PORGY: Interactive and Visual Reasoning with Graph Rewriting Systems

Bruno Pinaud, Jonathan Dubois and Guy Melançon * University of Bordeaux and INRIA Bordeaux Sud-Ouest, France Figure 1: Overview of the PORGY graph rewriting framework allowing end-users (here biologists) to explore, study and simulate a model for biochemical calculus. Graphs describing the states and bindings of molecules are being transformed through the application of rewriting rules. The simulation is driven from the visualization, where rules are seen as elementary programming instructions.

Graph rewriting systems are easily described and explained. They can be seen as a game where one iterates transformation rules on an initial graph, until some condition is met. A rule describes a local pattern (i.e. a subgraph) that must be identified in a graph and specifies how to transform this subgraph. The graph rewriting formalism is at the same time extremely rich and complex, making the study of a model expressed in terms of graph rewriting quite challenging. For instance, predicting whether rules can be applied in any order is often difficult. When modelling complex systems, graphical formalisms have clear advantages: they are more intuitive and make it easier to visualize a system and convey intuitions about it. This work focuses on the design of an interactive visual graph rewriting system which supports graphical manipulations and computation to reason and simulate on a system. PORGY has been designed based on regular exchanges with graph rewriting systems experts and users over the past three years. The design choices relied on a careful methodology inspired from Munzner's nested * E-mail: {bruno.pinaud, jonathan.dubois, guy.melancon}@labri.fr. This work was funded through the INRIA's Associate Team Porgy (see http: //gravite.labri.fr/?Projects_%2F_Grants:Porgy) in collaboration with King's College London and by a grant from the French National Research Agency (EVIDEN project, ANR-10-JCJC-0201). process model for visualization design and validation [START_REF] Munzner | A nested process model for visualization design and validation[END_REF].

GRAPH REWRITING BASICS

Each available or allowed modification (topology, node/edge's attributes) on a given graph G is called a rewriting rule. It captures the knowledge of experts about the system they study and describes how a (small) subgraph of G can be modified or rewritten. More complex modifications are realized by combining sequence of rules into expressions with various operators affecting rules applications called rewriting strategies. Strategies specify which/how/when/where rules apply (see [START_REF] Namet | A strategy language for graph rewriting[END_REF] for more details). Formally speaking, a rewriting rule is of the form r i : L i → R i where L i and R i are graphs, respectively called the left-hand side (lhs) and right-hand side (rhs) of the rule r i . Fig. 1 shows an example of such a rule in the bottom left panel. One of its effect is easily deduced from the drawing: assuming a graph contains a subgraph with five nodes in the given configuration, the edge connecting the blue and green nodes is deleted. The top left panel of Fig. 1 shows an example of application. Nodes of the subgraph being rewritten are red (top), the nodes of the output subgraph (below) are blue.

USERS' REQUIREMENTS

The first requirement of our users was to be able to graphically design rules. The main challenge is whether the rules adequately model the system's behavior. As a consequence, the second requirement was to be able to easily run a simulation after defining a rewriting strategy to observe the evolution of the system. The computing history of the calculus is managed using a derivation tree (bottom center panel of Fig. 1) which appears as a living scrapbook the user plays with. Its nodes hold all the graphs that can be derived by applying rules. Black edges show single rule applications while green curved edges correspond to the application of a strategy. Strategies may be applied from any already computed graph to produce a new branch in the tree. For the rest of this paper, the term graph will be reserved to talk about those graphs on which rules are applied, unless stated otherwise. The complexity of the rewriting system is, in a sense, captured within the derivation tree which obviously forms a central object to study the rewriting system. Needless to say, viewing and manipulating the derivation tree became the next strong priority expressed by our users.

The study of a rewriting system requires to oscillate between local views (rules, graphs), and a global view of the derivation tree. The main challenge is to understand how the behavior of the system at a global scale emerges from rules specifying how local modifications operate. It is precisely by looking at the graphs in the derivation tree, both at a local and global scale, that a domain expert can judge of the model's adequacy or check postulated properties.

CASE STUDY: BIOCHEMICAL NETWORK

We show how to use PORGY for modelling and reasoning about a biochemical network composed of different types of molecules at different concentrations who interact to maintain a regulation mechanism. The biologists' challenge is to come up with a model for the dynamic of molecules to explain this mechanism. Knowledge gained from (wet)lab experiments suggests: 1) the overall process is controlled through only four chemical reactions and 2) the regulation works if there is alternating short periods of time where the concentration of a specific molecule called A increases, and others where it remains constant [START_REF] Andrei | A Model and Analysis of the AKAP Scaffold[END_REF]. Graph rewriting appears as a natural device to build the model. At each time step, the state of the biological system is given as a graph where nodes correspond to molecules and edges correspond to physical bindings that took place. The chemical reactions are described as rewriting rules.

First, rules and the initial graph G are drawn and laid out using a visual graph editor. Next, after combining the rewriting rules into a strategy, the biologists can apply it to simulate this in silico biological system. The applicability of a strategy is computed in real-time to provide a visual feedback. Finally, the overall behavior of the system requires to be validated, by for instance making a plot of the evolution of the concentration of A molecules. The staircase shape of the plot (the top right panel of Fig. 1) confirms that the rules (biochemical reactions), the strategy (conditions) and the initial molecule concentration combine well to reproduce the expected behavior. Now, since all PORGY views are synchronized and because nodes are embedded into the plot, the user may select (in blue) part of the plot and query the derivation tree to visualize the time at which a given state is reached. Generally speaking, to ease the work of the user, most of the interactions are visual and interactive. We use drag and drop operations as often as possible.

IMPLEMENTATION DETAILS

Porgy is built on top of the Graph Visualization framework Tulip [START_REF] Auber | Tulip -a huge graph visualization framework[END_REF]. A first difficulty comes from the capability of showing a compound derivation tree. The tree acts as a top level structure, and nodes of the tree themselves contain graphs (on which rules apply). The tree structure encapsulates the computation history, where each branch is induced from a sequence of rule applications. Each node must therefore refer to a graph resulting from the application of a rule on its parent graph. Each edge stores the necessary information to recover the rule that was applied. In a sense, the paradigm we are dealing with is that of a dynamic graph which evolves in many ways according to rewriting rules. However, on the data structure level, we must have access to every single graph that was derived from the original graph. This imposes that all graphs derived from the initial graph share nodes, edges and their respective attributes to insure coherence and achieve scalability.

One basic task the system needs to perform is to find instances of the lhs of a rule. Indeed, applying a rule r : L → R to a graph G requires that we first identify a sub-graph H ⊂ G that is isomorphic to L. Hence, a rule r applies to a graph G if there exists at least a subgraph H ⊂ G such that L is isomorphic to H. Now, although the subgraph isomorphism problem is known to be NP-Complete over the class of unlabelled graphs, it becomes tractable in our case because we deal with labelled graphs. The implemented algorithm is inspired from [START_REF] Cordella | A (sub)graph isomorphism algorithm for matching large graphs[END_REF]. Subgraph isomorphism search is also triggered to contract the derivation tree into a quotient graph after isomorphic graphs are merged into a single node, called a metanode, and the edges are induced from edges of the derivation tree. As a consequence, the quotient graph may for instance contain cycles (the system returns to a previous state) or multiples black edges may point to the same metanode (local confluence).

Although the graphs are drawn using a force-directed layout, they may need to be drawn according to specific graphical conventions. As a consequence, our system can use any layout algorithm thanks to the Tulip plug-ins system. The layout of rules also required some attention. Most authors in graph rewriting theory use symmetry as a central aesthetics to emphasize the changes operated by a rule. The overall heuristics we implemented is to layout the rhs first to optimize its aesthetics and then try to symmetrically match the lhs as much as possible. Finally, care must be taken to draw the derivation tree. Although we referred to it as a tree, the presence of green edges for strategies turns it into a directed acyclic graph. Thus, we use a Sugiyama-typed [START_REF] Sugiyama | Methods for visual understanding of hierarchical systems structures[END_REF] layout where each node is being assigned to a layer coinciding with its depth in the tree.

