Cécile Couharde
email: cecile.couharde@u-paris10.fr

Issiaka Coulibaly
email: issiaka1.coulibaly@etu.u-pec.fr

Olivier Damette
email: olivier.damette@u-pec.fr

Misalignments and Dynamics of Real Exchange Rates in the CFA Franc Zone *

Keywords: CFA zone, misalignments, panel smooth transition model C23, F31, O1

In this paper, we analyse currencies' misalignments of the CFA zone countries and the adjustment process of their real effective exchange rates towards their equilibrium level over the period 1985-2007. To this end, we firstly estimate, using panel cointegration techniques, a long term relationship between the real effective exchange rate and economic fundamentals. Secondly, we estimate a panel smooth transition error correction model in order to take into account non linearities in the convergence process of real exchange rates towards their equilibrium level. Two main results emerge from our analysis. Firstly, the real appreciation of effective exchange rates in the CFA zone countries from the 2000s did not translate, in 2007, into a real overvaluation comparable to that occurring before the devaluation of the CFA franc in 1994. However, some countries are exceptions, indicating a strong heterogeneity within the CFA zone. Finally, the convergence process of real effective exchange rates towards their equilibrium level also differs substantially between country groups. These results tend to show the difficulty to apply a single exchange rate policy in the CFA zone and rather call for further coordination and policy harmonization between the countries.

Introduction

The recent crisis has highlighted the growth of global economic tensions and the slide toward international trade and currency wars; it has also revived the debate on using the exchange rate in order to improve competitiveness and to accelerate the exit from the crisis. For the countries of the CFA 1 Several studies have attempted to address the issue of misalignment's currencies in the Franc CFA zone. The underlying theoretical framework is usually based on equilibrium exchange rates approaches which consist in checking if real exchanges rates are in line with fundamentals, i.e. close to their equilibrium values. At the empirical level, estimates rely, in general, on a reduced form equation of the real effective exchange rate using mostly panel zone, this issue is not a new one: it had already arisen in the first half of the nineties. Indeed, the magnitude of the crisis at that time raised major concerns about the peg of their currencies to the French Franc and finally led them to devalue the CFA Franc. If this devaluation contributed to the recovery of the area, then again questions about competitiviness have raised since the 2000s. In particular, because of its peg to the euro, the CFA Franc has appreciated considerably over the last decade. Between 2000 and 2010, the dollar has lost 43% of its value against the euro, and therefore against the CFA Franc.

Currency appreciation may present a major drawback if it induces a real overvaluation that penalizes external competitiveness. [START_REF] Coudert | Do terms of trade drive real exchange rates? Comparing oil and commodity-currencies[END_REF] show that the anchor currency is not neutral: their estimates of equilibrium exchange rates for the CFA zone economies reveal that the CFA Franc tends to be overvalued in periods when the euro is strong. Now the issue of overvaluation is particularly acute in these economies. Indeed, export sectors often play a key role because of the narrowness of their domestic market, a low diversification of their production and the weakness of their human capital and technological potential. Thus for these countries, growth largely relies on export sectors which are the main source of foreign currency, the main provider of public revenues, and the main sectors attracting FDI [START_REF] Baffes | Single-Equation Estimation of the Equilibrium Real Exchange Rate[END_REF]. Given the current difficulties faced by the area, some consider the peg to the euro as a potential source of overvaluation and the question of a new devaluation is reemerging now. For others, the effects of devaluation are, however, uncertain as the exchange rate policy cannot entirely deal with structural problems faced by the area. 1 The CFA franc zone includes the countries of the West African Economic and Monetary Union (Benin, Burkina Faso, Ivory Coast, Guinea Bissau, Mali, Niger, Senegal, and Togo) and the countries of the Central Africa Economic and Monetary Community (Cameroon, Gabon, Equatorial Guinea, Congo, Central African Republic, and Chad). The appellation CFA franc means: "Communauté Financière Africaine" for the WAEMU members countries and "Coopération Financière en Afrique Centrale" for CAEMC's members countries. data cointegration methods, given the small size of samples. 2 The issue of nonlinearity is particularly relevant to the CFA zone countries. [START_REF] Elbadawi | Theory and Empirics of Real Exchange Rates in Sub-Saharan Africa and Other Developing Countries[END_REF] underline some inertia in the adjustment process of the real exchange rate in the CFA and the RMA (Rand Monetary Area) zones, two monetary unions of Sub-Saharan Africa.

They argue that economies with inflexible exchange rate regimes and rigid labour markets are likely to be characterized by nominal rigidities, which in turn, could dampen their automatic adjustment towards equilibrium. The issue is also crucial to policy-makers of the CFA zone in determining the opportunity and the extent of devaluation. Indeed, we may expect that the Real exchange rate and their fundamentals are found to be cointegrated and have a stable long-run equilibrium relation.

Nevertheless, fewer studies have focused on the short run dynamics of the real exchange rate in the CFA countries, i.e. the convergence process along which the real exchange rate converges to its long-run equilibrium value. Moreover, when this dynamics issue is analyzed, the short run dynamics is assumed to be linear and symmetric [START_REF] Elbadawi | Aid, Real Exchange Rate Misalignment and Economic Performance in Sub-Saharan Africa[END_REF].

However, several works show that the assumption of linearity may be quite restrictive. [START_REF] Flood | Exchange Rate Economics: What's Wrong with the Conventional Macro Approach?[END_REF] suggest that the adjustment to equilibrium may instead depend on the magnitude of the deviation from the equilibrium as well as on changes in underlying economic fundamentals. On the theoretical level, economists have proposed different explanations of nonlinearity in exchange rate dynamics. For example, [START_REF] Dumas | Dynamic Equilibrium and the Real Exchange Rate in a Spatially Separated World[END_REF] explains the non linear adjustment process of exchange rates towards the purchasing power parity (PPP) by the existence of transaction costs in goods and services markets. Behaviours of market and of policy makers can also induce a rapid convergence process of exchange rates towards equilibrium when deviations are large, while exchange rates may not converge or may converge slowly and unstably when deviations are small [START_REF] Taylor | Nonlinear adjustment, long-run equilibrium and exchange rate fundamentals[END_REF]. Most of researches in this area examine nonlinearities in the deviations of exchange rates from an equilibrium level suggested by monetary fundamentals. More recent works [START_REF] Béreau | Nonlinear Adjustment of the Real Exchange Rate Towards its Equilibrium Value: a Panel Smooth Transition Error Correction Modelling[END_REF] apply nonlinear panel models to the short run dynamics of real exchange rates, in a theoretical framework where their equilibrium level is defined by real fundamentals. Following a Behavioural Equilibrium Exchange Rate (BEER) approach, they show that the convergence process of real exchange rates toward their equilibrium level depends on the size of misalignments in emerging economies of the G20 countries.

2 However, some studies use single equations in order to estimate equilibrium exchange rates. See Baffes et al. (1997) in their study of Côte d'Ivoire and Burkina Faso ; [START_REF] Roudet | Estimation of Equilibrium Exchange Rates in the WAEMU: A Robustness Analysis[END_REF] test the robustness of their equilibrium exchanges rates' estimates for the WAEMU countries by using both time series econometrics and panel cointegration techniques. Also, [START_REF] Chudik | In Search of Equilibrium: Estimating Equilibrium Real Exchange Rates in Low-Income African Countries[END_REF] apply both methods on a set of 36 Sub-Saharan Africa countries; they show that the panel method is more robust and leads to better results. more overvaluation's episodes will be persistent and significant, the more a correction of the CFA Franc will be required. This article fits in these researches by addressing the opportunity of a nominal devaluation for the CFA zone. In particular, we investigate the following two questions. Has the appreciation of the CFA franc since the 2000s resulted in an overvalued real exchange rate on a scale comparable to that observed before the 1994 devaluation? How do real effective exchange rates converge toward their equilibrium level? But it distinguishes itself by several ways. Firstly, we use the most recent panel data unit roots and cointegration techniques to study the relationship between real effective exchange rates and their economic fundamentals. All previous studies rest upon first generation unit roots and cointegration tests that assume cross sectional independence among panel units. But, given several specificities shared by the CFA countries (peg to the same anchor currency, strong exposure to shocks), we also run second generation unit root and cointegration tests that relax the assumption of cross sectional independence as well as unit root tests that enable to accommodate structural breaks. Finally, we apply a Panel Smooth Transition Regression (PSTR) model, as proposed by González et al. (2005), to the short-run dynamics of real effective exchange rates. In particular, we follow the approach developed by Lopez-Villavicencio and Mignon (2010) and [START_REF] Béreau | Nonlinear Adjustment of the Real Exchange Rate Towards its Equilibrium Value: a Panel Smooth Transition Error Correction Modelling[END_REF] in order to check if the convergence process of real exchange rates acts differently when misalignments are in different regimes.

