Maty Konte
email: maty.konte@etu-univ-cezanne.fr.

Theo Eicher

A Curse or a Blessing? Natural Resources in a Multiple Growth Regimes Analysis *

Keywords: JEL Classification: O13-O47 Natural Resources, Mixture of regression, Multiple equilibria

The literature on the impact of an abundance of natural resources on economic performance remains inconclusive. In this paper we consider the possibility that countries may follow different growth regimes, and test the hypothesis that whether natural resources are a curse or a blessing depends on the growth regime to which economy belongs. We follow recent work that has used a mixture of regression method to identify different growth regimes, and find two regimes such that in one regime resources have a positive impact on growth, while in the other they have a negative impact or at best have no impact on growth. Our analysis of the determinants of whether a country belongs or not to the blessed resources regime indicates that the level of democracy plays an important role while education and economic institutions have no effect.

Introduction

During the last decade the question of the impact of an abundance of natural resources on growth and its transmission channels has received substantial attention. Despite the extensive literature on the topic, no consensus has emerged on whether natural resources are a curse or a blessing. On the one hand, there is evidence of a negative marginal impact of natural resources on economic performance (see [START_REF] Sachs | The big push, natural resource booms and growth[END_REF], [START_REF] Sachs | Natural resources and economic development the curse of natural resources[END_REF], [START_REF] Gylfason | Natural resources, education, and economic development[END_REF] and [START_REF] Leite | Does Mother Nature Corrupt? Natural Resources, Corruption, and Economic Growth[END_REF] among others). Different channels of transmission have been proposed to explain the curse, starting with the Dutch Disease [START_REF] Corden | Booming sector and Dutch Disease economics: Survey and consolidation[END_REF]). It has also been suggested that the curse can be due to rent-seeking behavior that increases tariffs and/or corruption, which in turn reduce growth (see [START_REF] Bardhan | Corruption and development: A review of the issues[END_REF] and [START_REF] Leite | Does Mother Nature Corrupt? Natural Resources, Corruption, and Economic Growth[END_REF]), and that natural resources crowd-out education [START_REF] Gylfason | Natural resources, education, and economic development[END_REF]) and quality of institutions [START_REF] Sachs | The big push, natural resource booms and growth[END_REF]). On the other hand, more recent evidence rejects the curse. For instance [START_REF] Manzano | Resource curse or debt overhang?[END_REF] find no evidence of the resource curse when adding country fixed-effects, while the results in [START_REF] Alexeev | The elusive curse of oil[END_REF] support a robust positive impact of natural resources on gdp. Moreover, the success of countries such as Botswana,1 rich in natural resources and with high growth rates, challenges the notion of curse.

Recent empirical evidence has thus started to determine conditions under which the curse can be turned into a blessing by allowing for heterogeneity in the coefficients on natural resources (see [START_REF] Bravo-Ortega | The relative richness of the poor? Natural resources, human capital and economic growth[END_REF], [START_REF] Mehlum | Institutions and resource curse[END_REF], [START_REF] Andersen | Constitutions and the resource curse[END_REF], [START_REF] Collier | Testing the neocon agenda: Democracy in resource-rich societies[END_REF]). The common approach in those papers is to interact natural resources with variables such as education or institutions, to determine whether for instance an increase of the level of education decreases the magnitude of the curse and at some level could turned the curse into blessing. This approach allows for heterogeneity in the impact of some variables, yet they impose, without testing, common coefficients on most of the regressors included in the models, thus neglecting heterogeneity on other regressors that may have an impact on the coefficients of our variable of interest, natural resources. This paper contributes to the literature addressing the heterogeneity in the resource curse by considering the fact that countries are heterogeneous and may follow different growth regimes or processes, and ask the question of whether the sign of the impact of natural resources depends on the growth regime that a given country belongs to. We suggest that there may be multiple growth regimes such that the marginal impact of explanatory variables on growth differs across regimes, enabling us to test whether an abundance of natural resources has a negative impact on growth in some regimes and a positive impact in other regimes. To shed light on the role of education and institutions, we employ a different strategy compared to the previous papers. We test whether education / or institutions affect the probability of a given country belonging to the blessed growth regimes. We estimate a finite mixture of regressions model, a semi-parametric method for modeling unobserved heterogeneity in the data, in which countries are sorted into regimes depending on the similarity of the conditional distribution of their growth rates given all the explanatory variables. This approach presents two main advantages. First, we relax the hypothesis of a single growth regime and allow the data to detect the number of regimes, which gives more flexibility and a better fit compared to the literature in which one growth regime is imposed. Second, instead of imposing a priori groups of countries (for instance some studies divide samples into high-and low-income countries, democracies and autocracies), we sort countries into blessed and cursed regimes in terms of their estimated posterior probability of being in one or another regime, which we endogenise and suppose to be a function of education, institutions and geographic features.

Our results indicate that the data is best generated by a model of two regimes, one in which an abundance of natural resources has a positive impact on growth and one in which it has a neutral or a negative impact depending on the measure of natural resources that we consider. We also find that more democracy increases the probability of a given country belonging to the blessed regime but economic institutions and education do not have an impact on that probability. The geographical location such as being a Sub-Saharan African or Latin-American country has no impact on the classification of countries into regimes. In the first regime the average annual growth rate is 2.32% and 42% of countries belongs to this group, while the annual growth rate in the second group is 1.5% with 58% of countries belonging to it. There is substantial heterogeneity within each group both in term of gdp levels and geographical location, indicating that democracy is not acting as a proxy for these features. This paper is related to three strands of literature on empirics of growth. First it contributes to the literature on the relationship between natural resources and economic performance.2 In their seminal work [START_REF] Sachs | The big push, natural resource booms and growth[END_REF] and [START_REF] Sachs | Natural resources and economic development the curse of natural resources[END_REF] provide evidence of a negative impact of natural resources on growth and find no support for the idea that geographic features or climate explain the resource curse. Further evidence on the resource curse has been provided by [START_REF] Gylfason | Natural resources, education, and economic development[END_REF], [START_REF] Leite | Does Mother Nature Corrupt? Natural Resources, Corruption, and Economic Growth[END_REF], [START_REF] Papyrakis | The resource curse hypothesis and its transmission channels[END_REF] and [START_REF] Papyrakis | Resource abundance and economic growth in the united states[END_REF], who analyze both the direct impact of natural resources on growth rates and the indirect one, operating through the effect of resources on physical and human capital investments.

Our analysis follows closely the literature focusing on the conditions under which a resource curse can be turned into a blessing, thus accounting for heterogeneity. [START_REF] Mehlum | Institutions and resource curse[END_REF] interact natural resources with an index of rule of law, ranging from 0 to 1, and find that the resource curse disappears when the index of rule of law is at least 0.93. This value decreases to 0.6 when they replace the export of primary goods in total gdp (also known as Sachs and Warner measure of natural resources) by the share of mineral production in national income. [START_REF] Bravo-Ortega | The relative richness of the poor? Natural resources, human capital and economic growth[END_REF] show how natural resources interact with education and find that a high level of education helps reduce the resource curse. [START_REF] Collier | Testing the neocon agenda: Democracy in resource-rich societies[END_REF] investigate whether democracy can offset the resources curse, and their results indicate that a combinaison of high resource rents and democracy is growth-reducing but this negative effect can be offset by setting checks and balances in resource rich countries. [START_REF] Andersen | Constitutions and the resource curse[END_REF] examine whether features of constitutions determine how an abundance of natural resources affects economic growth. They find that the curse is present in democratic presidential countries but not in parliamentary democracies, and that being parliamentary or presidential is more important than being a democracy or an autocracy. All of these papers assume that all countries follow the same growth process and allow for parameter heterogeneity only in some chosen variables. We propose a more flexible approach that considers parameter heterogeneity for all the variables of the model, so that countries can belong to different growth regimes. We then examine whether the impact of natural resources on growth differs across regimes. Furthermore, rather than imposing the interaction between resources and a particular variable, we consider several potential determinants of growth regime membership and test whether they help a given country to belong to the resource blessed regime.

Our paper is also related to the literature that tests for the existence of multiple growth processes.

Starting with the Classification Analysis and Regression Tree (named CART) proposed by [START_REF] Durlauf | Multiple regimes and cross-country behavior[END_REF] the question of multiple growth regimes has been addressed in numerous papers. Although the CART method is an endogenous grouping method based on thresholds of splitting variables selected a priori, its disadvantage is the lack of available asymptotic properties that would be useful for drawing inference on threshold variable choices and threshold values estimations. More sophisticated clustering methods have been presented in order to make the classification as flexible as possible. Recent work has applied the mixture of regression method to address the multiple regimes hypothesis, an approach that presents a number of advantages over previously used methods (see section 2.2 below). [START_REF] Owen | Do all countries follow the same growth process[END_REF] apply the mixture of regression method to answer the question Do all countries follow the same growth process? and find that their panel data is best generated by two different growth processes. Using the same methodology, [START_REF] Flachaire | Political versus economic institutions in the growth process[END_REF] examine the direct and indirect roles of economic and political institutions in the process of development, and their results indicate that political institutions are the main determinant of which growth regime a country belongs to, while economic institutions have an direct impact on growth rates within each of the two regimes. Mixture regressions have also been used by [START_REF] Bos | Do all countries growth alike[END_REF] and [START_REF] Vaio | Did globalization drive convergence? Identifying cross-country growth regimes in the long-run[END_REF] to examine respectively, growth in the very long-run (using historical data) and the possibility of countries switching regimes. Neither of these papers considers the role of natural resources, yet the framework is obviously suited to examine the question.

The paper proceeds as follows. Section 2 presents the econometric methodology. Section 3 describes the data while section 4 presents the main results. The next section checks the robustness of the results while some concluding comments are provided in section 6.

Econometric specifications

Standard specification

The standard parametric specification of the framework is in the following form:

growth i,t = β 0 + β 1 log(gdp 0,i,t ) + β 2 log(pop i,t + 0.05) + β 3 log(inv i,t ) + β 4 log(educ 0,i,t ) +β 5 NR 0,i,t + β 6 eco i,t + β 7 dem i,t + ε i,t (1)
The dependent variable is the average annual growth of real gdp per capita (growth i,t ) while the independent variables are initial gdp per capita (gdp 0,i,t ), the population growth rate (pop i,t ) plus a term 0.05 capturing depreciation and technological change, the average investment rate (inv i,t ), the initial level of education (educ 0,i,t ), the initial endowment in natural resources (N R 0,i,t ), the average level of economic institutions (eco i,t ) and the average level of democracy (dem i,t ).

We assume that the error terms ε it are identically and independently distributed and follow a normal distribution with mean zero and variance σ 2 . Our parameter of interest is the coefficient on the natural resources variable β 5 . A negative β 5 confirms the resource curse hypothesis while a positive β 5 implies that resources are a blessing. Economic institutions have been found to be a robust determinant of growth rates in many studies3 but there is only weak evidence that political institutions (here measured by democracy) are a robust regressor of growth rates. Political institutions (democracy), have been found

to have a weak direct impact on growth but a strong indirect impact through the effect that economic institutions and policies have on growth or through their impact on the choice of policies and economic institutions in a country. 4 We expect the coefficient β 6 on economic institutions to be positive and significant while we do not expect a particular sign on the coefficient on democracy, β 7 .

