Bastien Drut
email: bastien.drut@gmail.com

Social responsibility and mean-variance portfolio selection

Keywords: Socially Responsible Investment, Portfolio Selection, Mean-variance Optimization, Linear Constraint, Socially Responsible Ratings. JEL: G11, G14, G20

In theory, investors choosing to invest only in socially responsible entities restrict their investment universe and should thus be penalized in a mean-variance framework. When computed, this penalty is usually viewed as valid for all socially responsible investors. This paper shows however that the additional cost for responsible investing depends essentially on the investors' risk aversion. Social ratings are introduced in mean-variance optimization through linear constraints to explore the implications of considering a social responsibility (SR) threshold in the traditional Markowitz (1952) portfolio selection setting. We consider optimal portfolios both with and without a risk-free asset. The SR-efficient frontier may take four different forms depending on the level of the SR threshold: a) identical to the non-SR frontier (i.e. no cost), b) only the left portion is penalized (i.e. a cost for high-risk-aversion investors only), c) only the right portion is penalized (i.e. a cost for low-risk aversion investors only) and d) the whole frontier is penalized (i.e. a positive cost for all the investors). By precisely delineating under which circumstances SRI is costly, those results help elucidate the apparent contradiction found in the literature about whether or not SRI harms diversification.

1) Introduction

In [START_REF] Markowitz | Portfolio selection[END_REF] setting, portfolio selection is driven solely by financial parameters and the investor's risk aversion. This framework may however be viewed as too restrictive since, in the scope of Socially Responsible Investment (SRI) 1 , investors also consider nonfinancial criteria. This paper explores the impact of such SRI concerns on mean-variance portfolio selection. SRI has recently gained momentum. In 2007, its market share reached 11% of assets under management in the United States and 17.6% in Europe. 2 Moreover, by May 2009, 538 asset owners and investment managers, representing $18 trillion of assets under management, had signed the Principles for Responsible Investment (PRI) 3 . Within the SRI industry, initiatives are burgeoning and patterns are evolving rapidly.

In practice, SRI takes various forms. Negative screening consists in excluding assets on ethical grounds (often related to religious beliefs), while positive screening selects the best-SR rated assets (typically, by combining environmental, social, and governance ratings). [START_REF] Renneboog | Socially responsible investments: institutional aspects, performance, and investor behaviour[END_REF] describe "negative screening" as the first generation of SRI, and "positive screening" as the second generation. The third generation combines both screenings, while the fourth adds shareholder activism.

3 SRI financial performances are a fundamental issue. Does SRI perform as well as conventional investments? In other words, is doing "good" also doing well? A large body of empirical literature is devoted to the comparison between SR and non-SR funds. According to [START_REF] Renneboog | Socially responsible investments: institutional aspects, performance, and investor behaviour[END_REF], there is little evidence that the performances of SR funds differ significantly from their non-SR counterparts. Conversely, [START_REF] Geczy | Investing in socially responsible mutual funds[END_REF] find that restricting the investment universe to SRI funds can seriously harm diversification. Taken at face value, those statements seem hard to reconcile. Within [START_REF] Markowitz | Portfolio selection[END_REF] mean-variance theoretical framework, negative screening implies that the SR efficient frontier and the capital market line will be dominated by their non-SR counterparts because asset exclusion restricts the investment universe. [START_REF] Farmen | A cautionary note on the pricing of ethics[END_REF] notice that, in this case, risk aversion matters in the cost of investing responsibly. Positive screening corresponds to preferential investment in well-rated SRI assets without prior exclusion, with each investor being allowed to choose her own SR commitment [START_REF] Landier | Investing For Change[END_REF]. This translates into a trade-off between financial efficiency and portfolio ethicalness [START_REF] Beal | Why do we invest ethically[END_REF]. Likewise, [START_REF] Dorfleitner | Theory of social returns in portfolio choice with application to microfinance[END_REF] propose a theory of mean-variance optimization including stochastic social returns within the investor's utility function. However, to our knowledge, easily implementable mean-variance portfolio selection for second-generation SRI is still missing from the literature. Moreover, the impact of risk aversion on the cost of SRI has not been investigated so far. Our paper aims at filling those two gaps. By delineating the conditions under which SRI is costly, it will furthermore help elucidate the apparent contradiction found in the literature regarding SRI's influence on diversification.

This paper measures the trade-off between financial efficiency and SRI in the traditional mean-variance optimization. We compare the optimal portfolios of an SR-insensitive investor and her SR-sensitive counterpart in order to assess the cost associated with SRI. Our contribution is twofold. First, we extend the [START_REF] Markowitz | Portfolio selection[END_REF] model4 by imposing an SR threshold. This leads to four possible cases: depending on the link between the social ratings and the expected returns and on the strength of the SR threshold, we show that either the risk averse investors either the investors with low risk aversion are penalized.. Despite its crucial importance, practitioners tend to leave the investor's risk aversion out of the SRI story. Our paper on the other hand offers a fully operational mean-variance framework for SR portfolio management, a framework that can be used for all asset classes (stocks, bonds, commodities, mutual funds, etc.). It makes explicit the consequences of any given SR threshold on the determination of the optimal portfolio. To illustrate this, we complement our theoretical approach by an empirical application to emerging bond portfolios.

The rest of the paper is organized as follows. Section 2 proposes the theoretical framework for the SR mean-variance optimization in the presence of risky assets only.

Section 3 adds a risk-free asset. Section 4 applies the SRI methodology to emerging sovereign bond portfolios. Section 5 concludes.

2) SRI portfolio selection (risky assets)

In this section, we explore the impact of considering responsible ratings in the meanvariance portfolio selection. To do so, we first assess the social responsibility of the optimal portfolios resulting from the traditional optimization of [START_REF] Markowitz | Portfolio selection[END_REF]. Then we consider the case of an SR-sensitive investor who wants her portfolio to respect high SR standards, and we explore the consequences of such a constraint for optimal portfolios. Consider a financial market composed of n risky securities5 ) , .

    
, where pi  is the weight of the th i asset in portfolio p ,  '

1 ... 1   and 1 '    p .
In the traditional mean-variance portfolio selection [START_REF] Markowitz | Portfolio selection[END_REF], the investor maximizes her portfolio's expected return

   ' p p 
for a given volatility or variance

p p p      ' 2 , Let 0  
be the parameter accounting for the investor's level of risk aversion. The problem of the SR-insensitive investor is then written6 :

Problem 1   1 ' ' 2 ' max            to subject (1)
The solutions to Problem 1 form a hyperbola in the mean-standard deviation plane ) , ( p p   and will be referred to here as the SR-insensitive efficient frontier.

Let us now add an SR rating independent from expected returns and volatilities. Typically, this is an extra-financial rating relating to environmental, social, or governance issues. It can 6 also combine several ratings [START_REF] Landier | Investing For Change[END_REF]. Let i  be the SR rating associated with the i-th security and  '

... 2 1 n     
. We assume that the rating is additive.

Consequently, the rating p  of portfolio p is given by:

    n i i pi p p 1 '      (2)
This linearity hypothesis (see [START_REF] Barracchini | An ethical investments evaluation for portfolio selection[END_REF][START_REF] Drut | Nice but cautious guys: the cost of responsible investing in the bond markets[END_REF][START_REF] Scholtens | Measuring sustainability performance of investments; the case of Dutch bond funds[END_REF] is often used by practitioners to SR-rate financial indices 7 . The representation in eq. ( 2) holds for positive as well as negative screening 8 .

Even when investors are SR-insensitive (thus facing problem 1), their optimal portfolios can be SR-rated. Proposition 1 expresses those ratings p  associated with SR-insensitive efficient portfolios.

Proposition 1 (i)

Along the SR-insensitive frontier, the SR rating p  is a linear function of the expected return p  :

p p     1 0   (3) with 2 1 1 1 1 1 1 1 0 ) ' ( ) ' )( ' ( ) ' )( ' ( ) ' )( ' (                                 and 2 1 1 1 1 1 1 1 1 ) ' ( ) ' )( ' ( ) ' )( ' ( ) ' )( ' (                                 . (ii) If 0 1   , p  ranges from     1 1 ' '    
(for the minimum-variance portfolio) to   (when the expected return tends to the infinite).

7 See for instance the Carbon Efficient Index of Standard & Poor's with the carbon footprint data from Trucost PLC. 8 For negative screening, i  is binary and p  denotes the proportion of portfolio p invested in the admissible assets.

(iii

) If 0 1   , p  ranges from     1 1 ' '    
(for the minimum-variance portfolio) to   (when the expected return tends to the infinite).

Proof: see Appendix 1

Thus, Proposition 1 gives the SR rating p  of any portfolio lying on the SR-insensitive frontier. From the optimality conditions comes the fact that, along the efficient frontier, both the SR rating p  and the expected return p  are linear functions of the quantity  1 , so it is straightforward that the SR rating p  can be written as a linear function of the expected return p  , as in eq. ( 1). The direction of this link is determined by the sign of the parameter 1  . The parameter 1  can take both signs because, for instance, the assets with the highest returns can be the best or the worst SR-rated. Furthermore, the sign of the parameter 1  is crucial because it represents where the trade-off appears between risk aversion and SR rating. If

0 1   , resp. 0 1  
, the riskier the optimal portfolio, the better, resp. the worse, its SR rating. In other words, if

0 1   , resp. 0 1  
, the best SR-rated portfolios are at the top, resp. at the bottom, of the SR-insensitive frontier.

Consider now the case of an SR-sensitive investor. For instance, she requires a portfolio that is well-rated for environment. Henceforth, the SR rating p  is introduced in the mean-variance optimization by means of an additional linear constraint imposing a given threshold 0  on p  . For positive screening, the threshold value is left to the investor's discretion (Beal et al., 2005, Landier and[START_REF] Landier | Investing For Change[END_REF]. The SR-sensitive optimization is summarized by Problem 2.

