Alejandro S González-Martín
email: a.gonzalez-martin@umontreal.ca

Gisela Hernandes-Gomes
email: gisela.hernandes.gomes@umontreal.ca

The use of integrals in Mechanics of Materials textbooks for engineering students: the case of the first moment of an area

Keywords: Mathematics for engineers, teaching and learning of analysis and calculus, textbooks, anthropological theory of the didactic, first moment of an area

Research has reported on the difficulties engineering students face in relating the content of their mathematics courses to what is taught in their professional courses. One way to address these difficulties is by better understanding how mathematical notions are used in professional engineering courses. This paper analyses how the notion of first moment of an areawhich is defined as an integralis used in civil engineering courses. Basing our analysis on elements from the anthropological theory of the didactic, we are currently analysing a classic Mechanics of Materials book. Our findings indicate that although first moments are introduced as an integral, the textbook's tasks do not require students to use techniques typically introduced in a traditional calculus course.

INTRODUCTION

Engineering courses are usually organized into two groups: basic science courses (which are taught in the first two years, including foundational skills in mathematics and physics), and technical courses (which appear later in the programme and are more specific to each field of engineering). However, research in engineering education and mathematics education indicates that engineering students encounter many difficulties in their mathematics courses in the first years of study, which can lead to high failure rates, and in many cases, result in students dropping out of engineering programmes [START_REF] Ellis | Student perceptions of pedagogy and associated persistence in calculus[END_REF]. In this sense, "poor mathematics skills are a major obstacle to completing […] engineering programs" (Fadali, Johnson, Mortensen, & McGough, 2000, p. S2D-19).

Researchers have identified some negative situations for students who pass these mathematics courses. One situation is that these students often find it difficult to relate the learned mathematical content to the content of the professional courses. For Flegg, Mallet, and Lupton (2011, p. 718) "without the explicit connection between theory and practice, the mathematical content of engineering programs may not be seen by students as relevant". Another situation is that in spite of having passed the mathematics courses (with a rather rigid structure and rare concrete applications relevant to engineering), students must apply mathematics in their engineering courses, where many new mathematical notions appear without having been encountered in the previous mathematics courses (Hochmuth, Biehler, & Schreiber, 2014, p. 694). Faced with these problems, the mathematics and engineering education communities have been engaged in research and discussion on "how to improve engineering students' mathematics learning, and hence their service teaching" (Bingolbali, Monaghan, & Roper, 2007, p. 764).

Our current research program investigates how calculus notions are used in engineering courses, aiming at identifying possible ruptures between how notions are first introduced and used in calculus, and how they are later used in professional courses. First, we analyse how engineering textbooks present these notions, working under the principle that most tertiary instructors organise their teaching using textbooks as an important resource (e.g., [START_REF] Mesa | Textbook mediation of teaching: an example from tertiary mathematics instructors[END_REF]. The manner in which mathematics notions are used in professional courses has not been the subject of much research. However, we believe this type of research could help bridge the gap between two communities. On the one hand, mathematics lecturers in engineering programs could benefit from knowing how their course content is used in professional courses; on the other hand, professional course instructors could benefit from a critical analysis of their use of mathematics, to help their students make connections between the content of mathematics and professional courses. For example, our analysis of the way integrals are used to define bending moments for beams in strength of materials textbooks for civil engineering reveals different uses of "the same" object (González-Martín & Hernandes Gomes, 2017a). Although bending moments are defined as an integral, the tasks, techniques, and justifications used in calculus courses are very different from the ones presented in professional engineering courses; this may result in students not recognising "the same" object in two different courses, and they may question the relevance of integration techniques that are not used in tasks concerning bending moments. In this paper we develop the content of González-Martín & Hernandes-Gomes (2017b) as we explore the use of integrals to introduce another engineering notion: first moment of an area. We aim to address two questions: how is the content related to integrals used in engineering to work with first moments of an area, and how does this use relate to the content in calculus courses?

Defining first moment of an area

Moments of areas are topics commonly taught in engineering courses that cover strength of materials. Due to space limitations, in this paper we focus on the first moment of an area. In civil engineering, for example, to solve bending problems one must take into account some specific geometrical characteristics of cross-sections of a bar, which is the general term for structures that include beams [START_REF] Feodosyev | Strength of Materials[END_REF]. In this situation, the notion of first moment of an area is used to calculate the centroid of an area and the shearing stresses in transverse bending. The centroid of an area A is its geometrical barycentre and is the point C of coordinates and such that the following relationships hold true: Let A be an area situated in the xy plane (Figure 1), using x and y as the coordinates of an element of area dA. According to Beer, Johnston, DeWolf, and Mazurek (2012, p. A2), the first moment of an area A with respect to the x axis (resp. y axis) is mathematically defined as the integral

  A x dA y Q (resp.   A y dA x Q
). In both integrals, the index A in the integral sign indicates that the integral is calculated over the whole cross-sectional area. Both integrals characterize the sum of the products of each element of area dA and its distance to the respective axis (x or y) and are measured in cubic units [START_REF] Beer | Mechanics of materials[END_REF]. When an area possesses an axis of symmetry, the first moment with respect to that axis is zero, since every element of area dA of abscissa x (resp. ordinate y) corresponds to an element of area dA' of abscissa -x (resp. ordinate -y). This implies that when an area possesses an axis of symmetry, its centroid is located on that axis. For instance, in a rectangular cross-section (two axes of symmetry), its centroid C coincides with its geometric centre. Determining the position of the centroid is important, since several forces in a bar pass through its centroid.

To illustrate these definitions and their calculation with an example, let us consider the case of a bar with a rectangular cross-section (Figure 2). If we consider the expression above, . Calculating this integral throughout all the vertical extension of the rectangular cross section, we obtain:

  h x dy b y Q 0 . Calculating the integral, we obtain: 2 0 2 2 2 2 0 2 b h b y b Q h x    , therefore 2 2 h b Q x  .