CONCLUSION AND FUTURE WORKS

This work took place within the context of a project involving endusers and computer scientists. This opportunity allowed us to run several interviews and observe actual uses of early prototypes to converge towards domain problems characterization, and for choosing specific views and interactions to support tasks identified in earlier phases of the work. The PORGY framework is available to the graph rewriting community since about a year and we may expect users to provide more feedback and suggest improvements. We already have identified a variety of issues that need to be studied like dynamic graph drawing for graphs as they evolve through a multiscenario scheme just as if a same graph would be part of different sequences of time stamped graphs. PORGY should also soon migrate towards other application domains.


Les Auteurs

Ridha Nouira

Professor, Patrick Plane
email: p.plane@u-clermont1.fr

Khalid Sekkat
email: ksekkat@ulb.ac.be

Catherine Araujo Bonjean

Keywords: Exchange rate, Misalignment, Undervaluation, Exports diversification JEL Classification: O14, O24, O53

Introduction

The shift of resources from the primary to the secondary sector has been recognized as a driver of the development process. Most of the "pioneers" of the development economics from [START_REF] Lewis | Economic Development with Unlimited Supplies of Labour[END_REF] or Nurkse (1954) to [START_REF] Chenery | Growth and Transformation[END_REF] have supported this view. Several theoretical arguments underlie the need of stimulating manufacturing sector, especially through the increase of its exports, in the context of the global economy. First, the demand for manufactured goods increases more with income than the demand for primary products. Hence, growth prospects for a country's exports are higher through specializing in manufacturing (Page, 2011 andHausmann et al., 2007). Second, the development of the manufacturing sector induces substantial dynamic productivity gains, and consequently growth, arising from economies of scale, learning effects, and externalities among firms and industries [START_REF] Hirschman | The Strategy of Economic Development[END_REF][START_REF] Seers | The Mechanism of an Open Petroleum Economy[END_REF][START_REF] Matsuyama | Agricultural Productivity, Comparative Advantage, and Economic Growth[END_REF]). Third, with relatively higher price elasticities of both demand and supply, the economies are less susceptible to price swings [START_REF] Elbadawi | Can Africa Export Manufactures? Endowments, Exchange Rates and Transaction Costs[END_REF]. Although not directly addressing the validity of such channels, empirical analyses lend support to the role of manufactured exports in fostering growth. In a cross country analysis, [START_REF] Sachs | Economic Reform and the Process of Global Integration[END_REF] found that manufactured exports and economic growth are positively related. [START_REF] Jones | The anatomy of start-stop growth[END_REF] also relying on cross-country analyses show that growth accelerations and decelerations are associated with employment move into and out of manufacturing. [START_REF] Rodrik | Disequilibrium Exchange Rates as Industrialization Policy[END_REF][START_REF] Rodrik | Industrial Development: Stylized Facts and Policies[END_REF] finds that rapidly growing developing countries tend to have large manufacturing sector. [START_REF] Ostry | Prospects for Sustained Growth in Africa: Benchmarking the Constraints[END_REF] argued not only that manufactured exports was successful in many countries as a mode of escaping from underdevelopment but that improvement in the quality of institutions also occurs when growth is driven by manufacturing exports. To ease the attainment of these promising structural objectives, reforms have been launched in many developing countries by the mid-1980s. Trade liberalization, but also exchange rate management on which this paper focuses, were initially at the heart of such reforms.

The economic approaches to exchange rate management have evolved over the past decades.

Earlier work dealt with the trade dimension and more specifically analyzed the impact of the removal of relative price distortions penalizing exported goods (e.g. [START_REF] Krueger | Foreign Trade Regimes and Economic Development: Liberalization Attempts and Consequences[END_REF][START_REF] Balassa | Development Strategies in Semi-industrial Economies[END_REF]. Starting mid-eighties, a broader approach to exchange rate management emerged.

Exchange rate has to be perceived as an instrument to adjust the whole economy to changes in variables affecting a country's long term internal and external equilibrium, the so-called "fundamentals" (see [START_REF] Edwards | Exchange Rate Misalignment in Developing Countries[END_REF]. In this perspective the new approach questions the former CERDI, Etudes et Documents, E 2011.25 wisdom that an overvaluation could be seen as a potential vehicle for economic growth: the export-oriented agricultural sector being indirectly taxed while the manufactured sector would benefit from cheap imported inputs. [START_REF] Cottani | Real Exchange Rate Behavior and Economic Performance in LDCs[END_REF] and Ghura and Grennes (1993) evidenced a negative relation between overvaluation and economic growth. The normative conclusion then emerged that countries should keep their exchange rate as close as possible to the equilibrium level. [START_REF] Rodrik | The Real Exchange Rate and Economic Growth[END_REF][START_REF] Rodrik | Industrial Policy: Don't Ask Why, Ask How[END_REF] recently disputed such a perspective, especially for economies that have to achieve the structural changes we referred to above. He provided theoretical arguments calling for an active disequilibrium exchange rate strategy taking the form of a deliberate undervaluation of the real value of the national currency.

Referring to seven high growth rate countries over the period 1950-2004, Rodrik argued that, just , Rodrik argued that, just as overvaluation hurts growth, undervaluation facilitates it. More than the non-tradable sector, which may incorporate excess costs in domestic prices; tradable goods particularly suffer from domestic institutional weaknesses as well as market failures that remain sometimes prominent in low to middle per capita income countries. [START_REF] Collier | Globalization: What Should Be the African Policy Response?[END_REF] made a similar point asserting that manufacturing being one of the most transaction-intensive activities, high transaction costs due to a poor policy environment might have caused Africa's comparative disadvantage more than Dutch-disease phenomena. [START_REF] Freund | Export Surges: The Power of a Competitive Currency[END_REF] findings of a surge in manufacturing export following episodes of real exchange rate undervaluation and the above documented relationship between manufactured exports and economic growth provide support to the positive impact of undervaluation. The conclusion then arises in [START_REF] Rodrik | The Real Exchange Rate and Economic Growth[END_REF]'s paper that a systematic increase of the relative price of tradables acts as a "second-best" solution to partially alleviate relevant distortion and spur economic growth1 . The author qualifies somewhat this normative prescription in relation with global macroeconomic imbalances that drove to the 2008 financial crisis (see [START_REF] Rodrik | Growth after the crisis[END_REF].

The issue of deliberate undervaluation is the subject of many arguments between countries. The most prominent example is the Chinese-European-American controversy about the Renminbi (RMB). China is accused of maintaining the RMB rate below its equilibrium level to favor its exports (see [START_REF] Evenett | The US-Sino Currency Dispute: New Insights from Economics, Politics and Law, A VoxEU[END_REF] for an extensive discussion). Such blame is rejected by the Chinese authorities. To the extent that our sample contains China, the analysis in this paper could shed some light on this controversial debate.

The objective of this paper is not to study the relationship between the exchange rate and growth but to investigate whether developing countries are receptive to the spirit of a proactive exchange rate policy in accordance with price incentives for fostering manufactured exports. The first step toward the objective of the paper is to identify countries maintaining undervalued exchange rates.

The second step is to examine whether such a strategy has been pursued in order to foster manufactured exports.

In the first step, undervaluation is naturally defined as an observed exchange rate level below its equilibrium level. The latter is not observable. To identify its level, Edwards (1988)'s method is adopted. It consists of separating the evolution of the Real Effective Exchange Rate (REER) into two components reflecting the evolution of the Equilibrium Real Effective Exchange Rate (EREER) and the deviation of the observed REER from the equilibrium (i.e. misalignment), respectively.

In the second step, we will use Granger causality tests to examine whether countries having undervalued exchange rate (Especially if undervaluation is maintained for some time) are doing so with the objective of providing price incentives for fostering manufactured exports. If this is the case, the country will seek to set the exchange rate in order to improve the price competitiveness of manufactured exports. Hence, the changes in the exchange rate will precede and explain changes in the price competitiveness. In econometric terms, this means that the changes in the exchange rate "Granger-cause" the changes in the price competitiveness of manufactured exports.