Problem 2

  0 ' 1 ' ' 2 ' max                  p to subject (4)
We derive the analytical solutions to this problem by following [START_REF] Best | The efficient set mathematics when mean-variance problems are subject to general linear constraints[END_REF] methodology. Proposition 2 summarizes the results.

Proposition 2

The shape of the SR-sensitive efficient frontier depends on the sign of 1  and on the threshold value 0  in the following way:

0 1   0 1   0 1 1 ' '           For 0   , the SR-sensitive
frontier is another hyperbola lying below the SR-insensitive frontier. For 0   , the SR-sensitive frontier is identical to the SRinsensitive frontier.

(see Figure 3)

The SR-sensitive frontier is identical to the SR-insensitive frontier (see Figure 1)

0 1 1 ' '          
The SR frontier differs totally from the SR-insensitive frontier.

(see Figure 4) For 0   , the SR-sensitive frontier is identical to the SRinsensitive frontier.

For 0   , the SR-sensitive frontier is another hyperbola lying below the SR-insensitive frontier (see Figure 2)

With              1 0 1 1 1 1 0 ) ' ' ( ) ' )( ' ( ) ' )( ' (              .
The associated expected return 0 E and the expected variance 0 V are:

) ) ' ( ) ' )( ' (( 1 ' ( ' 1 2 1 1 1 0 1 1 0                         E ) ) ' ( ) ' )( ' (( 1 1 ( ' 1 2 1 1 1 2 0 1 2 0 0                       V Proof: see Appendix 2.
Proposition 2 makes explicit the situations in which there is an SRI cost. The impact of the constraint on the SR ratings depends on the parameter 1  and on the strength of the constraint. As showed in Proposition 1, if

0 1   , resp. 0 1  
, the best SR-rated portfolios are at the top, resp. at the bottom, of the SR-insensitive frontier: by consequence, the SR constraint impacts first the efficient frontier at the bottom, resp. at the top. In addition, the more the investor wants a well-rated portfolio, that is to say the higher the threshold 0  , the bigger the portion of the efficient frontier being displaced. In the case where the threshold 0  is below the minimum rating of the SR-insensitive frontier, the efficient frontier is even not modified at all. We illustrate the four possible cases through Figures 1 to 4.

In the case where 1), the SR-sensitive and the SR-insensitive frontiers are the same and there is no SRI cost at all. This is the most favourable case. In the case where 0 3), the SR-sensitive and the SR-insensitive frontiers are the same below the corner portfolio ) , ( 0 0 V E . For portfolios with higher expected returns and variances, the SRI constraint induces less efficient portfolios.

0 1   and 0 1 1 ' '           (see Figure
1   and 0 1 1 ' '           (see Figure
There is only an SRI cost for investors whose risk aversion parameter is below the threshold 0

 . In the case where 0 1   and 4), the SR-sensitive and the SRinsensitive frontiers are totally different. The SRI constraint induces less efficient portfolios for every investor. There is an SRI cost for everybody. This is the worst case.

0 1 1 ' '           (see Figure

3) Portfolio selection with a risk-free asset

In this section, we assume the existence of a risk-free asset and we explore, in this case, the impact of considering responsible ratings in the mean-variance portfolio selection. Indeed, the social responsibility of this risk-free asset should also be taken into account. So, we assess first the social responsibility of the optimal portfolios obtained by an SR-insensitive investor.

And then we study whether an SR-sensitive investor is penalized by requiring portfolios with high SR standards.

Denote by r the return of the risk-free asset and by r  the fraction of wealth invested in this risk-free asset. The standard mean-variance portfolio selection in the presence of a riskfree asset has been extensively studied by [START_REF] Lintner | The valuation of risky assets and the selection of risky investment in stock portfolios and capital budgets[END_REF] and Sharpe (1965). It corresponds to Problem 3.

Problem 3

The investor wants to solve the following program:

  1 ' ' 2 ' max      r r to subject r           (5)
In the mean-standard deviation plan, the set of optimal portfolios is referred as the well-known Capital Market Line (CML). As the investor does not consider responsible ratings in her optimization, we refer it here as "SR-insensitive capital market line".

As in Section 2, we add responsible ratings to the story. Henceforth, we denote *  as the responsible rating of the risk-free asset and the portfolio rating is defined as * '

     r p  
. In the following, we seek to determine the portfolio ratings p  of the optimal portfolios on the "SR-insensitive capital market line".

Proposition 3 (i)

Along the SR-insensitive capital market line, the responsible rating p  is a linear function of the expected return p  :

p p     * 1 * 0   (6) with ) ( )' ( ) ( )' * ( * 1 1 * 0            r r r r           and ) ( )' ( ) ( )' * ( 1 1 * 1           r r r          (ii) If 0 * 1   , p
 ranges from *  (for the minimum-variance portfolio) to   (when the expected return tends to the infinite.) 6). It is striking that this relationship expressed by eq. ( 6) has the same form as eq. ( 3) in the case without a risk-free asset. Note that the portfolio of an infinitely risk averse investor would be fully invested in the risk-free asset and would have its Similarly to Section 2, we now consider the case of SR investors wishing high SR standards and so, requiring the portfolio rating * '

(iii) If 0 * 1   ,
     r p  
to be above a threshold 0  .

This corresponds to Problem 4.

Problem 4

The investor wants to solve the following program:

  0 * ' 1 ' ' 2 ' max                         r p r r to subject r (7)
In Problem 4, the constraints in the mean-variance optimization are also linear. Thus, we employ [START_REF] Best | The efficient set mathematics when mean-variance problems are subject to general linear constraints[END_REF] methodology, as we did for Problem 2. Proposition 4 summarizes the results.

Proposition 4

The shape of the SR-sensitive capital market line depends on the sign of * 1  and on the threshold value 0  in the following way:

0 * 1   0 * 1   0 *    For * 0    , the SR-sensitive
capital market line is a hyperbola lying below the SR-insensitive capital market line.

For * 0    , the SR-sensitive capital market line is identical to the SR-insensitive capital market line. (see Figure 7)

The SR-sensitive capital market line is the same as the SRinsensitive capital market line (see Figure 5)

0 *   
The SR-sensitive capital market line differs totally from the SRinsensitive capital market line and becomes a hyperbola.

(see Figure 8) For * 0    , the SR-sensitive capital market line is identical to the SR-insensitive capital market line.

For * 0    , the SR-sensitive capital market line is a hyperbola lying below the SR-insensitive capital market line.

(see Figure 6)

With *) ( ) * ( )' ( 0 1 * 0               r
The associated expected return * 0 E and the expected variance * 0 V are:

) ( )' ( 1 1 * 0 * 0      r r r E       ) ( )' ( 1 1 2 * 0 * 2 0 * 0       r r V       Proof: see Appendix 4
Proposition 4 makes explicit the situations in which there is an SRI cost in the presence of a risk-free asset. As in Proposition 2, the impact of the constraint on the SR ratings depends on the parameter * 1  and on the strength of the constraint. As showed in Proposition 3,

if 0 * 1   , resp. 0 * 1  
, the best SR-rated portfolios are at the top, resp. at the bottom, of the SR-insensitive capital market line: by consequence, the SR constraint impacts first the capital market line at the bottom, resp. at the top. However, contrary to the case without a risk-free asset, the modified part of the capital market line has a different mathematical form: for this segment, the capital market line becomes a hyperbola in the mean-standard deviation plan.

Figures 5 to 8 illustrate the four cases.

In the case where 0 * 1   and 0 *    (see Figure 5), the SR-sensitive and the SR- insensitive capital market lines are the same and there is no SRI cost at all. This is the best case. There is an SRI cost only for investors with a risk aversion parameter below the threshold * 0  .  and 0 *    (see Figure 8), the SR-sensitive and the SR- insensitive capital market lines differ entirely. The SR-sensitive capital market line is no longer a line but a hyperbola. This is the most disadvantageous case: there is an SRI for all the investors.

4) Application to an emerging bond portfolio

This section illustrates the results of Sections 2 and 3 by considering the case of a responsible US investor on the emerging bond market.

We consider the EMBI+ indices from JP Morgan as proxy for emerging bond returns. 3. Here, the portfolio EPI is defined in the same way as in eq. ( 2). We start by estimating the portfolio EPI along the SR-insensitive frontier, which corresponds to estimating the relationship (3) of Proposition 1. We obtain the following estimates for the parameters 0 As an illustration of Problem 2, we seek to determine the impact of SR attempts on the efficient frontier and we impose a set of constraints 0    p on the portfolio EPI. Figure 9 exhibits the SR-sensitive frontiers for several thresholds 0  . The corner portfolios for which there is a disconnect between the SR-sensitive and SR-insensitive frontiers are in Table 4.

          
, the SR-sensitive frontier is the same as the SR-insensitive frontier. For 26

. 78 ' ' 1 1 0           
, the SR-sensitive frontier differs from the SR-insensitive frontier at the bottom and is the same at the top. For instance, with a threshold equal to 84 on the portfolio EPI, the SR-sensitive and the SR-insensitive frontiers are the same for expected returns above 26.84%/year and differ for expected returns below 26.84%/year. In the case of emerging bonds, improving the portfolio EPI costs more for investors with high risk aversion.