THEORETICAL FRAMEWORK

As stated above, we are interested in analysing how calculus notions are used in professional engineering courses, aiming at identifying possible breaks from the content in calculus courses. For our research, we use tools from the anthropological theory of the didactic (ATD - [START_REF] Chevallard | L'analyse des pratiques enseignantes en théorie anthropologique du didactique[END_REF] because it considers human activities as institutionally situated. In this sense, knowledge about these activities and their raison d'être is also institutionally situated (Castela, 2016, p. 420). In particular, ATD offers a general epistemological model of mathematical knowledge, where mathematics is seen as a human activity through which various types of problems are studied (Barbé, Bosch, Espinoza, & Gascón, 2005, p. 236).

The key element we use in our analysis is the notion of praxeology (or, in our case, mathematical organisation or mathematical praxeology -MO hereinafter), which is formed by a quadruplet [T/τ/θ/Θ] consisting of a type of task T to perform, a technique τ which allows the task to be completed, a discourse (technology) θ that explains and justifies the technique, and a theory Θ that includes the discourse. The first two elements [T/τ] are the practical block (or know-how), whereas the knowledge block [θ/Θ] describes, explains, and justifies what is done. These two blocks are important elements of the ATD model of mathematical activity that can be used to describe mathematical knowledge. Furthermore, ATD distinguishes different types of MO: punctual, which are associated with a specific type of task; local, which integrate multiple punctual MOs that can be explained using the same technological discourse; and regional, which integrate local MOs that accept the same theoretical discourse (Barbé et al., 2005, pp. 237-238).

Praxeologies, like knowledge in general, may move from the institution where they emerge to other institutions that find them useful [START_REF] Castela | Des mathématiques à l'automatique: étude des effets de transposition sur la transformée de Laplace dans la formation des ingénieurs[END_REF]. This is the case, for instance, of mathematical notions that are used to solve engineering problems. In this process, there are transposition effects on the concerned praxeologies [START_REF] Castela | Des mathématiques à l'automatique: étude des effets de transposition sur la transformée de Laplace dans la formation des ingénieurs[END_REF][START_REF] Chevallard | L'analyse des pratiques enseignantes en théorie anthropologique du didactique[END_REF]. We consider the work of [START_REF] Castela | When praxeologies move from an institution to another: an epistemological approach to boundary crossing[END_REF], who identified that "when a fragment of social knowledge, produced within a given institution I, moves to another one I U in order to be used, the ATD's epistemological hypothesis states that such boundary crossing most likely results in some transformations of knowledge, called transpositive effects" (p. 420). In this boundary-crossing process, some (or all) elements of the original praxeology may evolve. Therefore, it is important to analyse the types of tasks and techniques as well as the discourses and theories employed. To that end, our research identifies specific local MOs present in professional courses; we analyse how calculus notions are used (practical block) and whether this use relates to the way the notions are usually presented in calculus courses (knowledge block).

METHODOLOGY

It is worth noting that, in order to understand how calculus notions are used in engineering courses, we have had several exchanges with an engineering teacher holding bachelor's and master's degrees in civil engineering, with more than 28 years of experience teaching a variety of professional engineering courses at Brazilian universities. This teacher has explained notions related to his field and has helped us identify course content in which first-year calculus notions are used.

At this teacher's university, first moments of area are introduced during the third semester of the programme (second year), in the Strength of Materials for Civil Engineering course (students take calculus in their first two semesters). The course's reference book is [START_REF] Beer | Mechanics of materials[END_REF]. First moments are initially cited in chapter 4 (4.2. Stresses and deformations in the elastic range). We proceeded in two stages:

 First, we analysed the general structure of the content related to integrals in the calculus courses. We identified the main tasks proposed to students, grouping them according to the technological elements needed, identifying therefore the main local MOs that structure this content.

 Second, we started our analyses of the reference book for the Strength of Materials course. We identified all instances where first moments appear in the book (using key words to search in an electronic version of this book). For each occurrence of this notion, we are currently analysing the tasks presented in the book where first moments are used. For each task, we are analysing the techniques and discourses (technologies) the textbook uses. As the notion of first moment is used in different chapters of the book, where different professional notions are introduced and explained, the technological discourses are quite varied, giving place to various MOs. The next section provides specific details of our analysis.

DATA ANALYSIS AND DISCUSSION

Calculus is taught in the first year of the program over two semesters in two courses: Calculus I and Calculus II. Up until a few years ago, integrals appeared only in Calculus II, but some content was moved to Calculus I because Physics II (a course in the second semester) requires a knowledge of integrals. Integrals appear towards the end of the first course and are the main topic in the second course (the second author of this paper has taught Calculus I for 15 years and Calculus II for two years).

The content covers indefinite integral (antiderivative of f), Riemann sum and definite integral, applications for the calculation of areas, integration by substitution, volumes (Calculus I), and integration techniques, improper integrals, and arc length (Calculus II). The main source for the calculus courses is the classic book by [START_REF] Stewart | Calculus[END_REF]. The content concerning integrals is basically structured using two local MOs. The first, MO M1 , introduces techniques for calculating indefinite integrals (immediate integration to begin with, followed by various integration techniques); however, theoretical elements justifying the different integration methods are mostly absent and those present are explained without a proof. The second MO, MO M2 , introduces Riemann sums to formally define integrals and interpret them as areas, and leads to the Fundamental Theorem of Calculus and the calculation of definite integrals using Barrow's rule; this leads to some applications of the integral (area, volume …). Many of the techniques used in MO M2 are derived from MO M1 .

We are currently analysing the use of first moments and centroids in the engineering textbook [START_REF] Beer | Mechanics of materials[END_REF], which numbers more than 800 pages. So far, our first analyses indicate that although this content is introduced as an integral, the techniques employed do not call for integration. Our ongoing analyses of the use of first moments in the textbook are summarised in Figure 3.