The analysis is conducted for 52 developing countries over the period 1980-2005. To take advantage of the time series-cross section dimensions of the sample, the econometric analysis is based on the recent developments in the panel-data-co-integration methodology. Section 2 identifies countries having an undervalued exchange rate. Section 3 examines whether these countries are doing so with the objective of providing price incentives for fostering manufactured exports. Section 4 concludes.

Undervaluation across time and countries

The first step of our analysis is to identify countries with undervalued exchange rates. To this end, we will compare each country's observed exchange rate with the value it should have under the hypothesis that the macroeconomic equilibrium is to be maintained. The observed exchange rate considered here is the Real Effective Exchange Rate (REER), which is the most commonly used in this respect. As for the exchange rate compatible with macroeconomic equilibrium we use a model based on [START_REF] Edwards | Exchange Rate Misalignment in Developing Countries[END_REF] which allows computing Equilibrium Real Effective Exchange Rate (EREER). A level of the REER below the one of the EREER is associated with undervaluation.

The Real Effective Exchange Rate

One major issue with the construction of the REER is the debated subject about the appropriate price index. On a long-term basis, we hypothesize that exporters cannot deviate from the "law of one price". Then, our concern is to find an index allowing comparisons of domestic costs of production across countries that may reflect relative long run ability to produce while remaining profitable. The IMF regards the unit labor cost (ULC) in manufacturing as a simple and useful index in this respect. However, if its evolution offers a reliable gauge of the profitability of traded goods, most developing countries lack the data to calculate it.

The Wholesale Price Index (WPI) does not prove to be an appropriate alternative to the ULC. Not only it is also available for few countries, generally industrialized economies, but it under-weighs non-traded goods that condition price competitiveness for traded goods, especially manufactured ones. Therefore, it does not reflect the long run profitability as reallocations may exist in the short run between wages and profits. Accordingly, the Consumption Price Index will be preferred for the construction of the REER. This index is available over a long period and incorporates a significant non-traded component. In addition, the CPI tends to be correlated with production costs as salary arrangements generally rely on its evolution. However, one limitation underlying the use of this index is that nominal wages and unit labor costs are supposed to be related in the same way across countries. In other words, the effect of the change in labor productivity on wages is assumed not to differ much across the trading partners incorporated in the calculation of the REER. For a given country, the real exchange rate index comes as follows:

ܴሻܧܧܴ݃ሺܮ ൌ ∑ ቈݓ * ݃ܮ ቆ݁ * ୀଵ ୀଵ ൬ ܫܲܥ ܫܲܥ ൗ ൰ቇ
ሺ1ሻ where:

CPI is the Consumer Price Index of the country; CPI j is the Consumer Price Index of the country's partner j; e j is the nominal bilateral exchange rate of the country as regard partner j;

w j is the weight of the j-th partner in the whole bilateral imports of the country.

The weighting pattern refers to the 10 largest trading partners over the period 1999-2003 excluding oil exporting countries (i.e. those for which petroleum related products represent at least 50% of their exports). Weights are calculated by considering the structure of national imports at the end of the period of observations in order to focus on the diagnosis for the most recent years. This choice allows taking into account the increasing contribution of some large emerging countries such as China, India or Brazil in the international trade. Because of its better statistical properties, a geometric rather than an arithmetic mean of the relative prices has been used to compute the REER over the period 1980-2005. An increase of the REER means an appreciation.

The Equilibrium Real Effective Exchange Rate

Because of misconceived policies or imperfect functioning of the exchange market, the REER may be a poor indicator of the macroeconomic equilibrium of an economy. Misconceived economic policies can maintain exchange rate away from the one corresponding to such equilibrium level. However, a country can also be willing to keep an over evaluated exchange rate in order to reduce the cost of importing machinery and other inputs for domestic firms. The resulting misalignment has been found to be damaging to economic performance [START_REF] Edwards | Exchange Rate Misalignment in Developing Countries[END_REF][START_REF] Cottani | Real Exchange Rate Behavior and Economic Performance in LDCs[END_REF]) implying that the REER should be maintained as close as possible to its equilibrium level (i.e. EREER).

Over the last thirty years, the economic literature on the exchange rate has developed in a way that allowed determining the influence of a limited range of variables affecting the long run real value of a currency (e.g. [START_REF] Williamson | Estimating Equilibrium Exchange Rates[END_REF][START_REF] Edwards | The Mexican Peso Crisis: How Much Did We Know? When Did We Know It?[END_REF]. These variables, called the "fundamentals", include external (e.g. the international terms of trade) as well as internal factors (e.g. government expenditure). The impact of these determinants can be estimated through an econometric regression and are used to calculate the EREER as well as the potential accompanying misalignment of the actual rate. Practically, the REER is decomposed into the CERDI, Etudes et Documents, E 2011.25 EREER and misalignment. [START_REF] Edwards | Exchange Rate Misalignment in Developing Countries[END_REF] was the first to propose an approach that makes it possible to distinguish between the two sources of REER variations. The latter is regressed on external and domestic ''fundamentals'', which bring about changes in the EREER if sustained over a long time period and do not create misalignment, unless price adjustment is extremely sluggish. In estimating the impact of these factors, we use the following empirical model [START_REF] Edwards | Real and Monetary Determinants of Real Exchange Rate Behavior: Theory and Evidence from Developing Countries[END_REF]:

Log (REER) = α 0 + α 1 Log (Open) + α 2 Log (Cap) + α 3 Log (ToT) + α 4 Log (rDebt) + α 5 Log (Gov) + α 6 Log (GDPgap) + α 7 Log (BalSam) + ε (2)
For clarity, we do not mention the year and country indices. The REER is defined in Equation 1,

ToT is the terms of trade (the ratio of export to import prices); Open is the ratio of export plus imports to GDP; Cap is the net capital inflow scaled by GDP; Gov is government consumption in percentage of the GDP; rDebt is the country debt services including interest payments and reimbursements as a share of GDP; GDPgap is the difference between the average per capita GDP growth rate within the whole sample and the growth performance of the BalSam is the ratio between the country's real per capita GDP and the geometric mean (weighted in a similar way as the exchange rate) of the same variable in the 10 major trading partners.

It is expected that trade openness exerts downward pressures on the relative price of tradable to non-tradable goods, thereby leading to an appreciation in the equilibrium REER; α 1 is expected to be negative. Higher capital inflows involve stronger demand for both tradables and non-tradables and lead to a higher relative price of non-tradables and REER appreciation. This is needed for domestic resources to be diverted toward production in the non-tradable sector in order to meet increased demand; α 2 is expected to be positive. The rise in the terms of trade is assumed to appreciate the equilibrium REER to the extent that it improves the trade balance; the income effect dominating the substitution effect; α 3 might be positive. The higher the country debt services the higher will be the demand for foreign currencies inducing depreciation of exchange rate; α 4 is expected to be negative. Government consumption has a similar effect: stronger demand for non-tradables increases their relative prices leading to an appreciation in the equilibrium REER; then we expect a positive sign for α 5 . The coefficient of the per capita GDP gap, α 6, is supposed to be negative, supporting the idea that a lower economic growth rate means BalSam reflects a productivity gap and aims at capturing the potential Balassa-Samuelson effect.

Assume the prices for tradable sectors homogeneous across countries and their productivity higher than in non-tradable sectors. The increase in wages in the tradable sectors due to higher productivity spills over the wages in non-tradable sectors. The latter induce an increase in inflation and an appreciation of the REER; α 7 is expected to be positive.

The results

Equation (1) will be used to estimate the EREER and potential misalignment on a sample of 52 developing countries from Africa, Asia and Latin America over the period 1980-2005 (See Appendix A). The sample is determined according to the availability of data with the major source of information we used (i.e. the World Development indicators and the International Financial Statistics). As explained above, the EREER concerns the long-term relationship between the REER and the fundamentals. In order to determine such a relationship, one should, therefore, use the co-integration methodology [START_REF] Engle | Co-integration and Error Correction: Representation, Estimation and Testing[END_REF]. The latter allows separating the long and short-term relationships between the REER and the fundamentals.