In order to illustrate Problems 3 and 4, we rely on the US 1-month interbank rate as a riskfree asset.12 Its responsible rating corresponds to the EPI of the United States

   

, the SR-sensitive capital market line differs from the SR-insensitive one at the bottom and is the same at the top. Here also, the SRI cost appears for investors with high risk aversion. We notice that the corner portfolios have particularly high expected returns and volatilities (see Table 5): this can be explained by the particularly low sensitivity * 1  . For example, if we consider a threshold 82 0   , the corner portfolio has an expected return of 50.01%/year and an expected volatility of 63.06%/year, meaning that for expected returns below 50.01%/year, the SR-sensitive and SR-insensitive capital market lines are disconnected. However, we observe in Figure 11 that the SRinsensitive and SR-sensitive capital market lines are very close for expected returns slightly above 20%/year. This numerical application highlights that the cost implied by high environmental requirements an emerging bond portfolio differs according to the investor's risk aversion.

In this particular case, it costs more to be green for risk averse investors. Let us now focus on a typical investor. Sharpe (2007) suggests that the "representative investor" has a risk aversion parameter 7 . 0 2   in the traditional mean-variance optimization of eq. ( 1). We seek to determine the consequences of SR thresholds for this "representative investor" by computing the optimal portfolios for different thresholds on the portfolio EPI. Figure 12 displays these portfolios (the means and variances of the optimal portfolios are given in Appendix 6).

Figure 12

Displaced optimal portfolios for the "representative investor" For the "representative investor", the constraint on the portfolio EPI has no cost while the threshold is below 82.37, which is slightly above the average EPI rating of the sample's countries. When the threshold is above 82.37, an SRI cost appears and the optimal portfolio is no longer on the SR-insensitive frontier. This SRI cost rises with the strength of the constraint. In this case, the "representative investor" is directly concerned by the disconnect between SR-sensitive and SR-insensitive frontiers for reasonable SR thresholds.

5) Conclusion

The rapid growth of the SRI fund market have given birth to a burgeoning academic literature. Most academic studies show that there is little difference between financial returns of SRI funds and conventional funds. However, [START_REF] Geczy | Investing in socially responsible mutual funds[END_REF] highlight that limiting the investment universe to SRI funds can seriously harm diversification. To shed light on this debate, our paper aimed at modelling SRI in the traditional mean-variance portfolio selection framework [START_REF] Markowitz | Portfolio selection[END_REF].

In our study, SRI is introduced in the mean-variance optimization as a constraint on the average responsible rating of the underlying entities. Our results are detailed so that they are ready to use by practitioners. Indeed, we show that a threshold on the responsible rating may clearly matters in the potential cost of investing responsibly, this cost being zero in some cases. We strongly believe that this finding could help portfolio managers of SRI funds.

As the calculations in our paper are very general, we believe it could find other applications in the asset management industry, notably for portfolio selection with asset liquidity constraints. However, one limitation of our study is that it assumes expected returns to be independent from responsible ratings: further research could focus on modelling the impact of an SRI constraint in the mean-variance optimization when expected returns and volatilities depend on responsible ratings.

                                                                p p
As a consequence, it possible to write

p p     1 0   with                                                   ) ' )( ' ( ) ' ( ) ' ( ) ' ( 2 ' 1 1 2 1 2 0 1 1 0 1 2                                 Case 0 1  
In this case, the portfolio rating decreases linearly with the expected return in the traditional mean-variance optimization. The maximal portfolio rating is

    1 1 ' '     . If 0 1 1 ' '           , the constraint on the portfolio rating is binding. If 0 1 1 ' '          
, the constraint on the portfolio rating is binding at the top of the efficient frontier and inactive at the bottom. Indeed, the constraint is binding for 0    .

The equation of the portion of the efficient frontier for which the constraint is binding is the same as for the case 0 1   .

Appendix 3

Following [START_REF] Best | The efficient set mathematics when mean-variance problems are subject to general linear constraints[END_REF], in the traditional mean-variance case, the portfolio solutions stand as:

  ) ( 1 1     r       ) ( ' 1 1 1      r r     
In the mean-variance plan, these portfolios are:

  ) ( )' ( 1 1         r r r r r p           ) ( )' ( 1 ' 1 2 2         r r p       
The responsible rating of the efficient portfolios is a linear function of

 1 :   ) ( )' * ( 1 * * ' 1             r r p        
As the expected return P  is also a linear function of  1 , it is possible to express the responsible rating P  of the efficient portfolios as a linear function of the expected return

P  :   ) ( )' * ( ) ( )' ( * * ' 1 1                 r r r r p r p             
As a consequence, it possible to write

p p     * 1 * 0   with ) ( )' ( ) ( )' * ( * 1 1 * 0            r r r r           ) ( )' ( ) ( )' * ( 1 1 * 1           r r r          Appendix 4
The mean-variance optimization with the linear constraint on the portfolio rating has the same portfolio solutions as the standard mean-variance optimization while the constraint is not binding. This is verified if the portfolio rating of the efficient portfolio from the traditional mean-variance optimization is above the threshold 0  . Two cases have to be distinguished:

( )' ( 1 1 2 * 0 * 0      r r V     
To compute the portion of the efficient frontier for which the linear constraint on the portfolio rating is binding, we apply the results of [START_REF] Best | The efficient set mathematics when mean-variance problems are subject to general linear constraints[END_REF]:

) ) * ( )' * ( )) ( )' * (( ) ( )' (( 1 *) ( ) * ( )' * ( ) ( )' * ( 1 2 1 1 0 1 1                                                       
                                             r r r p
Indeed, when the constraint on the portfolio rating is binding, the Capital Market Line is no longer a linear function in the mean-standard deviation plan but a hyperbola.

Figure 1 E

 1 Figure 1 SR-sensitive frontier versus SR-insensitive frontier with 0 1   and

Figure 2

 2 Figure 2 SR-sensitive frontier versus SR-insensitive frontier with 0 1   and

Figure 3

 3 Figure 3 SR-sensitive frontier versus SR-insensitive frontier with 0 1   and

Figure 4

 4 Figure 4 SR-sensitive frontier versus SR-insensitive frontier with 0 1   and

p

  ranges from *  (for the minimum-variance portfolio) to   (when the expected return tends to the infinite). Proof: see Appendix 3 Proposition 3 attributes an SR rating of any portfolio of the SR-insensitive capital market line. From the optimality conditions comes the fact that, along the capital market line, both the SR rating p  and the expected return p  are linear functions of the quantity  1 It is therefore straightforward that the SR rating p  can be written as a linear function of the expected return p  as in eq. (

  SR rating * . Here, the direction of this link is determined by the sign of the parameter * 1  . In the same way as in Section 2, the sign of the parameter * 1  is crucial because it represents where the trade-off appears between risk aversion and SR rating. portfolio, the better, resp. the worse, its SR rating. In other words, SR-rated portfolios are at the top, resp. at the bottom, of the SR-insensitive capital market line.

Figure 5 E

 5 Figure 5 SR-sensitive capital market line versus SR-insensitive capital market line with

Figure 6

 6 Figure 6 SR-sensitive capital market line versus SR-insensitive capital market line with

Figure 7

 7 Figure 7 SR-sensitive capital market line versus SR-insensitive capital market line with

Figure 8

 8 Figure 8 SR-sensitive capital market line versus SR-insensitive capital market line with

  These indices track total returns for actively traded external debt instruments in emerging markets. 10 The indices are expressed in US dollars and taken at a monthly frequency from January 1994 to October 2009. They are extracted from Datastream. Descriptive statistics are available in Appendix 5. In the same way as Scholtens (2009), we use the Environmental Performance Index (EPI) as responsible ratings. The EPI 11 is provided jointly by the universities of Yale and Columbia in collaboration with the World Economic Forum and the Joint Research Centre of the European Commission. EPI focuses on two overarching environmental objectives: reducing environmental stress to human health and promoting ecosystem vitality and sound management of natural resources. These objectives are gauged using 25 performance indicators tracked in six well-established policy categories, which are then combined to create a final score. EPI scores attributed in 2008 are reported in Table

  EPI increases with the expected return on the SR-insensitive efficient frontier: a 1%/year increase in expected returns corresponds to an increase of 0.30 in the EPI portfolio. The minimal EPI portfolio on the SR-insensitive frontier is obtained for the minimum-variance portfolio and is equal to 26

Figure 9

 9 Figure 9 SR-sensitive frontiers versus SR-insensitive frontier for the EMBI+ indices,

Figure10

  Figure10 SR-insensitive capital market line for the EMBI+ indices, January 1994 to October

  impact the efficient frontier in four different ways, depending on the link between the returns and the responsible ratings and on the strength of the constraint. The SR-sensitive efficient frontier can be: a) identical to the SR-insensitive efficient frontier (i.e. no cost at all), b) penalized at the bottom only (i.e. a cost for high risk-aversion investors only), c) penalized at the top only (i.e. a cost for low risk-aversion investors only), d) totally different from the SRinsensitive efficient frontier (i.e. a cost for every investor). In other words, if portfolio ratings increase (resp. decreases) with the expected return along the traditional efficient frontier, the SRI cost arises first at the bottom (resp. at the top) of the frontier. The results are the same in the presence of a risk-free asset. Our work highlights the fact that the investor's risk aversion



  , the portfolio rating increases linearly with the expected return in the traditional mean-variance optimization. The minimal portfolio rating is * is inactive and the solutions are the same as in the traditional meanvariance optimization: the Capital Market Line is not modified. If 0 *    , the constraint on the portfolio rating is binding at the bottom of the efficient frontier and inactive at the top. corresponds to the portfolio with the expected return:

)



  the portfolio rating is always active: the entire Capital Market Line becomes a hyperbola in the mean-standard deviation plan. If 0 *    , the constraint on the portfolio rating is binding at the top of the Capital Market Line. The modification of the Capital Market Line occurs for the same risk aversion parameter * 0

Table 3

 3 Environmental Performance Index 2008

	ARGENTINA	81.78
	BRAZIL	82.65
	BULGARIA	78.47
	ECUADOR	84.36
	MEXICO	79.80
	PANAMA	83.06
	PERU	78.08
	PHILIPPINES	77.94
	RUSSIA	83.85
	VENEZUELA	80.05
	Mean	81.00
	Standard Deviation	2.44
	UNITED STATES	81.03

Sources: Universities of Yale and Columbia.