Description of use Terms used Chapter -Sections

The term appears in a theoretical explanation. It appears with an expression using the integral sign, but no calculation is required. Here, due to space limitations, we describe our analysis of two MOs present in the textbook at points where first moments come into play. It is worth noting the book advises students that they should already have completed a course in statics, that the properties of moments and centroids are explained in Appendix A, and that this material can be used to reinforce the discussion of the determination of normal and shearing stresses in beams in chapters 4, 5, and 6 (Preface, p. x).

First case: MO E1

The initial use of first moments, MO E1 , concerns stresses and deformations in the elastic range (section 4.2 of the book). Its aim is to calculate the maximum stress that beams can resist, resulting in some recommendations about the size and shape of beams. Using some formulae, the book arrives at   0 ydA and concludes: "This equation shows that the first moment of the cross section about its neutral axis must be zero. Thus, for a member subjected to pure bending and as long as the stresses remain in the elastic range, the neutral axis passes through the centroid of the section" (p. 245, italics in the original). This is the first apparition of first moments in the book; however, they are not explained and the authors refer readers to Appendix A. In Appendix A, first moments and their link with the centroid are introduced in a similar manner as in this paper, using implicitly theoretical elements from MO M2 (namely, the interpretation of an integral). However, the book makes the connection with the centroid and deduces many integrals using geometric considerations (and the properties of the centroid), and adds "Centroids of common geometric shapes are given in a table inside the back cover" (p. A3). Therefore, this content is justified vaguely through some basic integral content (present in MO M2 ), but mostly by using geometric considerations. The tasks in MO E1 calculate stresses and bending moments in known geometrical shapes. In the case of a rectangle (Figure 4left), the coordinates of the centroid are deduced using geometry (and not techniques derived from MO M1 or MO M2 ); the same approach is used in the case of a semicircular cross-section (Figure 4-right).

Thus, although the notions of first moment and centroid are necessary to solve tasks in MO E1 , the techniques employed are not based on elements derived from MO M1 or MO M2 . Students can solve the tasks present in this MO E1 without using any of the techniques learned in MO M1 or MO M2 , or hardly any of the technological elements present in them.

Second case: MO E2

First moments and centroids are also used in chapter 6. In section 6.1A, Shear on the horizontal face of a beam element, MO E2 seeks to determine the horizontal shear per unit length (or shear flow) on a beam. Defining Δx as the length of a section of the beam, V as the shear force, ΔH as the horizontal shearing force exerted on the lower face of the element, Q as the first moment, and I as the centroidal moment of inertia, and using techniques and technological elements covered in this and previous chapters, the horizontal shear per unit length (q) is deduced as:

q = I VQ x H   
. It is worth noting that the techniques used to arrive at this expression involve integrals, but they are referred to in terms of notions belonging to MO E2 . The above expression is used to solve tasks such as the one in Figure 5.

The resolution of the task is based on the determination, via different expressions, of Q and I (since V = 500N is provided) to find the horizontal force exerted on the lower face of the upper plank. For the first moment, Q, the following technique is presented: "Recalling that the first element of an area with respect to a given axis is equal to the product of the area and of the A beam is made of three planks, 20 by 100 mm in crosssection, and nailed together. Knowing that the spacing between nails is 25 mm and the vertical shear in the beam is V = 500N, determine the shearing force in each nail. distance from its centroid to the axis, Q = A y " (p. 422). The area of the cross-section of the upper plank is calculated as 0.020m × 0.1m, and the coordinate of the centroid of this horizontal plank with respect to the axis of symmetry of the cross-section is 0.05m + 0.01m (that is, half the measure of the central plank, plus half the measure of the horizontal plank). Q is thus obtained as: Q = A y = (0.020m × 0.100m)(0.060m) = 120 × 10 -6 m 3 . We see that, once more, the tasks to solve in this MO E2 involve cross-sections with geometrical shapes that make use of geometrical considerations, thus avoiding techniques belonging to MO M1 or MO M2 .

Although the technological elements of MO E2 refer to elements that imply the use of integrals, tasks are presented in such a way that previously deduced formulae can be used and magnitudes can be deduced using these formulae and geometrical considerations. The book later provides a table with values (Figure 6). Therefore, it is possible for students to simply memorise the formulae or use the tables to solve the given tasks without actually using any technical or technological element derived from MO M1 or MO M2 .

FINAL CONSIDERATIONS

The data presented here, together with the data from González-Martín & Hernandes Gomes (2017a), indicate that two notions used in civil engineering (bending moment and first moment) are defined as integrals. This may often be used to justify the fact that "engineers need to learn integrals". However, our analyses show that the types of tasks and the techniques developed are not actually derived from praxeologies explored in a calculus course. In the two cases presented in this paper, both MO E1 and MO E2 have their own set of tasks and techniques, and both develop their own technological discourse, which uses the notion of integral to define their own notions and deduce properties. As Figure 3 shows, this seems to be the general situation throughout the textbook.

As [START_REF] Castela | When praxeologies move from an institution to another: an epistemological approach to boundary crossing[END_REF] states, when a fragment of knowledge (in this case, the notion of integral) produced within a given institution moves to and is used by another institution, this process results in a transformation of knowledge. In the case analysed here, it is clear that all the technological discourse proper to a calculus (or even an analysis) course pertaining to the notion of integral is transformed when it is used to define first moments (and centroid) in a professional course, where explanations mostly rely on basic geometric considerations. In this case, it seems that the transpositive effects cause the notion of integral to be used very differently in both courses. The techniques presented in the Strength of Materials course make use of given formulae and geometric considerations, rendering the techniques introduced in the calculus course irrelevant for the use of first moments in MO E1 and MO E2 . This may result in students not recognising the object "integral" when they move from MO M1 and MO M2 to MO E1 and MO E2 . Students may encounter many difficulties in learning MO M1 and MO M2 , but this knowledge is not necessary to solve tasks in engineering courses, so students may question the need to learn these MOs.