While co-integration analysis has been for a long time applied to "pure" time series (e.g. a given country over time), in this paper we take advantage of the time series and the cross-section dimensions of the sample to study the relationship in Equation (1) using recent developments of panel-data-co-integration analysis. The latter allows for more efficient estimation and testing, especially when the number of time periods is limited (e.g. [START_REF] Lin | Unit Root Test in Data: Asymptotic and Finite Sample Properties[END_REF]Im, Pesaran and Chin, 2003;[START_REF] Moon | Testing for a Unit Root in Panel With Dynamic Factors[END_REF][START_REF] Chang | Nonlinear IV Unit Root Tests in Panels with Cross-sectional Dependency[END_REF][START_REF] Pesaran | A Simple Panel Unit Root Test in the Presence of Cross Section Dependence[END_REF][START_REF] Pedroni | Panel Cointegration: Asymptotic and Finite Sample Properties of Pooled Time Series Tests with an Application to the PPP Hypothesis[END_REF]Kao andChiang, 1998).

Pooling the data potentially improves the robustness of estimations with misalignments being determined according to a "normal" behavior given by the average estimated coefficients over the sample. However, panel data being vulnerable to the heterogeneity of countries, country fixed effects are introduced in the empirical model. Time fixed effects, which did not prove statistically significant over the period, have been dropped. In order to avoid too much technicality in the main text, the panel-data-co-integration analysis is presented in Appendix B. The resulting longterm relationship between the REER and the explanatory variables is given in Table 1. It has a good overall quality of fit and all the coefficients are significant with the expected sign. Using the coefficients in Table 1, one can compute the extent of the REER misalignment. Recall that misalignment refers to the difference between the REER and the EREER. The latter is given by the fitted values using together the estimates in Table 1 and the long run values of the explanatory variables. To get such long run values, we use the Hodrik-Precsott filter to separate the permanent and temporary components of each variable. We define misalignment as:

Mis = (REER / EREER -1) * 100 (3)
The positive values correspond to overvaluations and the negative to undervaluation. period was characterized by exchange rate overvaluation, the period 1991-2005 exhibits a reverse feature. Overvaluation was not only more frequent in the first sub-period but also much higher. In the second sub-period, undervaluation was more frequent and much larger than in the first period. 1991-1995 1996-2000 2001-2005 While exchange rate undervaluation might foster manufactured exports, the literature points to the importance of its persistence. ranging from about 65% in Ghana to less than 1% in Rwanda. Except for Ghana and Algeria, no country displays an average undervaluation higher than twice the standard deviation (in absolute term). For 14 countries, including China, the undervaluation is higher than one standard deviation (in absolute term).2

As mentioned in the introduction, China is accused of maintaining the RMB rate below its equilibrium level to favor exports. Cheung et al. ( 2007) conducted an empirical analysis that found little evidence of the RMB undervaluation. [START_REF] Eichengreen | Comment on Cheung, Chinn and Fujii: The Overvaluation of Renminbi Undervaluation[END_REF] refuted that their findings could be interpreted as a rejection of the RMB undervaluation hypothesis because their empirical strategy (i.e. an extended PPP approach) encounters fundamental problems. In particular, their empirical strategy focuses exclusively on price comparisons and forgets the other dimensions of the macroeconomic equilibrium [START_REF] Cottani | Real Exchange Rate Behavior and Economic Performance in LDCs[END_REF]Ghura andGrennes, 1993 andRazin andCollins, 1997). In the present paper, we adopted a different strategy which addresses such problems.

From Table 2, we also notice that, in all countries, undervaluation during the period 1991-2005 occurred at least in 8 years (half of the period). However, in a majority of countries (26 out of 41)

undervaluation occurred during at least 12 years (80% of the period). In 10 countries, undervaluation stayed for the whole period. Finally, among the 14 countries exhibiting an average undervaluation higher than one standard deviation (in absolute term) none shows a percentage lower than 80% (a number of years equal to 12 out of 14) except Iran (73%).

To sum up, the first step of our analysis confirms the existence of countries having undervalued exchange rate during the period 1991-2005. Undervaluation is in some instances both very high and very persistent. Depending on the criteria we use (i.e. duration, level), the number of concerned countries is at least 14 out of 52 in the whole sample (i.e. slightly less than 30%). The second step of our analysis, presented in the next section, focuses on whether countries having undervalued exchange rate, especially if undervaluation is maintained for some time, have pursued a deliberate strategy aiming at fostering manufactured exports through price incentives.

Price incentives for manufactured exports and undervaluation

The Exports Price Competitiveness Index

Both the REER and the EREER refer to macroeconomic conditions. However, exchange rate adjustments that respond to macroeconomic conditions do not necessarily meet requirements of microeconomic competitiveness of exporters of manufactured products. Microeconomic competitiveness is defined as the ability of national producers to trade across national boundaries i.e. to have costs of products that do not significantly depart from those of the main international competitors. Assuming that the "law of one price" holds at the 4-digit level of the Standard International Trade Classification (SITC), movements of relative prices, as measured by CPI of exporters, can be interpreted as a proxy of the movements in cost differences across the producers of the individual product. Therefore, such relative prices can be used as an indicator of exports price competitiveness.

The indicator of exports price competitiveness, hereafter denominated EPCI, is computed following [START_REF] Goldberg | Industry-Specific Exchange Rates for the United States[END_REF]. The first step to build the indicator consists in disaggregating the international trade of each country according to the 4-digit of the SITC. Each 4-digit-SITC item is referred to as a single product for which we compute a separate series of EPCI. In the construction of a specific ECPI, we take into account the ten largest worldwide exporters of the corresponding product. The weight attributed to each exporter depends on its relative importance among the ten exporters of this product. Hence, for a given year t and a given product p, the indicator of exports price competitiveness denominated EPCI pt is calculated as follows:

(

)

∑ = =                     = 10 1 * * j j j j jp pt CPI CPI e Log w ECPI Log (4)
where :

CPI is the Consumer Price Index of the country;

CPI j is the Consumer Price Index of the country's partner j; e j is the nominal bilateral exchange rate of the country as regard partner j;

w jp is the weight of the j-th partner in total international trade of the ten most important exporters of product p. . The same calculation is replicated as many times as the number of products exported by the country requires, provided that the product represents at least 1% of its average national exports over the period 1999-2003. A weighted average of all EPCI pt can be calculated by country as:

( ) ( ) [ ] ∑ = = = P p p pt p ECPI Log q ECPI Log 1 * (5)
where q p is the weight of the p-th good in the country's total exports. A decrease in ECPI means an improvement in the price competitiveness. Countries pursuing active exchange rate policies in the line of what [START_REF] Rodrik | The Real Exchange Rate and Economic Growth[END_REF][START_REF] Rodrik | Industrial Policy: Don't Ask Why, Ask How[END_REF] recommends for developing economies, target such exports price competitiveness in order to provide incentives to domestic producers to export.

To our best knowledge, [START_REF] Goldberg | Industry-Specific Exchange Rates for the United States[END_REF], focusing on the USA, was the first to construct sectorspecific indicators of price competitiveness. She found that the period-to-period percentage changes in the indicators and the REER could differ substantially. Using the impact of exchange rate changes on producers' profits as an illustration, [START_REF] Goldberg | Industry-Specific Exchange Rates for the United States[END_REF] showed that using aggregate exchange rate indexes instead of sector-specific indicators could underestimate the empirical importance of exchange rates for producers. One can, therefore, expect that the use of aggregate instead of industry-specific rates also affects the estimated incentive for producers to export.

Exports price competitiveness and macroeconomic equilibrium

For a number of countries, the previous section has established high and persistent undervaluation of the real value of the domestic currency (1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005); in this section, we examine whether such an undervaluation reflected or not the desire to foster manufactured exports.