Ann. Standard Deviation (%/year) Ann. Mean (%/year) SR-insensitive Frontier SR 80 SR 82 SR 84 SR 86 SR 88

	30.00%
	25.00%
	20.00%
	15.00%
	10.00%
	5.00%
	0.00%
	0.00%	10.00%	20.00%	30.00%	40.00%	50.00%

Table 4

 4 Corner portfolios for which the SR constraint is binding

	0 	0 	Expected return 0 E	Expected volatility 0 
					(%/year)	(%/year)
	82	3.14			20.13	22.22
	84	2.05			26.84	32.17
	86	1.52			33.55	42.48
	88	1.21			40.26	52.93
	As expected from Proposition 2, for	0	' ' 1 1	26 . 78

Table 5

 5 Figure 11 SR-sensitive capital market lines versus SR-insensitive capital market lines for the EMBI+ indices, January 1994 to October 2009

	displays

Table 5

 5 Corner portfolios for which the SR constraint is binding

	0 						0 	Expected return 0 E	Expected volatility * 0 
								(%/year)	(%/year)
	82				1.16	50.01	63.06
	84				0.38	144.97	193.08
	86				0.23	239.93	323.11
	88				0.16	334.89	453.13
	As expected, for		0	 	*		03 . 81 , the capital market line is the same as the
	SR-insensitive capital market line. For	0	*	03 . 81

See Steinbach (2001) for a literature review on the extensions of the[START_REF] Markowitz | Portfolio selection[END_REF] model.

Notations of Lo (2008) are used here.

For sake of simplicity, short sales are allowed here.

This section highlights the impact of a constraint on the portfolio rating in the mean-variance optimization.However, the cost of investing responsibly, if non-zero, may be non-significant. The significance of the meanvariance efficiency loss may be assessed using the test of[START_REF] Basak | A direct test of mean-variance efficiency of a portfolio[END_REF] or any spanning test (see[START_REF] De Roon | Testing for mean-variance spanning: a survey[END_REF] for a literature review).

Argentina, Brazil, Bulgaria, Ecuador, Mexico, Panama, Peru, Philippines, Russia, Venezuela.

The EPI index is computed every two years since 2006.

This variable is extracted from Datastream.

Acknowledgments

The author thanks Marie Brière, Benjamin Lorent, Valérie Mignon, Kim Oosterlinck, Hugues Pirotte, Ombretta Signori, Ariane Szafarz and Kokou Topeglo for their helpful comments.

Social Investment Forum, 2007. Report on socially responsible investing trends in the United States. Available at: http://www.socialinvest.org/resources/pubs/documents/FINALExecSummary_2007_SIF_Tre nds_wlinks.pdf . Sharpe, W., 1965. Capital asset prices: a theory of market equilibrium under conditions of risk. Journal of Finance 19, 425-442. Sharpe, W., 2007. Expected utility asset allocation, Financial Analysts Journal 63, 18-30. Steinbach, M., 2001. Markowitz revisited: mean-variance models in financial portfolio analysis. Society for Industrial and Applied Mathematics Review 43, 31-85.

Appendix 1

Following [START_REF] Best | The efficient set mathematics when mean-variance problems are subject to general linear constraints[END_REF], in the standard mean-variance case, the weights vector that solves the problem is:

The corresponding expected return P  stands as:

And the expected variance 2 P  stands as:

As the expected return is also a linear function of  1 , it is possible to express the responsible rating as a linear function of the expected

.

Appendix 2

The mean-variance optimization with the linear constraint on the portfolio rating has the same portfolio solutions as the standard mean-variance optimization, while the constraint is not binding. This is verified if the portfolio rating of the efficient portfolio from the traditional mean-variance optimization is above the threshold 0

 . Two cases have to be distinguished:

and where 0 1   .

Case 0 1   In this case, the portfolio rating increases linearly with the expected return in the traditional mean-variance optimization. The minimal portfolio rating is

, the constraint on the portfolio rating is inactive and the solutions are the same as in the traditional mean-variance optimization. If

, the constraint on the portfolio rating is binding at the bottom of the efficient frontier and inactive at the top. Indeed, the constraint is binding

In the mean-variance plan, this corner portfolio is the one for which the portfolio rating is 0  .

To compute the portion of the efficient frontier for which the linear constraint on the portfolio rating is binding, we apply the results of [START_REF] Best | The efficient set mathematics when mean-variance problems are subject to general linear constraints[END_REF]:


Audrey Sallenave
email: audrey.sallenave@u-paris10.fr.

Real exchange rate misalignments and economic performance for the G20 countries *

Keywords: JEL classification : C23, F31, O47 Equilibrium Real Effective Exchange Rate, Group of Twenty, Growth, Misalignments, Panel Cointegration

We evaluate the growth effects of real effective exchange rate misalignments for the G20 countries over the period 1980-2006. To this end, we first estimate real effective equilibrium exchange rates relying on the behavioral approach BEER, from which misalignments are derived. Second, we estimate a dynamic panel growth model in which among the traditional determinants of growth, our measure of misalignments is included. Our findings put forward some important differences between developed and emerging economies. The magnitude of the misalignments is more pronounced in the case of emerging countries, and the speed of convergence towards the estimated equilibrium exchange rate is slower for industrialized ones. Turning to our growth regression analysis, we find that misalignments have a negative effect on the economic growth. As a consequence, an appropriate exchange rate policy would close the gap between real exchange rates and their equilibrium level.

Introduction

The question of currencies misalignments, often viewed as a key indicator of external competitiveness have a strong interest for policy makers. Indeed, persistent misalignments, whatever we consider an over-or-under valuation of the currencies may generate instability and are likely to affect the economic performance of countries. As [START_REF] Kaminsky | Leading Indicators of Currency Crisis[END_REF] and [START_REF] Razin | Real Exchange Rate Misalignments and Growth[END_REF] underline, an overvaluation of the currencices is often the sign of the inconsistency of the decisions of macroeconomic policies that may lead to an unsustainable current account deficit, increasing external debt and the risk of possible speculative attacks. 1 On the opposite, in case of real exchange rate undervaluation, competitiveness is reinforced, which stimulates investment and exports, the current account is then improved, so is the GDP. Consequently, an important question concerns the mesure of misalignments, that is the evaluation of equilibrium exchange rates.

Currency misalignment measures are far from consensual. Between the two extreme views -market equilibrium (short term) and purchasing power parity (very long term) -a large research avenue has been developed to provide numerous equilibrium exchange rates concepts [START_REF] Bénassy-Quéré | How Robust are Estimated Equilibrium Exchange Rates ? A panel BEER Approach[END_REF]. The analysis of the real equilibrium exchange rate could be divided into two main categories, the fundamentals (normative) et behavorial (positive) ones. The fundamental equilibrium exchange rate (FEER) developed by [START_REF] Williamson | Estimates of FEERs[END_REF] defines the equilibrium exchange rate as the one that satisfies simultaneously internal and external balances. Internal balance is identified as the level of output consistent with both full employment and sustainable rate of inflation, and external balance can be characterized by a current account which is consistent with external debt and sustainability [START_REF] Clark | Exchange Rates and Economic Fundamentals: A Methodological Comparison of BEER s and FEER s[END_REF]. Aspect normativity of this approach, given by the slighty arbitrary definition of "medium-term" fundamentals led to the desired equilibrium exchange rate (DEER), where the real exchange rate is conditioned on some measure of optimal fiscal policy. Similar to the spirit of this approach is the natural rate of exchange rate (NATREX), that conversely to the FEER does not only consider the medium term but also the long run, when capital stock and foreign debt are assumed to converge to their long run steady-state (Frait & al. (2004)). The NATREX is considered as a "'positive"' conception to the extend the equilibrium real exchange rate is jointly determined by real fundamentals factors and macroeconomics policies that 1 As illustrated by crisis in Latin American as well as in Asian Economies. don't need to be optimal. Turning now to the behavioural models, the behavioural real exchange rate (BEER) supported by [START_REF] Clark | Exchange Rates and Economic Fundamentals: A Methodological Comparison of BEER s and FEER s[END_REF] is rather a statistical approach linking the real exchange rate to a set of macroeconomic variables through a single equation. This model offers advantages to use a modelling technique which captures movements in real exchange rate over time [START_REF] Driver | Concepts of Equilibrium Exchange Rates[END_REF] and to be easily implemented.