It is therefore important that mathematics lecturers in engineering programs become aware of how the notions they teach are used in professional courses. Once they develop a better understanding of the techniques and tasks used in professional courses, mathematics instructors may be prompted to reflect on the mathematical praxeologies developed in their own courses and make stronger connections with the techniques used in professional courses. This could help students transition from mathematics courses to professional courses, enabling them to relate mathematical content to the content of their professional courses and better understand its relevance [START_REF] Flegg | Students' perceptions of the relevance of mathematics in engineering[END_REF].

We plan to continue analysing the use of integrals in professional courses in engineering. This will be the source of future papers.

  take dA as the area of the grey rectangle, whose dimensions are b and dy. Substituting dA in the integral, we have that

Figure 1 :

 1 Figure 1: General area A with infinitesimal area dA in the xy plane (Beer et al., 2012, p. A2).

Figure

  Figure 2: Determination of the first moment with respect to the x-axis of an area with rectangular cross-section.

Figure 3 :

 3 Figure 3: Synthesis of uses of first moments in Beer et al. (2012).

Figure 4 :

 4 Figure 4: Left: The centroid is placed calculating the half measure of each side of the rectangle (Beer et al., 2012, p. 247). Right: The centroid is placed using geometric formulae (p. 248).

Figure 5 :

 5 Figure 5: Task and diagrams used concerning horizontal shear (Beer et al., 2012, p. 422).

Figure 6 :

 6 Figure 6: Areas and centroids of common shapes (Beer et al., 2012, p. 654).

ACKNOWLEDGEMENTS

The authors wish to thank Januário Pellegrino Neto, the engineer who participated in this project, for sharing his knowledge and experience and for making himself available for the interview and our many follow-up questions. The research presented here was funded by grant 435-2016-0526 of the Social Sciences and Humanities Research Council (SSHRC) of Canada's Insight program.


Keywords: Trade Openness, Economic Growth, Labor flexibility

Thanks God, for giving me my childhood dream

International trade openness and its effect on economic growth in Latin American Countries 1. Introduction

Is trade openness good or bad for economic growth in developing countries? In the last few decades most of the Latin American countries (LAC) and East Asian countries (EAC) have sought to reverse the protectionist policies which dominated the regions for centuries. After that, both regions have experience a rapid trade liberalization, which has been characterized by the elimination of quotes, reduction in tariffs, multilateral and regional agreements. For instance, between 1980 and 1999 the average tariff reduction in Latin America was from 30% to 10% similar to OECD levels. Nowadays LAC countries have many Free Trade Agreements (FTAs) with industrialized countries North American Free Trade Agreement (NAFTA). These measures were also accompanied by macroeconomic and other structural reforms like strengthening fiscal and monetary discipline to promote economic growth. [START_REF] Ferranti | Trade for Development in Latin America and the Caribbean[END_REF] - [START_REF] Nenci | Does Tariff Liberalization Promote Trade? Latin America in the Long-run( 1900-2000[END_REF])

However, the level of trade openness was not the same across Latin America countries.

While in 2013 for countries like Costa Rica the share of trade in goods and services over the GDP represented more than 70%, in Argentina this share was about 30%. We also notice that Latin American countries are still behind in relationship to East Asian.

For instance, in 2013 the average share of trade for LAC was about 50% while for EAC more than 60%. [START_REF] Ferranti | Trade for Development in Latin America and the Caribbean[END_REF].

On the other hand, comparing the trade lies between Latin American and East Asia countries, we observed that countries like China has targeted the world as its market while Latin America trade is still focus in most of the case in United States and Brazil.

Furthermore, while East Asian countries have experience a rapid and extensive economic growth after trade liberalization, the success of different reforms taken in Latin America has been widely criticized, suggesting that LAC are still not getting all the possible benefits from the virtuous circle of more integration with neighbors and the world. That is the reason why there is a lively academic and political debate about whether trade liberalization is good or not for developing countries. (The World Bank's report "Latin America and the Rising South: Changing World, Changing Priorities", 2015). In this sense, the present work contributes to the existing literature by providing an empirical analysis from the relationship between trade openness and economic growth for Latin America countries by taking into account the degree of labor market flexibility.

There are many studies in favor of trade openness. For instance, there exists a positive correlation between trade openness and economic growth (Harrison, 1995). There is also a positive and significant relationship between trade openness and per capita income. International Trade increases productivity [START_REF] Frankel | Does Trade Cause Growth?[END_REF][START_REF] Frankel | Does Trade Cause Growth?[END_REF][START_REF] Broda | Globalization and the Gains from Variety[END_REF][START_REF] Broda | Globalization and the Gains from Variety[END_REF]. A direct relationship between trade openness and manufacturing labor productivity is observed for some industries in different Latin American countries [START_REF] Paus | Trade liberalization and productivity growth in Latin American manufacturing, 1970-98[END_REF]. Some of the channels through which trade openness generates a positive impact on the economic growth are:

learning by doing in the exports of goods, access to import products of high-tech and a bigger variety of products. The fact of being exposes to different developed and innovative products may bring new ideas to local producers, improving the quality of domestic products. Basically, developing countries can enjoy from trade openness because of knowledge already accumulated in the industrialized world. [START_REF] Grossman | Trade, Knowledge Spillovers, and Growth[END_REF].