Our results firstly demonstrate that the real appreciation of effective exchange rates in CFA zone countries from the 2000s did not translate, in 2007, into a real overvaluation comparable to that occurring before the devaluation of the CFA Franc in 1994. However, there are country-specific exceptions, indicating a strong heterogeneity within the CFA zone. Secondly, our estimates support the idea that the convergence process of real effective exchange rates towards their equilibrium level also differs substantially between country groups. Indeed, only the WAEMU countries seem to be prone to persistent overvaluation.

The remaining of the article is organized as follow: section 2 outlines the theoretical framework and provides a brief literature review on equilibrium exchange rates approaches in developing economies. Section 3 presents the methodology used in order to estimate equilibrium exchange rates and displays misalignments results. Section 4 discusses the process of convergence of real effective exchange rates to their equilibrium value. Section 5 concludes and draws some policy implications for the CFA zone countries.

Equilibrium exchange rates in CFA zone countries

Among the models of real equilibrium exchange rate (REER thereafter), some deal more specifically with the dynamics of the real exchange rate in developing economies [START_REF] Edwards | Real and monetary determinants of real exchange rate behavior: Theory and evidence from developing countries[END_REF][START_REF] Elbadawi | Estimating Long Run Real Exchange Rates[END_REF][START_REF] Hinkle | Exchange Rate Misalignment: Concepts and Measurement for Developing Countries[END_REF]. These models highlight the role played by a number of fundamentals in determining equilibrium exchange rates, following models of industrialized economies. In particular, from these theoretical models, a reduced equation of real exchange rate can be derived, in conformity with the so-called Behavioral Equilibrium Exchange Rate (BEER) approach. These models, since they take into account several specificities of developing economies, generally include some fundamentals that are usually omitted in the determination of equilibrium exchange rates of industrialized countries and emerging economies.

Theoretical background

Most models consider a small open economy with two sectors (tradables and non-tradables) in which the REER is the internal real exchange rate that ensures both internal and external balances 3 ( ) ( )

0 , 0 , 1 , < ∂ ∂ < ∂ ∂ + - = + = ξ θ ξ N N N N N N y q y g qc g c q y
(see for example [START_REF] Montiel | Determinants of the Long-Run Equilibrium Real Exchange Rate: An Analytical Model[END_REF]. Internal balance holds when markets for labour and non-traded goods clear:

(1)

With q the internal real exchange rate defined by the domestic price of tradables in terms of domestic price of non-tradables goods 4 N y , , the supply of non-tradables consistent with full employment ; c , total private consumption measured in terms of tradables goods ; θ , the share of spending on traded goods ; N g , government spending on non-tradables, and ξ , a productivity shock in favour of the tradable sector.

The external balance is defined, in turn, by the long term condition of external sustainability, i.e. the steady equilibrium value of the net external position:

( ) ( ) 0 , 0 , 0 , > ∂ ∂ > ∂ ∂ = + + + - - = + + = ξ φ θ ξ T T T T y q y rf z c g q y rf z b f  (2)
3 Knowing that the exogenous variables have reached their equilibrium values and that economic policies are sustainable. 4 An increase in stands for a real depreciation.

With f , the net foreign asset ; b , the trade balance ; z , net transfers, measured in prices of tradables goods ; φ , transaction costs associated with private spending on long-term determined by the foreign inflation rate, w π ; r , real interest earned on the net external position.

The REER, * q , corresponds to the internal real exchange rate leading to the simultaneous achievement of internal balance (1) and external balance (2):

            + = - ξ π , , , , * * * * W T N z f r g g q q
(3) With * denoting long run equilibrium value

What determinants of the real equilibrium exchange rate in CFA zone?

From the previous model, several factors explaining the long-run equilibrium level of the real exchange rate can be derived: the productivity differential in favour of the tradable sector, public expenditure on non-tradable and tradable goods, the foreign inflation rate, international transfers or the real interest earned on net foreign balance.

The productivity differential in favour of tradable goods refers to the "Balassa-Samuelson" effect. Increased productivity in the tradable sector leads to higher wages in this sector (to maintain equality with international prices). This induces a rise in relative prices in the nontradable sector, where productivity has not increased, and an appreciation of the REER.

Usually models specified for developing economies [START_REF] Edwards | Real and monetary determinants of real exchange rate behavior: Theory and evidence from developing countries[END_REF][START_REF] Elbadawi | Estimating Long Run Real Exchange Rates[END_REF] and for the CFA zone countries [START_REF] Baffes | Single-Equation Estimation of the Equilibrium Real Exchange Rate[END_REF][START_REF] Roudet | Estimation of Equilibrium Exchange Rates in the WAEMU: A Robustness Analysis[END_REF] consider public spending as an another factor affecting equilibrium exchange rates. However, its impact is ambiguous since it depends on its distribution between tradables and non-tradables. An increase in public expenditure in non-tradables induces an excess demand in that market and must be offset by an appreciation of the REER. Conversely, higher public spending in the tradable sector leads to a deterioration in the trade balance: a depreciation of the REER is therefore necessary to restore external balance. Capital inflows (interest earned on the investment position, international transfers), as that they can relax the constraint on trade in goods and services, lead to an appreciation of the REER. Generally, in the case of developed economies, capital flows are approximated by the net external position. However, alternative variables that could also account for these flows5 can be found in studies relative to the CFA zone countries. For example, Dufrenot and Yehoue (2005) take into account in their estimates of real equilibrium exchange rate equilibrium, for a sample of 64 developing countries, the net income from abroad and official development assistance. [START_REF] Aydin | Exchange Rate Assessment for Sub-Saharan Economies[END_REF] takes as determinants of capital flows in Sub-Saharan economies, the net external position, the official development assistance and private transfers measured by remittances from workers. Other studies seek to estimate a current account equilibrium balance. [START_REF] Elbadawi | Estimating Long Run Real Exchange Rates[END_REF]Soto (2005, 2008) estimate the sustainable level of current account by regressing from panel data imports over exports, the official development assistance, the debt service, and the change in external debt. [START_REF] Baffes | Single-Equation Estimation of the Equilibrium Real Exchange Rate[END_REF], in turn, measure the external balance, by taking into account the limited access of developing economies to international financial markets. In their framework, the external equilibrium is approximated by the trade balance in volume and adjusted from the terms of trade.

The previous model can be extended to three sectors, with tradables splitted between exported and imported goods. The relevant real exchange rate is no more the internal real exchange rate but instead the external real exchange rate which measures the price competitiveness of the domestic economy vis-à-vis its trade partners. With this extension other explanatory variables of equilibrium exchange rates which are particularly relevant for CFA zone countries can been highlighted as trade policy and terms of trade [START_REF] Baffes | Single-Equation Estimation of the Equilibrium Real Exchange Rate[END_REF][START_REF] Edwards | Real and monetary determinants of real exchange rate behavior: Theory and evidence from developing countries[END_REF][START_REF] Elbadawi | Estimating Long Run Real Exchange Rates[END_REF]. The effect of trade liberalization (reduction of import tariffs or export subsidies) depreciates the real exchange rate equilibrium in the long term. The impact of the terms of trade is ambiguous since they exert different effects on the REER. Thus, a rise in exportable goods price has a positive income effect, which combined with a substitution effect in supply, causes an appreciation of the REER. However, consumers can be encouraged to substitute their consumption basket in the non-traded goods by imported goods which become cheaper. This substitution effect from the demand side results in a depreciation of the REER. A simplifying assumption usually made is to assume that the income effect dominates the substitution effect from the demand side or that commodities are entirely exported. Under these hypotheses, the impact of commodities prices on domestic demand can be omitted [START_REF] De Gregorio | Terms of trade, productivity and the real exchange rate[END_REF] and an improvement in the terms of trade leads to an appreciation of the REER.