The specification in equation 1 assumes that there is a single growth model which explains the process of development for all countries. If the observations of our dataset are not generated by a single growth regime, the estimation of equation 1 will produce biased results. A biased estimate of the coefficient β 5 could thus lead to the wrong conclusion on whether or not there is a resource curse. For instance if for some countries β 5 is positive and for others β 5 is negative, in a single regression it may turn out insignificant. To overcome this problem we propose to use the mixture-of-regression method.

Finite-mixture-of-regression models

Finite-mixture-of-regression models, also known as Generalized Mixture Regression Models, are semiparametric methods for modeling unobserved heterogeneity of the population in the estimation of a regression model. We relax the hypothesis of one growth regime and assume K different homogeneous growth regimes such that the growth determinants have different marginal impacts across regimes. Thus we are able to test whether the marginal impact of an abundance of natural resources on growth differs across regimes.5

Let us consider (Y, X) = (y i , x i ) n i=1 a pair of a random variable y i and a set of explanatory variables

x i . By definition, the mixture of regression based on the density of Y conditional on X is expressed as follows:

f (y|x, Θ) = K k=1 π k f k (y|x; β k , σ k ) ( 2
)
where K is the number of groups or regimes, π k is the probability of belonging to group k, and

f k (y |x; β k , σ k ) is a conditional probability distribution characterized by a set of parameters (β k , σ k )
and of covariates x. Both β k and σ k are unknown and hence estimated. We suppose f k is a Gaussian distribution with conditional expectations equal to E(y|x) = xβ k .

To illustrate, if K = 1, then all observations are generated by the same data-generating process given by:

y = xβ + ε, ε ∼ N (0, σ 2 ) (3)
In this case the standard specification in equation 1 is sufficient to study the impact of natural resources on the growth rate. If K = 2 then a mixture of linear regressions assumes that an observation belonging to the first group and one belonging to the second group would not be generated by the same data-generating process. The mixture model with two components reduces to:

Group 1: y = xβ 1 + ε 1 , ε 1 ∼ N (0, σ 2 1 ), Group 2: y = xβ 2 + ε 2 , ε 2 ∼ N (0, σ 2 2 ), (4)
where ε 1 and ε 2 are independent and identical normally distributed error terms within each group, with variances of σ 2 1 and σ 2 2 , respectively. In this setting the impact of natural resources on growth could be different in the two regimes because the environment in which growth occurs is different across regimes.

Since we are also interested in testing whether institutions and/or education help to classify countries into growth regimes, we extend the model in equation 2 by adding a set of additional variables ω, also known as concomitant variables, that explain group membership. Concomitant variables play the same role as covariates in a multinomial regression model designed to explain group membership. They directly affect the probability of a given country being in one or another growth regime, implying that parameter π k (.) becomes endogenous. The roles of standard covariates x and of concomitant variables ω are different: standard covariates help to explain variations within groups, whereas concomitant variables explain variations between groups. Equation 2 with concomitant variables becomes:

f (y|x, ω, Θ) = K k=1 π k (ω, α k )f k (y|x; β k , σ k ), (5)
where α k is a vector of parameters on concomitant variables ω and its sign helps to determine how a variation of ω impacts the probabilities of countries being in one or another regime.

For a given number of components K we estimate the finite mixture model by maximum likelihood with the EM algorithm of [START_REF] Dempster | Maximum likelihood from incomplete data via EM algorithm (with discussion)[END_REF], which is the most common approach for the maximum likelihood estimation of finite mixture models. To avoid a singularity problem we ensure that the estimated parameter of σ k is different from zero. The number of groups K is a priori unknown and the selection of the optimal value is crucial since it gives the true number of growth regimes generated by the data. We choose the optimal value of K by minimizing the Bayesian Information Criterion (BIC) developed by [START_REF] Schwarz | Estimating the dimension of a model[END_REF], and the Corrected Information Criterion (CAIC, see [START_REF] Burnham | Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach[END_REF]). Those criteria are defined as follow:

BIC = -2 ˆ + (#param) log n (6) CAIC = -2 ˆ + (#param)2n n -(#param) -1 (7)
where ˆ is the estimated value of the log-likelihood and n is the number of observations. Once parameters are estimated, we can use Bayes rule to compute the probability that a given country is allocated to a given group k. The equation is written as follows:

πik = π k (w i , αk )f k (y i |x i ; βk , σk ) K k=1 π k (ω i , αk )f k (y i |x i ; βk , σk ) (8)
For classification purposes, a given country i will be allocated in group k rather than group l if and only if πik > πil .

We will apply the mixture of regression method to equation 1, using as concomitant variables average levels of economic institutions ( eco), democracy (dem) and the initial level of education (log(educ 70 )), as well a Sub-Saharan Africa dummy and a Latin-America dummy to control for geographical location.

The use of the mixture of regression models has at least three advantages. First, it allows to treat endogenously unobserved heterogeneity by considering simultaneously all the covariates and allowing them to have different marginal impacts across regimes. Second, countries are sorted into regimes in terms of probabilities which are a function of concomitant variables, thus we can compare the role of education, geography and institutions in allocating countries into regimes. Finally, the number of homogeneous growth regimes is a priori unknown and are selected optimally with respect to some information criterion.

This means that if there are more than two ways in which resources affect growth, we should be able to identify them. It is important to note that our approach does not consider the indirect impact of natural resource through variables such as investment or education, a question that has received substantial attention in the literature (See [START_REF] Gylfason | Natural resources, education, and economic development[END_REF]). In addition our model constrains countries not to be in different regimes at different periods since the concomitant variables are constant. 6 3 Data and descriptive statistics

We build a 5-year panel of developed and developing countries for the period 1970-2005, which yields 7 periods: 1970-1975, 1975-1980, 1980-1985, 1985-1990, 1990-1995, 1995-2000 and 2000-2005. All the variables used except education, the measures of natural resources and institutions are from the Penn World Tables (version 6.3). Education comes from [START_REF] Barro | A new data set of educational attainment in the world[END_REF] and is measured by the average years of schooling in the population aged over 25. Our main measure of natural resource abundance is the share of exports of primary goods in total GDP (xgdp) which includes fuel and non-fuel goods.

This measure, first proposed by [START_REF] Sachs | The big push, natural resource booms and growth[END_REF], has been extensively used in the literature.

The data are provided by the World Development Indicators (WDI). Non-fuels goods comprise metals and ores, agricultural raw materials and food. In our analysis we will first use the aggregate measure of natural resources (xgdp). [START_REF] Sachs | Natural resources and economic development the curse of natural resources[END_REF] argue that the natural resources effect should be linked to the magnitude of economic rents they generate and it is possible that different types of resources yield higher or lower rents 7 , hence we will distinguish minerals from agricultural goods since minerals yield in general higher rents. We will hence disaggregate xgdp into its three components 8 : metal and ores (M etal -Ores), agricultural raw materials and food (Agri -f ood) and fuel (F uel). Some authors (for instance [START_REF] Gylfason | Natural resources, education, and economic development[END_REF]) define the share of primary exports as natural resources intensity rather than natural resources abundance, 9 so we will also use the rent per capita, 10 as a measure for natural 6 The question of regime migration is a complex one and has been recently addressed by [START_REF] Bos | Do all countries growth alike[END_REF]. 7 The different types of natural resources may have a difference in term of factors intensity, ownerships and costs of extraction which may imply a difference quantities of extracted rents (See [START_REF] Leite | Does Mother Nature Corrupt? Natural Resources, Corruption, and Economic Growth[END_REF]).

8 As documented in the World Bank data Agricultural raw materials exports correspond to the SITC section 2 excluding divisions 22, 27 (crude fertilizers and minerals excluding coal, petroleum, and precious stones), and 28 (metalliferous ores and scrap); Food exports Food comprises the commodities in SITC sections 0 (food and live animals), 1 (beverages and tobacco), 4 (animal and vegetable oils and fats) and SITC division 22 (oil seeds, oil nuts, and oil kernels); Ores and metals comprise the commodities in SITC sections 27 (crude fertilizer, minerals nes) 28 (metalliferous ores, scrap), and 68 (non-ferrous metals) and Fuel exports comprise SITC section 3 (mineral fuels).

9 The idea behind is that a country like Norway, has a low share of exports of primary products in total GDP because it has also developed the others sectors of the economy.

10 Rent is defined as total revenue from natural resources divided by the population. The rent is provided by the WDI and it includes rent from energy, minerals and forest. Energy refers to crude oil, natural gas and coal, and mineral refers to bauxite, copper, iron, lead, nickel, tin, zinc, gold and silver. The rent of a unit of resource is defined as the gap between its world price and its country-specific extraction costs both expressed in US dollars, the obtained measure is then multiplied by the total quantity of resources extracted.

resources abundance in the robustness section.

Turning to the measures of institutions, we distinguish political institutions from economic institutions. Political institutions refer to how political choices are made while economic institutions refer to the consistency of those choices with voluntary exchange and the protection of property rights. We measure political institutions by the index of democracy from Polity IV, and economic institutions by the index of the Economic Freedom in the world from the Fraser Institute compilation. 11 The democracy index takes into account the competitiveness of executive recruitment, the openness of executive recruitment, the constraints on the executive, and the competitiveness of political participation. It ranges between 0 and 10, with a value of 0 denoting an autocratic government and a value of 10 full democracy. Economic freedom measures the extent to which property rights are protected and the freedom that individuals have to engage in voluntary transactions. This measure takes into account the respect of personal choices, the voluntary exchanges coordinated by markets, freedom to enter and compete in markets, and protection of persons and their property from aggression by others.

Table 1 shows the descriptive statistics and data sources. Note that eco, dem, log(educ 1970 ), Sub-Afri and Latin are concomitant variables, where eco and dem are the average value of economic institutions and democracy over the period 1970-2005, educ 1970 is the level of education in 1970 and Sub-Afri and Latin are respectively dummy for Sub-Saharan Africa countries and dummy for Latin-America dummy. Table 2 shows the correlation coefficients between variables. The correlation between the growth rate and the aggregate natural resources variable (xgdp) is negative, in line with the resource curse theory. In addition xgdp is negatively correlated with investment in physical and human capital (log(inv), log(educ 0 )) and these variables are in turn positively correlated with the growth rate. This suggests that there may be an indirect negative impact of natural resources on growth through the investments in physical and human capital as already found in the literature (see [START_REF] Gylfason | Natural resources, education, and economic development[END_REF], [START_REF] Atkinson | Savings, growth and the resource curse[END_REF], [START_REF] Papyrakis | The resource curse hypothesis and its transmission channels[END_REF]). Turning to the correlations between natural resources and institutions, the natural resource measure (xgdp) is negatively correlated with both measures of institutions but the correlation with democracy is much higher. When we consider the disaggregated measures of natural resources only the measure of fuel (F uel) is positively correlated with the growth rate, initial gdp per capita and investment in physical capital.

Results and discussion

Standard model results

We start by reproducing some of the results found in the literature in cross section analysis, reported in Table 3 column (1). The dependent variable, the growth rate and the explanatory variables (except for initial gdp, education and natural resources) are averaged for the entire 35-year period. We measure initial gdp, education and natural resources at the starting year 1970. We use the aggregate measure of natural resources (xgdp). In this and all subsequent tables N R always denotes natural resources, which can be measured in different ways. The coefficient on natural resources is negative and significant at the conventional level 1%, suggesting that an abundance of natural resources reduces growth. The coefficient on N R (-0.044) is roughly comparable to that in [START_REF] Sachs | Natural resources and economic development the curse of natural resources[END_REF], table 2 columns (2) and ( 3), where the resource curse hypothesis is analyzed for the period 1970-1989. One issue with the cross-section data is the low number of observations (71 obs) due to the limitation of the number of countries. The low number of observations may also be a problem when estimating the mixture model since the number of parameters increases with the number of growth regimes K, requiring more observations. One possibility to increase the number of observations in growth regressions is to use panel data. Thus the rest of the paper is based on panel data.