On the other hand, the effect of trade on welfare for Least Developed Countries (LDC) is ambiguous [START_REF] Young | Learning by Doing and the Dynamic Effects of International Trade[END_REF]. The positive link between trade openness and growth is stronger if countries have the enough human capital to absorb the advantages of more commerce [START_REF] Harrison | Openness and Growth: A Time-Series, Cross-Country Analysis for Developing Countries[END_REF]. Countries that export products with higher quality and greater variety growth faster than those who do not, which implies that some countries might have a negative impact from trade openness (Huchet-Bourdon, Le [START_REF] Huchet-Bourdon | The relationship between trade openness and economic growth: some new insights on the openness[END_REF]. In addition, trade gains will be influenced by the degree of labor market flexibility [START_REF] Chang | Openness can be good for growth: The role of policy complementarities[END_REF]. After Brazil trade liberalization [START_REF] Daumal | The Impact of International Trade Flows on Economic Growth in Brazilian States[END_REF] found trade openness is more beneficial to states with a high level of income, contributing to income disparities between Southeast and North regions in Brazil. While, after the China Opening Up [START_REF] Sun | International Trade and its Effects on Economic Growth in China[END_REF] found that net export shares in GDP and high-tech export have a significant positive effect on efficiency. However, authors mentioned that the unbalanced development in high-tech exports between rich and poor regions widens the income gap. In this sense, according to the OECD analysis reducing income inequality would promote economic growth.

Income inequality hurt human capital accumulation through a reduction in education opportunities for individuals in the bottom of the income distribution, which lower social mobility and skills development (Focus on Inequality and Growth OECD 2004).

According to these results, trade liberalization will hurt economic growth under a framework of low human and physical capital, which implies that the level of investment and aid for building productive capacity, developed human skills and the introduction of complementary macroeconomic policies will be crucial to promote growth in developing countries [START_REF] Huchet-Bourdon | The relationship between trade openness and economic growth: some new insights on the openness[END_REF].

We observe in the previous paragraphs that the empirical evidence about the effect of trade on economic growth is not conclusive. In determining the relationship about trade openness and economic growth some of the potentials problems are: two-way causality between trade and economic growth due to the omission of relevant variables. On the other hand, openness indicators are not robust to the inclusion of different macroeconomic variables. For instance, the inclusion of different variables such as quality of institutions, and government expenditures makes disappear the relationship between trade and economic growth [START_REF] Rigobon | Rule of Law, Democracy, Openness and Income: Estimating the Interrelationships[END_REF] and [START_REF] Levine | A Sensitivity Analysis of Cross-Country Growth Regressions[END_REF]). Another problem is the simultaneity, which means that trade openness variables are related to the level of income [START_REF] Ha | Once Again, is Openness Good for Growth?[END_REF]. Another issue, it is that the level of strength in the relationship between trade openness will depend on the data used cross section or panel data [START_REF] Harrison | Openness and Growth: A Time-Series, Cross-Country Analysis for Developing Countries[END_REF] and Quah and Rauch (1990)). Last but not least, another problem, it is which variable or combinations of variables are used as proxies of trade openness.

Trade openness can be measure such as the share of trade in goods and services over the GDP, an annual index of trade openness based on exchange rate and commercial policies, an index based on tariffs and non-tariff Barriers, a black-market premium [START_REF] Harrison | Openness and Growth: A Time-Series, Cross-Country Analysis for Developing Countries[END_REF]. Which one should be used as measure of trade openness?

By using the General Method Moment the present paper aims at assessing how international trade openness affects the economic growth in Latin America countries from a long-run perspective. Can international trade openness serve as an "engine of growth" for this region? What kind of economic policies might be implemented to promote higher welfare from trade openness? I will use two broad categories as measures of trade openness: trade volume and trade restrictions. And by trying to control for specific political features of the region, I include the interaction term between Trade openness and Labor flexibility indicator as a possible explanatory variable of econom ic perform ance, this variable will tell us if labor market flexibility in Latin American countries might be or not a possible channel to enjoy greater benefits from trade. Essentially, I will try to determine if the fact of allowing enterprises to adapt the kind of employees to changing environments observed in international markets influences the impact of trade openness on economic growth.

For the present analysis, I consider two data sets the World Development and Doing Business Indicators. According to this data, I build an annual panel data over the period 2005-2012 for 14 Latin American Countries. In this sense, the main contribution of this paper will be to consider a Labor Market Flexibility Indicator from the recently created Doing Business Project.

Estimations show that under a long time framework. Trade openness encourages the growth of LAC where there is less rigidity in the labor market related to redundancy rules, therefore contributing to more flexible labor market policies make LAC to enjoy greater benefits from trade openness. All else equal, empirical results show that trade openness is likely to benefit more LAC where it is legal to terminate the employment contract of a worker due to redundancy than those where it is forbidden.

The paper is organized as follows. Section1 presents the introduction of the dissertation, While section 2 the theoretical and empirical literature on trade openness. Section3 describes a standard growth equation. Section 4 the data sources and definitions. The empirical analysis and explanation of the main findings are presented in section 5.

Finally, Section 6 concludes and gives recommendations.

Related Literature

Since many years economists have explored the relationship between international trade and economic growth. Trade openness applied to trade policy will be neutral if the incentives are neutral between a unit imported and a unit exported, trade policies might be oriented to promote exports through export subsidies and finally, trade policies might be inward oriented through the creation of tariff, quotas, and licenses. A government might take neutral policies in some sectors and inward oriented in others [START_REF] Harrison | Openness and Growth: A Time-Series, Cross-Country Analysis for Developing Countries[END_REF].

The neoclassical theory suggests that trade openness will generate static gains. Gains will be obtained through country specialization in the production of goods in which their relative cost is lower in relationship to the world, and countries import goods in which they are less efficient. Free commerce allows countries to devote labor to activities in which is most effectively and most economically, which implies an increase of benefits and production. Due to the scarcity of land and diminishing marginal productivity, isolated nation will have a falling rate of profit and an increase in prices which will decrease economy growth (Ricardo, 1817).

On the other hand, international trade generates a reallocation of resources which implies perfect mobility of factors between traded and non-trade sectors within each nation. According to this, under nations with the same technology, the difference in resource endowments is enough reason to cause trade between countries. International trade of products is a substitute for trade in factors that allow them to compensate for any uneven distribution, which will result in the economic convergence across nations.

(Heckscher- Ohlin-Samuelson, 1941).