Undervaluation induces a cost in term of macroeconomic equilibrium. Hence, fostering manufactured exports by adopting an undervaluation strategy means that the country deliberately accepts incurring the cost of a macroeconomic disequilibrium. In other words, in this country improving the price competitiveness of manufactured exports and maintaining macroeconomic equilibrium can not be achieved at the same time. An important question is, therefore, whether this is an issue in some of the countries under study.

To highlight the potential incompatibility between improving the price competitiveness of manufactured exports and maintaining macroeconomic equilibrium, Table 3 compares the evolution of the EREER, REER and the ECPI over 3 sub-periods. 3 To save on space, the Table focuses on selected countries and the three most important groups of exported manufactured products in each country. The whole results are available from the authors.

3 Appendix C gives correlations. Overall, Table 3 suggests not only that there are instances where the objectives of manufactured exports promotion and macroeconomic equilibrium are incompatible but also that some countries seem to favor manufactured exports promotion. The results in Table 3 are, however, descriptive statistics and a more rigorous econometric analysis is needed to confirm that the REER is managed in order to foster the price competitiveness of manufactured exports.

The choice of the econometric approach that enables addressing our question is based on the fact that favoring the price competitiveness of manufactured exports means that the country will seek to change the REER in order to improve the ECPI. Hence, changes in the REER will precede changes in the ECPI which implies that observing the evolution of the former one can predict the evolution of the latter. In econometric terms, this means that the REER "Granger cause" the

ECPI.

The seminal paper by Granger in 1969 presented a simple test of causality. Consider two stationary variables X and Y. Variable Y is causing X if one is able to better predict X using past information on Y than without using such information. Note x t and y t the realizations at time t of X and Y respectively (with t = 1, 2, 3, .., T). In practice, an equation is estimated where x t is regressed on x t-k and y t-k (with k = 1, 2, 3, .., K). If Y causes X, the statistic pertaining to the joint significance of the coefficients of the y t-k should be above the critical level.

Like for co-integration, the Granger test was for a long time conducted in a pure time series context. Now, new tests taking advantage of both the time series and the cross-section exist.

Instead of observing one couple of variable (X, Y) over time, one can observe a set of couples (X i , The dependent and explanatory variables are first differences of log. Countries with "undervalued currencies" refer to countries showing undervaluation on average higher than one standard deviation in absolute term (see Table 2) over the period 1991-2005. The three most important products are those presented in Appendix C. ** = significant at 5%, * = significant at 10% Table 4 presents the results of two sets of the causality analysis. The first set concerns the weighted average of ECPIs over all manufactured products while the second focuses on the weighted average of the three most important products in each country. Following the results in Section 2.3 (see Figures 1 and2), undervaluation was especially prevalent after 1990 and especially high (above one standard deviation in absolute term) and persistent in some countries (see Table 2). Hence, each set comprises four results according to the period of observation (the 1980-2005 period versus the period 1991-2005) and to the countries included (all countries or countries with high and persistent undervaluation). The aim is to check the robustness of our conclusion. If countries use undervaluation to foster the price competitiveness of manufactured exports, causality running from changes in the REER to changes in the ECPI should exist only, or at least be stronger, with the sub-samples including countries with high and persistent undervaluation between 1991 and 2005. The results show that this is, indeed, the case independently on whether the average over all products or only over the three most important products is considered. In both cases, non-causality between changes in the REER to changes in the ECPI is rejected only for countries with high and persistent undervaluation over the period 1991 and 2005. With these sub-samples, changes in the REER precede changes in the ECPI which, in our framework, support the hypothesis that on average the concerned countries used undervaluation to foster the price competitiveness of manufactured exports over the period 1991-2005.

Conclusion

In search of economic growth, developing countries have been seeking the promotion of the industrialization of their economy. A majority of them relied on import substitution strategy, which turned out to be a failure. Industrialization did not occur and the productive systems suffered greatly from high trade barriers and distorted relative prices. A major policy shift then took place by the mid-1980s emphasizing trade liberalization and exchange rate management with a similar objective as before, i.e. enhancing growth by moving from primary commodity exports to manufactured exports. In this perspective exchange rate management was assigned a specific role on which this paper focused on.

Over the past decades, the literature on exchange rate management has evolved significantly.

Earlier work focused on the trade dimension. In the turmoil of the eighties, exchange rate was seen as an instrument to adjust the whole economy to internal and external equilibrium. This equilibrium concept was used to shed light on the negative relation between a misalignment of the exchange rate and economic growth. This implies that countries should keep their exchange rate as close as possible to the equilibrium level. However, subsequent theoretical and empirical analyses suggest that having exchange rate departing from such equilibrium level could be a good strategy for some emerging countries. A proactive exchange rate strategy taking the form of real undervaluation of the national currency could be conductive to higher export of manufactured goods and long run growth. It follows that such countries might be obliged to choose between maintaining macroeconomic equilibrium and providing price incentive to export manufactured goods.

In this paper we have investigated whether some developing countries choose a proactive exchange rate policy in accordance with price incentives for fostering manufactured exports. The approach consists of two steps. The first one seeks to identify countries maintaining undervalued exchange rates. The second step examines whether such strategy is adopted in order to foster manufactured exports.

The results pertaining to the first step revealed a contrast between the periods before and after 1990. The period 1980-90 was characterized by exchange rate overvaluation in a large majority of countries while the period 1991-2005 exhibited exchange rate undervaluation in a large majority of countries. Overvaluation was not only more frequent in the first sub-period but also much higher than in the second. The reverse feature characterized the second sub-period with more frequent and much larger undervaluation than in the first period. This contrast fits with the fact that the 1990s have witnessed an acceleration of exchange rate reforms in many LDCs with the aim of fostering development through manufactured exports expansion. Focusing on the period 1991-2005, undervaluation was also found to be persistent and of non-negligible level (i.e. higher than one the standard deviation in absolute term) in 14 out of the 52 countries in the sample; among which China, Ghana and Algeria.

Regarding the second step, the analysis first showed that there are instances where the objectives of manufactured exports promotion and macroeconomic equilibrium are incompatible. The important question became, therefore, whether some countries favor the price competitiveness of manufactured exports over macroeconomic equilibrium. The question is addressed using the Granger-causality test in a panel data framework. The intuition underlying our test is that favoring the price competitiveness of manufactured exports means that the country will seek to set the exchange rate in order to improve such competitiveness. Hence, changes in the exchange rate will precede and explain changes in the price competitiveness which corresponds to the definition of Granger-causality. Applying the test on the whole sample and on different variants in order to check for the robustness of the conclusion, the results showed that during the "undervaluation period" (i.e. 1991-2005) the changes in the exchange rate precede changes in the price competitiveness of manufactured exports in a number of countries. In our framework, this result does not reject the hypothesis that on average the concerned countries used undervaluation to foster the price competitiveness of manufactured exports over the period 1991-2005.

B.1 Stationarity tests

To examine stationarity, we should, therefore, use a test that incorporates the interdependence of individuals. Among the existing test, the one by [START_REF] Pesaran | A Simple Panel Unit Root Test in the Presence of Cross Section Dependence[END_REF] is the most adequate because it is targeted toward a situation where N (the number of individuals) is higher than T (the number of years). In addition, the test allows analyzing non-stationarity within a heterogeneous panel framework, i.e. a panel in which each country is allowed to evolve according to its own dynamics. The test builds on the well-known augmented Dickey-Fuller regressions. Practically, consider y it pertaining to the individual i at time t. Run the regression:

Δݕ ௧ ൌ ߙ ߩ ݕ ௧ିଵ ߛ ݕ ത ௧ିଵ ߜ ݕ∆ ത ௧ ߴ ௧ (B.