We report in columns ( 2)-( 4) of table 3 respectively the pooled, the fixed effects and the random effects estimations when using panel data. The coefficient on natural resources is negative in almost all columns but it is never significant. This confirms the results in [START_REF] Manzano | Resource curse or debt overhang?[END_REF] who find that the resource curse hypothesis disappears once panel data with fixed-effects are used. Turning now to the other variables in the regression, the negative signs on initial gdp log(gdp) are consistent with the beta-convergence hypothesis between countries and the coefficients on the economic institutions, eco, have the expected sign and are significant at the 1% level. Not surprisingly more democracy does not stimulate growth, as already found in previous work. 12 The Hausman test of the appropriateness of the random-effects model gives a low p-value of 0.001 which suggests that the random-effects model is less appropriate than the fixed-effects one.

It is well-known fact that both institutional quality and educational attainment may be determined by economic performance, and the literature on natural resources has also discussed the problem of causality between natural resources and economic performance. For instance the denominator of our main measure for NR is gdp per capita. Thus if two countries export the same amount of natural resources, the country with a lower level of gdp per capita will be resource rich while that with a higher level of gdp will be considered as resource poor. To deal with this possible endogeneity, we use IV estimation with the first lags of education, NR and both institutions as instruments. The last two columns in table 3 present estimation results with instrumental variables for the pooled and random-effects models. The estimations in column (5) are close to those in column (2) except that education and democracy now become insignificant. The estimates in columns ( 4) and ( 6) are very similar. In all specifications the coefficient of the variable of interest, natural resources, remains insignificant.

These results support neither a resource curse nor a resource blessing when using standard models on panel data. One possible cause for the absence of significant coefficients on natural resources is that there exists unobserved heterogeneity in the data. In fact the assumption that all countries follow the same growth regime may be too constraining, raising a doubt on the estimates and enabling us to figure out whether natural resources are a curse or a blessing. Hence we suppose that our data could be generated by multiple growth regimes, and that an abundance of natural resources may have different marginal impacts across regimes. Under this assumption we apply the mixture of regression method to take into account heterogeneity. Although the panel fixed-effect takes into account the heterogeneity in the constant term the mixture of regression method has the advantage of taking into account endogenously the heterogeneity on the explanatory variables by allowing them to have different marginal impacts across growth regimes.

Mixture-of-regression results

We next estimate the mixture model with concomitant variables and allow the number of groups K to vary between 1 and 4, estimating 4 models. As in the previous panel data estimations, our dependent variable is the annual rate of growth averaged over five-years and the standard covariates are the initial gdp per capita, the population growth rate averaged over five-years, the initial level of education, the initial quantity of natural resources, and the five-years average of investment, economic institutions and democracy. As concomitant variables we use the average level of democracy and of economic institutions over the 35-year period, the initial level of education in 1970, a Sub-Saharan Africa dummy and a Latin-America dummy. We report the values of the BIC and CAIC in table 4. Both of the information criteria are minimized for K=2, allowing us to select the model with two growth regimes as the model that best fits the data. According to the two test statistics, the two-regime model presents a substantial improvement over estimating a single regime model (BIC=2282.6 for K=2 versus BIC=1353.8 for K=1).

Recall that the estimations of the model where K=1 is reported in column (2) of table 3, where we found no impact of natural resources on growth rate.

Table 5 shows the estimated parameters of the selected mixture model. The coefficients on natural resources support our hypothesis that an abundance of natural resources has different impacts on growth across regimes. While there is a resource blessing in the first regime, an abundance of natural resources is neutral in the second regime. We also test whether the coefficients on N R are statistically different across regimes, reporting the Wald test in column 3. The null hypothesis under which the coefficients on N R are equal across the two growth regimes is statistically rejected by the Wald test at the 5% level.

The coefficients on initial income, on investment in physical and human capital and on institutions are also statistically different across regimes. Investments in physical and human capital have a positive and significant impact on growth for the first group, but education does not affect growth for the second one. Economic institutions are beneficial for growth in both regimes while political institutions do not matter for the second regime but affect negatively the growth rate in the first group. Recent literature has tried to explain why it has been so difficult to find a robust positive effect of political institutions on growth and suggests that in contrary to the economic institutions their impact on growth may be indirect. For instance Acemoglu et al. (2005) propose the hierarchy of institutions hypothesis , which indicates that political institutions set the stage in which economic institutions and policies operate. The results in [START_REF] Flachaire | Political versus economic institutions in the growth process[END_REF] find support for the hierarchy of institutions hypothesis when using the mixture-of-regression approach in a panel of developped and developping countries covering.

We turn now to the coefficients on the concomitant variables. Recall that the concomitant variables play the same role as covariates in the multinomial logit estimations, so that only the signs of the coefficients have an interpretation. Our group of reference here is the first one, the one for which resources have a positive impact on growth. The results show a negative and very significant coefficient on democracy, indicating that an increase of the level of democracy decreases the probability for a given country to be in the second regime rather than in the first regime. Both economic institutions, education and the geographical location do not affect the regime membership probability.

We find that 42% of countries are in the first group against 58% in the second group. Table 6 shows the classification of countries into growth regimes with their respective probability. Some countries from different regions and countries with different levels of development follow the same growth process. For instance Bangladesh, Botswanna and the Republic of Congo and Mali are in the same group as most of the Western countries, while Ireland and Portugal are in the same group as most of poor countries.

The bottom panel of Table 6 reports the average values of the dependent and main independent variables for the two groups as well as the within group standard deviations in parenthesis. The average growth rate is equal to 2.32% for the first group against 1.50% for the second group. The standard deviation is much lower in the first group than in the second group which could be explained by the high diversity of countries in the latter group. The average value of exports of primary goods is twice as low in the first group as in the second. Regarding institutions, there is only a small difference on the average values of economic institutions but the level of democracy is much higher in the first group than in the resource blessing group.

As already discussed in the section 4 above, the endogeneity issue is important in the literature but still finding good institutions for natural resources and in particular for institutions remains difficult. Also we are not aware of a procedure that allows to estimate mixture models using instrumental variables and proceed in two step. This last point could be an interesting contribution in the mixture of regression framework. To consider the endogeneity problem we perform a standard IV estimations for each of the group derived previously from the mixture of regression estimation. We use as instruments one-period lags of education, natural resources and institutions. The results are reported in Table 7 and show that coefficients are very closed to those reported in Table 5.

Robustness Analysis

To test the robustness of our results we run a number of further estimations. First, we use different measures for natural resources, the disaggregated components of our main measure xgdp and the rent per capita in logs. Second, we use alternative measures of political institutions which we have found to be important for the classification of countries into growth regimes. Lastly, we will include an interaction term between natural resources and education.

Alternative measures for natural resources

Table 8 shows additional evidence on the existence of two growth regimes when we use alternative measures of natural resources, as the information criterion selection always gives 2 growth regimes. We first focused on the disagragated measures of xgdp, our main measure of natural resource abundance in the previous estimations. It is important to shed light on how the different components of xgdp affect growth in a multiple growth regime analysis. There may be different reasons to believe that the different components of xgdp may have different impacts on growth across regimes. For example mineral sectors yield in general higher rents than agricultural sectors and fuel sectors (see [START_REF] Sachs | Natural resources and economic development the curse of natural resources[END_REF]). [START_REF] Leite | Does Mother Nature Corrupt? Natural Resources, Corruption, and Economic Growth[END_REF] mention that although those components are different in term of factor intensity, they also have differences in term of ownership and in term of time of extraction, implying different costs and different processes, and thus different rents.

We report the estimations of the K=2 mixture models in table 9. For M etal-Ores, the results support the existence of a resource blessing in the first regime and a resource curse in the second regime. The level of democracy helps to split countries into regimes, with more democracy increasing the probability for a given country to be in the resources blessed regime. The Wald test, which is not reported, rejects the hypothesis of the equality of the coefficients on natural resources across regimes. Similarly, when we consider agricultural raw and food (Agri-Food) as the measure of natural resource abundance, we find again a resource blessing in the first regime and resources curse in the second regime. For Fuel we have no effect of natural resources on growth in the second regime and a positive one in the first. In all cases the level of democracy is an important determinant of the probability for countries to be classified into regimes, while education and regional dummies tend to play no role. Only in the case of Fuel the Latin American dummy decreases the probability to be in the resources blessing regime. Note that the magnitude of the coefficient on natural resources in absolute value is higher for M etal -Ores than for Agri -f ood and F uel. One possible explanation is that mineral sectors yield in general higher rents than agricultural sectors and fuel sectors due to the difference in term of costs and in term of capital intensity as already mentioned in the previous paragraph.

Considering rent per capita as our measure of resources, we find resource blessing in the first group but no impact in the second one. As before, the level of democracy enhances the classification of countries into regimes, while the Sub-Africa dummy is now significant indicating that being a Sub-Africa country reduces the probability to belong to the blessed resource group.

Alternative measures for democracy

Our second specification to check the robustness of our results is to change the measure of democracy that we find important in the classification of countries. We replace the Polity IV measure with data from [START_REF] Golder | Democratic electoral system around the world[END_REF]. These data provide measures for a wide range of institutions including regime type, the electoral system and the assembly size. Data are available for a large number of countries over the 1946-2000. We use demautoc, a dummy which is equal to 1 for democracies and 0 for autocracies.

As explanatory variable we take the initial value of demautoc at the beginning of each period and as concomitant variable the value in 1970. We will also add to the concomitant variables a dummy denoted presdem 70 which is equal to 1 for presidential democracies in 1970 and 0 for parliamentary or mixed democracies. 13 Results are reported in table 10. We find again two growth regimes whereby an abundance of natural resources is beneficial in one regime and negative or neutral in the other. Being a democracy remains a key determinant of the probability of being in the blessed regime but the type of democratic system does not matter for the classification of countries into regimes. These results differ from the conclusion in [START_REF] Andersen | Constitutions and the resource curse[END_REF], where the authors interact in a single growth regime natural resources resources with institutional features. They provide evidence that the curse is present in presidential democracies but not in parliamentary democracies, while being an autocracy does not explain the curse.

Education and natural resources

Education has been found to be important in the resource curse literature (see [START_REF] Gylfason | Natural resources, education, and economic development[END_REF] and Bravo-Ortega and De-gregorio ( 2007)) but our previous results do not show that education helps to split countries into blessed and cursed regimes. One explanation could be that education has a different role, from that of institutions. Following [START_REF] Bravo-Ortega | The relative richness of the poor? Natural resources, human capital and economic growth[END_REF] who interact education and natural resources in order to examine whether an increase in the level of education decreases the negative impact of natural resources on growth, we add the term (log(educ) * N R) to the regressors. For ease of computation we also exclude all the concomitant variables that where never significant in the previous estimations. The values of the information criteria are not reported, but the model with two growth regimes is again selected for each of the measures of natural resources we consider.