Considering the New Trade Theory (NTT), we face different challenges such as: 1) the introduction of the scale economies in production, which are linked to the size of firms and market structure.2) Imperfect markets and 3) Product differentiation. There might be some losses for small producers that are unable to get scale economies but they can be compensated by an increase in the welfare due to a greater consumption basket [START_REF] Bhattacharjea | Trade and Competition Policy[END_REF]. After trade liberalization small countries can enjoy economies arising at an international level [START_REF] Helpman | A simple theory of international trade with multinational corporations[END_REF]. For developing countries, trade openness is an economic tool to expand and overcome the limitations of the domestic market and also allocate the surplus of products in foreign markets (Myint, 1958). The scale of the world economy gives greater to get scale economies and more opportunities to success in the investment of research and development (Krueger, 1978-Grossm an andH elpm an, 1991). Under cheap and greater communication across borders, countries can enjoy from spillovers effects (Krueger, 1978).

Considering an enough product differentiation, both trading countries can benefit from intra-industry specialization. Essentially, if countries have similar factors endowments there will be intra-industry instead of inter-industry commerce. Under a dominant intraindustry trade, the access to a bigger market after trade liberalization will allow them to overcome any kind of distributional effect. And trade openness allows countries to allocate their resources to area/countries where is more efficient to produce, which implies mutual benefits for all trading nations due to increasing returns on a global [START_REF] Krugman | Intraindustry Specialization and the Gains from Trade[END_REF] Indeed, it is interesting to note that both Traditional and New trade theory are unable to manage the dynamic implications of trade related to growth and development, especially for developing countries. Both theories do not explain changes in resource endowments, consumer preferences, technological possibilities and income distribution [START_REF] Bhattacharjea | Trade and Competition Policy[END_REF]. That is the reason why it is necessary to consider endogenous models based on technological progress and accumulation of knowledge. Under this framework, an outward orientation will generate a faster economic growth and a higher economic well-being than those observed in protectionist trade economies (inward orientation), because of different channels such as learning by doing in the exports of goods, access to import products of high-tech. The fact of being exposes to different developed and innovative products may bring new ideas to local producers, improving the quality of home products. Basically, developing countries can enjoy from trade openness because a vast stock of knowledge already accumulated in the industrialized world. [START_REF] Grossman | Trade, Knowledge Spillovers, and Growth[END_REF], which implies that developing countries will get more benefits from trade with developed countries than less developed countries. (Halit Yanikkaya, 2003).

But opposing arguments are not too hard to build. For instance, under imperfect markets there might be reciprocal dumplings of exports, or countries that have a big great advantage in the production of goods (Brander and Spencer 1985;Krugman and Obstfeld 1992.). Furthermore, there might be a decline in barter terms of trade for developing countries, which are mainly the primary producing and exporting countries which may contribute to divergence across countries and a transfer of resource from poorest countries to richest one (Prebisch-Singer, 1950). On the other hand, the existence of marked differences between developed and developing countries give a framework able to explain the observed divergence in economic growth between trading partners, which implies that the initial conditions of each economy will be decisive to go toward an underdevelopment trap or toward prosperity (Darity and Davis 2005: 29, pag. 165). Moreover, Multinational Corporation (MNC) practices relating to subsidiaries, threat of denying market access, generate a hegemonic power from developed countries on weaker nations (Bhagwati and Krueger 2001). Considering the Harris-Todaro model where trade gains will be influenced by the degree of labor market flexibility Chang, Kaltani, Norman V. Loayza, ( 2009) found that the effect of trade openness will be positive on average to economic growth but the effect will depend on different complementary reforms such as educational investment, financial depth and labor market flexibility which implies that complementary reforms are crucial to enjoy greater benefits from trade openness.

If we consider imperfect markets such as dumpling of exports, or greater advantages in the production of goods. The government intervention trough subsidies that allow "infant industry" to reach scale economies is justified (Brander and Spencer 1985;

Krugman and Obstfeld 1992). In addition, a decline in barter terms of trade for developing countries might be generated by two reasons: a secular decline in the long run price of primary products in relationship to manufactured products, and a reduction in the demand for exportable from developing countries due to technological progress.

As a consequence the diversification of exports into manufactures, technological capacity building, and development of human capital in developing countries becomes crucial (Prebisch-Singer, 1950). On the other hand, the fact that market differences will affect prosperity implies that history and good fortune are key in the battlefield for understanding economic growth (Darity and Davis 2005: 29). In addition, to overcome with Multinational Corporation (MNC) practices some steps have been taken. For instance, the creation of the United Nations Conference on Trade and Development (UNCTAD) (1964), SAFTA in South Asia to more( 2004) or the Mercosur (1991) in Latin America. However, there is still an evident power and economic divergence between rich and poor countries.

Moreover, the effect of trade openness on economic growth will be affected by complementary reforms (Lipsey and Lancaster, 1956). For instance, in high regulated countries, trade openness will not promote growth due to the inability of flowing of resources to productive sectors. Basically, under inflexible economies, trade expands in the production of wrong goods which prejudice growth [START_REF] Bolaky | Trade, Regulations, and Growth[END_REF].