Although real exchange rate misalignments have not been a key variable of neo-classical growth models that traditionally focus on savings, investment or education among others, some authors shed in light its prominence role. Among the empirical studies dealing with the misalignmentgrowth nexus, many papers focus on developing countries. A great majority of them find a negative correlation between exchange rate misalignments and growth since the 1970 s ; the more overvalued the currency, the smaller the per capita growth rate. This is for instance the case of Ghura & Greenes (1993), who negatively link growth and misaligned currencies for Sub-Saharan Africa. They concluded that inappropriate domestic macroeconomic, trade, and exchange rate policies appear to be one of the important factors that contributed to the economic distress in all Sub-Saharan African countries. We also note the contributions of [START_REF] Cavallo | Real Exchange Rate Behaviour and Economic Performance in LDC s[END_REF][START_REF] Dollar | Outward-Oriented Developing Economies Really Do Grow More Rapidly: Evidence from 95 LDC s , 1976-1985[END_REF], [START_REF] Easterly | Has Latin America's Post-Reform Growth Has Been Disappointing[END_REF], [START_REF] Domaç | Real Exchange Rate Behavior and Economic Growth: Evidence from Egypt, Jordan, Morocco, and Tunisia[END_REF], [START_REF] Bleany | The Impact of Trade and Real Exchange Rate Volatility on Investment and Growth in Sub-Saharan Africa[END_REF], [START_REF] Toulaboe | Real Exchange Rate Misalignments and Economic Growth in Developing Countries[END_REF] as well as [START_REF] Gala | Exchange Rate Misalignment and Growth: old and New Econometric Evidence, Anais do XXXIV Encontro National de Economia 93[END_REF] which still point the negative link between misalignments and growth for a large sample of emerging countries. While some empirical studies negatively link economic growth and misalignment volatility (see for example Ghura & Greenes (1993), [START_REF] Aghion | Exchange rate volatility and Productivity Growth: The Role of Financial Development[END_REF]), others, as [START_REF] Razin | Real Exchange Rate Misalignments and Growth[END_REF] and [START_REF] Béreau | Currency Misalignments and Growth: A New Looking Using Nonlinear Panel Data Methods[END_REF] show that it is the real exchange rate misalignment and not its volatility that can be associated with slower growth. More specifically, they found that while high overvaluations appear to be associated with slower growth, moderate to high undervaluations seem to stimulate growth. In this paper, we will investigate the impact of both the level and the volatility of the misalignment on economic growth.

The aim of this paper is to investigate the relationship between real exchange rate misalignments and economic growth for the group of twenty (hereafter G20). The choice to work on this sample is caused by the willigness to work on a sample that accounts for approximatively 80% of the world GDP. Furthermore, its allows us to take the context of growing global imbalances into consideration. To this end, we proceed in three steps. First, we investigate the impact of various potential determinants of the real exchange rate using the more recent panel unit root and cointegration techniques for the (G20). Second, based on cointegration results, we estimate equilibrium paths for the G20 real exchange rates and then compute the degree of misalignment between the observed and the equilibrium real exchange rates. Third, we assess the relationship between economic growth and a set of explanatory variables, by paying a special attention to the impact of real exchange rate misalignments.

The rest of the paper is organized as follows. Section 2 briefly presents the potential determinants of exchange rates in a BEER context. Section 3 outlines the data. Section 4 presents the panel unit root and cointegration tests. Section 5 deals with the empirical estimation of both real equilibrium exchange rates and currency misalignments. Section 6 is devoted to the growth model and presents the empirical results. Finally, Section 7 provides some concluding remarks.

The BEER framework

We rely on the BEER approach introduced by Clark and MacDonald (1998), and more specifically on the stock-flow model developed by [START_REF] Alberola | Global Equilibrium Exchange Rates: Euro, Dollar, 'Ins','Out' and Other Major Currencies in a Panel Cointegration Framework[END_REF][START_REF] Alberola | Misalignment, liabilities dollarization and Exchange Rate Adjustment in Latin America[END_REF], where the real exchange rate is jointly determined by external balance as well as internal balance. The real exchange rate q is defined as the relative price of domestic goods. With p * denoting the foreign price index and p the domestic one, and s standing for the nominal exchange rate defined as the price of foreign currency in terms of domestic currency, all variables being in logarithms, we have:

q = s -p * + p (1)
Denoting2 α the share of tradable goods in the price index, p T the price level of tradable goods, and p NT the price level of non-tradable goods, the real exchange rate can also be written as follows :

3 q = (p T -(s + p T * ) q T + α p NT -p T -α * (p NT * -p T * ) q NT
(2)

The first term denoted q T , refers to the relative price of tradable goods accross countries. It is determined by the equilibrium condition of the balance of payments when net capital flows correspond to normal adjustment of the net foreign asset position f towards its desired level f .

Defining the equilibrium for the external exchange rate q T as the exchange rate consistent with f = f i-e the exchange rate consistent with asset holdings at their targeted level, it follows that : 4

q T = (i * -g) γ f γ > 0 ( 3
)
where g is the growth rate of nominal GDP and i * the international interest rate. The second term, q NT refers to the Balassa-Samuelson effect, which is driven by relative productivity in the tradable relative to non-tradable sector. The internal contribution to the equilibrium exchange rate q NT can be expressed as:

q NT = (1 -α) y T -y NT -y T * -y NT * (4)
where y i stands for labor productivity in sector i, (i = NT, T).

From (3) et (4), we get the real equilibrium exchange rate, denoted q:

q = (i * -g) γ f + (1 -α) y T -y NT -y T * -y NT * (5)
The real exchange rate q is expected to be a positive function of both the net foreign asset position f and the relative productivity differential.

Data: sources and construction

As mentioned in the introduction, we consider both industrial and emerging countries by concentrating on fifteen countries or areas belonging to the group of the twenty (G20). 5 More specifically our sample includes Argentina (ARG), Australia (AUS), Brazil (BRA), Canada (CAN), China (CHN), the United Kingdom (GBR), Indonesia (IND), India (IND), Japan (JPN), Korea (KOR), Mexico (MEX), South Africa (ZAF), Turkey (TUR), the United States (USA) and the Euro area (ZZM). 6

Data are annual and cover the period 1980-2006.

The dependent variable is the real effective echange rate q and the explanatory variables are (i) the stock of net foreign assets n f a and the relative productivity in the tradable relative to non-tradable 4 See [START_REF] Alberola | Misalignment, liabilities dollarization and Exchange Rate Adjustment in Latin America[END_REF] for details. 5 Our sample covers all G20 countries except Russia ans Saudi Arabia because of data availability. 6 France, Germany and Italy are grouped into the Euro area. EUR/USD exchange rate is extracted from datastream.

rprod, q and rprod are in logarithms, n f a being expressed as share of GDP in percentage points.

q t = f (n f a t , rprod t ) (6)
The real effective exchange rate for each country, extracted from the International Financial Statistics, is calculated as a weighted average of real bilateral exchange rate against each partner. We apply the usual definition of a real effective exchange rate: 7

rer i = n j=1, j i w i j (s j$ -p j -(s i$ -p i )) (7)
where s j$ (resp s i$ ) is currency j (resp i)'s bilateral exchange rate (defined as the price of foreign currency in terms of domestic currency). p j (resp p i ) is country j (resp i)'s consumer price index 8

(CPI) and n denotes the number of partner countries. All variables are based 100 in 2000 and taken in logarithms. w i j are the weights put on currency j for country i s real effective exchange rate. Here we define them on the whole period 1980-2006, as country j s share in the world gross domestic product 9 (GDP) in USD, which is calculated excluding country i. This can be written as follows:

w i j = GDP j n k=1,k i GDP k (8)
The weights w i j are reported in Appendix. The net foreign asset position is built using the Lane and Milesi-Ferretti database. 10 According to portfolio-balances considerations, this variable influences the real exchange rate. For instance, a deficit in the current account creates an increase in the net foreign debt of a country, which has to be financed by international investors which, in order to adjust their portfolio, demand a higher yield. At a given interest rate, this can be only achieved Concerning the relative productivity of tradables versus non-tradables, we follow [START_REF] Alberola | Global Equilibrium Exchange Rates: Euro, Dollar, 'Ins','Out' and Other Major Currencies in a Panel Cointegration Framework[END_REF] in using a proxy given by the ratio of the consumer price index (CPI) to the producer price index (PPI). 11 The reason for such approximation is that the CPI contains more non-tradable goods than the PPI. According to the IMF International Financial Statistics, the producer price index doesn't include services. In this sense, it makes it an acceptable proxy for tradable good prices.

For each country, we calculate the ratio rprod both for the domestic economy and for an aggregate foreign economy which is a weighted average of foreign partners, using the same weights as for the real effective exchange rate:

rprod it = ln CPI PPI it - j i w i j ln CPI PPI jt (9)
rprod refers to the Balassa-Samuelson effect which states that relatively larger increases in productivity in the traded goods sector are associated with a real appreciation of the currency of a country.

Having introduced macroeconomic fundamentals for calculating real exchange rate misalignments, we are now in position to investigate the impact of real exchange rate misalignments on the economic performance. From this perspective, we add misalignments among explanatory variables in our growth regression. We consider a model of the following form:

y i,t -y i,t-1 = αy t-1 + βX i,t + µ t + η i + i,t (10)
The dependent variable is the growth rate of real GDP per capita, extracted from the Penn World Table 6.2. Turning to the growth determinants, we follow [START_REF] Béreau | Currency Misalignments and Growth: A New Looking Using Nonlinear Panel Data Methods[END_REF] and rely on the neoclassical growth theory by considering the usual determinants: initial value of GDP per capita, a proxy of human capital, trade openess, terms of trade, government burden and investment. The initial value of GDP per capita proxies for conditional convergence. We expect, according to the theory, the sign of this variable to be negative. Our mesure of cyclical reversion is the difference between (the log of) the actual GDP and ( the log of) potential (trend) GDP. To this end we im-11 PPI are from Datastream.

plement the Hodrick-Prescott filter 12 to decompose GDP in trend and cycle. 13 Human capital is proxied by the gross-secondary school enrollment rate. Our source is the Barro & Lee's educational attainment data, 1960-2000. 14 Trade openness is the log of the ratio of exports and imports to GDP, and the terms of trade are defined as the home country's export price to import price ratio. The data are respectively obtained from the PWT 6.2 and the World Development Indicators. Government burden is proxied as the ratio of government consumption to GDP and the data are extracted from the PWT. Importance of capital accumulation is proxied by investment (as percentage of GDP)

and data are from the PWT 6.2. Volatility of both the terms of trade and the real exchange rate misalignments is estimated from a GARCH (1,1). 15