The estimations of the selected models are reported in table 11. Our result that natural resources have a positive impact in one regime but a negative or neutral effect in the other is robust, and democracy still helps to split countries into regimes. When we use the aggregated measure xgdp and the rent per capita Rent as the measures of natural resource the coefficient on the interact term (log(educ)*NR) indicates that more education decreases the marginal effect of natural resource on growth in the blessed regime (or group 1). However, when we replace the measure of natural resource by Ores -M etal results show that more education decreases the resource curse. There are no other important changes in the coefficients on the other explanatory variables.

Conclusion

This paper has tested a new hypothesis that has not yet been addressed by the literature that has tried to understand the conditions under which natural resources can be a blessing. We go beyond existing studies and test whether the impact of natural resources depends on the growth regime to which an economy belongs. To do so we consider that countries may follow different growth processes or regimes such that the marginal impact of explanatory variables on growth differs across regimes, enabling us to test whether natural resources are a curse or a blessing within each regime.

Our results indicate that for the period 1970-2005 the data is best fitted by a model of two regimes.

In one regime an abundance of natural resources has a significant positive impact on growth, while in the other regime an abundance of natural resources does not enhance growth. The analysis of the determinants of whether a country belongs or not to the blessed resources regime indicates that the level of democracy plays a crucial role, while education and economic institutions have no effect. We also find that the form of government (such as being parliamentary or presidential democracy) matters less for the regime membership than being democratic or autocratic. Moreover, once we control for the degree of democracy being a Sub-Saharan African or a Latin-American does not seem to be relevant to determine whether a country belongs to the blessed regime.

The policy implication of this analysis is that, resource rich countries that have suffered from their endowment in natural resources should try to figure out how to move to the resource blessed regimes, thus changing the environment in which growth occurs. External aid aimed at improving education (although it has benefits in itself) will not help countries to use their natural resource endowments in a growth-enhancing manner but promoting democracy (parliamentary or presidential) would increase the probability of the resource rich countries to be in the environment in which natural resources could be beneficial for their development. This last point supports the 'neocon agenda' defined by [START_REF] Selden | Neoconservatives and american mainstream[END_REF] that emphasizes the importance of encouraging democratic institutions in resource-rich economies.

Our analysis has only considered the direct impact of natural resources, future works on the link between natural resources and economic development should consider the indirect mechanism of the curse in a multiple growth regimes analysis by modeling a system of simultaneous equations using a mixture of regression approach. Also the two step stage method in the mixture model framework remains suited for the endogeneity issue.

Table 1 :

 1 Data descriptive and sources

	Variable	Obs. Mean	SD	Min	Max Description				Data source
	growth	498 1.82	2.75	-13.60 11.07 Average annual growth rate	PWT 6.3
	log(gdp)	498 8.77	1.01	6.43 10.64 Log of initial real GDP per capita	PWT 6.3
	log(pop + 0.05) 498 1.89	.16	1.49	2.33 Log of population growth + technol-	PWT 6.3
							ogy growth + depreciation rate
	log(inv)	498 3.01	.50	1.25	4.05 Log of investment rate		PWT 6.3
	log(educ)	498 1.58	.68	-1.64	2.57 Log of initial average years of educa-	Barro and Lee 2010
							tion of the total population aged over
							25
	dem	498 5.83	3.99	0	10 Political institutions:	degree of	www.systemicpeace.org,
							democracy (Polity IV)		Polity IV project
	eco	498 6.01	0.81	2.68	8.66 Economic institutions: index of Eco-	www.freetheworld.com,
							nomic Freedom of the World	version 2009
	xgdp	498 12.92 12.43	.23 76.07 Initial level of exports of primary	World Development In-
							goods over total gdp			dicators(2010)
	Metal-Ores	492 2.14	5.74 < 0000 55.44 Initial level of exports of metal and	World Development In-
							ores over total gdp			dicators(2010)
	Agri-food	498 6.92	7.25	.001 44.15 Initial level of exports of agriculture	World Development In-
							and food goods over total gdp	dicators(2010)
	Fuel	482 4.01	9.08 < 0000 63.12 Initial level of exports of fuel over to-	World Development In-
							tal gdp				dicators(2010)
	log(educ1970)	91 1.58	0.89	-1.64	2.39 Log of initial average years of educa-	Barro and Lee 2010
							tion of the total population aged over
							25
	dem	91 5.19	3.54	0	10 Political institutions:	degree of	www.systemicpeace.org,
							democracy (Polity IV)		Polity IV project
	eco	91 1.01	1.07	4.31	8.14 Economic institutions: index of Eco-	www.freetheworld.com,
							nomic Freedom of the World	version 2009
		growth log(gdp) log(pop) log(inv) log(educ) dem	eco	xgdp Metal-Ores Agri-Food Fuel
	growth	1.00
	log(gdp)	0.06	1.00
	log(pop)	-0.21	-0.66		1.00
	log(inv)	0.24	0.58		-0.43	1.00
	log(educ)	0.11	0.77		-0.59	0.45	1.00
	dem	0.07	0.63		-0.62	0.38	0.63	1.00
	eco	0.26	0.58		-0.41	0.33	0.51	0.46	1.00
	xgdp	-0.07	-0.16		0.33	-0.06	-0.12	-0.28 -0.08 1.00
	Metal-Ores -0.16	-0.06		0.19	-0.06	-0.04	-0.20 -0.01 0.45	1.00
	Agri-Food	-0.04	-0.31		0.27	-0.11	-0.15	-0.13 -0.05 0.52	-0.01	1.00
	Fuel	0.03	0.04		0.13	0.02	-0.05	-0.18 -0.07 0.68	-0.01	-0.08	1.00

Table 2 :

 2 Coefficients of correlation

		Cross-Section		Panel Data
	Variable	Ols	Ols		FE		RE		OlS-IV	RE-IV
		(1)	(2)	(3)	(4)	(5)	(6)
	log(gdp)	-1.150	* * *	-1.469	* * *	-5.130	* * *	-2.298	* * *	-1.454	* * *	-2.483	* * *
		(0.311)		(0.219)		(0.509)		(0.276)		(0.263)		(0.334)
	log(pop+0.05)	-0.911		-5.151	* * *	-5.858	* * *	-6.305	* * *	-5.592	* * *	-6.364	* * *
		(1.652)		(1.035)		(1.669)		(1.276)		(1.157)		(1.448)
	log(inv)	1.420	* * *	1.402	* * *	2.109	* * *	1.590	* * *	1.526	* * *	1.918	* * *
		(0.432)	(0.280)	(0.520)	(0.360)	(0.340)	(0.423)
	log(educ)	0.619		0.637	* *	0.252		0.972	* * *	0.515		1.182	* *
		(0.314)	(0.285)	(0.628)	(0.373)	(0.381)	(0.496)
	NR	-0.044 * * *	-0.006		0.019		-0.002		-0.032		-0.009
		(0.012)		(0.009)		(0.019)	(0.013)		(0.019)		(0.013)
	eco	0.606	* *	0.991	* * *	1.409	* * *	1.363	* * *	0.815	* * *	1.064	* * *
		(0.266)	(0.142)	(0.216)	(0.175)	(0.176)	(0.239)
	dem	-0.005	0.092	* *	-0.131	* *	-0.069		-0.085	-0.032
		(0.081)		(0.040)	(0.054)		(0.046)		(0.0565)		(0.078)
	Constant	4.899		13.34	* * *	18.97	* * *	19.84	* * *	15.03	* * *	21.48	* * *
		(4.721)	(2.864)	(3.485)	(3.565)	(3.209)	(3.866)
	time dummies	..		..	..	..	..
	nobs	71		498		498	498		388		388
	ncountries	71		91		91		91		83		83
	R-squared	0.44		0.23		0.36		0.32	0.25	0.22
	Hausman test							< 0.001
								(3)-(4)

Table 3 :

 3 Standard estimations. We use the aggregate measure of exports of primary goods xgdp for the natural resources variable. Time dummies are include for panel data estimations. For Hausman test, the p-value is reported. For IV estimation, first lags of log(educ), NR, eco and dem are used as instruments. Standard Errors are in parenthesis, *** significant at 1%, ** significant at 5%.

		BIC	CAIC
	K=1	2353.8	2368.8
	K=2 2280.3 2316.3
	K=3	2299.4	2356.4
	K=4	2304.3	2382.3

Table 4 :

 4 Panel data: selection of the mixture models. BIC and CAIC criterion are reported. K is the number of regimes. We use the aggregate measure of natural resources xgdp to measure NR. Selected model in bold.

	Variable		Mixture		Wald test
		group 1	group 2	statistic p-value
		(42%)	(58%)
	Intercept	15.409	* * *	13.092	* * *	0.22	0.64
		(2.791)		(4.149)
	log(gdp)	-1.937	* * *	-1.255	* * *	3.05	0.08
		(0.247)		(0.311)
	log(pop+0.05) -3.476	* * *	-5.935	* * *	1.91	0.17
		(0.929)		(1.507)
	log(inv)	2.542	* * *	0.640		14.64 < 0.001
		(0.261)	(0.413)
	log(educ)	1.348	* * *	0.501		2.662	0.1
		(0.278)	(0.423)
	NR	0.036	***	-0.015		8.29	0.004
		(0.009)	(0.014)
	eco 5	(0.129) 0.311 * *	(0.212) 1.298 * * *	15.53 < 0.001
	dem 5	(0.040) -0.201	* * *	0.058 -0.039		5.143	0.023
	time dummies	..		..
	Concomitant
	Intercept	-		1.880
				(2.962)
	eco	-		-0.145
				(0.509)
	dem	-		-0.297	* *
				(0.128)
	log(educ 1970 )	-		0.053 (0.545)
	Sub-Afri	-	0.737
				(0.851)
	Latin	-		5.084
				(2.882)
	R 2	0.56		0.26

Table 5 :

 5 Panel data: estimation results of the selected mixture model in table4where the measure of natural resources is xgdp. There are 91 countries and 498 observations. Time dummies are include. Standard errors in parenthesis. *** significant at 1%, ** significant at 5%.