Considering the Harris-Todaro model Chang, Kaltani, Norman V. Loayza, ( 2009) trade openness benefits will be greater under a framework of more public infrastructure, labor flexibility, more access to credits, and education. While the positive effect of trade openness will be lower with more inflation and corruption. Basically, domestic firms will be able to compete in international markets when they have more educated labor force, and a stable macroeconomic and political environment. Labor market flexibilities will allow domestic companies to adapt to changes observed in international markets. In this model, there are two sectors, if a trade reforms reduce the price in sector1 and it has a fixed salary the increase of product wage in that sector will induce firms to reduce the number of workers, while in sector 2 firms will hire more workers which implies a decreasing marginal productivity of labor and a lower wage in sector 2. The impact on total unemployment is ambiguous. Trade openness will increase per capita income if labor market distortions are sufficiently small. According to this, the basic premise is that complementary policies are required to enjoy greater benefits from international trade. On the other hand, trad e liberalization can red uce or increase w age inequality and the effect on unem ploym ent rate w ill d epend how m an y w orkers are m atched and hired , w hich im plies m ost prod uctive agents w ill be able to profit from exports [START_REF] Oleg | International Trade and Labor Markets: Unemployment, Inequality and Redistribution[END_REF]. In this sense, according to the OECD analysis reducing income inequality would promote economic growth. Income There is a positive and significant relationship between trade openness and per capita income [START_REF] Frankel | Does Trade Cause Growth?[END_REF]. In addition, by using a simultaneous equations system to estimate the effect of trade policy on different determinants for growth and a panel data of 57 countries between 1970 and 1989 [START_REF] Wacziarg | Measuring the Dynamic Gains from trade[END_REF] found that trade policy openness promotes economic growth. Author considers a neoclassical production (Solow decomposition) function in which economic growth depends mainly on the level of technology, physical capital, human capital, labor; government consumption. The measure of trade openness is based on a weighted average of three indicators: tariff revenues, non tariff barriers, and an indicator of overall outward orientation. Berg and Krueger (2003) mentioned the positive link between openness and economic growth.

Moreover, there is a positive impact of trade in productivity [START_REF] Broda | Globalization and the Gains from Variety[END_REF]. Furthermore, by using a panel data for 27 industries in seven Latin American countries from 1970 to 1998 and the Arellano-Bond GMM [START_REF] Paus | Trade liberalization and productivity growth in Latin American manufacturing, 1970-98[END_REF] found a positive relationship between trade openness and manufacturing labor productivity. In addition, by trying to control for endogeneity problems because of simultaneity between trade openness and growth, Luca Antonio Ricci, and Roberto Rigobon (2004) use the identification through heteroskedasticity over a panel data for about 100 countries and found that measures of openness such as size of trade, a tariff indicator, and black market premium 1 would have a positive effect on growth, even after controlling for the effect of growth to openness.

In these studies, some of the channels through which trade openness generates a positive impact on the economic growth are: learning by doing in the exports of goods, access to import products of high-tech and a bigger variety of products [START_REF] Sun | International Trade and its Effects on Economic Growth in China[END_REF]. Moreover, trade liberalization promotes more investment, foreign direct investment (FDI) and macroeconomic policy quality, macroeconomic policies taken to comply with the framework of international trade agreements, a framework that implies a better settlement of law, the promotion of competitive markets and macroeconomic stability like inflation-preventive policies. [START_REF] Wacziarg | Measuring the Dynamic Gains from trade[END_REF]. Trade liberalization may increase productivity growth by forcing surviving firms to be more competitive, and commercial reforms might bring access to cheaper and higher quality technology imports. Export promotion might bring learning of "best practice", increase contacts with foreign partners and an increase of higher productivity multinationals [START_REF] Paus | Trade liberalization and productivity growth in Latin American manufacturing, 1970-98[END_REF].

On the other hand, by using an endogenous growth model in which learning by doing will generate spillover across all goods [START_REF] Young | Learning by Doing and the Dynamic Effects of International Trade[END_REF] found that the effect of trade on (2004) restrictions. Author considers an economic growth function which depend on physical and human capital per person (telephone mainlines and life expectancy rates were used as proxy variables respectively), initial GDP per capital level (as a proxy for the stock of capital for a country), trade openness measures, war deaths, type of regime and geographical factors. As trade volumes variables, author considers the sum of export and import over GDP and population densities, and found that countries with higher densities grow faster than those with lower densities. While for trade restriction variables author uses an index combining import and export taxes, total taxes on international trade, bilateral payments arrangements BPAs2, and non tariff barriers. In addition, by using a GMM estimator for 26 Brazilian states over the period 1989-2002 [START_REF] Daumal | The Impact of International Trade Flows on Economic Growth in Brazilian States[END_REF] found that the effect of trade openness (which consists in the sum of import and exports over the GDP) on the economic growth of Brazilian states depends on the initial income level of each state. The results of this research suggest that trade openness is more beneficial to states which a high level of income, contributing to income disparities between Southeast and North regions in Brazil and that trade openness contributes more to industrialized states than agricultural states.

Moreover, considering a cross-country, panel-data evidence and a GMM estimator Chang, Kaltani, Norman V. [START_REF] Chang | Openness can be good for growth: The role of policy complementarities[END_REF] found that trade openness might deteriorate economic growth under a framework of big labor market distortions. In addition, by using cross-country regressions and after controlling for simultaneity [START_REF] Bolaky | Trade, Regulations, and Growth[END_REF] found that excessive regulations on business entry and labor reduces the positives benefits from trade openness.

Less developed countries will be unable to catch up DC if DC have a greater population and the initial income gap is too big [START_REF] Young | Learning by Doing and the Dynamic Effects of International Trade[END_REF]. Trade openness is more beneficial to states which a high level of income and developed industries due to more developed human capital which implies that trade benefits can be deprived by a low human capital [START_REF] Daumal | The Impact of International Trade Flows on Economic Growth in Brazilian States[END_REF]. For these authors the important question is not to open or not but to know the pattern of imports and exports before trade liberalization, the type of products to trade, and the benefits of trade openness in the pattern of imports and exports. The unbalanced development in high-tech exports between rich and poor regions widens the economic gap [START_REF] Sun | International Trade and its Effects on Economic Growth in China[END_REF]. On the other hand, labor market and financial rigidities will deteriorate the international trade benefits due to inability of flowing of resource to most productive sectors. And trade openness will promote economic growth if there is enough development human capital [START_REF] Chang | Openness can be good for growth: The role of policy complementarities[END_REF].