Estimation of real equilibrium exchange rates

To estimate the equilibrium exchange rates of CFA countries, we use -like most of studies developed in this area -the BEER approach. In this framework, the REER is the solution of a long run relationship between real exchange rate and economic fundamentals as specified by the following equation:

(4)
Where subscripts i and t represent respectively country and time indexes,

Data

Our study covers 13 countries of the CFA zone: Benin, Burkina Faso, Ivory Coast, Guinea Bissau, Mali, Niger, Senegal, Togo, Cameroon, Gabon, Equatorial Guinea, Congo, Central African Republic, and Chad. 7 The data are annual and cover the period from 1985 to 2007. Real effective exchange rates are calculated using real bilateral exchange rates of the top ten trading partners of each country 8 6 For developing and emerging economies, it is generally more convenient to use the BEER approach for estimating equilibrium exchange rates. The FEER approach requires to estimate trade elasticity's and to calculate the potential output of the various countries concerned, which is often made difficult by the lack of data availability. Therefore, apart from some studies of the International Monetary Fund (Aydın, 2010; [START_REF] Abdih | FEER for the CFA franc[END_REF], most studies on CFA countries rely on the BEER approach. 7 Guinea Bissau is not taken into account insofar as it is a member of WAEMU since 1997. 8 See Appendix, Table A.

, weighted by their share in foreign trade of the country over the period 1999-2007. Bilateral exchange rates are extracted from the database World Development Indicators (WDI) of the World Bank while shares of partners' countries are calculated using data of the Direction of Trade Statistics (International Monetary Fund).

Terms of trade are calculated in a similar fashion to that developed by [START_REF] Cashin | Commodity Currencies and the Real Exchange Rate[END_REF] and employed by [START_REF] Coudert | Do terms of trade drive real exchange rates? Comparing oil and commodity-currencies[END_REF]. They are defined as a weighting price of the three main export commodities for each country, deflated by the price index of manufactured exports of OECD countries. Commodities prices are extracted from the database International Financial Statistics of the International Monetary Fund. Weights are calculated over the period 2005-2007 and are derived from commodity trade flows available from the International Trade Center9 . For oil exporters, the terms of trade reflect only oil prices, deflated by the same foreign index price. The Balassa effect is measured by relative living standards (PPP GDP per capita), which are considered as a proxy for relative productivity differences between sectors. PPP GDP per capita data are taken from the World Bank's World Development Indicators (WDI) database; Calculations for weights are identical to those used for real effective exchange rates. Finally, the openness rate is measured by the share of imports and exports in GDP. Import and export data is obtained from the database WDI as well as public spending data. Net external positions come from the database developed by Lane and Milesi-Ferretti (2007). 10In order to analyse the time properties of the variables, we mobilize several unit root tests

Estimating the long run relationship

We determine first the order of integration of each variable and then test the existence of a cointegration relationship by applying non-stationary panel methods. Indeed, the use of panel data has the distinct advantage of allowing working with small sample size in the temporal dimension -as is often the case in African countries -and thus to overcome the classic problem of low power tests in small sample. 11 and in particular the so-called second (2 nd ) and third (3 rd ) generation tests. These latter tests present the advantage of taking into account, respectively, the dependence between countries and the presence of break points in the stochastic process of the series. We justify this choice by several specificities shared by the countries of our sample. Indeed, the strong correlation between real effective exchange rates, explained by their peg to the same anchor currency, means that the inter-individual independence assumption underlying the first generation tests may be no relevant. 12 3rd generation tests are then mobilized to check the existence of structural breaks. We only consider unit root tests that have the best properties in finite samples i.e. that remain relatively strong with a limited number of observations: 1rst generation tests of [START_REF] Im | Testing for Unit Roots in Heterogeneous Panels[END_REF] and Madalla and Wu (1999); 2 nd generation tests of [START_REF] Pesaran | A simple panel unit root test in the presence of cross-section dependence[END_REF] and [START_REF] Choi | Combination Unit Root Tests for Cross-Sectionally Correlated Panels[END_REF], and the 3 rd generation test developed by [START_REF] Carrion-I | Breaking the panels: An application to GDP per capita[END_REF] which takes into account both interindividual dependence and the existence of structural breaks. From an econometric point of view, 2 nd generation panel unit root tests account for cross sectional dependence by assuming a common factor representation:

it t i it F x µ λ + ′ =
where t F is a vector of unobserved common factors. In this general specification, the number of factor is supposed to be unknown. i λ ′ is a vector of factor's coefficients by country, i.e. the country specific sensitivity to the common components. it µ is the idiosyncratic error term. Particularly, the tests of [START_REF] Choi | Combination Unit Root Tests for Cross-Sectionally Correlated Panels[END_REF] and [START_REF] Pesaran | A simple panel unit root test in the presence of cross-section dependence[END_REF] assume that there is one common factor. Choi's test supposes that countries have the same sensibility to the common factor ( λ λ = i ) while Pesaran's test suggests that countries can react differently to the common component ( [START_REF] Hadri | Testing for Unit Roots in Heterogeneous Panel Data[END_REF] test in panel) for the case of multiple structural breaks. Thus this test allows the presence of multiple breaks (the number of break is unknown) under the null hypothesis of stationarity and does not impose the independence of cross section in the errors terms through boostraping. Table 1 summarizes the results of these different tests.

i i λ λ = while 1 = i à 13 ).
Overall, first-generation unit root tests indicate that that all variables are integrated of order one. Tests of 2 nd and 3 rd generations lead to the same conclusions, except the degree of openness which appears to be stationary. 13CFA zone. In these studies, as only first generation tests are used, the degree of openness is found I(1) and then appeared as an explanatory variable in the long run relationship [START_REF] Roudet | Estimation of Equilibrium Exchange Rates in the WAEMU: A Robustness Analysis[END_REF]Dufrenot and Yehoue, 2005;Abdih and Tsangarides, 2006, etc..) We then consider in the long run relationship the only variables that share the same order of integration with the real effective exchange rate: the terms of trade, productivity shocks, the net foreign asset position and public expenditure. The existence of a cointegration relationship is tested by using firstly the now well-known [START_REF] Pedroni | Critical values for cointegration tests in heterogeneous panels with multiple regressors[END_REF][START_REF] Pedroni | Panel cointegration. Asymptotic and finite sample properties of pooled time series tests with an application to the PPP hypothesis[END_REF] tests and the recent [START_REF] Westerlund | Testing for Error Correction in Panel Data[END_REF][START_REF] Westerlund | Panel cointegration tests of the Fisher effect[END_REF] tests. These tests are similar to Engle and Granger (1987)'s test in the time series context and lead to a unit root test on the residues of the cointegration model. [START_REF] Pedroni | Critical values for cointegration tests in heterogeneous panels with multiple regressors[END_REF][START_REF] Pedroni | Panel cointegration. Asymptotic and finite sample properties of pooled time series tests with an application to the PPP hypothesis[END_REF] proposes seven statistics to test the null hypothesis of no cointegration.