	Group 1		Group 2
	Country		proba Country	proba Country	proba
	Australia	0.99 Algeria	1 Paraguay	1
	Austria		0.99 Argentina	1 Peru	1
	Bangladesh	0.84 Bahrain	1 Philippines	1
	Belgium		0.94 Bolivia	1 Portugal	0.95
	Benin		0.52 Brazil	0.99 Sierra Leone	0.67
	Botswana	0.75 Cameroon	0.99 Syria	1
	Canada		0.99 Central African Rep,	1 Tanzania	0.74
	China		0.97 Chile	1 Thailand	0.99
	Congo.Rep,	0.96 Colombia	0.85 Togo	1
	Cyprus		0.99 Costa Rica	0.98 Trinidad Tobago	1
	Denmark	0.99 Cote d'Ivoire	0.97 Uganda	0.58
	Finland		0.98 Dominican Rep,	0.99 Uruguay	1
	France		0.99 Ecuador	1 Venezuela	0.99
	Germany	0.99 Egypt	0.99 Zambia	1
	Greece		0.97 El Salvador	1 Zimbabwe	1
	India		0.99 Fiji	0.99
	Israel		0.99 Ghana	1
	Italy		0.99 Guatemala	1
	Japan		0.99 Guyana	1
	Korea.Rep,	0.99 Haiti	0.99
	Malaysia	0.95 Honduras	1
	Mali		0.87 Hungary	0.99
	Netherlands	0.99 Indonesia	0.99
	New Zealand	0.91 Iran	1
	Norway		0.99 Ireland	0.96
	Pakistan		0.99 Jamaica	1
	Poland		0.93 Jordan	1
	Senegal		0.74 Kenya	1
	Singapore	0.99 Lesotho	0.93
	South Africa	0.91 Malawi	1
	Spain		0.99 Mauritius	0.99
	Sri Lanka	0.89 Mexico	1
	Sweden		0.99 Mozambique	1
	Switzerland	0.99 Nepal	0.94
	Tunisia		0.99 Nicaragua	1
	Turkey		0.99 Niger	0.99
	UK		0.99 Panama	1
	US		0.99 Papua New Guinea	1
	Group 1		Group 2
			Means of key variables by group
	Group 1		Group 2
	growth	2.55		1.24
	(1.87)		(3.17)
	NR	8.78		16.21
	(11.36)		(12.27)
	log(educ0)	1.79		1.42
	(0.71)		(0.61)
	eco5	6.37		5.72
	(1.08)		(0.98)
	dem5	7.57		4.44
	(3.51)		(3.82)

Table 6 :

 6 Classification obtained from the selected mixture model with xgdp as the measure of natural resources. The numbers are the group membership posterior probabilities

		Group 1		Group 2
	Intercept	18.20	* * *	14.51	* * *
		(2.858)	(4.575)
	log(pop+0.05)	-4.345	* * *	-6.273	* * *
		(0.995)		(1.655)
	log(gdp 0 )	-2.102	* * *	-1.055	* * *
		(0.267)		(0.358)
	log(inv 5 )	2.513 (0.280) * * *	0.636 (0.452)
	log(educ 0 )	1.490 (0.309) * * *	0.271 (0.548)
	NR 0	0.027 (0.012) **	-0.028 (0.018)
	dem 5	-0.232	* * *	-0.012
		(0.057)		(0.077)
	eco 5	(0.149) 0.378 * *	(0.278) 0.965 * * *
	Observations	183	224
	R-squared	0.56		0.27
	Under test.	< 0.001		< 0.001
	Weak instr.	51.5	86.0

Table 7 :

 7 Panel data: IV estimations by groups, from the classification obtained in Table6. Standard errors in parenthesis. Time dummies are include. For under identification test, the p-value is reported. For weak instruments tests, the value of the first-stage-F statistic is reported. Standard errors in parenthesis.

			Xgdp Components
		Metal-Ores Agri-food Fuel	Rent
		(1)	(2)	(3)	(4)
	K=1	2315.8

*** significant at 1%, ** significant at 5%

Table 9 :

 9 Panel data: estimations of the selected models in Table8for alternative measures of natural resources. Time dummies are include. Standard errors in parenthesis. *** significant at 1%, ** significant at 5%. Data for fuel for Honduras and Malawi are not available, which reduces the number of countries to 89 for the estimation of the models with fuel.

				xgdp		Metal-Ores				Rent
		group1			group2		group1		group2			group1		group2
		(π1=45%)	(π2=55%)	(π1=43%)	(π2=57%)		(π1=41%)	(π2=59%)
	Intercept	16.824	* * *	11.407	* * *	16.958	* * *	11.955	* * *	19.015	* * *	-3.774
		(3.295)			(4.218)		(2.919)		(4.389)			(2.743)		(2.845)
	log(gdp)	-2.016	* * *	-1.446	* * *	-2.271	* * *	-1.449	* * *	-2.324	* * *	-1.044	* * *
		(0.287)			(0.327)		(0.243)		(0.328)			(0.251)		(0.377)
	log(pop + 0.05)	-3.559		* * *	-5.222	* * *	-3.823	* * *	-5.068		* * *	-4.445	* * *	0.088
		(1.036)			(1.410)		(1.002)		(1.437)			(0.919)		(0.616)
	log(inv)	2.489		* * *	0.979	* *	3.138	* * *	0.608			2.956	* * *	0.509
		(0.296)	(0.417)	(0.293)	(0.398)	(0.314)	(0.366)
	log(educ)	1.287		* * *	0.823	* *	1.135	* * *	0.855		* *	1.339	* * *	0.806
		(0.339)	(0.416)	(0.265)	(0.426)	(0.353)	(0.422)
	NR	0.039		***	-0.018		0.278	***	-0.086		***	0.088	*	0.119
		(0.01)			(0.017)		(0.079)	(0.033)			(0.045)	(0.104)
	eco	0.201		* * *	1.306	* *	0.346	* * *	1.319	* * *	0.273		1.762	* * *
		(0.135)	(0.214)	(0.132)	(0.22)			(0.165)	(0.252)
	demautoc	-1.328	* * *	-0.169		-1.302	* * *	-0.117		-1.120	* * *	0.226
		(0.322)			(0.399)		(0.291)		(0.393)			(0.314)		(0.455)
	time dummies	..			..	..		..	..		..
	Concomitant
	Intercept	-			0.512		-		0.624			-		0.299
					(0.396)			(0.385)				(0.501)
	demautoc 70	-			-1.882	* * *	-		-2.058	* * *	-		-2.575	* * *
					(0.700)				(0.671)					(0.899)
	pres 70	-		-1.916		-		-1.971			-		-3.445
					(2.215)				(2.339)					(2.533)
	Sub-afri	-									-		2.783	* *
														(1.356)
	Latin	-	-4.766	* *	-		4.733	* *	-		5.223	* *
					(2.128)				(2.151)				(2.434)
	R 2	0.53		0.28		0.59	0.28			0.54		0.25

Table 10 :

 10 Panel data: estimations with alternative measures of institutions. We replace the variable dem by a binary variable demautoc which takes the value of 1 for democracies and 0 for autocracies. The variable pres in the concomitant variable is equal to 1 for presidential democracies and 0 for parliamentary or mixed democracies. Time dummies are include. Standard errors in parenthesis. *** significant at 1%, ** significant at 5%, * significant at 10%

	Variable			Xgdp		Ores-Metal				Rent
		group1		group2	group1			group2		group1		group2
		(42%)			(58%)		(π1=41%)	(π2=59%)	(π1=50%)	(π2=50%)
	Intercept	14.952	* * *	13.367	* * *	16.060	* * *	13.922	* * *	3.056	* *	7.929
		(2.732)			(4.205)		(2.559)			(4.269)		(1.492)	(4.917)
	log(gdp 0 )	-1.985		* * *	-1.272	* * *	-2.192	* * *	-1.218	* *	-1.810	* * *	-1.013	* * *
		(0.243)			(0.313)		(0.234)			(0.311)		(0.232)		(0.385)
	log(pop + 0.05) -3.355		* * *	-5.749	* * *	-3.608	* * *	-6.019	* * *	0.115		-4.306	* *
		(0.919)			(1.551)		(0.866)			(1.512)		(0.3)		(1.738)
	log(inv)	2.544		* * *	0.707		2.969		* * *	0.441		2.957	* * *	0.569
		(0.259)	(0.421)	(0.278)	(0.404)	(0.239)	(0.454)
	log(educ)	1.754		* * *	0.039		1.333		* * *	0.022		2.437	* * *	-0.509
		(0.329)	(0.568)	(0.256)	(0.478)	(0.286)	(0.736)
	NR	0.098		***	-0.065		0.388		**	-0.232	***	0.962	***	-0.222
		(0.032)		(0.045)		(0.192)		(0.079)		(0.168)	(0.261)
	log(educ) * N R -0.039		**	0.032		-0.069			0.123	**	-0.402	***	0.159
		(0.019)			(0.027)	(0.111)			(0.055)	(0.077)		(0.174)
	eco	0.290		* *	1.305	* * *	0.407		* * *	1.339	* * *	0.398	* * *	1.527	* * *
		(0.127)	(0.217)	(0.126)	(0.214)	(0.151)	(0.246)
	dem	-0.186	* * *	-0.039	-0.192	* * *	-0.046		-0.140	* * *	0.055
		(0.039)			(0.059)		(0.038)			(0.060)		(0.040)		(0.070)
	time dummies	..	..		..	..		..	..
	Concomitant
	Intercept	-			1.438	* * *	-		1.597	* * *	-		0.396
					(0.546)				(0.562)			(0.599)
	dem	-		-0.343	* * *	-		-0.363	* * *	-		-0.228	* *
					(0.092)					(0.095)				(0.091)
	Latin	-	4.683		-		5.329	* *	-		5.037
					(2.483)				(2.623)			(2.672)
	Sub-afri											-		0.411
														(0.730)
	R 2	0.27		0.56	0.28			0.59	0.28		0.57

Table 11 :

 11 Panel data: stimation results of the mixture model with the interact term between education and natural resource. Time dummies are include. Standard errors in parenthesis. *** significant at 1%, ** significant at 5%. We include to the concomitant variables a Latin American dummy Latin and a Sub-African dummy Sub-afri to controle for geography.

Also, Norway, Canada and the United States are examples of countries rich in natural resources but do not suffer from the curse of natural resources.

For a survey of the existing hypotheses and analyses see[START_REF] Ploeg | Natural resources: Curse or blessing?[END_REF].

See Glaeser et al. (2004) and[START_REF] Flachaire | Political versus economic institutions in the growth process[END_REF] among others.

See Acemoglu et al. (2005),[START_REF] Eicher | Institutions and economic performance: Endogeneity and parameter heterogeneity[END_REF] and[START_REF] Flachaire | Political versus economic institutions in the growth process[END_REF].

Since this approach has been used before to analyze growth regimes we do not give all the steps of the functional form of the mixture of regression methods for panel data. For more details the reader is invited to refer to[START_REF] Owen | Do all countries follow the same growth process[END_REF].

These two measures are used in[START_REF] Flachaire | Political versus economic institutions in the growth process[END_REF] where authors explain how political and economic institutions enhance differently the economic development of countries

[START_REF] Barro | Democracy and growth[END_REF],[START_REF] Glaeser | Do institutions cause growth[END_REF] and[START_REF] Flachaire | Political versus economic institutions in the growth process[END_REF] support that the empirical evidence does not establish a direct link between political institutions and economic performance.

See Persson (2005) for the role of constitutions on economic development and[START_REF] Andersen | Constitutions and the resource curse[END_REF] for natural resources and constitutions.


Gilles De Truchis

Approximate Whittle Analysis of Fractional Cointegration and the Stock Market Synchronization Issue Gilles de Truchis Approximate Whittle Analysis of Fractional Cointegration and the Stock Market Synchronization Issue

Keywords: Fractional cointegration, Frequency domain, Full-band estimator, Monte-Carlo simulation, Parametric estimation JEL: C32, C15, C58, G15

I consider a bivariate stationary fractional cointegration system and I propose a quasi-maximum likelihood estimator based on the Whittle analysis of the joint spectral density of the regressor and errors to estimate jointly all parameters of interest of the model: the long run coefficient and the long memory parameters of the regressor and errors. I lead a Monte Carlo experiment which reveals the good finite sample properties of this estimator, even when the parameter space is extended to the non-stationary regions. An application to the stock market synchronization is proposed to illustrate the empirical relevance of this estimator.