Panel unit root and cointegration tests

The econometric methodology used in this paper is based on panel unit root and cointegration tests. Fisrt, we test for unit root in various series. Second, we test for cointegration between the real effective exchange rate and the underlying macroeconomic fundamentals. Finally, we estimate the long-run parameters that we later use for computing the real equilibrium exchange rates and the corresponding misalignements. Given our relatively short time span (T = 27), examining the long run behavior of real exchange rates by using non stationarity panel econometrics instead of relying on individual time series yields substantial benefits. Firstly, as underlined by Carrera & Restout (2008) panel unit root and cointegration tests outperform their conventional time series counterparts. 16 Secondly, recent panel unit root and cointegration tests take account of the heterogeneity 12 Other methodologies are routinely used in pratice (see [START_REF] Cette | Actualisation des Evaluations de Croissance Potentielle et d' Ecart de PIB[END_REF] for details.) such as the Baxter-King filter. Since the litterature is somewhat divided over the choice of this two filters (see for instance [START_REF] Guay | Do the Hodrick-Prescott and Baxter-King Filters Provide a Good Approximation of Business Cycles?[END_REF] or Woitek (1998)) we made the choice to enforce the H-P filter. 13 Here we use a smoothing parameter value of 100 (λ=100) Our choice is motivated by the statistical view of Hodrick-

Prescott filter according which it is great adviced to choose a λ consistent with the frequency of the data [START_REF] Hodrick | Postwar U.S. Business Cycles: An Empirical Investigation[END_REF]. Note that recent studies as [START_REF] Agenor | Macroeconomic Fluctuations in Developing Countries: Some Stylized Facts[END_REF] implemented a modified version of the Hodrick-Prescott using specific smoothing parameters for their series. However, the arbitrariness of the decision of requiring variant value for λ led us to impose the same exogenous smoothing parameter for our database. 14 http://www.cid.harvard.edu/ciddata/ciddata.html 15 Here we follow the methodology enforced by [START_REF] Bleany | The Impact of Trade and Real Exchange Rate Volatility on Investment and Growth in Sub-Saharan Africa[END_REF] and [START_REF] Wong | Terms of Trade and Economic Growth in Japan and Korea: an Empirical Analysis[END_REF] based on annual data where the GARCH (1,1) model is estimated using a regression of a change in the logarithm of the variables on a constant. 16 See Carrera & Restout for details.

accross different members of the panel (see [START_REF] Hurlin | Une Synthèse des tests de Racine Unitaire sur données de panel[END_REF]. This allows us to test the presence of unit root and the existence of a cointegration relationship in the panel while permitting the short run dynamics or fixed effects to be heterogeneous among individuals countries. Finally, here, panel estimation permits us to take into account the rising share of emerging countries in global imbalances since the mid-1990s. [START_REF] Levin | Unit Root Test in Panel Data: Asymptotic and Finite Sample Properties, University of California at San Diego[END_REF], 1993), [START_REF] Breitung | The Local Power of Some Unit Root Tests for Panel Data[END_REF] and [START_REF] Hadri | Testing for Unit Roots[END_REF]

Panel unit root

∆y i,t = γz i,t + ρ i y i,t-1 + p i j=1 θ i, j ∆y i,t-j + i,t (11)
where z i,t is the deterministic component, i,t are assumed to be i.i.d. The null and alternative hypotheses are defined as:

           H 0 : ρ i = 0 ∀ i = 1, ..., N. H 1 : ρ i < 0 for i=N 1 + 1, N 1 + 2, ..., N. (12)
Thus, under the alternative hypothesis, IPS allows for ρ i to be individual specific, and in this sense, is more general than the homogeneous alternative, i-e ρ i = ρ < 0 for all i.

The results of the panel unit root tests applied to the (log) of real exchange rate q, net foreign asset position n f a and relative productivity rprod are reported in table 1.

In accordance with empirical studies such as [START_REF] Calderon | Real Exchange Rates in the Long and the Short Run: A Panel Co-Integration Approach[END_REF]

Cointegration tests

To test for cointegration between real exchange rate, the sectoral productivity differential and the net foreign asset position, we follow the methodology proposed by [START_REF] Pedroni | Critical for Cointegration Tests in Heterogeneous Panels with Multiple Regressors[END_REF]. 18 He developed tests that allow for considerable heterogeneity across individuals and also allow the cointegration vector to differ across members under the alternative hypothesis. These tests are based on the null hypothesis of no cointegration. [START_REF] Pedroni | Critical for Cointegration Tests in Heterogeneous Panels with Multiple Regressors[END_REF] considers the following cointegration model with k regressors for a panel:

y it = γz it + β 1,i x 1,it + β 2,i x 2,it + ... + β k,i x k,it + it (13)
where z it is the deterministic component and x it are the k regressors which are assumed to be I(1)

and no cointegrated with each other. [START_REF] Pedroni | Critical for Cointegration Tests in Heterogeneous Panels with Multiple Regressors[END_REF][START_REF] Pedroni | Panel Cointegration Asympotic and Finite Sample Properties of Pooled Time Series Tests with an Application to the PPP Hypothesis[END_REF]) approach focuses on testing for unit roots in panel estimates of:

êi,t = ρ i êi,t-1 + υ i,t (14)
where êi,t are the estimated residuals and υ i,t are assumed to be iid. [START_REF] Pedroni | Critical for Cointegration Tests in Heterogeneous Panels with Multiple Regressors[END_REF][START_REF] Pedroni | Panel Cointegration Asympotic and Finite Sample Properties of Pooled Time Series Tests with an Application to the PPP Hypothesis[END_REF]) considered seven tests based on residuals from the regression below. Four are based on pooling data along the within dimension and three are calulated by pooling data along the between dimension of the panel. Using the within approach, the test of the null of no cointegration is H 0 :

ρ i = 1∀i
against the alternative hypothesis H 1 : ρ i = ρ < 1∀i. Thus, all within statistics presume a common value ρ i = ρ, whereas the between estimators are less restrictive in that they allow for considerable heterogeneity since the alternative hypothesis is H 1 : ρ i = ρ i < 1∀i. The between statistics provide an additional source of heterogeneity since the autoregressive coefficients, ρ i , are allowed to vary across individual members of the panel. [START_REF] Pedroni | Panel Cointegration Asympotic and Finite Sample Properties of Pooled Time Series Tests with an Application to the PPP Hypothesis[END_REF] explored finite sample performances of the seven statistics. He showed that in terms of power all the proposed statistics do fairly well for T > 90 and N = 20. Moreover Pedroni's (1997) simulations showed that for small time span (T < 20), the between group parametric-t statistic is the most powerful. Given our relatively short time span (T = 27), we will pay a particular atention to the group parametric-t statistic when testing for cointegration. The result of panel cointegration tests are displayed in table 2. As it can be seen below, the results are somewhat mixed (see among others [START_REF] Bénassy-Quéré | World Consistent Equilibrium Exchange Rates[END_REF][START_REF] Wong | Terms of Trade and Economic Growth in Japan and Korea: an Empirical Analysis[END_REF]). 19 Since simulations made by [START_REF] Pedroni | Panel Cointegration, Asymptotic and Finite Sample Properties of Pooled Time Series Tests with an Application to the PPP Hypothesis: New Results[END_REF] show that, in small samples, the group-mean parametrict-test is more powerful than the other tests, we can conclude that the null hypothesis of no cointegration is rejected in our study, and now turn to the estimation of the long run relationship between the real effective exchange rate and its determinants.

Equilibrium exchange rates and currency misalignments

Having established that the variables are integrated and that a cointegration relation indeed exists, the long run parameters can be estimated. Various procedures exist, such as the Ordinary Least Squares (OLS),20 the Fully-Modified Ordinay Least Squares (FM-OLS)21 method proposed by [START_REF] Phillips | Statistical Inference in Instrumental Variables Regression with I(1) Processes[END_REF], the error correction pooled mean-group (PMG)22 by [START_REF] Pesaran | Pooled Mean Group Estimation of Dynamic Heterogeneous Panels[END_REF] or the Dynamic Ordinay Least Squares (DOLS)23 method introduced by [START_REF] Saikkonen | Asymptotically Efficient Estimation of Cointegration Regressions[END_REF]. Here, we propose to use the panel DOLS24 procedure that consists in augmenting the cointegrating relationship with lead and lagged differences of the regressors to control for the endogeneous feedback effect, that is:

y it = βx it + ∞ k=-∞ δx it+k + it (15)
where x it are the k regressors and it are assumed to be i.i.d. The cointegration vector estimated through the DOLS method with country fixed effects are reported in table 3. From these results, consistent with the literature named above using the DOLS methodology, 25 we can highlight that both n f a and rprod are significant and correctly signed. A rise in the n f a position (i-e an improvement in the current account) as well as in the CPI to PPI ratio (Balassa-Samuelson effect) leads to a real exchange rate appreciation.

The estimation of equation ( 6) gives the real equilibrium exchange rate (hereafter qit ) for each considered country. The misalignments m it are then obtained as the deviation of the real exchange rate from its equilibrium level:

m it = q it -qit (16)
Figure 1 reports the real exchange rate misalignments for each country. Our results highlight two points. First, average misalignments in emerging economies are higher than in advanced countries [START_REF] Aguirre | Real Exchange Rate Misalignments and Economic Performance[END_REF], meaning that real exchange rates in industrial countries are closer to macroeconomic fundamentals. Second, the adjustment to equilibrium seems to be smoother in advanced economies than in emerging ones.