B.2 Co-integration tests

The best-known tests are due to Pedroni (1995[START_REF] Pedroni | Panel Cointegration: Asymptotic and Finite Sample Properties of Pooled Time Series Tests with an Application to the PPP Hypothesis[END_REF]. They allow taking account of heterogeneity among individuals. The author proposed 7 versions of the co-integration test: 4 are suitable when studying the relationship of the variables within countries and 3 pertain to the relationship between variables of different countries. The former set of tests is the most suitable for our study. The procedure is the following. Consider a dependent variable y it and set of explanatory variables x kit observed for individual i at time t. To conduct the test, proceed in the 5 following steps:

1. Estimate the following co-integration regression over the panel:

ݕ ௧ ൌ ߙ ߜ ݐ ߚ ଵ௧ ݔ ଵ௧ ߚ ଶ௧ ݔ ଶ௧ ⋯ ߚ ௧ ݔ ௧ ߝ ௧
2. Differentiate the original series for each member, and estimate the following regression over the panel:

ݕ∆ ௧ ൌ ܾ ݔ∆ ଵ௧ ⋯ ܾ ݔ∆ ௧ ߟ ௧ 3. Calculate L 2
11i as the long-run variance of η it using, for instance, the [START_REF] Newey | A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix[END_REF] estimator.

4. Apply a DF and ADF regressions to the residuals ε it and compute the long-run (σ i 2 ) and the simple variances (s i 2 ) from of the residuals of the DF regression as well as the simple variances (s i *2 ) from of the residuals of the ADF regression.

5. Using the above parameters, the following four statistics can be computed to test for cointegration:

Panel v-statistic:

ܶ ଶ ܰ ଷ/ଶ ܼ ௩ே,் ≅ ܶ ଶ ܰ ଷ ଶ ሺ ܮ ଵ ିଶ ் ௧ୀଵ ே ୀଵ ߝ̂ ,௧ିଵ ଶ ሻ ିଵ Panel ρ-statistic: ܶ√ܼܰ ఘ ෝே,் షభ ≅ ܶ√ܰ ൭ ܮ ଵ ିଶ ் ௧ୀଵ ே ୀଵ ߝ̂ ,௧ିଵ ଶ ൱ ିଵ ܮ ଵ ିଶ ் ௧ୀଵ ே ୀଵ ൫ߝ̂ ,௧ିଵ ∆ߝ ,௧ െ ߣ መ ൯ Panel t-statistic: ܼ ௧ே,் ≅ ൭ߪ ே,் ଶ ܮ ଵ ିଶ ் ௧ୀଵ ே ୀଵ ߝ̂ ,௧ିଵ ଶ ൱ ି ଵ ଶ ܮ ଵ ିଶ ் ௧ୀଵ ே ୀଵ ൫ߝ̂ ,௧ିଵ ∆ߝ ,௧ െ ߣ መ ൯ Panel ADF statistic: ܼ * ௧ே,் ≅ ൭̃ݏே ,் * ଶ ܮ ଵ ିଶ ் ௧ୀଵ ே ୀଵ ߝ̂ ,௧ିଵ * ଶ ൱ ି ଵ ଶ ܮ ଵ ିଶ ் ௧ୀଵ ே ୀଵ ൫ߝ̂ * ,௧ିଵ ∆ߝ̂ * ,௧ െ ߣ መ ൯ where λ i = 0.5 (σ i 2 -s i 2 )
Pedroni (1995,1997) showed that, with a slight correction, the statistics converge toward a normal distribution. Actually:

ݔ ே் െ ߤ√ܰ √ߥ ↝ ܰሺ0,1ሻ
where x NT is one of the 4 statistics and µ and ν are tabulated by [START_REF] Pedroni | Critical Values for Cointegration Tests in Heterogeneous Panels with Multiple Regressors[END_REF]. The results of the co-integration tests applied to Equation 2 are presented in Table B.3. Two tests suggest that the variables are co-integrated but two others suggest the reverse. We follow [START_REF] Pedroni | Panel Cointegration: Asymptotic and Finite Sample Properties of Pooled Time Series Tests with an Application to the PPP Hypothesis[END_REF] who being faced with the same type of results concluded that the variables are co-integrated (See also [START_REF] Barisone | Are our FEERs Justified?[END_REF].

B.3 Estimation of the coefficients

Although the variables are co-integrated, the OLS estimate of the parameters is convergent but not efficient [START_REF] Kao | International R&D Spillovers: An Application of Estimations and Inference in Panel Cointegration[END_REF]. Two methods are available to get efficient estimate of the parameters. One, labeled dynamic OLS (DOLS), was developed by Kao and Chiang (1998) and consists of adding to the co-integration equation lags of the explanatory variables in order to "clean" the error term from any autocorrelation and heteroskedasticity. The other, called Fully

Modified OLS (FMOLS), was proposed by Pedroni (2000). It is little bit more complicated to explain in a non-technical way. Roughly explained, it consists in running an OLS estimate of the co-integration equation and using the residuals to compute their variance-covariance matrix. This is, then, used to perform a "sort of GLS" on the co-integration equation. Both methods were applied to Equation 2 and the results are presented in Table B.4. The overall quality of fit is good.

Except for the variable Cap, the sign, level and significance of the coefficients are broadly similar. In the text, we will focus on the DOLS results.

a

  loss of economic opportunity in comparison with what the other countries do. The variable CERDI, Etudes et Documents, E 2011.25

Figures 1

 1 Figures 1 and 2 present, on comparable scales, the extent of the 5 year average exchange rate misalignment during the periods 1980-90 and 1991-2005, respectively. We set the year 1990 as a separator between the two figures in order to highlight possible change in exchange rate management. The 1990s have witnessed an acceleration of exchange rate reforms in many LDCs with the aim of fostering development through manufactured exports expansion. Comparisons over the two sub-periods do not reject the presence of contrasted evolutions. While the 1980-90

Figure 1 :

 1 Figure 1: Exchange rate misalignments: 1980-1990

Figure 2 :

 2 Figure 2: Exchange rate misalignments 1991-2005

  For instance, Hausmann et al. (2005) examining growth episodes (i.e. growth acceleration by at least two percentage points lasting for at least eight years) found that real previous depreciation is among the factors significantly associated with these episodes. An increase of undervaluation by around 10% which is sustained for five years precedes growth episodes.[START_REF] Freund | Export Surges: The Power of a Competitive Currency[END_REF] also found a surge in manufacturing exports following episodes of RER undervaluation. To illustrate the persistence dimension, Figure3gives the percentage of years during which exchange rate were undervalued during the periods1980-90 and 1991-2005, respectively. The figure shows that, in general, the percentage of years during which exchange rate were undervalued is higher during the 1991-2005 than during 1980-90. Moreover, this percentage is high during the 1991-2005. It is frequently higher or equal to 70%.

Figure

  Figure 3: Years (in % of the period) of exchange rate undervaluation

Table 1 : Panel data estimation results of the REER (1980-2005)

 1

		Equation (2)
	Variables	Coefficients
	Cap	0.00***
		(4.02)
	Open	-0.52***
		(14.01)
	BalSam	0.38***
		(7.90)
	rDebt	-0.11***
		(6.11)
	Gov	0.25***
		(6.25)
	ToT	0.12***
		(3.31)
	GDPgap	-0.01*
		(1.75)
	Adjusted-R 2	0.60

Note: Absolute t-statistics are in parentheses. *** = significant at 1%, * = significant at 10%

  Table2focuses on 1991-2005; a period during which undervaluation was the most frequent. It provides further insights on the occurrence of undervaluation and its acuteness by presenting average undervaluation for countries exhibiting such undervaluation and the percentage of years during which exchange rate was undervalued. The Table also gives the estimated standard deviation of misalignment computed using equations 1 and 2, the sample observations and the estimation results in Table1. Out of the 52 countries in the sample, 41 exhibit an undervalued currency over the period 1991-2005. Among these countries the undervaluation highly differs;