Introduction

Consider the following triangular bivariate fractional cointegration representation

(1 -L) γ (y t -βx t ) = ε 1t , (1 -L) δ x t = ε 2t , t = 1, 2, ..., n, (1)
where δ ∈ [0, 1/2), γ ∈ (-1/2, 1/2) and (1 -L) α is the fractional filter, further denoted ∆ α and defined by its binomial expansion

(1 -L) α = +∞ k=0 a j (α)L j , a j (α) = Γ(k -α) Γ(k + 1)Γ(-α) L k (2)
Email address: gilles.de-truchis@univ-amu.fr (Gilles de Truchis ) 1 Aix-Marseille School of Economics, Aix-Marseille University, Château La Farge, Route des Milles 13290 Aix-en-Provence. Tel.: 00 33 (0)4 42 93 59 60; fax: 00 33 (0)4 42 38 95 85.

Γ(z) = +∞ 0 t z-1 e -t dt, (3)
with L the lag operator. Following the general and seminal definition of the cointegration offered by [START_REF] Granger | Developments in the study of cointegrated economic variables[END_REF], in equation ( 1), y t is said cointegrated if the error term, ν t = y t -βx t , satisfies ν t ∼ I(γ) with γ < δ and x t ∼ I(δ). The estimation of equation ( 1) usually operates in two steps. The first step is to estimate the long run coefficient, β, whereas the second step is to estimate the order of integration of the residuals, γ. Many studies restrict their analysis to integer integration orders. In most cases, x t is assumed to possess a unit root (i.e. δ = 1) and the traditional cointegration also imposes γ = 0. More recently, has emerged the idea that cointegration relationship can exist between stationary variables (that is δ < 1/2). Some studies have suggested adapted estimators for β. For instance, [START_REF] Robinson | Semiparametric analysis of long-memory time series[END_REF] develops a consistent semiparametric Narrow-Band Least Squares estimator (NBLS) of β that essentially performs the time domain Least Square Estimator (LSE) on a degenerating band of frequencies around the origin.

Then, [START_REF] Christensen | Asymptotic normality of narrow-band least squares in the stationary fractional cointegration model and volatility forecasting[END_REF] demonstrate the asymptotic normality of the NBLS when δ + γ < 1/2 and [START_REF] Nielsen | Fully modified narrow-band least squares estimation of weak fractional cointegration[END_REF] extend it to the weak fractional cointegration2

(that is δ-γ < 1/2). In most studies, these estimators are combined with semi-parametric estimators of long memory (see for instance [START_REF] Marinucci | Semiparametric fractional cointegration[END_REF], [START_REF] Christensen | Asymptotic normality of narrow-band least squares in the stationary fractional cointegration model and volatility forecasting[END_REF] and [START_REF] Nielsen | Fully modified narrow-band least squares estimation of weak fractional cointegration[END_REF]). We can cite among other the well-known logperiodogram regression (LPE) of [START_REF] Geweke | The estimation and application of long memory time series models[END_REF] but also, [START_REF] Künsch | Statistical aspects of self-similar processes[END_REF], [START_REF] Robinson | Gaussian semiparametric estimation of long range dependence[END_REF] and Andrews and Guggenberger (2003). [START_REF] Velasco | Gaussian semi-parametric estimation of fractional cointegration[END_REF] suggests to estimate simultaneously δ and γ but requires a consistent estimator of β. This innovative approach of estimating jointly several parameters is extended to β, δ and γ by [START_REF] Nielsen | Local whittle analysis of stationary fractional cointegration and the implied-realized volatility relation[END_REF]. This consists in a local Whittle analysis of the joint spectral density of x t and ν t . This methodology has the advantage of being invariant to the miss-specification of short-term dynamics but is only √ mconsistent where m depends on the bandwidth selection. For practical purpose, the bandwidth selection is important because of the variance of the estimator that can increase. For instance, a too high bandwidth can deteriorate the variance if the process possess a short run dynamics because of the confusion in the frequency domain between the low and high frequencies. Simultaneously, [START_REF] Hualde | Root-n-consistent estimation of weak fractional cointegration[END_REF] have developed a √ n-consistent parametric estimator of weak fractional cointegration following the suggestion of [START_REF] Robinson | Cointegration in fractional systems with unkown integration orders[END_REF] and exploiting an error correction form of (1). This estimator has the advantage of covering a wide range of integration orders, however, it requires a more complex optimization procedure than [START_REF] Nielsen | Local whittle analysis of stationary fractional cointegration and the implied-realized volatility relation[END_REF].

In this paper, I propose a one step estimator of fractional cointegration. It is a parametric approach that is sensible to miss-specification but that simulations suggest to be √ n-consistent whereas than the one of Nielsen ( 2007) is only √ m-consistent. It also contrasts with those of [START_REF] Hualde | Root-n-consistent estimation of weak fractional cointegration[END_REF] and [START_REF] Nielsen | Local whittle analysis of stationary fractional cointegration and the implied-realized volatility relation[END_REF] because according to the Monte Carlo simulation, it can be applied to strong, weak and stationary cointegration cases. It is based on a frequency domain Whittle approximation of the likelihood further termed Whittle Quasi-Maximum Likelihood Estimator (Whittle QMLE). The remainder of the paper is laid out as follows. In the section 2 some generalities on the long memory are exposed and the Whittle QMLE is developed. In the section 3 the Monte Carlo simulation is described and performed.

In the section 4, an application on the stock market synchronization is proposed to illustrate the empirical relevance of the Whittle QMLE. The section 5 concludes.

The stationary fractional cointegration model

The multivariate Whittle estimator of fractional cointegration

In this section, the model is developed with respect to the stationary regions of long memory parameters (that is δ and γ are less than 1/2). In a more general form than the equation (2), the Gaussian process x t (equivalently ν t , also assumed to be Gaussian) can be restated as follows

x t = ∞ j=0 κ( j; δ)ε 1t-j , ∞ j=0 κ( j; δ) 2 < ∞, κ(0; δ) = 1, t ∈ Z (4)
for κ(.; δ) ∈ R. In order to state the spectral density of x t , let g(λ; δ) = ∞ j=0 κ( j; δ)e i jλ be the transfer function. Then, the spectral density of x t is defined by,

f x (λ; δ) = σ 2 2π |g(λ; δ)| 2 , σ 2 = var(ε 2t ), (5)
where |g(.)| is the complex modulus of g(.). This results in that the well-known Whittle estimator of δ is defined as δn = arg min δ∈D Q n (δ) with D a compact subset of R 3 and

Q n (δ) = -n π -π log f x (λ j ; δ) dλ + π -π f x (λ j ; δ) -1 I xx (λ j ) dλ , (6)
where π -π log f x (λ j ; δ) dλ < ∞ is assumed, implying that x t is non-deterministic. In equation ( 6), I xx (λ j ) denotes the periodogram of x t defined as

I xx (λ j ) = w x (λ j )w x (λ j ), w x (λ j ) = 1 2πn n t=1 x t e itλ j , (7)
with w x (λ j ) the Fourier transform of x t and λ j = (2π j/n) the angular frequency. In the following, it will be preferred the discrete version of (6) that is

Q n (δ) = - n j=1 log f x (λ j ; δ) + f x (λ j ; δ) -1 I xx (λ j ) (8)
Notice that in Q n (δ) the zero frequency is left out of the summation, implying this estimator is invariant to the presence of nonzero mean. One can attempt to estimate step by step the equation

(1) using a consistent estimator of β. However, it is more efficient to estimate jointly β, δ and γ. That is the reason why I consider a multivariate extension of the Whittle estimator described above.

Let w t be a bivariate Gaussian sequence such as w t = (ν t , x t ) then let define θ = (θ 1 , θ 2 ) , θ 1 = (γ, δ) and θ 2 = (β). Rewriting equation (4) in a multivariate framework, we obtain

w t = ∞ j=0 K( j; θ 1 )ε 1t-j , ∞ j=0 tr K( j; θ 1 )Σ(θ)K( j; θ 1 ) < ∞, K(0; δ) = I, (9)
where elements of K are all real, t ∈ Z and Σ is a nonsingular 2 × 2 matrix. It follows the transfer matrix G(λ; θ 1 ) = ∞ j=0 K( j; θ 1 )e i jλ and the joint spectral density function

f w (λ, θ) = 1 2π G(λ; θ 1 ) -1 Σ(θ)(G(λ; θ 1 ) -1 ) * , (10)
where the superscript asterisk denotes the conjugate transpose. Similarly to the univariate case, the multivariate Whittle estimator of θ is defined as θ = arg min

θ∈D Q n (θ) with D a compact subset of R 2 and Q n (θ) = - n j=1
log det f w (λ j ; θ 1 ) + tr f w (λ j ; θ 1 ) -1 I ww (λ j ; θ 2 ) (11)

With respect to the periodogram in the multivariate case, we have

I ww (λ j ; θ 2 ) = w w (λ j ; θ 2 )w w (λ j ; θ 2 ) * , w w (λ j ; θ 2 ) = (2πn) -1 n t=1           ν t x t           e itλ j (12)
It follows that

I ww (λ j ; θ 2 ) =           I yy (λ j ) -2βI xy (λ j ) + β 2 I xx (λ j ) I xy (λ j ) -βI xx (λ j ) I xy (λ j ) -βI xx (λ j ) I xx (λ j )           , (13)
with I ab (λ j ) the cross-periodogram of a t and b t defined by

I ab (λ j ) = w a (λ j )w b (λ j ) (14)

The fractionally integrated VAR(p) model of cointegration

Now, I develop the model when (ν t , x t ) follows a vector autoregressive fractionally integrated (VARFI) process. In this case, let the system of equations in (1) be

          ϕ 11 (L) ϕ 12 (L) ϕ 21 (L) ϕ 22 (L)                     (1 -L) γ (1 -L) δ                     ν t x t           =           ε 1t ε 2t           (15)           ε 1t ε 2t           ∼ i.i.d N                     0 0           ,           σ 11 σ 12 σ 21 σ 22                     (16)
with ϕ i j (L) the lag polynomial of order p, where ϕ i j (L) = p k=1 1 -φ i j (k)L k and has all its eigenvalues less than 1 in modulus. Let G(λ; θ 1 , φ) be the transfer function of ( 15) and defined as

G(λ; θ 1 ) = ∞ j=0 K( j; θ 1 )e i jλ A( j; φ)e i jλ = ∞ j=0 Λ(e i jλ )Φ(e i jλ ), ( 17
)
where φ = φ i j (k) for {i, j} = {1, 2} and k = {1, ..., p}. Thus, the autocorrelated model has a spectral density expressed by

f w (λ, θ, φ) = 1 2π Λ(e i jλ ) -1 Φ(e i jλ ) -1 Σ(θ, φ)(Φ(e i jλ ) -1 ) * (Λ(e i jλ ) -1 ) * (18)

Finite sample investigation

In this section, I propose a Monte Carlo simulation in order to investigate the finite sample performance of the multivariate Whittle estimator of fractional cointegration. The study of asymptotic properties will be the subject of a forthcoming paper. For now, the consistency of the multivariate Whittle estimator of long-range dependent process is provided by [START_REF] Hosoya | A Limit theory for long-range dependence and statistical inference on related models[END_REF] in the stationary case. However, this experiment is not confined to the stationary regions of δ and γ because I anticipate that the multivariate Whittle estimator is still consistent when estimator in these cases because some empirical stylized fact imply the stationary, the weak or the strong (that is δγ > 1/2) fractional cointegration cases. For instance, volatility data are often found to be stationarity while macroeconomics data often possess unit root. The simulations are conducted in the following model considering some regular restrictions:

δ ∈ [0, 1/2) (1/2, 1] and γ ∈ (-1/2, 1/2) (1/2, 1]. A
          ∆ γ ν t ∆ δ x t           =           φ 11 φ 12 φ 21 φ 22                     ∆ γ ν t-1 ∆ δ x t-1                     ε 1t ε 2t           , ( 19
)
where φ i j (k), k = 1 is denoted φ i j . According to equation (17), Λ(e i jλ ) is simply

Λ(e i jλ ) =           |1 -e i jλ | γ 0 0 |1 -e i jλ | δ           , ( 20
)
and φ i j enters the transfer matrix through

Φ(e i jλ ) = I -          
φ 11 e i jλ φ 12 e i jλ φ 21 e i jλ φ 22 e i jλ

          (21)
From the system of equations in (19) I set up two models. For each model, I generate 1000 artificial series for sample size n = {256; 512}. I also constrain φ 12 = φ 21 = φ 22 = 0 to preserve the weak exogeneity of x t .

i) Model A:

         (1 -L) δ x t = ε 2t (1 -L) γ ν t = ε 1t , ρ = corr(ε 1t , ε 2t ) = 0;
ii) Model B:

         (1 -L) δ x t = ε 2t (1 -0.5L)(1 -L) γ ν t = ε 1t , ρ = corr(ε 1t , ε 2t ) = 0;
y t is generated from (1) with β = 1. The case of the stationary fractional cointegration is explored for δ = 0.4 and γ = {0.0, 0.2, 0.3, 0.4} where γ = 0.4 corresponds to spurious fractional regression. The case of the weak fractional cointegration is investigated when δ = {0.6, 0.8, 1.0} and δγ ≤ 1/2. Alternatively, the case of the strong fractional cointegration is considered when δ = {0.6, 0.8, 1.0} and δγ > 1/2. Finally, the standard cointegration occurs when δ = 1 and γ = 0. When δ = γ = 1, the regression is spurious. For each simulation, I report the bias and the root mean squared error (RMSE), defined by 1

I I i=1 (E[ θ i -θ]) var( d) + (Bias[ d|d]) 2 .
All computations are performed using RATS 8.013 .

The model A and B are consistent with the model presented in section 2. Nonetheless, it increases in complexity with B because of the presence of short run dynamics. Conversely, the model A is very simple and describes a multivariate fractional white noise. I also perform an unreported investigation of model A and B in presence of nonzero correlation between ε 1t and ε 2t . Consequently, Σ is no longer block-diagonal and one can anticipate some complication in this case. Notably, the model cannot identify separately ρ and β and estimate β + ρ. As regards the stationary fractional cointegration, the bias and the RMSE of β are very low for all sample size. Results of δ and γ are particularly subject to higher bias and variances when γ is close to 1/2. Overall, the bias and the variance decrease when the sample size increases.

Compared with the results of [START_REF] Nielsen | Local whittle analysis of stationary fractional cointegration and the implied-realized volatility relation[END_REF] and [START_REF] Hualde | Root-n-consistent estimation of weak fractional cointegration[END_REF], these results are slightly more biased but display lower variance. When δ is greater than 1/2, the assumption δ ∈ [0, 1/2) is violated. However, results are suggesting that the Whittle QMLE of fractional cointegration is still consistent for some non-stationary regions of δ and γ including the unit root case. When δ = {0.6, 0.8} the bias is still very low but the RMSE increases when δ = γ. No significant differences appear between the cases of strong (δ -γ > 1/2) and weak (δ -γ ≤ 1/2) fractional cointegration. Concerning the long memory parameters, results are similar to the stationary case. Since [START_REF] Hualde | Root-n-consistent estimation of weak fractional cointegration[END_REF] essentially investigate the finite sample properties of their estimator on β, results cannot be compared. [START_REF] Nielsen | Local whittle analysis of stationary fractional cointegration and the implied-realized volatility relation[END_REF] does not explore the non-stationary cases and similarly, results cannot be confronted in this case. I give a special attention to the results when δ = 1 because this case is the most investigated in the literature.

Note that in this case, the results are not significantly different. Moreover, in the case of the spurious regression, the Whittle QMLE does not seem to have an additional bias. This seems to confirm the conjecture that the estimator is still consistent when δ = 1. The Model B is increasing in complexity. Again, it is difficult to compare the results with the literature but clearly the short-run dynamics negatively impact the bias and the variance.

Observe that the bias in the estimate of γ is less pronounced in the case of stationary fractional cointegration, that is δ = 0.4 and γ ≤ 0.4 in this simulation. While the Whittle QMLE poorly estimates the model B when the sample size is n = 256, the bias considerably decreases when the sample size increase. Notice that the Whittle QMLE seems inconsistent in the classical spurious regression case, that is δ = 1.0 and γ = 1.0. Globally, the bias concerning γ increases when δ = 1.0. Unreported experiment investigates the case of a non-null correlation between ε 1t and ε 2t , termed ρ. In this case, Σ is no-longer block-diagonal and one can anticipate some complication in this case. Regarding to this specification, the estimates of the integration orders are moderately impacted but the model cannot identify separately ρ and β and estimate β + ρ.

Empirical illustration

In this section, I investigate the question of the stock market synchronization in order to illustrate the empirical relevance of the Whittle QMLE. This issue has found a greater interest in the last decades with the creation of the Economic and Monetary Union (see for instance Adjaout and Danthine ( 2004) and [START_REF] Gilmore | Bilateral and multilateral cointegration properties between the German and Central European equity markets[END_REF]) and has many implications in terms of portfolio diversification. Indeed, the stock market synchronization is closely related to monetary integration because of the reduction in the exchange rate volatility that promotes economic trade and financial integration. Consequently, it can be expected that the creation of the EMU has increased the stock market synchronization of the member countries. The question can be asked concerning the non-member European countries but also for some non-European countries because of the raise in trade intensity, international shocks and portfolios diversification. A convenient way to test for stock market synchronization is to explore the presence of comovement (Wälti ( 2011)) or long run correlation between stock market returns or volatility. [START_REF] Gilmore | International portfolio diversification: US and Central European equity markets[END_REF], [START_REF] Gilmore | Bilateral and multilateral cointegration properties between the German and Central European equity markets[END_REF] and has notably been impacted by the creation of the euro. Thus we also consider sub-periods, before and after the creation of the euro.

I estimate the equation (1) for each bilateral relation and I test the lag structure against the hypothesis of a vector fractional white noise process. The V ARFI(1, δ, γ) process hypothesis can never be rejected. The star tags do not identify the significance of the result at 10 percent but a stationary fractional cointegration relationship.

The full sample estimation reveals several long-run relationship (table 5). Concerning the two European countries, the dimension reduction occurs with the IBEX 35 and the CAC 40 suggesting a market synchronization. Similar relations appear between the FTSE 100 and the CAC 40, the IBEX 35 and the FTSE and the SMI and the CAC although the United Kingdom and the Switzerland are not in the euro zone. In most of cases there is no evidence of cointegration on bilateral basis between European countries and non European countries, except for the SMI 20 and the S&P500 and the IBEX 35 and S&P500.

The first sub-sample covers the period before the creation of the euro (table 6). During this period, the monetary integration was insured by a basket of the currencies of the European Community member states: the European Currency Unit (ECU). This is supported by one cointegration relationship between the CAC 40 and the IBEX 35 implying that the CAC 40 squared returns' depended on the IBEX 35 in the long run. A few Similar long-term correlations appear between the SMI 20 and the FTSE 100 and the SMI 20 and the IBEX 35.

In order to appreciate the impact of the creation of the euro, I consider now the second sub-sample that covers the period 1999-2011 (table 7). Clearly there is more cointegration relationships in comparison with the first sub-period but the impact is moderated. As in previous estimates, the IBEX 35 and the CAC 40 are correlated in the long run. The IBEX index is also cointegrated with the FTSE 100 and the S&P 500. A similar cointegration relationship can be observed between the SMI 20 and the CAC40, the FTSE and the S&P 500. In comparison with the ECU system, there is less benefit for US investors to invest in these stock index, in terms of portfolio diversification, since the creation of the euro. Indeed, the S&P 500 is cointegrated with the CAC 40 and the FTSE 100. as the CAC 40 and the FTSE 100.

To summarize, the creation of the euro has seemingly increased the stock markets synchronization of the countries considered but moderatly. This has led to a greater monetary integration than the ECU system. This implies an impact in terms of portfolios diversification and results can help to clarify the investors horizons.

Final comments

I considered a parametric Whittle multivariate approach of a bivariate system of fractional cointegration. I suggested to jointly estimate all parameters of interest of the model and possibly others nuisance parameters. A Monte Carlo experiment is proposed and confirms the good finite sample properties of this estimator in the stationary regions of the residuals and the regressor (that is δ and γ are less than 1/2). This also reveals that the Whittle QMLE can be extended to the analysis of the weak and strong fractional cointegration cases. These results slice with other fractional cointegration estimators that concentrate on specific cases. A concise empirical analysis of the question of the stock market synchronization is presented. It points out that the stationary fractional cointegration model is appropriated to investigate this question and highlights several long-term relationship between different stock market indexes. Conclusions in terms of portfolio diversification can be deducted.

  and Égert and Kocenda (2007) investigate the stock market synchronization issue in the long-run through the traditional cointegration but find no strong evidence of long-term correlation. In this paper I bring the new perspective of the fractional cointegration. In contrast to Wälti (2011) that leads a panel analysis and examines the synchronization causes, this study is more interested by the question of the existence of the synchronization phenomenon in a bivariate context. A similar methodology is used by[START_REF] Nielsen | Fully modified narrow-band least squares estimation of weak fractional cointegration[END_REF] in order to analyze how the volatility of a particular stock depends on the volatilities of two stock market indexes.In the following, I consider the squared returns of six national stock indexes: CAC 40, IBEX 35, SMI 20, FTSE 100, S&P 500, NIKKEI 225. Weekly average data are used from January 1994 to December 2011 and expressed in local currency 4 . The weekly frequency is preferred here to avoid the issue of non-synchronous trading hours encountered with daily data and because of the lack of information provided by monthly data. Concerning the monetary inegration, obviously the French index and the Hispanic index are strongly related while the Switzerland index and the British index represent a lower degree of integration. The American and Japanese stock indexes are investigated although they are not European countries because of the interest of these countries in terms of portfolio diversification. Several empirical studies point out that the financial integration can vary over time(Cappiello et al. (2006), Égert and[START_REF] Ègert | Time-varying synchronization of European stock markets[END_REF]

  Adjaout, K., Danthine, J.P., 2004. Equity returns and integration: is Europe changing? Oxford Review of Economic Policy, 20,555-570. Andrews, D. W. K., Guggenberger, P., 2003. A bias-reduced log-periodogram regression estimator for the long memory parameter. Econometrica, 71(2), 675-712. Cappiello, L., Hrdahl, P., Kadareja, A., Manganelli, S., 2006. The Impact of the Euro on Financial Markets. ECB, Working Paper 598.

