783
	Train driver	0.874
	Taxi Driver	0.954
	Bottom 10 occupations	Probability
	Packing worker	0.972
	Truck driver	0.972
	Hotel worker	0.974
	Tourist Bus Driver	0.974
	Road patrol worker	0.974
	Computer-Assisted-Design operator	0.982
	Data entry keyer	0.982
	Industrial waste collection and transportation worker	0.982
	Mail Deliverer	0.982
	Computerized typesetting operator	0.982

Table 2 :

 2 Share of employment by level of risk(%)

	Level of risk Total	Men	Women	Regular Temporary Part-time jobs jobs jobs
	High risk	55.611 55.827 55.018	56.147	73.120	55.587
	Middle risk 25.413 24.643 26.424	21.572	20.876	34.439
	Low risk	18.977 19.530 18.559	22.281	06.004	09.973

Table 5 :

 5 Variables description

Table 6 :

 6 Variable importance

	Rank Variables	Type of tasks	% increase in MSE
	1	Originality	Creative intelligence	8.06676
	2	Manual dexterity	Perception and manipulation	7.01464
	3	Instructing	Social intelligence	5.41735
	4	Negotiation	Social intelligence	4.56105
	5	Persuasion	Social intelligence	3.09784
	6	Judgment and decision making Appreciation	2.18357
	7	Fine Arts	Creative intelligence	1.04819
	8	Social perceptiveness	Social intelligence	0.96448
	9	Coordination	Social intelligence	0.42546
	10	Service orientation	Social intelligence	-2.58361

Table 7 :

 7 Probability of Automation by Occupation

	Index Occupation	Probability
	1	Speech therapist	0.014
	2	Lawyer	0.019
	3	Stylist	0.021
	4	Classical Musician	0.025
	5	Theatre Decorator	0.025
	6	Stage director	0.031
	7	High school teacher	0.033
	8	Vocational school teacher	0.033
	9	Make-up artist	0.035
	10	Radio director	0.038
	11	Hairdresser	0.043
	12	Nail Artist	0.058
	13	Teacher to deaf and blind people	0.062
	14	Artistic Director	0.068
	15	Midwife	0.071
	16	Illustrator	0.073
	17	Fashion Designer	0.073
	18	Sports Instructor	0.077
	19	Ballet Dancer	0.081
	20	Junior high school teacher	0.083
	21	Floral designer	0.084
	22	Chef and Head Cook	0.084
	23	Primary school teacher	0.084
	24	Sushi chef	0.088
	25	Japanese Teacher	0.104
	26	Pre-school Teacher	0.104
	27	Interior Designer	0.107
	28	Film director	0.107
	29	Clinical engineer	0.108
	30	Ship engineer	0.114
	31	Forging engineer	0.114
	32	Fair Trade Commission employee	0.114
	33	Professional footballer	0.118
	34	Surgeon	0.118
	35	Nurse	0.118

Table 10 :

 10 Probability of Automation by Occupation

	Index Occupation

Table 12 :

 12 Probability of Automation by Occupation

	Index Occupation

Table 14 :

 14 Probability of Automation by Occupation

	Index Occupation	Probability
	246	Editor	0.461
	247	Photojournalist	0.461
	248	Mason (interior)	0.463
	249	Cooks (Chinese food)	0.463
	250	opérateur Computer-Assisted-Design	0.472
	251	Botanist	0.472
	252	Fine art restoration worker	0.482
	253	Tofu producer	0.487
	254	Professional golfer	0.489
	255	Production and quality control engineer	0.489
	256	Dental hygienist	0.493
	257	Chinese Masseur	0.503
	258	Chiropractor	0.503
	259	Computer equipment saleman	0.510
	260	Service station worker	0.510
	261	Game center employee	0.510
	262	Park ranger	0.510
	263	Nutritionist	0.510
	264	Breeding staff member (zoo)	0.510
	265	Parking Lot Attendant	0.510
	266	Electrical appliance salesperson	0.510
	267	Veterinary technician	0.510
	268	Amusement park worker	0.510
	269	Swordsmith	0.537
	270	Numerical controled milling machine operator	0.537
	271	Fruit grower	0.537
	272	Furniture worker	0.537
	273	Sign language interpreter	0.547
	274	Dispatcher	0.554
	275	Housing and property sales assistant	0.554
	276	Credit union liaison officer	0.554
	277	Damage service clerk	0.554
	278	Actuary	0.557
	279	Estate Agent Valuer	0.557
	280	Advertising photographer	0.558

Table 15 :

 15 Probability of Automation by Occupation

	Index Occupation

Table 18 :

 18 Probability of Automation by Occupation

	Index Occupation

Moreover, Japan not only employs robots but is a major producer with 127491 robots produced in 2014 of which 98882 were exported (Japan Robotics Association, 2015).

For this reason, we consider the following expressions as synonym: computer technology , computer and communication technologies , Information Technology (IT), Information and Communication Technologies (ICT).

[START_REF] Vivarelli | Innovation, employment and skills in advanced and developing countries: A survey of the literature[END_REF] identify six types of compensation mechanisms.

Each input is an aggregate. Routine tasks are composed of routine cognitive tasks and routine manual tasks. Non-routine tasks can be non-routine analytic tasks, non-routine interactive tasks or non-routine manual tasks.

[START_REF] Frey | The future of employment: How susceptible are jobs to computerization?[END_REF] define Computerisation as follow: We refer to computerisation as job automation by means of computer-controlled equipment . To avoid unpleasant repetitions, we also use the usual term of automation .

For estimation, we use R Package randomForest version 4.6-10 ([START_REF] Liaw | Classification and regression by randomforest[END_REF]. We consider a forest containing

trees. We doesn't need more iterations because the study of the execution of the algorithm shows that the Mean Square Error (MSE) stabilizes around 40 trees.10 Given the particular structure of data (y = 1 or y = 0), we could use classification tree but we would a more nuanced view. By using regression tree instead, we could get all values between 0 and 1.11 CART part of the "Top 10 Algorithm in data mining"[START_REF] Wu | Top 10 algorithms in data mining[END_REF].

Bagging refers to Bootstrap AGGregatING .

In CART, Weakest Link Pruning is used.

Note that[START_REF] Frey | The future of employment: How susceptible are jobs to computerization?[END_REF] model has AUC equal to 0.894.

It represents approximatively 6% of the employed population.

We have also used the median instead of the mean in the aggregation procedure. We obtain similar results

See also[START_REF] Kitano | Roboethics -a comparative analysis of social acceptance of robots between the west and japan[END_REF].