Table 2 : Forty one countries experiencing undervaluation between 1991 and 2005

 2

	Country	Average undervaluation	Percentage of years
	Algeria	-48.62 +	100
	Bolivia	-23.84 +	100
	Burkina Faso	-8.85
	Cameroon	-16.20
	Chad	-13.92
	Chile	-14.01
	China	-24.25 +
	Colombia	-11.43
	Congo	-13.93
	Costa Rica	-3.49
	Cote d'Ivoire	-19.81
	Ecuador	-15.16
	Egypt	-15.15
	Gabon	-34.49 +
	Gambia	-24.14 +
	Ghana	-64.70 +	100
	Guatemala	-16.48	100
	Guinea-Bissau	-34.90 +	100
	Honduras	-19.82
	India	-34.57 +	100
	Iran	-38.80 +
	Jordan	-19.93 +
	Lesotho	-5.32
	Madagascar	-17.72
	Malaysia	-24.45 +
	Mali	-17.00
	Mauritania	-19.63
	Mauritius	-3.47
	Morocco	-8.03	100
	Niger	-22.22 +
	Pakistan	-1.58
	Panama	-17.48	100
	Paraguay	-30.32 +	100
	Philippines	-16.70
	Rwanda	-0.56
	Senegal	-19.92 +
	Sierra Leone	-2.53
	Swaziland	-5.45
	Thailand	-15.73
	Tunisia	-13.56	100
	Venezuela	-6.69
	Standard Deviation	19.90	-
	Note: + means above standard deviation in absolute term

Table 3 : Annual growth rates (ECPI, REER and EREER): Selected countries and most important manufactured products (4-digit level)

 3 Names of the 4-digit groups of products and weights are reported in Appendix C. ECPI1, ECPI 2 and ECPI 3 refer respectively to the first, second and third most important groups in the country In Table3, the most noticeable illustration of incompatibility is Iran. The REER and the ECPIs appreciate or depreciate by almost the same amounts across the 3 periods. This is inline with high correlation coefficients (above 98%) reported in Appendix C. Moreover, such evolutions seem disconnected from the EREER. For instance, between 1990 and 1994 the REER depreciated and the ECPI improved while the EREER appreciated; the REER didn't follow the EREER. During this period 2000-2005, the REER depreciated much more than the EREER but kept on track with the EREER.Although the magnitudes are lower than in Iran, China exhibits a similar pattern. Between 1990 and 1994, the REER depreciated and the ECPI improved by almost the same amount while the EREER appreciated; the REER didn't follow the EREER. Between 2000 and 2005, a similar picture emerged; although less pronounced. Appendix C also shows that the REER and the ECPIs are highly correlated (99%). Similar observations can be made regarding the evolution of the three variables for countries from different continents.

	Country	Variable	1991-1995	1996-2000	2001-2005
	Bolivia	ECPI 1	-3.02	3.46	-1.49
	Bolivia	ECPI 2	-0.61	2.96	-7.29
	Bolivia	ECPI 3	-1.46	5.01	-5.20
	Bolivia	REER	-3.22	2.15	-1.87
	Bolivia	EREER	0.71	-1.13	4.01
	China	ECPI 1	-4.08	5.09	-2.09
	China	ECPI 2	-4.10	4.06	-2.48
	China	ECPI 3	-3.34	3.18	-1.93
	China	REER	-5.31	4.46	-0.87
	China	EREER	2.60	-2.61	1.26
	Colombia	ECPI 1	7.83	0.49	0.36
	Colombia	ECPI 2	4.24	1.96	-2.65
	Colombia	ECPI 3	7.21	1.46	-0.17
	Colombia	REER	7.28	-2.51	0.70
	Colombia	EREER	-2.31	-0.42	2.82
	Ghana	ECPI 1	-1.71	-2.80	-0.15
	Ghana	ECPI 2	-4.67	-5.85	2.29
	Ghana	ECPI 3	-6.28	-4.80	3.46
	Ghana	REER	-5.43	-5.38	1.77
	Ghana	EREER	0.46	2.68	-3.11
	Iran	ECPI 1	-33.44	19.77	-20.81
	Iran	ECPI 2	-33.84	19.47	-21.64
	Iran	ECPI 3	-36.12	22.31	-20.88
	Iran	REER	-35.14	23.96	-22.07
	Iran	EREER	6.46	-3.11	-4.06
	Malaysia	ECPI 1	-0.28	-2.94	-1.28
	Malaysia	ECPI 2	0.79	-3.02	-1.83
	Malaysia	ECPI 3	0.07	-2.27	-1.87
	Malaysia	REER	-0.70	-3.78	0.12
	Malaysia	EREER	-0.63	3.17	2.53
	Tunisia	ECPI 1	1.99	-5.52	0.00
	Tunisia	ECPI 2	1.97	-3.21	-0.85
	Tunisia	ECPI 3	1.16	-5.59	-0.45
	Tunisia	REER	1.39	-0.20	-3.81
	Tunisia	EREER	0.83	-0.47	1.36
	Note:

Table 4 : Results of the causality tests between the REER and the ECPI

 4

	Null hypothesis: No causality running from REER to ECPI
	All products
	Computed statistics, all countries, 1980-2005 period	1.39
	Computed statistics, countries with "undervalued currencies", 1980-2005 period	0.73
	Computed statistics, all countries, 1991-2005 period	1.36
		2.11
	Computed statistics, countries with "undervalued currencies",1991-2005 period	**
	Three most important products
	Computed statistics, all countries, 1980-2005 period	1.04
	Computed statistics, countries with "undervalued currencies", 1980-2005 period	0.24
	Computed statistics, all countries, 1991-2005 period	1.09
		1.84
	Computed statistics, countries with "undervalued currencies",1991-2005 period	*

Note:

Table B .1. Tests of the independence of the variables across individuals

 B CERDI, Etudes et Documents, E 2011.25

	Variables	Calculated statistics
	Cap	7.28***
	Open	16.06***
	rDebt	6.48***
	Gov	3.34***
	ToT	2.43***
	REER	14.32***
	GDPgap	12.04***
	BalSam	                        10.09***
		Note: *** = significant at 1%

Table B .2. Test of the stationarity of the variables

 B

	Variable	Stationarity in
		Level First difference
	Cap	-2.01	-5.78***
	Open	-2.06	-4.89***
	rDebt	-1.75	-5.24***
	Gov	-1.80	-4.55***
	ToT	-1.93	-5.33***
	REER	-1.98	-4.65***
	GDPgap	-2.09	-4.03***
	BalSam	-1.92	-4.15***
	ଵ ே is used to test for stationarity but it does not have a standard distribution. We follow Pesaran ∑ ݐ ே ୀଵ ሺܰ, ܶሻ (B.3)
	(2005) and simulate the critical values using the Monte Carlo approach. If the computed statistics
	(CIPS) is above the critical value, one cannot reject the null hypothesis of stationarity.

2)

and take the calculated Student statistics of ρ i ; t i . Where ŷ t is the average of y it over all individuals at time t. The statistics:

ܵܲܫܥ ሺܰ, ܶሻ ൌ Note: *** = significant at 1%

Table B .

 B 2 presents the results. The tests reveal that all variable are I (1). Hence, if we find a relationship among the variables which gives stationary residuals, these variables will be considered as co-integrated.

Table B .3. Test of co-integration

 B CERDI, Etudes et Documents, E 2011.25

	Statistics	Calculated value
	Panel v-statistic	-3.18***
	Panel ρ-statistic	4.37***
	Panel t-statistic	-1.10
	Panel ADF statistic	0.28
	Note: *** = significant at 1%

Table B .4. Estimation results of Equation (2)