But the alternative hypothesis depends on the dimension considered. The within dimension implies that the cointegration vector is homogeneous across countries while the between dimension supposes that the vector is heterogeneous across countries. Thus, the four "within dimension" statistics (panel statistics) are more restrictive than the three "between dimension" statistics (group statistics). Pedroni's statistics are reported in the table 2 below. Globally, they lead to reject the null hypothesis of no cointegration. Since we find evidence of crosssectionally correlation among our variables, we then run the cointegration tests developed by [START_REF] Westerlund | Panel cointegration tests of the Fisher effect[END_REF] and [START_REF] Westerlund | A panel bootstrap cointegration test[END_REF]. The Westerlund cointegration test (2008), based on the Durbin-Hausman principle, is very similar to the panel unit root test with 14 However, it is possible that the degree of openness has a short-term effect on the real exchange rate. In other words, the degree of openness may influence the dynamics of exchange rate but not its equilibrium level. 15 Results still hold with alternative specifications.

common factors. It consists here in estimating a common component from the regression errors of the equation ( 5) and then deriving the test on the residual idiosyncratic component.

As [START_REF] Westerlund | Panel cointegration tests of the Fisher effect[END_REF] explains, because the test is constructed under the assumption of a unit root in the idiosyncratic errors, the null hypothesis is the absence of cointegration, while the alternative is that there are at least some countries for which there is a cointegrated relationship. The Westerlund and Edgerton test (2007) After having demonstrated the existence of a long run relationship, we finally estimate the cointegrating vector between real effective exchange rates and macroeconomic fundamentals.

To this end, we implement the estimator Dynamic Ordinary Least Squares (DOLS) in panel data developed by Kao and Chiang (2000) and [START_REF] Mark | Cointegration Vector Estimation by Panel DOLS and Longrun Money Demand[END_REF] as it outperforms both the OLS and fully modified OLS estimators. Indeed, although the OLS estimator of the cointegrating vector is super-convergent, the distribution of coefficients is asymptotically biased and depends on nuisance parameters associated with the presence of unit roots. Thus, usual tests are not valid and OLS is not optimal for inference. In addition, Kao and Chiang (2000) show that in finite sample size distortions from the DOLS estimator are lower than those of OLS and FMOLS and that DOLS performs well in cointegrated panels. Compared to these latest estimators which suppose homogeneous coefficients in both short and long runs, the DOLS approach also presents the advantage to consider heterogeneous coefficients in the short run, while being homogeneous in the long run. According to several papers, this seems to be more pertinent in the context of equilibrium exchange rate studies (see Lopez-Vallavicencio, 2006).

Neglecting leads and lags, the results of the estimation are summarized by the following equation: (5)

( ) ( ) ( ) ( )
The coefficients are statistically significant 16 16 Values in brackets are the associated t statistics.

and their signs are consistent from what is expected, meaning that the theoretical model is relevant for the countries of our sample. In particular, an increase of the terms of trade leads to an appreciation of the equilibrium exchange rate, suggesting that the substitution effect is lower than the income effect in the CFA zone. Our estimated value is similar to the one of [START_REF] Elbadawi | Aid, Real Exchange Rate Misalignment and Economic Performance in Sub-Saharan Africa[END_REF]. A rise in government spending implies an appreciation of the equilibrium exchange rate. This result is consistent with the empirical literature on CFA and others developing countries that usually finds that government spending is dominated by non-tradable goods. The estimated coefficient is lower, compared to other studies, but is similar in magnitude to the one found by [START_REF] Mongardini | Grants, Remittances, and the Equilibrium Real Exchange Rate in Sub Saharan African Countries[END_REF]. Our results also confirm the existence of the Balassa-Samuelson effect in the CFA zone since an increase of the productivity gap between tradable and non-tradable goods implies an appreciation of the equilibrium exchange rate. Finally, an improvement of the net foreign position also leads the equilibrium exchange rate to appreciate, but its estimated coefficient is small which is also in accordance with most previous findings (see Aydın, 2010;[START_REF] Elbadawi | Aid, Real Exchange Rate Misalignment and Economic Performance in Sub-Saharan Africa[END_REF][START_REF] Mongardini | Grants, Remittances, and the Equilibrium Real Exchange Rate in Sub Saharan African Countries[END_REF]etc...).

Misalignments

The equilibrium value of the real exchange rate is derived from the estimated cointegration relationship summarized by equation ( 5). In most cases, it is calculated by taking into account the permanent component (estimated using a Hodrick-Prescott filter) of fundamentals. The permanent component, insofar as it is supposed to capture the sustainable level of fundamentals, seems to be more consistent with the concept of equilibrium exchange rates.

Then misalignments can be deduced from the difference between the observed values of real effective exchange rates and their equilibrium values. However, as pointed out by Elbadawi et al. (2008), this method to calculate misalignments, when the latter are estimated in panel data, can lead to permanent distortions (under or overvaluation) of the real exchange rate. 17

For the whole CFA zone, the misalignments observed in 1993 and 2007 lead to mixed results.

Only some countries experience in 2007 an overvaluation higher than the one observed before the devaluation of the CFA Franc. Moreover, there is no clear distinction between the two monetary unions of the zone: the Central Africa Economic and Monetary Community Therefore, these authors propose an alternative method that has the advantage to overcome this problem and thus avoid misspecifications of misalignments. This method consists in constraining to zero the expected misalignment of each country over the sample period; in order words, this method assumes that the real exchange rate adjusts always, more or less rapidly, towards its equilibrium value, in accordance to the concept of cointegration and misalignment. In this paper, we choose this method in order to assess misalignments.

Figure 1 reports the percentage of misalignments in 2007 and 1993 (before the devaluation of the CFA Franc) for comparison. Figures A1 andA2 in Appendix display respectively the evolution of real effective exchange rates (observed and equilibrium) and of misalignments over the sample period and for the 13 considered countries of the CFA zone. 17 We encountered the same problem when we calculated misalignments of the countries in our sample. These countries are also included in the study by Elbadawi et al. (2008). For more details, cf. the paper of these authors.

(CAEMC) and the West African Economic and Monetary Union (WAEMU). [START_REF] Abdih | FEER for the CFA franc[END_REF] calculate confidence intervals for real exchange rates of the CAEMC and WAEMU countries and conclude that they were close to their equilibrium values in 2005. Our results suggest the same conclusion, with values slightly higher: the simple mean (i.e. non weighted) of misalignments is respectively 8% for the CAEMC, 3% for the WAEMU and 5% for the whole CFA.

WAEMU CAEMC

Note: A positive (resp. negative) corresponds to an overvaluation (resp. undervaluation)

Among the CAEMC countries, which are oil exporters, only Equatorial Guinea, Congo and Central African Republic are characterized, in 2007, by an overvaluation of their currencies higher than in 1993. Except Central African Republic which is non-oil exporter, the CAEMC economies have benefited from an improvement of their terms of trade from the 2000s that allows them to record a stable or an appreciation of their equilibrium exchange rates (Appendix, Figure A1). Overall, even if those countries have seen their real exchange rate appreciating since the 2000s, the appreciation has been moderate for Cameroon, Gabon and Chad. So this explains why misalignments of their currencies exhibit in 2007 a rather low magnitude. The WAEMU countries are, for their part, mainly exporters of agricultural commodities (cotton, coffee or cocoa). Three of these economies (Benin, Ivory Coast and Togo) suffer from a continued depreciation of their REER that results in 2007 by a real overvaluation of their currencies on a scale comparable to or well above that ones found in 1993. The other countries have benefited, like CAEMC members, from an improvement or a stability of their REER. Combined with a moderate real appreciation, this has resulted in a low real undervaluation of their currencies in 2007. In total, the real appreciation of currencies observed in the CFA zone countries from the 2000s does not seem to have translated in 2007 by a real overvaluation, on a scale comparable to that occurring before the devaluation of the CFA franc in 1994. In 2007, currencies are characterized by rather small misalignments.

However, this movement is not general: some countries (Ivory Coast, Central African Republic and to a lesser extent Chad and Togo) undergo significant overvaluation in 2007 compared to 1993. These results are close to those found by previous studies that reveal also a real overvaluation for the four countries mentioned above (Ivory Coast, Central African Republic, Chad and Togo). On the other side, currencies of Burkina Faso, Mali and Senegal are found to be clearly undervalued. The rest of the CFA countries record mixed situations depending on the studies. 18 Despite several articles devoted to currency's misalignments in Sub-Saharan Africa, very few analyze the convergence process of the real exchange rate toward its equilibrium level, i.e. its short term dynamics.