Regarding the particular countries, the United States know a phase of overvaluation between 1982 and 1987 where the dollar reaches a value at 23 %, then followed by a period of undervaluation about ten years between 1988and 1998[START_REF] Bénassy-Quéré | World Consistent Equilibrium Exchange Rates[END_REF][START_REF] Lopez-Villavicencio | Real Equilibrium Exchange Rates: A panel Data Approach For Advanced and Emerging Economies[END_REF], period characterized by a trade gap in constant increase.

Symetrically the euro is undervalued over the period 1982-1987. Then the European currency knew phases of successive under and overvaluations (Maeso-Fernandez & al., 2001). At the beginning of 1999, the euro is overvalued by 5 % but in January 2002, wich coincides with the period around the launch of the euro and the moment when the European Central Bank took over responsability for the monetary policy of the EMU members states, the euro is strong. In the last few years, the real equilibrium exchange rate reaches a level similar to the ones observed during the nineties.

India, Indonesia and Korea have all the same profile before the 1997 crisis, their currencies are overvalued then fall brutally during the explosion of the crisis. 26 However this overvaluation does not last and most of the currencies show a return towards their equilibrium value or, at least to their initial level, as underlined by [START_REF] Lopez-Villavicencio | Real Equilibrium Exchange Rates: A panel Data Approach For Advanced and Emerging Economies[END_REF]. By the end of the period, esti-25 For instance, cointegration's coefficient of both n f a and rprod respectively vary from 0.001 to 0.149 for [START_REF] Aguirre | Real Exchange Rate Misalignments and Economic Performance[END_REF] and from 0.484 to 0.771 for [START_REF] Bénassy-Quéré | World Consistent Equilibrium Exchange Rates[END_REF] who considered the same database as ours. 26 With the exception of India. mated misalignments in China, Japan, Indonesia are quite insignificant compared with the other countries. 27 Turning to the pound sterling, after a peak of appreciation in 1985, it depreciates from 1987 to 2001.

At the end of the period the currency is undervalued by around 21%.

Among the Latin American countries of our sample, Argentina, Brazil and Mexico, the two first present the most important misalignments, both before the explosion of the crisis and just after.

Mexico departs from the two other countries seems to be an exception because since the 2000s it is close to its equilibrium value. The case of Mexico is however similar to that of Brazil because the Tequila crisis has carried along an undervaluation of the peso about 37%, to finish at the end of the period with a 2% appreciation.

Given these misalignment series, let us now investigate their impact on the economic performance of the different countries.

27 With the exception of Korea.

Figure 1: Real exchange rate misalignments, 1980-2006

Note: positive misalignment: overvaluation, negative misalignment: undervaluation.

6 Growth regression analysis

Econometric methodology

The econometric framework follows the traditional litterature of growth regressions (see for instance [START_REF] Barro | Economic Growth in a Cross Section of Countries[END_REF] and [START_REF] Barro | La Croissance Economique[END_REF]). As mentioned before, GDP per capita growth rate is the dependent variable which is expected to depend on a vector of variables representing growth determinants X it , together with the initial GDP per capita level for each country i on a

given time period t. The theoretical model is given by:

y i,t -y i,t-1 = αy t-1 + βX i,t + µ t + η i + i,t (17)
where η i represents unobserved country-specific factors and µ t is a period specific effect. As underlined by [START_REF] Gala | Exchange Rate Misalignment and Growth: old and New Econometric Evidence, Anais do XXXIV Encontro National de Economia 93[END_REF], using the initial level of per capita income on the right hand side of the previous equation for convergence analyses might cause possible biases on the estimators in a panel context. Thus, we chose to use the Generalized-Method-of-Moment (GMM) estimators developped for dynamic models of panel data that were introduced by [START_REF] Arellano | Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Evidence[END_REF]. Taking advantage of the data's panel nature, these estimators are based on, first, differencing regressions and/or instruments to control for unobserved effects, and second, using previous observations of explanatory and lagged-dependent variables as instruments.

Estimation

Following [START_REF] Dufrénot | The Trade Growth Nexus in the Developing Countries: A Quantile Regression Approach, Document de travail du CEPII[END_REF], we estimate our growth model first on the whole period and on two sub-periods, namely 1980-1995 and 1996-2006. 28 In table 4 we report our regression estimates using the GMM difference estimation technique.

For the three regressions, we find evidence of conditional convergence, i-e, all things being equal, countries with lower income per capita tend to grow faster. Over the periods 1980-2006 and 1980-1995, speeds of convergence are respectively given by 7.2% and 16.7% corresponding to half-lives of 10 and 4.5 years respectively. Our estimates, although close to those obtained by [START_REF] Easterly | Has Latin America's Post-Reform Growth Has Been Disappointing[END_REF], [START_REF] Bleany | The Impact of Trade and Real Exchange Rate Volatility on Investment and Growth in Sub-Saharan Africa[END_REF], and [START_REF] Aguirre | Real Exchange Rate Misalignments and Economic Performance[END_REF] seem to be somewhat too high compared to other empirical studies (see [START_REF] Barro | La Croissance Economique[END_REF], [START_REF] Ramey | Cross Country Evidence on the Link Between Volatility and Growth[END_REF] and [START_REF] Easterly | National Policies and Economic Growth: a Reappraisal, Handbook of Economic Growth[END_REF]) where the speed of convergence is between 2% and 5% corresponding to half-lives of 25 to 40 years. Our results over the last sub-period are consistent with those obtained by [START_REF] Barro | La Croissance Economique[END_REF] and [START_REF] Loayza | Economic Growth in Latin America and the Caribbean: Stylized Facts, Explanations, and Forecasts[END_REF] with a speed of annual convergence of 1.7% and a half-life of 40 years. Estimated output gap coefficients are negative, but non significant, over the whole period and the 1980-1995 sub-period and significant with a positive sign over the 1996-2006 period. Therefore we don't find any cyclical reversion.

The trade openness coefficient is positive and statistically significant for all estimations. Thus, the more countries are outward-oriented the more this contributes favorably to economic growth. The estimated coefficients of the open variable vary from 0.001 in 1980-2006 to 0.07 over the period 1996-2006, and these results are in line with those found by [START_REF] Cavallo | Real Exchange Rate Behaviour and Economic Performance in LDC s[END_REF], Calderon & al. (2004) and [START_REF] Dufrénot | The Trade Growth Nexus in the Developing Countries: A Quantile Regression Approach, Document de travail du CEPII[END_REF], and, more generally with the neoclassical approach according to which the positive impact of trade on growth is explained by comparative advantages, be they in ressource endowment or differences in technology (see [START_REF] Béreau | Currency Misalignments and Growth: A New Looking Using Nonlinear Panel Data Methods[END_REF]. The terms of trade, 29 which capture both changes in international demand for a country's export and the cost of production (Loayza & al., 2004), are negative and statistically insignificant except on the 1996-2006 sub-period. Toulaboe (2004) and [START_REF] Gala | Exchange Rate Misalignment and Growth: old and New Econometric Evidence, Anais do XXXIV Encontro National de Economia 93[END_REF] also reported a negative and statistically insignificant coefficient for the terms of trade. On the other hand, this same variable enters significantly on the third regression but with the opposite sign, just like [START_REF] Cavallo | Real Exchange Rate Behaviour and Economic Performance in LDC s[END_REF] and [START_REF] Bleany | The Impact of Trade and Real Exchange Rate Volatility on Investment and Growth in Sub-Saharan Africa[END_REF]. In the perspective to be oversubtle, we included in our estimation a measurement of the volatility of the terms of trade. The results are conform with those obtained by [START_REF] Bleany | The Impact of Trade and Real Exchange Rate Volatility on Investment and Growth in Sub-Saharan Africa[END_REF] since our variable voltot enters significantly and positively over all the periods.

In accordance with the theoretical model of Solow, population growth is negative and significant.

The coefficient of the investment (as a percentage of GDP) variable is positive and significant, 29 There is no consensus about the impact of terms of trade and terms of trade volatility on economic growth. While some studies point the fact that an increase in terms of trade lead to an increase in investment and thus economic performance [START_REF] Bleany | The Impact of Trade and Real Exchange Rate Volatility on Investment and Growth in Sub-Saharan Africa[END_REF], [START_REF] Blattman | The terms of Trade and Economic Growth in the Periphery 1870-1983[END_REF]), other, as [START_REF] Eicher | Dynamic Effects of Term of Trade Shocks: The Impact on Debt and Growth[END_REF] show that an improvement in terms of trade decreases economic growth in the long term. In this sudy, we expect a positive sign of this both variables, reflecting the income effect according which a rise in terms of trade lead to foster accumulation and thus economic growth [START_REF] Wong | Terms of Trade and Economic Growth in Japan and Korea: an Empirical Analysis[END_REF]).

reflecting the importance of capital accumulation for developing countries.

Gross secondary school enrollment variable is, following [START_REF] Barro | La Croissance Economique[END_REF]), Toulaboe (2004), and [START_REF] Gala | Exchange Rate Misalignment and Growth: old and New Econometric Evidence, Anais do XXXIV Encontro National de Economia 93[END_REF] significant but with a negative sign, which means that obtaining a secondary diploma seems to adversely impact economic growth. For [START_REF] Barro | La Croissance Economique[END_REF], the affected sign of schooling variable depends on the sex (male or female)30 and of the level of schooling. It is worth noting that Barro (1994) reported a positive coefficient for male secondary schooling, but found the initial level of female secondary education to be negatively correlated with economic growth. Government spending enters positively and non significantly, although, as underlined by Toulaboe (2004), there seems to be a consensus that consistent and increasing government balance in a economy can hinder economic growth.