 B

	Costa Rica	Parts,data proc. etc.mch		34.93		0.811 Panama	Bananas, fresh or dried	19.86	0.774
	Costa Rica	Bananas, fresh or dried		13.37		0.435 Panama	Fish,frozen ex.fillets	10.58	0.497
	Costa Rica	Othr.medical instruments			6.64		0.876 Panama	Crustaceans, frozen	10.57	0.144
	Ecuador	Variables Estimation methods Bananas, fresh or dried 22.46	0.976 Paraguay	Oil-cake,oilseed residue	9.30	0.997
	Ecuador Ecuador Egypt Egypt	Crustaceans, frozen Cap Fish,prepard,presrvd,nes Cotton yarn,excl. thread Rice,milled,semi-milled	DOLS 0.00*** (4.02)	8.10 FMOLS 6.91 0.00 3.33 (0.25) 3.14	0.865 Paraguay 0.949 Paraguay 0.901 Philippines 0.936 Philippines	Bovine meat,frsh,chilled Maize, other unmilled Electronic microcircuits Parts,data proc. etc.mch	5.24 3.95 41.16 8.26	0.941 0.948 0.992 0.926
	Egypt	Open Household linens	-0.52*** -0.55*** 2.92 0.956 Philippines	Input or output units	7.19	0.844
	Gabon	Veneer,plywood sheets	(14.01)		0.89	(7.48)	0.969 Rwanda	Fabrc<85%syn.stp.fbr+ctn	36.27	0.835
	Gabon Gabon Gambia	BalSam Plywood,solely of wood Helicopters Fish,frozen ex.fillets	0.38*** (7.90)	0.64 0.34*** 0.662 Rwanda 0.63 0.974 Rwanda (6.64) 8.39 0.991 Senegal	Metal fencing,gauze etc. Batteries,accumulators Inorganic acid,oxide etc	27.23 0.78 19.11	0.861 0.720 0.974
	Gambia	rDebt Crustaceans, frozen	-0.11*** -0.05*** 8.06 0.654 Senegal	Crustaceans, frozen	7.62	0.643
	Gambia	Soap		(6.11)		5.87	(3.12)	0.987 Senegal	Oil-cake,oilseed residue	5.65	0.904
	Ghana	Cocoa beans	Gov	0.25*** 23.16 0.17*** 0.998 Sri Lanka	Spices,ex.pepper,pimento	18.25	0.664
	Ghana Ghana Guatemala Guatemala	Alum.,alum.alloy,unwrght ToT Fish,prepard,presrvd,nes Coffee, not roasted Sugars,beet or cane, raw	(6.25) 0.12*** (3.31) 22.84 7.96 4.41 0.10*** 0.999 Sri Lanka (11.67) 1.000 Sri Lanka 0.705 Swaziland (6.83) 11.83 0.628 Swaziland	Trousers, breeches etc. Trousers,breeches,etc. Flavours,industrial use Food preparations, nes	6.15 5.69 36.69 10.72	0.559 0.631 0.345 0.255
	Guatemala	GDPgap Bananas, fresh or dried	-0.01*	11.39	-0.01** 0.703 Swaziland	Sugars,beet or cane	9.64	0.500
	Honduras	Coffee, not roasted	(1.75)	18.70	(2.45)	0.907 Syria A. R.	Cotton yarn,excl. thread	1.75	-0.249
	Honduras	Fruit,fresh,dried, nes		10.68		0.840 Syria A. R.	Durum wheat, unmilled	1.75	-0.221
	Honduras India	A-R 2 Bananas, fresh or dried Diamonds.excl.industrial	0.60	10.08 30.12	0.57	0.889 Syria A. R. 0.971 Thailand	Tomatoes,fresh,chilled Parts,data proc. etc.mch	1.57 15.76	-0.198 0.972
	India	Cotton yarn,excl. thread			5.69		0.900 Thailand	Electronic microcircuits	9.85	0.991
	India	Gold,silver jewelry,ware			5.06		0.996 Thailand	Rice,milled,semi-milled	4.90	0.200
	Iran	Carpets etc.knotted			2.44		0.980 Tunisia	Trousers,breeches,etc.	13.93	0.444
	Iran	Edible nuts fresh,dried			1.82		0.996 Tunisia	Oth.garments,not knitted	8.79	0.389
	Iran	Cyclic hydrocarbons			0.42		0.999 Tunisia	Insultd wire,etc.condctr	6.76	0.723
	Jordan	Medicaments, nes		11.07		0.980 Uruguay	Oth.bovine,equine leathr	12.88	0.873
	Jordan	Shirts				6.30		0.732 Uruguay	Bovine meat, frozen	12.59	0.787
	Jordan	Nitrogenous chem.fertlzr			6.00		0.947 Uruguay	Rice,milled,semi-milled	7.15	0.654
	Kenya	Tea			32.57		0.599 Venezuela	Alum.,alum.alloy,unwrght	2.61	0.963
	Kenya	Coffee, not roasted			9.42		0.708 Venezuela	Pellets,etc.pig iron,etc	1.10	0.982
	Kenya	Oth.frsh,chll.vegetables			7.89		0.893 Venezuela	Flat,cold-rolld,prod.irn	0.68	0.985

Note: Absolute t-statistics are in parentheses. *** = significant at 1%, * = significant at 10%

Another way to promote the diversification is to improve productivity more than competitors do. However, improvement of productivity is not an easy target in LDCs. Because increased uncertainty about future profitability pushes domestic producers to limit their investment, which further affects their technological upgrading. Rigidity on the labor markets limits greatly the possibility of rationalizing the use of labor by firms and, hence, improvement in labor productivity.

Note that these are average over the period and, hence, undervaluation might be much higher for a given year. This was the case of course for Ghana in 2001 (more than 100%) but also for China in 1994 (almost 60%).

There are other approaches to test for co-integration (e.g.[START_REF] Johansen | Maximum Likelihood Estimation and Inference on Cointegration -with Applications to the Demand for Money[END_REF]. It is not the aim of the paper to discuss them.

Acknowledgements

The authors thank two anonymous referees and the editor of the journal for very constructive comments that allow substantially improving the paper. They also acknowledge very useful feedbacks on an earlier version of this paper from Ibrahim Elbadawi, Sylviane Guillaumont, Marcelo Olarreaga, Steve O'Connell and Nadeem Ul Haque as well as from participants to the ERF 16th Annual Conference (Shocks, Vulnerability and Therapy, Cairo, Egypt, 7-9 November 2009). The usual disclaimers apply.

Y i ) over time (with i = 1, 2, 3, .., N). Hurlin (2004) proposed a test of causality on a mix of time series and the cross-section data which is similar in spirit to [START_REF] Pesaran | General Diagnostic Tests for Cross Section Dependence in Panels[END_REF] presented in Appendix B. The idea is to compute for each individual i a Wald statistic (W i ) pertaining to the joint significance discussed above. Then, calculate the average of W i over i : (6) When N and T tend to infinity, Hurlin (2004) shows that this simple mean converges to a normal distribution. For finite N and T, the author provides critical values. In the rest of this section, we apply the causality analysis to the REER and the ECPIs.

Appendix B: Co-integration analysis and estimation of Equation 4

To present co-integration simply, consider two time series x and y that are integrated of order one; I (1). This means that their first differences (i.e. ∆x and ∆y) are stationary; I (0). If the regression of x on y (that are I (1)) gives a time series of residuals that is I (0), the two series are called co-integrated. This means that there exists a long-term relationship between them. The latter is given by the regression coefficients of x on y. However, the OLS estimate of the coefficient is convergent but not efficient and other estimation techniques need to be used. 4 The methodology comprises 3 major steps. First, test whether the variables are I (1). Second, test whether the variables are co-integrated. Third, estimate the long-term relationship.

First developed in a "pure" time series context, co-integration analysis has been subsequently extended to data combining both the time series and the cross-section (commonly referred to as panel data) dimensions. The 3 steps for the analysis are the same as above except that the nature of the data (i.e. time series and the cross-section) involves a preliminary check regarding whether individuals (e.g. countries) are interdependent or not. This is important for the tests to be used in the co-integration analysis. This Appendix applies the panel-data-co-integration analysis to Equation 2.

To examine whether individuals are interdependent, we use a test suggested by [START_REF] Pesaran | General Diagnostic Tests for Cross Section Dependence in Panels[END_REF].

The test is based on the average of the correlations between the residuals from a regression on each individual separately. Practically, consider the variable y i pertaining to the individual i. The variable is regressed on its first lag and the residuals are collected to compute ρ ij which is the correlation coefficient between the residuals from individual i and j regressions. The statistics:

is shown to have a N (0, 1) distribution under the null hypothesis of independence. Where N is the number of individuals and T is the number of years.

The results of the test applied to our sample are presented in Table B.1. For all variables, the test rejects the null hypothesis of independence of individuals at the 1% level.

Appendix C: Correlations between the REER and the ECPI (Most important 4-digit groups of products, by country)