(see [START_REF] Chudik | In Search of Equilibrium: Estimating Equilibrium Real Exchange Rates in Low-Income African Countries[END_REF][START_REF] Mongardini | Grants, Remittances, and the Equilibrium Real Exchange Rate in Sub Saharan African Countries[END_REF][START_REF] Roudet | Estimation of Equilibrium Exchange Rates in the WAEMU: A Robustness Analysis[END_REF][START_REF] Elbadawi | Aid, Real Exchange Rate Misalignment and Economic Performance in Sub-Saharan Africa[END_REF]. Finally, the assessment of misalignments reveals a strong heterogeneity and the lack of a convergence process between the CFA zone countries.

The adjustment process of real effective exchange rates to their equilibrium value

19 18 Congo's misalignment is not reported in the quotes papers. The reader can refer to the paper of Francis (2009).

Niger is only studied in [START_REF] Roudet | Estimation of Equilibrium Exchange Rates in the WAEMU: A Robustness Analysis[END_REF]. 19 To our knowledge only [START_REF] Elbadawi | Theory and Empirics of Real Exchange Rates in Sub-Saharan Africa and Other Developing Countries[END_REF], through the Pooled Mean Group estimator (PMG) of Pesaran (1999), have tried to interpret the short-run dynamics of exchange rates in SSA.

To take into account this dynamic adjustment, we estimate a panelbased vector error correction model (VECM). The classical VECM, that we firstly estimate, suppose that the adjustment process is linear and with a constant rate. These assumptions seem however too restrictive. Indeed, several theoretical arguments, which are particularly relevant for the CFA zone countries, can justify the nonlinear dynamics of real exchange rates: changes in economic policy regime, the behaviour of some macroeconomic variables that do not necessarily react instantaneously to macroeconomic fluctuations (e.g., price rigidity), the presence of macroeconomic shocks such as terms of trade shocks. Moreover, evidence of nonlinearities can be observed in the evolution of real effective exchange rates of our sample. Indeed, they are characterized by persistent distortions from their equilibrium value (see Appendix, Figure A2). In order to take into account potential asymmetries, persistence and nonlinearities in the dynamics of real exchange rates in the CFA Franc zone, we also estimate a nonlinear panel-based VECM following the approach developed by Lopez-Villavicencio and Mignon (2010), [START_REF] Béreau | Nonlinear Adjustment of the Real Exchange Rate Towards its Equilibrium Value: a Panel Smooth Transition Error Correction Modelling[END_REF].

The linear dynamics of real exchange rates

We consider a linear Error Correction Model (ECM) described by the following equation:

it it it it it it i it NFA LDEP LPROD LTOT MES LTCER ε λ λ λ λ θ α + ∆ + ∆ + ∆ + ∆ + + = ∆ - 4 3 2 1 1 (6)
With ∆ , the difference operator and 1 -it MES , the lagged value of the misalignment.

We first test the endogeneity of the variation of REER by estimating equation ( 6), in dynamic form by the method of instrumental variables (MVI) and the generalized method of moments (GMM). Given the small individual size of the panel (13 countries), estimation results from GMM are not retained. As the coefficient associated with the lagged value of the endogenous variable is not significant, we use the within estimator to estimate the linear VECM.

The coefficients of equation ( 6) are estimated using the panel OLS estimator 20 20 The model was also estimated by one-step method of Pesaran (Pooled Mean Group). The results, available upon request, are very similar, except the coefficient associated with public spending.

for the whole CFA zone and for each monetary union of the zone (WAEMU and CAEMC). Results are reported in Table 3. They show that in the short term, an improvement of terms of trade leads to a depreciation of the real effective exchange rate (about 11% for a 1% increase). An increase of 1% of public expenditure and of 1 point of the net foreign position induces an appreciation of respectively 6% and 13% of the real effective exchange rate. Regarding productivity differentials, they exert no significant impact. Moreover, the estimated average adjustment parameter is -0.26 for the whole CFA zone. This value is close to -0.20 obtained by [START_REF] Elbadawi | Aid, Real Exchange Rate Misalignment and Economic Performance in Sub-Saharan Africa[END_REF] who estimate an error-correction for a world panel comprised by annual data for 83 countries for 1980-2004, including 36 Sub Saharan African economies.

Considering only Sub Saharan African countries, [START_REF] Mongardini | Grants, Remittances, and the Equilibrium Real Exchange Rate in Sub Saharan African Countries[END_REF] find error correction parameters between -0.28 and -0.17, which is also in line with our estimations.

These estimated coefficients values suggest that, overall, real effective exchange rates converge relatively slowly toward their equilibrium levels, suggesting some inertia in their adjustment process. Some difference in the adjustment process between the WAEMU and the CAEMC economies can be highlighted. The estimated error correction parameter for the WAEMU (-0.23) is lower than the one found for the CAEMC (-0.29). Thus, real effective exchange rates converge to their equilibrium value more quickly in the CAEMC than in the WAEMU. This result is supported by most of previous studies on this area. For example, [START_REF] Elbadawi | Theory and Empirics of Real Exchange Rates in Sub-Saharan Africa and Other Developing Countries[END_REF] report the estimated error correction term of five WAEMU and two CAEMC countries 21 and show that the mean adjustment parameter of the WAEMU (-0.13) is lower than one of the CAEMC (-0.23). This difference could be explained by specific features: smaller and less rigid economies of the CFA zone, like Chad, adjust relatively faster than others, such as Ivory Coast (see [START_REF] Elbadawi | Theory and Empirics of Real Exchange Rates in Sub-Saharan Africa and Other Developing Countries[END_REF][START_REF] Elbadawi | Real Exchange Rate Regimes and Macroeconomic Adjustment in Sub-Saharan Africa and Other Developing Countries[END_REF][START_REF] Baffes | Single-Equation Estimation of the Equilibrium Real Exchange Rate[END_REF]. [START_REF] Mongardini | Grants, Remittances, and the Equilibrium Real Exchange Rate in Sub Saharan African Countries[END_REF] also highlight that the adjustment process is faster in oil exporters than in non oil countries. This could then explain the observed difference between the two zones as the CAEMC countries are mainly oil exporters unlike the WAEMU countries. 22

21 Burkina Faso, Bissau Guinea, Ivory Coast, Senegal and Togo for the WAEMU; Gabon and Chad for the CAEMC. However, the means reported here exclude Ivory Coast and Togo. Indeed, Ivory Coast has a positive adjustment parameter 0.09 and Togo, according to the authors, has a very high implausible adjustment parameter -0.83. Moreover, [START_REF] Roudet | Estimation of Equilibrium Exchange Rates in the WAEMU: A Robustness Analysis[END_REF] find the same value (-0.13) for all WAEMU economies by using Johansen time series method. 22 Only the study of [START_REF] Abdih | FEER for the CFA franc[END_REF] leads to an opposite conclusion. Using time series method, the authors find that the adjustment path of the real exchange rate to its equilibrium value is faster in the WAEMU than in the CAEMC. Their results show that the half of shocks on real exchange rate is absorbed in the WAEMU in 3 years while 7 years is required in the CAEMC.