Regarding now our variable of interest, both the global period and 1980-1995, only the volatility misalignment contracts economic growth, with estimated coefficients of -0.01 and -0.003 respectively. On the other hand, over the period 1996-2006, the volatility misalignment is non significant and positive, but we find a negative and significant relationship between growth and real exchange rate misalignment (as in [START_REF] Cavallo | Real Exchange Rate Behaviour and Economic Performance in LDC s[END_REF], [START_REF] Dollar | Outward-Oriented Developing Economies Really Do Grow More Rapidly: Evidence from 95 LDC s , 1976-1985[END_REF], [START_REF] Bleany | The Impact of Trade and Real Exchange Rate Volatility on Investment and Growth in Sub-Saharan Africa[END_REF], Toulaboe (2004), [START_REF] Aguirre | Real Exchange Rate Misalignments and Economic Performance[END_REF] and Haussmann & al. (2004)). This result implie that growth would decline in response to increase in the real exchange rate misalignment.

More generally, this result corroborates the view that exchange rate policies continue to play a vital role in the economic growth, and an appropriate exchange rate policy should to focus on the real exchange rate misalignment reduction. 1980-2006 (resp. 1980-1995, 1996-2006) 4. Instruments used for GMM are lagged values of the endogenous and explanatory variables.

Conclusion

This paper investigates the link between real exchange rate misalignments and economic growth for a panel of countries including both emerging and industrial economies. As the real exchange rate misalignment is not observable, equilibrium exchange rates have been estimated relying on the BEER methodology. Misalignment series are then obtained by the deviation of the observed real exchange rate from its equilibrium level. We have then assessed their impact on economic growth using dynamic panel data techniques in order to address both the issue of unobserved country-specific effects and the possibility of endogeneous regressors. Explaining the real effective exchange rate by the net foreign asset position and the Balassa-Samuelson effect, our results show that average misalignments in emerging countries are higher than in advanced ones. Moreover the adjustment towards equilibrium tends to be smoother in industrial economies. Turning to the growth regression analysis, our finding puts forward a negative and significant relationship between growth and real exchange rate misalignments on the recent 1996-2006 period. This result highlights that countries that pursue major and appropriate exchange rate reforms to reduce real exchange rate misalignment are very likely to record gains in real per-capita GDP. In other words, it should be relevant for countries, especially emerging countries, to maintain their real exchange rate at its appropriate level.

There are many directions in which the present analysis can be extended. In particular, it would be interesting (i) to pay a special attention of the asymetric imact of under and overvaluations on economic growth [START_REF] Béreau | Currency Misalignments and Growth: A New Looking Using Nonlinear Panel Data Methods[END_REF], (ii) to take into account the rest of the world in the analysis, and (iii) to rely on higher frequency data and other exchange rate determinants.

  through an immediate depreciation of the currency of the debtor country. The 2005 and 2006 data are calculated by adding the current account position to the 2004 and 2005 n f a value. 7 We define real exchange rate as the price of foreign currency in term of domestic one using CPI deflator. Other narratives, as Rodrik (2007) or Carrera & Restout (2008) use a definition of relative price. To what extend the large majority of studies use the same definition as ours, we implement real exchange rate misalignments with it.8 CPI are from World Development indicators. 9 GDP are from World Development indicators. 10 http://www.imf.org/external/pubs/cat/longres.cfm?sk=18942.9

  tests are based on a common unit root process, except the Hadri test which uses the null of unit root. All these tests are designed for cross sectionally independent panels, i-e there is no cointegration between pairs or groups of individuals in the cross section dimension. Im & al. (2003) (hereafter IPS) proposed a test that allows for residual correlation, and heterogeneity of the autoregressive root and error variance accross individual members of the panel. IPS is based on the augmented Dickey-Fuller (ADF) test to each individual series. If we consider a sample of N individuals observed over T time periods, ADF estimation for each individual i = 1, ...N is:

Table 1 : Panel unit root tests

 1 ,Carrera & Restout (2008) or[START_REF] Coudert | Currency Misalignments and Exchange Rate Regimes in Emerging and Developing Countries, CEPII[END_REF] both n f a and rprod contain a unit root at the 10% significance level for the four tests. 17 Concerning the effective real exchange rate, the unit root hypothesis is rejected only by the

		q t	rprod t	n f a t
		N=15
	LL	-0.39 (0.34)	-0.95 (0.17) -0.89 (0.18)
	Breitung	-1.07 (0.12)	-1.09 (0.86) -0.43 (0.33)
	IPS	-2.81 (0.002)*** -0.70 (0.24) -0.61 (0.26)
	Hadri	6.33 (0)***	7.25 (0)***	8.62 (0)***
	Note: This table reports the results of the following panel unit root tests: Levin & Lin (LL); Breitung; Im, Pesaran and Shin

(IPS); Hadri. All tests but Hadri are based on the unit root null hypothesis. p-value are given in parentheses. * (resp.**,***): rejection of the null hypothesis at 10% (resp. 5%, 1%) significance level. IPS t-bar. The three other tests indicate that this series is non stationary at the 10% significance level.

Table 2 : Panel cointegration tests

 2

		Panel cointegration tests
	v -stat	rho -stat	pp -stat	ad f -stat
	-0.41 (0.36) 3.51*** (0.00) -0.80 (0.28) -1.83 (0.07)*
		Group mean cointegration tests
		rho -stat	pp -stat	ad f -stat
		4.58*** (0.00) -1.56 (0.11) -2.00** (0.05)

Note: This table reports the results of the seven tests proposed by

[START_REF] Pedroni | Critical for Cointegration Tests in Heterogeneous Panels with Multiple Regressors[END_REF]

. All tests are based on the null hypothesis of no cointegration. p-value are given in parentheses. *(resp.**,***): rejection of the null hypothesis at the 10% (resp. 5%, 1%) significance level.

Table 3 : Cointegration vector

 3

		coefficient t-stat
	n f a	0.57	5.97
	rprod	0.54	8.11

Note: This table reports the estimation of the cointegration vectors using the DOLS procedure.

Table 4 : GMM Regressions 1980-2006, 1980-1995 and 1996-2006

 4

	Dependent variable: per-capita real growth rate
		(1)	(2)	(3)
		GMM
	Real GDP (-1)	-0.29* (0.107)	-3.16* (0.02)	-0.01* (0.04)
	Output gap	-0.15 (0.149)	-0.02 (-0.11)	0.39* (0.121)
	Government balance	18.17 (9.406)	14.25 (6.89)	-0.01 (0.26)
	Investment share	0.02* (0.040)	0.01* (0.003)	0.01* (0.003)
	Misal	0.01 (0.01)	0.03 (0.01)	-0.06* (0.02)
	VolMisal	-0.01* (0.004) -0.003 (0.005)	0.001 (0.003)
	Terms of trade	-0.04 (0.75)	-0.08 (0.07)	0.004* (0.03)
	VolTot	0.05* (0.014) 0.008* (0.020) 0.004* (0.005)
	Open	0.02* (0.010) 0.001* (0.001) 0.007* (0.007)
	Population growth	-0.96* (0.864)	-0.97* (0.66)	-1.50* (0.68)
	School	-0.01* (0.019) -0.02* (0.118)	0.01* (0.014)
	No. countries	15	15	15
	No. observations	345	345	345
	R 2	0.24	0.25	0.78
	Specification test p-value
	-2nd Order Correlation	0.41	0.50	0.61
	Note:
	1. *(resp.**,***): rejection of the null hypothesis at the 10% (resp. 5%, 1%) significance level.
	2. Standard deviations are given in parentheses.
	3. (1) (resp. (2), (3)):

We refer to foreign variables with a star.

Thus, an increase in q represents an appreciation of the real exchange rate.

Note that[START_REF] Coudert | Currency Misalignments and Exchange Rate Regimes in Emerging and Developing Countries, CEPII[END_REF] provide som extensive panel unit root.

Kao (1999) also proposed residuals based test for panel cointegration, see for instance[START_REF] Calderon | Real Exchange Rates in the Long and the Short Run: A Panel Co-Integration Approach[END_REF] for an implementation of this test.

WhereBenassy-Quéré (2006) derive panel cointegration test for a closed G20 dataset and an another with the rest of the World.

SeeCaderon (2002) and[START_REF] Bénassy-Quéré | Burden Sharing and Exchange-Rate Misalignments Within the Group of Twenty[END_REF].

see for instance[START_REF] Calderon | Real Exchange Rates in the Long and the Short Run: A Panel Co-Integration Approach[END_REF].

See[START_REF] Lopez-Villavicencio | Real Equilibrium Exchange Rates: A panel Data Approach For Advanced and Emerging Economies[END_REF] for details, and[START_REF] Béreau | Currency Misalignments and Growth: A New Looking Using Nonlinear Panel Data Methods[END_REF].

Note that DOLS estimator allows to correct the asymptotic biais contained in OLS estimates. Moreover, it has the same asymptotic distribution as the FM-OLS one but has smaller size distortion. We consquently enforce the former.

See Calderon (2002),[START_REF] Aguirre | Real Exchange Rate Misalignments and Economic Performance[END_REF] as well as[START_REF] Bénassy-Quéré | World Consistent Equilibrium Exchange Rates[END_REF][START_REF] Wong | Terms of Trade and Economic Growth in Japan and Korea: an Empirical Analysis[END_REF].

As underlined by[START_REF] Dufrénot | The Trade Growth Nexus in the Developing Countries: A Quantile Regression Approach, Document de travail du CEPII[END_REF], justifications for these sub-periods come from different trade policies. Up until the first half of the 1990s, trade policies concentrated on market-oriented development and led to only short-lived recoveries in Latin America countries and a few take offs in Africa. As a consequence, from the mid-nineties, trade policies were complemented by reforms putting a stronger focus on other macroeconomic and social policies.

Here we considered a sample including both men and women.