Table 1 :

 1 Model An = 256 -φ 11 = 0

	n = 256	θ	Bias	RMSE	Bias	RMSE	Bias	RMSE	Bias	RMSE
	δ = 1.0	γ	0		0,4		0,6		1,0
		β	0.000	0.012	-0.003	0.040	0.000	0.067	-0.007	0.263
		γ	-0.027	0.068	-0.124	0.155	-0.091	0.133	-0.044	0.103
		δ	-0.034	0.086	-0.036	0.090	-0.037	0.094	-0.029	0.086
	δ = 0.8	γ	0		0,4		0,6		0,8
		β	0.000	0.024	-0.003	0.061	0.002	0.087	-0.001	0.127
		γ	-0.026	0.068	-0.117	0.149	-0.084	0.128	-0.049	0.112
		δ	-0.076	0.121	-0.079	0.125	-0.080	0.129	-0.069	0.117
	δ = 0.6	γ	0		0,2		0,4		0,6
		β	0.000	0.040	-0.003	0.057	0.001	0.080	0.000	0.094
		γ	-0.023	0.067	-0.105	0.130	-0.109	0.142	-0.082	0.129
		δ	-0.076	0.121	-0.079	0.125	-0.080	0.129	-0.069	0.117
	δ = 0.4	γ	0		0,2		0,3		0,4
		β	0.000	0.057	0.000	0.070	0.002	0.083	-0.001	0.084
		γ	-0.021	0.066	-0.100	0.125	-0.109	0.137	-0.109	0.143
		δ	-0.106	0.137	-0.106	0.140	-0.107	0.142	-0.097	0.132

Table 2 :

 2 Model An = 512 -φ 11 = 0

	n = 512	θ	Bias	RMSE	Bias	RMSE	Bias	RMSE	Bias	RMSE
	δ = 1.0	γ	0		0,4		0,6		1,0
		β	0.000	0.007	0.000	0.025	0.000	0.047	-0.002	0.246
		γ	-0.010	0.029	-0.085	0.094	-0.071	0.084	-0.050	0.064
		δ	-0.047	0.058	-0.048	0.060	-0.045	0.058	-0.045	0.057
	δ = 0.8	γ	0		0,4		0,6		0,8
		β	0.000	0.014	0.000	0.037	0.000	0.050	-0.001	0.072
		γ	-0.009	0.028	-0.082	0.091	-0.067	0.081	-0.047	0.066
		δ	-0.044	0.062	-0.047	0.065	-0.043	0.063	-0.041	0.061
	δ = 0.6	γ	0		0,2		0,4		0,6
		β	0.000	0.024	0.000	0.035	0.000	0.043	-0.001	0.044
		γ	-0.008	0.028	-0.069	0.077	-0.079	0.089	-0.068	0.081
		δ	-0.066	0.079	-0.069	0.082	-0.066	0.079	-0.064	0.077
	δ = 0.4	γ	0		0,2		0,3		0,4
		β	0.001	0.035	0.001	0.040	0.000	0.043	-0.001	0.041
		γ	-0.007	0.027	-0.067	0.075	-0.077	0.086	-0.080	0.090
		δ	-0.080	0.088	-0.081	0.091	-0.079	0.088	-0.077	0.087

Table 3 :

 3 Model Bn = 256 -φ 11 = 0.4

	n = 256	θ	Bias	RMSE	Bias	RMSE	Bias	RMSE	Bias	RMSE
	δ = 1.0	γ	0		0,4		0,6		1,0
		β	0.001	0.020	0.002	0.064	0.001	0.106	-0.006	0.438
		γ	-0.098	0.172	-0.236	0.404	-0.349	0.564	-0.319	0.641
		δ	-0.098	0.200	-0.109	0.232	-0.095	0.225	-0.162	0.382
	δ = 0.8	γ	0		0,4		0,6		0,8
		β	0.001	0.037	-0.001	0.081	-0.001	0.103	0.001	0.152
		γ	-0.088	0.165	-0.179	0.343	-0.197	0.411	-0.214	0.483
		δ	-0.084	0.195	-0.092	0.221	-0.106	0.268	-0.113	0.280
	δ = 0.6	γ	0		0,2		0,4		0,6
		β	-0.001	0.055	-0.003	0.074	-0.002	0.081	-0.001	0.089
		γ	-0.074	0.167	-0.116	0.237	-0.139	0.287	-0.164	0.364
		δ	-0.096	0.193	-0.106	0.204	-0.101	0.197	-0.116	0.228
	δ = 0.4	γ	0		0,2		0,3		0,4
		β	-0.003	0.066	-0.003	0.074	-0.003	0.075	-0.002	0.076
		γ	-0.064	0.151	-0.108	0.220	-0.112	0.247	-0.122	0.275
		δ	-0.124	0.184	-0.121	0.183	-0.122	0.183	-0.122	0.184

Table 4 :

 4 Model Bn = 512 -φ 11 = 0.4

	n = 512	θ	Bias	RMSE	Bias	RMSE	Bias	RMSE	Bias	RMSE
	δ = 1.0	γ	0		0,4		0,6		1,0
		β	0.000	0.010	0.000	0.037	0.000	0.065	0.009	0.371
		γ	-0.012	0.161	-0.119	0.461	-0.071	0.403	-0.057	0.433
		δ	-0.017	0.102	-0.020	0.077	-0.013	0.117	-0.028	0.219
	δ = 0.8	γ	0		0,4		0,6		0,8
		β	0.000	0.021	0.000	0.043	0.002	0.050	0.003	0.085
		γ	-0.008	0.163	-0.063	0.367	-0.047	0.354	-0.018	0.341
		δ	-0.002	0.086	-0.001	0.126	-0.002	0.123	-0.003	0.142
	δ = 0.6	γ	0		0,2		0,4		0,6
		β	0.000	0.032	0.001	0.039	0.001	0.041	0.001	0.041
		γ	0.000	0.148	-0.031	0.280	-0.052	0.336	-0.009	0.267
		δ	-0.011	0.097	-0.010	0.099	-0.009	0.079	-0.011	0.118
	δ = 0.4	γ	0		0,2		0,3		0,4
		β	0.001	0.039	0.001	0.040	0.001	0.039	0.001	0.038
		γ	0.005	0.147	-0.015	0.245	-0.026	0.278	-0.024	0.283
		δ	-0.022	0.144	-0.023	0.148	-0.023	0.146	-0.014	0.101

Table 5 :

 5 Estimating for bilateral stationary fractional cointegration for the period1994-2011 (n = 934)

	y t		CAC			FTSE			NIKKEI
	x t	β	δ	γ	β	δ	γ	β	δ	γ
	CAC				0.452* 0.236* 0.137*	0.090	0.236	0.129
					(0.027) (0.032) (0.039) (0.033) (0.035) (0.041)
	FTSE	0.459	0.231	0.745				0.114	0.231	0.127
		(0.027) (0.035) (0.039)				(0.033) (0.038) (0.042)
	NIKKEI	0.098	0.147	0.226	0.108	0.147	0.219
		(0.033) (0.040) (0.033) (0.032) (0.038) (0.039)
	S&P	0.287	0.220	0.208	0.269	0.220	0.180	0.077	0.220	0.133
		(0.034) (0.035) (0.033) (0.032) (0.034) (0.039) (0.032) (0.034) (0.042)
	IBEX	0.392	0.191	0.170	0.340	0.191	0.170	0.100	0.191	0.134
		(0.033) (0.035) (0.032) (0.029) (0.033) (0.038) (0.033) (0.034) (0.041)
	SMI	0.341	0.179	0.178	0.325	-0.780	0.158	0.082	0.179	0.137
		(0.031) (0.035) (0.032) (0.029) (0.015) (0.037) (0.031) (0.035) (0.039)
	y t		S&P			IBEX			SMI
	x t	β	δ	γ	β	δ	γ	β	δ	γ
	CAC	0.261	0.236	0.194 0.365* 0.236* 0.101* 0.355* 0.236* 0.099*
		(0.032) (0.031) (0.033) (0.028) (0.032) (0.036) (0.031) (0.030) (0.039)
	FTSE	0.279	0.231	0.177 0.347* 0.231* 0.120* 0.371* 0.231* 0.098*
		(0.034) (0.038) (0.035) (0.031) (0.037) (0.035) (0.033) (0.037) (0.039)
	NIKKEI	0.105	0.147	-0.373	0.104	0.147	0.182	0.085	0.147	0.173
		(0.035) (0.039) (0.014) (0.033) (0.040) (0.033) (0.035) (0.039) (0.037)
	S&P				0.205* 0.220* 0.149* 0.228* 0.220* 0.134*
					(0.034) (0.034) (0.036) (0.035) (0.035) (0.037)
	IBEX	0.213	0.191	0.869				0.346	0.191	0.128
		(0.032) (0.035) (0.045)				(0.033) (0.034) (0.038)
	SMI	0.209	0.179	0.185	0.313	0.179	0.139
		(0.031) (0.034) (0.034) (0.031) (0.036) (0.035)

Table 7 :

 7 Estimating for bilateral stationary fractional cointegration for the period1999-2011 (n = 674)

	y t		CAC			FTSE			NIKKEI
	x t	β	δ	γ	β	δ	γ	β	δ	γ
	CAC				0.512* 0.254* 0.111*	0.099	0.254	0.083
					(0.032) (0.039) (0.050) (0.039) (0.040) (0.050)
	FTSE	0.556	0.241	0.167				0.144	0.241	0.071
		(0.035) (0.045) (0.041)				(0.040) (0.047) (0.050)
	NIKKEI	0.089	0.113	0.244	0.118	0.113	0.221
		(0.040) (0.048) (0.039) (0.039) (0.045) (0.045)
	S&P	0.390	0.209	0.219	0.352	0.209	0.157	0.078	0.209	0.094
		(0.038) (0.041) (0.039) (0.037) (0.039) (0.048) (0.039) (0.040) (0.048)
	IBEX	0.416	0.192	0.190	0.371	0.192	0.163	0.129	0.192	0.087
		(0.038) (0.039) (0.042) (0.038) (0.041) (0.044) (0.041) (0.040) (0.047)
	SMI	0.419	0.195	0.193	0.348	0.195	0.152	0.115	0.195	0.090
		(0.036) (0.039) (0.041) (0.039) (0.042) (0.046) (0.039) (0.044) (0.048)
	y t		S&P			IBEX			SMI
	x t	β	δ	γ	β	δ	γ	β	δ	γ
	CAC 0.370* 0.254* 0.160* 0.387* 0.254* 0.090* 0.409* 0.254* 0.106*
		(0.036) (0.038) (0.039) (0.034) (0.040) (0.041) (0.035) (0.040) (0.049)
	FTSE 0.368* 0.241* 0.131* 0.376* 0.241* 0.107* 0.373* 0.241* 0.107*
		(0.038) (0.046) (0.042) (0.035) (0.042) (0.036) (0.039) (0.046) (0.045)
	NIKKEI	0.065	0.113	0.201	0.121	0.113	0.180	0.099	0.113	0.187
		(0.039) (0.048) (0.043) (0.038) (0.042) (0.039) (0.038) (0.045) (0.039)
	S&P				0.293* 0.209* 0.129* 0.314* 0.209* 0.123*
					(0.034) (0.039) (0.039) (0.038) (0.041) (0.044)
	IBEX	0.303	0.192	0.153				0.344	0.192	0.150
		(0.038) (0.040) (0.040)				(0.037) (0.039) (0.042)
	SMI	0.309	0.195	0.143	0.330	0.195	0.142
		(0.037) (0.044) (0.042) (0.035) (0.044) (0.039)

The terms weak and strong fractional cointegration mean here the intensity with which deviations from the long-run equilibrium will disappear.

RATS codes and unreported results are available upon request.

Data are collected from http://fr.finance.yahoo.com/.

 Analysis, 24, 345-378. Wälti, S., 2011.Stock market synchronization and monetary integration. Journal of International Money and Finance, 30, 96-110.