Nonlinear dynamic adjustment

As previously noted, in the CFA zone countries, real exchange rates show some inertia in the convergence process to their long-run values. However, this result has been found, assuming that this convergence process was linear. In order to investigate more deeply this issue, we now check if the hypothesis of linearity is relevant for the CFA zone countries and more particularly if the dynamics of real exchange rates in these countries varies according to the nature of misalignments. To capture this potential non linearity, we develop a Panel Smooth

Transition Regression (PSTR) model (González et al., 2005) which allows the dynamics of real exchange rates to vary from one regime to another, depending on the value (threshold) of a transition variable, identified here by misalignments. 23 In these models, the transition from one regime to another is smooth or gradual because of some inertia (due to transaction costs, to uncertainty or rigidity). 24

( )

it it it it i it c MES g x x LTCER ε γ β β α + ′ + ′ + = ∆ - , , 1 1 0
We then apply this specification to equation ( 6) of the previous section. In the context of two regimes, the model can be described as follows: (  )

1 1 1 1 exp 1 , , - = - -               - - + = ∏ m j j it it c MES c MES g γ γ ( 8
)
23 While the transition variable can be chosen among several variables (see [START_REF] Béreau | Nonlinear Adjustment of the Real Exchange Rate Towards its Equilibrium Value: a Panel Smooth Transition Error Correction Modelling[END_REF][START_REF] Aydin | Exchange Rate Assessment for Sub-Saharan Economies[END_REF], it can also be chosen in accordance with economic theory. Currency's misalignment is considered here as the transition variable as we can expect that the adjustment process of the real exchange rate towards its equilibrium value depends on the amplitude of the misalignment 24 Instead of a Panel Transition Regression (PTR) model. These models, introduced by [START_REF] Hansen | Threshold effects in non dynamic panels: Estimation, testing and inference[END_REF], have the same features of PSTR models but allow the regression coefficients to change suddenly or abruptly when moving from one regime to another. ( )

This function is a continuous function of the transition variable

0 1 0 SSR SSR SSR TN LM - =
with 0 SSR is the sum of squared residuals of the model with fixed effects and 1 SSR is the sum of squared residuals of the alternative equation (PSTR model with two regimes). However, the authors derive a Fisher LM-test which has better 25 Thus, when γ tends to infinity, the transition function collapses to an indicator function and the PSTR model corresponds to a PTR model from [START_REF] Hansen | Threshold effects in non dynamic panels: Estimation, testing and inference[END_REF] described by an abrupt change from one regime to one other.

When γ tends to zero, the transition function g becomes constant and the model reduces to a usual panel linear regression model with fixed effects and homogenous coefficients. When γ is in the interval ] [ 0, ∞ , the function, the slope coefficient is a weighted average of 0 β and 1 β and the coefficients may be not directly interpretable.

properties in finite sample and is asymptotically distributed as a ( ) ( )

1 , + - - k m N TN mk F : ( ) ( ) mK N TN SSR mK SSR SSR LM - - - = 0 1 0
. Results of the Fisher LM-test are reported in table 4. They show that the hypothesis of homogeneity is rejected for the variable misalignment and evidence a two-regime model (

1 = r
).

Next we have to determine the order m of the logistic function. Following Granger and Teräsvirta (1993)'s and Teräsvirta (1994)'s methodology, Gonzảlez et al. (2005) proposed a sequential test for choosing between

1 = m or 2 = m
. We apply this test to the equation ( 9) below, considering also the case ) for all samples considered 26

[ ] (

) However, considering the small time dimension of panel studies, this test is not very relevant (see Gonzảlez et al., 2005). The second test allows checking if some nonlinearity, which is not taken into account in the estimated model, remains. This test also permits to choose the adequate value of the parameter r (the number of regimes). There again, the process of choosing the value of r is sequential. Firstly, we compare the one regime model (homogeneous model, ). Results of this test are reported in the table 4 below. They show that the null hypothesis of

it it it it it it it it it it it it i it c MES g NFA LDEP LPROD LTOT MES NFA LDEP LPROD LTOT MES LTCER ε γ λ λ λ λ θ λ λ λ λ θ α + ∆ + ∆ + ∆ + ∆ + + ∆ + ∆ + ∆ + ∆ + + = ∆ - - - , ,
1 = r
is accepted for all samples, since the associated probabilities are higher than 5%. Table 5 reports the values of key parameters from the estimation: the error correction term, the threshold value and the speed of adjustment. For the CFA zone, the estimated threshold value is 0.03 and identifies the two following regimes: a first regime corresponding to undervalued real exchanges rates and also real exchange rates for which overvaluation is below the threshold of 3%; This regime is distinct from the second one where real overvaluation is more than 3%. But, our findings suggest a strong symmetry in terms of adjustment between these two regimes as the estimated correction terms are fairly close (-0.29 against -0.28). Thus, when real exchange rates are undervalued or overvalued, there is a similar convergence process towards the equilibrium level. While real exchange rates' adjustment is comparable between the two regimes in the overall CFA zone, results for the two specific areas (CAEMC and WAEMU) reveal strong differences. The dynamics of real exchange rates in the CAEMC countries is characterised by the same two regimes as in the CFA zone: a first regime corresponding to undervalued exchange rates (misalignment below the threshold of 2%) and a second regime of overvalued exchange rates (misalignment above 2%). Nevertheless, for this area, the estimated error correction coefficients show that the adjustment is increasing slightly in the second regime (overvaluation). Thus, when the real exchange rate is above the threshold (overvalued), there is a convergence process towards the equilibrium level, while in case of undervaluation, the adjustment process, while being effective, seems to be slower. This result highlights the asymmetric property of real exchange rates' adjustment towards their equilibrium level and may reflect that the misalignment of the real exchange rate is not neutral on the degree of pass-trough from nominal exchange rate to inflation. For the WAEMU zone, the threshold is much lower (-13%). Moreover, the results show a stronger asymmetry for these countries as the correction term is much lower in the second regime (overvaluation regime) than in the first one (undervaluation regime). In other words, only real exchanges rates undervalued more than 13% converge towards their equilibrium level; otherwise, they do adjust but very slowly.

The low threshold value can be explained by the fact that, in some countries of the WAEMU (Burkina Faso, Mali, Niger and Senegal) real exchange rates have not converged towards their equilibrium value but have recorded instead a stable and rather slight undervaluation, since the CFA Franc's devaluation of 1994 (Appendix, Figure A2). Finally, the adjustment parameter is lower in the WAEMU (-0.18) than in the CAEMC (-0.37) as in the linear case.

Indeed, real exchange rates of the CAEMC countries converge to their equilibrium exchange rates in both regimes. On the contrary, in the WAEMU zone, real exchange rates, while converging more quickly than in the CAEMC countries in case of undervaluation, are strongly rigid when they are overvalued. Theoretically this feature of the WEAMU countries could be explained by the existence of hysteresis effects (in trade and/or in labour market, inter alia) induced by overvalued exchange rates which impede the adjustment path of fundamentals towards their equilibrium level. Moreover, as currencies are pegged, external imbalances must be corrected by internal adjustment which can be more difficult than a flexible exchange rate adjustment. In particular, the speed with which domestic prices can adjust downward in case of overvaluation (and the degree to which they do) may be a critical factor in the WAEMU zone. The discrepancies between the two zones can be observed from Figure A3 in Appendix in which the transition function is plotted against the value of the gap between misalignment and the threshold parameter. Clearly, results show that the slope parameter is higher in the CAEMC countries than in the WAEMU countries, suggesting that the former react more rapidly to an overvaluation and are also able to correct it more quickly.

On the contrary the transition from the overvaluation regime to the undervaluation tends to be smoother in the CAEMC zone.

Conclusion

The real appreciation observed in currencies of the CFA zone over the last decade has reopened the discussion on the opportunity of a new devaluation of the CFA Franc. This issue has also come in a world context of currency tensions induced by the recent crisis. To investigate this issue, we have analysed and assessed currency's misalignments of 13 CFA zone countries and the convergence process of their real effective exchange rates to their equilibrium levels over the period 1980-2007. Equilibrium real exchange rates have been derived from a set of fundamentals which appear the most relevant for CFA countries, following the BEER approach. Using non stationary panel econometrics, our results show that the real appreciation of effective exchange rates in CFA zone countries from the 2000s did not translate, in 2007, into a real overvaluation comparable to that occurring before the devaluation of the CFA franc in 1994. However, some countries experience significant overvaluation, reflecting a high heterogeneity and the lack of a convergence process within the CFA Franc zone.

While the stable long-run relationship between real exchange rates and other macroeconomic variables may serve as a guideline for exchange rate policy, the short-run dynamics is also crucial to policy-makers in determining the timing and extent of a potential intervention. To this end, we have investigated more deeply the adjustment process of real effective exchange rates towards their equilibrium levels, by estimating an error correction model in panel data.

We have first assumed a linear dynamic process of real exchange rates, and then we have applied a smooth transition model to the adjustment process. This last specification allows the dynamics of real exchange rate to be nonlinear, which is likely in the CFA countries given the evolution of misalignments. Indeed, our results highlight the existence of two distinct regimes, an undervaluation regime and an overvaluation regime, whatever the considered zone. However, there are marked differences in the convergence process of real exchange rates between country groups. In the CAECM countries, real effective exchange rates tend to converge to their equilibrium level more quickly when they are overvalued. On the contrary, real exchange rates of the WAEMU countries must record a higher undervaluation in order to ensure a return to macroeconomic equilibrium; otherwise they converge very slowly towards their equilibrium level. Accordingly, a nominal devaluation seems to be appropriate only for the WAEMU zone which seems more prone to persistent overvaluations.

Overall, our results highlight the strong heterogeneity between the countries of the CFA zone.

They tend to show the difficulty to apply a single exchange rate policy in the considered zone and rather call for further coordination and policy harmonization between the countries. 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 Note: An increase (resp. decrease) of the real effective exchange rate indicates an appreciation (resp. depreciation). 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 Note: An increase (resp. decrease) of the real effective exchange rate indicates an appreciation (resp. depreciation). 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 Note: A positive (resp. negative) value corresponds to an overvaluation (resp. undervaluation). 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 Note: A positive (resp. negative) value corresponds to an overvaluation (resp. undervaluation). Note: LM test is asymptotically distributed as chi-squared with ((13*(13-1))/2) degrees of freedom and the Pesaran's CD test follows a Gaussian centered reduced. However the LM test is adapted only to the large time dimension ( ) and fixed number of country (N) when the Pesaran's test is suitable to a large individual dimension of panel (

Appendix

Figure A1b. Real effective exchange rate (observed and equilibrium level), WAEMU countries

Figure A2a. Misalignments in CAEMC countries

Figure A2b. Misalignments in WAEMU countries

BENIN

) and sufficient large time dimension. When the value of the statistics is lower than the critical values, we can reject the null hypotheses of cross section independence between countries. Note: * We chose 2 maximum breaks points. The optimum break date is chosen by considering the modified Schwarz information criterion (LWZ) of Liu, Wu, and Zidek (1997) which performs better than the Bayesian information criterion BIC when individual trends are included in the specification according to [START_REF] Carrion-I | Breaking the panels: An application to GDP per capita[END_REF].

Table C. The breaks dates for the REER by country and the optimal break point

Table D. Tests for choosing m, the type of non linearity (with maximum m=3)

  intercepts and disturbance terms, LREER denotes the real effective exchange rate, LTOT the terms of trade, LPROD the relative per capita productivity, LOPEN the degree of openness, LDEP public spending relative to GDP, NFA the net foreign position relative to GDP and it ε the error term. The coefficients β represent the parameters to be estimated. All variables are in logarithm, except the net foreign position.

  Choi's test consists in testing the unit root from a transformation of the observed series it x , allowing to eliminate inter-individual correlations and possible components of deterministic trend. Pesaran's test consists in adding to the standard well-known IPS test, the mean and the lagged mean of the observed series (respectively is sufficient to filter asymptotically the effects of unobserved common component when the number of countries tends to infinity. Finally, the Carrion ( ) λ LM test is a generalization of the univariate KPSS test usually computed in time series (and of the

Figure

  Figure 1. Misalignments in 1993 and 2007 (in %)

α

  is a vector of individual fixed effects; it x the vector of dimension k of explanatory variables (the terms of trade, the relative per capita productivity, the degree of openness, public spending relative to GDP, net foreign position relative to GDP).

  the coefficients associated with explanatory variables in the first and second regimes. it ε , the error term independently and identically distributed. function which can be specified by the following logistic function of order m : ( )

  i.e. the speed of transition from one regime to another one (the highest this parameter is, the more sudden is the transition). 251 = m According to Gonzalez et al. (2005), the transition function can be of order one (logistic function) or order two (quadratic function) in order to capture the non linearities derived from the regime switching. For , the model implies that the two extreme regimes are associated with high and low values of the transition variable ( increases, where the change is centered around 1 c (see Appendix, Figure A3). The methodology used to estimate the PSTR is sequential. We first test the null hypothesis of homogeneity specification. The associated tests are not standard tests because of the presence of nuisance parameters which are unidentified (like the parameter c ) under both null hypothesis. Following the methodology of Luukkonen et al. (1988), Gonzảlez et al. (2005) proposed to test the null hypothesis of ( to overcome the problem of nuisance parameters. After reparameterization, this leads to consider the following regression: homogeneity consists in applying the LM-test developed by Gonzảlez et al. (2005):

  work and are associated with high and low values of deviations from equilibrium. In order words, as in Lopez-Villavicencio and Mignon (2010), the type of asymmetry distinguishes between high or low misalignments. Thus we proceed to estimating the following Panel Smooth Transition Error of the error correction term of respectively the linear and the non linear regimes. These latest parameters are the interest parameters of this study. The estimation's step is a relative application of the fixed effects estimator. It consists to demeaning variables by removing individual-specific means before applying the nonlinear least squares to obtain the coefficient's estimations. Finally, we evaluate the quality of the regression. Gonzảlez et al. (2005) suggest two tests: the parameters constancy over time test and the no remaining nonlinearity test. The first one reduces to the stability test of the parameters usually performed in time series studies.

  , if we accept the hypothesis of non homogeneity in the first step, we compare the two regimes model to the three regimes model ( 2 = r

Figure

  Figure A1a. Real effective exchange rate (observed and equilibrium level), CAEMC countries

Figure

  Figure A3. Transition functions

  in brackets are the associated probabilities (P-values).

  6

	it LREER	=	U	i	+	β	it LTOT 1	+	β	2	LPROD	it	+	β	3	LOPEN	it	+	β	4	it LDEP	+	β	5	it NFA	+	ε	it

Table 1 . Unit roots tests

 1 .14

		1 st generation				2 nd generation		3 rd generation
	Variables	Im and al.	Madalla and	Pesaran		Choi	Carrion et al.
			Wu
		IPS	Z	MW	CIPS	*	Pm	Z	( ) λ LM
	TCER	1.76 (0.96)	18.33 (0.86)	-2.29 (0.49)	-1.93 (0.97)	1.66 (0.95)	20.43 (0.00)
	TOT	2.31 (0.99)	67.79 (0.00)	-2.74 (0.07)	-0.98 (0.84)	3.61 (0.99)	29.17 (0.00)
	PROD	0.23 (0.59)	15.96 (0.94)	-2.68 (0.10)	0.16 (0.45)	-0.63 (0.27)	19.57 (0.00)
	NFA	4.77 (1.00)	12.95 (0.98)	-2.52 (0.22)	-1.74 (0.96)	2.24 (0.99)	15.85 (0.00)
	OPEN	-0.62 (0.27)	70.15 (0.00)	-1.93 (0.27)	10.50 (0.00)	-5.61 (0.00)	0.02 (0.49)
	DEP	-1.26 (0.10)	41.78 (0.03)	-2.41 (0.34)	3.56 (0.00)	-2.46 (0.01)	8.85 (0.00)

Notes: trends and individual constants are introduced in all specifications

15

, except for the variable OPEN. The values in brackets are the associated probabilities. The test of

[START_REF] Carrion-I | Breaking the panels: An application to GDP per capita[END_REF]

, based on the KPSS test, tests the null hypothesis of stationarity, unlike the other tests presented here.

Table 2 . Cointegration tests

 2 appears to be a good complement as it was developed on the null hypothesis that takes cointegration for the panel as a whole. Crosssectional dependence is taken into account by boostraping. We first test the presence of cointegration via the Westerlund test (2008) (

	g DH and	p DH ) and then check this result using

N

LM ) for the whole panel. The results, presented in table 2, show that we can reject the null hypothesis of the absence of cointegration regarding the Westerlund test. Indeed, there are some countries that exhibit a long run or equilibrium relationship between the real exchange rate and its covariates. Results of the Westerlund and Edgerton test also lead to accept the null hypothesis of a cointegration relationship for the panel as a whole. Finally, first and second-generation cointegration tests provide clear support of a long-run cointegration relationship between the real exchange rate and its fundamentals. a refers to bootstrap p-values.*, **, ***, indicates the rejection of the null hypothesis of no cointegration at the 10%, 5% and 1% significance level, respectively.

Table 3 . Within estimation

 3

	Variables	CFA zone	CAEMC	WAEMU
	∆	MES	it	1 -	-0.26***	-0.27***	-0.23***
	∆	it LTOT	-0.11***	-0.10***	-0.11***
	∆	LPROD	it	-0.08	-0.04	-0.23*
	∆	it LDEP	0.06***	0.05*	0.08**
	∆	it NFA	0.13***	0.11***	0.17***

Note: ***, ** and * mean respectively that the variable is significant at 1%, 5% and 10%.

Table 4 . Linearity and no remaining nonlinearity tests with misalignment as threshold variable.

 4

	Hypothesis	CFA Zone	CAEMC	WAEMU
		Fisher LM	P.value	Fisher LM	P.value	Fisher LM	P.value
		stat		stat		stat
	H0: r=0 versus H1: r=1	4.94	0.00	3.076	0.01	2.357	0.04
	H0: r=1 versus H1: r=2	1.198	0.31	1.139	0.34	0.35	0.88
	Note: The first line corresponds to the non linearity test and the second allows testing the no remaining
	nonlinearity also call no remaining heterogeneity in the panel context. Briefly, this last test permit to choose the
	number of regimes of the model (r=1 or 2). In this case we accept r=1.

Table 5 . Estimated PSTR with two regimes and m=1

 5

			Regime 1			Regime 2	Transition
		θ	0	T-stat	0 θ +	θ	1	T-stat	γ	c
	CFA Zone	-0.29	-4.19	-0.28		-4.24	33.72	0.03
	CAEMC	-0.29	-2.79	-0.37		-3.55	36.22	0.02
	WAEMU	-0.32	-1.97	-0.18		-2.20	8.01	-0.13
	Note: The Schwarz's criterion (BIC) was used to choose the form of the transition function that
	is to say the adequate value of parameter m (logistic or quadratic).

Table A .

 A Main partners of CFA zoneNote: Weights (in %) correspond to the share of partner in the total trade of each CFA country. CAEMC countries in italics

	BENIN		BURKINA FASO	IVORY COAST	GUINEA BISSAU	MALI
	Partners	weight Partners	weight Partners	weight Partners	weight Partners	weight
	Chine	30.4 Ivory Coast	18.9 France	18.7 India	22.8 France	12.0
	France	9.1 France	18.9 Nigeria	12.9 Portugal	11.7 Ivory Coast	10.2
	United States	6.5 Chine	6.7 Netherlands	8.2 Senegal	11.4 Senegal	9.6
	Thailand	5.5 Singapore	3.7 United States	6.4 Brazil	7.1 China	5.3
	India	5.1 Togo	3.7 Germany	3.5 Nigeria	5.4 Germany	3.8
	Malaysia	3.7 Belgium	3.6 Italy	3.3 Italy	4.4 Belgium	2.8
	Netherlands	3.1 Italy	3.0 Spain	2.8 Thailand	3.6 South Africa	2.3
	Ivory Coast	2.9 India	2.5 England	2.7 Uruguay	3.4 India	1.9
	Belgium	2.9 Ghana	2.5 Chine	2.3 Chine	2.9 Italy	1.8
	Ghana	2.4 Libya	2.5 Burkina Faso	2.0 Netherlands	2.7 United States	1.8
	NIGER		SENEGAL		TOGO	CAMEROON
	Partners		weight Partners	weight Partners		weight Partners	weight
	France		21.5 France	19.5 France		12.5 France	16.2
	Nigeria		12.2 Nigeria	7.3 China		7.9 Spain	10.5
	United States		7.4 India		5.2 Ghana		7.4 Italy	10.4
	China		6.9 Mali		4.6 Benin		5.1 Nigeria	6.0
	Ivory Coast		5.1 Thailand	4.1 Netherlands	4.8 Netherlands	5.9
	French Polynesia		4.1 Spain		4.0 Burkina Faso	4.7 China	5.8
	Japan		3.0 Italy		4.0 Ivory Coast	3.9 United States	5.7
	Belgium		2.8 Chine		3.8 Nigeria		3.5 Belgium	3.6
	Netherlands		2.6 Ivory Coast	3.0 India		3.1 South Korea	3.0
	Algeria		2.1 Germany	2.5 Belgium		3.1 England	2.9
	CENTRAL AFRICAN	CONGO REPUBLIC	GABON		GUINEA	CHAD
	REPUBLIC					EQUATORIALE
	Partners	weight Partners	weight Partners	weight Partners	weight Partners	weight
	Belgium	20.4 United States	26.7 United States	31.0 United States	24.3 United States	62.1
	France	13.9 China	22.9 France	19.9 China	16.9 France	7.5
	Cameroon	5.4 France	9.1 China	9.3 Spain	15.5 China	6.3
					Trinidad et
	United States	5.2 South Korea	4.7	Tobago	2.4 France	5.8 Cameroon	3.9
	Netherlands	4.4 India	3.1 Spain	2.4 Japan	4.5 Germany	2.0
	Spain	3.6 Italy	2.8 Italy	2.0 Italy	4.3 Portugal	1.8
	China	2.8 North Korea	2.1 Japan	1.9 Canada	3.2 Japan	1.7
	Italy	2.6 Germany	1.6 Netherlands	1.8 Portugal	3.0 Netherlands	1.2
	South Korea	2.4 Netherlands	1.5 Germany	1.6 Netherlands	2.9 Belgium	1.1
	Democratic
	Republic of
	Congo	2.2 Brazil	1.5 South Korea	1.4 South Korea	2.4 Saudi Arabia	1.1

Table B .

 B Cross Section Dependance Tests

	Statistics	TCER	TOT	PROD	NFA	OPEN	DEP	Critical Value at	Critical Value at
								5%	1%
	LM test	1006.34	129.09	111.42	400.30	281.83	110.74	99.62	109.96
	CD test	31.04	3.24	6.08	17.05	14.71	0.11	1.96	2.58

[START_REF] Roudet | Estimation of Equilibrium Exchange Rates in the WAEMU: A Robustness Analysis[END_REF] excludes capital flows considered as negligible in their estimation of equilibrium exchange rates of the WAEMU countries.

www.intracen.org Moreover, these countries are characterized by a strong exposure to common shocks (devaluation or structural adjustment plan in 1994, terms of trade's shocks).

http://www.imf.org/external/pubs/ft/wp/2006/data/wp0669.zip

We have run several tests before using tests of second and third generations. These tests are the interindividual dependency test of Pesaran (CD), the Breush-Pagan test (LM test) and the LM test of the number of breakpoints developed by[START_REF] Carrion-I | Breaking the panels: An application to GDP per capita[END_REF]. The results of these tests are reported in table B (Cross section dependence tests of all variables) and table C (breaks dates of the REER by country and the optimal number of break) in the Appendix.

 12 See for instance O'Connel (1998) and[START_REF] Westerlund | Testing for panel cointegration with multiple structural breaks[END_REF] for details about this invalidity.

Choi's test also leads to reject the presence of a unit root for public spending. However, the test of Pesaran (CD) does not confirm the presence of inter-individual dependence and therefore the use of test Choi. In addition, CIPS tests conclude to the character I (1) of this series. This result contrasts with previous studies on the

[START_REF] Béreau | Nonlinear Adjustment of the Real Exchange Rate Towards its Equilibrium Value: a Panel Smooth Transition Error Correction Modelling[END_REF] proposed an alternative method by using the Schwarz's criterion (BIC). They suggest choosing the function that minimises this criterion. Applying this method leads to the same conclusion: m=1.