As we can see empirical evidence about trade openness for developing countries is not On the other hand, [START_REF] Harrison | Openness and Growth: A Time-Series, Cross-Country Analysis for Developing Countries[END_REF] found that the correlation between trade openness and economic growth depends on the time period of dataset. In general, the positive effect becomes significant for longer periods of time. Another issue, it is which variable or combination of variables is used as a proxy of trade openness because it is difficult to aggregate the data in one index. For instance, trade openness can be measure by using the following proxies: exports plus imports over the GDP, an annual index of trade liberalization based on exchange rate and commercial policies, an index of trade liberalization based on tariffs and nontariff Barriers, a black-market premium, or the Dollar index. Finally, there is a clear difference between collected rates and official tariff rates (Pritchett and Sethi, 1994) In lights of the aforem entioned literature, we can expect that the effect of trade liberalization in Latin American countries will depend on different factors such as export and import patterns, human capital dexterity and different political policies. In this sense, the main contribution of this research will be to determine the relationship betw een econom ic grow th and openness consid ering a labor m arket flexibility ind icator. The inclusion of the interaction term between Trade openness volume and Labor flexibility Indicator as possible explanatory variable w ill tell us if Latin Am erican countries should or not establish a m ore flexible labor m arket fram ew ork to experience greater benefits from trad e liberalization.

Empirical Framework

The Growth Equation

To our knowledge, this study will contribute to the empirical evidence by trying to explore the causal relationship between trade openness and economic growth by taking into account the degree of labor market flexibility in Latin America Countries, using the Solow growth model. The Solow decomposition is a neoclassical production function in which economic performance depends on the level of technology, physical and human capital. In this model, there are diminishing returns to a single factor and constant returns to scale. Authors such as [START_REF] Dollar | Prod uctivity and Grow th: What d o We Really Know ?[END_REF], [START_REF] Sun | International Trade and its Effects on Economic Growth in China[END_REF] and [START_REF] Daumal | The Impact of International Trade Flows on Economic Growth in Brazilian States[END_REF] have used the Solow growth equation.

The empirical analysis conducted in this study will use a panel data set for Latin American Countries over the period 2005-2012, and an extension of the conventional Solow growth equation. According to this, for Latin America Countries, the economic growth will be explained by the following equation:

Eq. 1)

Where the dependent variable is the economic performance or growth of country i at year t. The measure of trade openness is part of the independent variables and it is subclassified in two groups: trade volume and trade restrictions [START_REF] Harrison | Openness and Growth: A Time-Series, Cross-Country Analysis for Developing Countries[END_REF]. Labor market flexibility indicator and the interaction term between this indicator and trade openness volume are also included as explanatory variables. This interaction term is the core of the present research. It will capture the effect of trade openness on economic growth given the degree of flexibility in the labor market of each country. In other words, it will tell us whether or not the growth due to trade openness is conditioned by labor market flexibility and whether Latin American benefits from trade are greater for countries with flexible labor markets than those with more rigid labor markets.

According to the previous statement, the economic growth generated by trade openness for developing countries considering labor market flexibility will be the sum of coefficients ( + ). The rest of explanatory variables are part of which is divided in three categories: Physical and Human Capital, and Macroeconomic features. On the other hand, represents unobserved and constant individual-specific effect that might affect economic growth (environment and political factors, quality of institutions) (Rodriguez and Rodrik, 2004); is an unobserved time-specific effect and is the stochastic error term. The log-linear functional form is adopted to reduce likely heteroscedasticity and to measure the coefficients as elasticities.

As it was mentioned in the previous section the empirical evidence about the effect of trade on economic growth is not conclusive due to different problems such as lack of long period data, omission of relevant variables, and different proxies of trade openness.

One of the main challenges about this type of empirical analysis is the endogeneity generated by simultaneity, which means that trade openness variables such as trade share ( import plus exports over GDP) are related to the level of income [START_REF] Ha | Once Again, is Openness Good for Growth?[END_REF].

Here, the GMM will be used as a method of estimation. It is an estimator based on different moments, which are features of a population. For instance, the average population used as a measure of central tendency, the variance used as a measure of spread in a distribution. However, in practice we use the sample information. Here, I will use a panel data set for Latin American Countries over the period 2005-2012.

Different estimators as OLS and Two-Stage Least Squares are particular cases of the GMM, where the number of sample moments is equal to the number of unknown parameters to estimate. Nevertheless, in some cases this equality fails (there are more sample moments than number of unknown parameters). In this sense, the GMM combines different moments to minimize the asymptotic variance, which implies that moments conditions with higher variance will receive less weight and vice versa.

According to this, GMM improves the OLS estimation in the presence of heteroskedasticity of unknown form. Here, since we are working with countries from the same region but with different economic and geographical features we may afford heteroskedasticity problems. Moreover, the GMM does not require any distributional assumptions about the error. On the other hand, the fact of having more moments that unknown parameters allow us to introduce variables properly excluded (lag variables) from the model as instrument variables, which might be used to control for endogeneity.

Considering the above mention panel data, here the GMM process will be. First, differencing to eliminate the unobserved heterogeneity and then the lags included will be instrumental variables for the differenced lagged dependent variable. To summarize, the GMM estimator is used to avoid possible heteroskedasticity, serial correlation3 and nonlinearities.

However, one of the disadvantages of using the GMM is that only consistence is guaranteed, no unbiased like in the OLS. Because in the GMM we can add more moment conditions that do not add much information, meaning that small samples size will be a problem to apply the GMM. In the next section the reader will find the data description to do the empirical analysis.

Data Description

In this thesis, I use two data sets providing information on Latin American Countries, the World Development and Doing Business Indicators. According to this data, I build an annual unbalanced panel data over the period 2005-2012 for Latin American

Countries. The World Development Indicators were obtained from the World Data Bank and the Doing Business Indicators from the Doing Business Project generated by the World Bank Group.

The World Development Indicators (WDI) are obtained from international sources and they consider national, regional and global estimates. While the Doing Business Project was recently created in 2002 with the idea of providing different measures of business regulations and their enforcement (189 economies are included). It considers domestic small and medium-size companies and how these measures are applied to them. In most of the case, the largest business city is considered in each country, expect for (Bangladesh, Brazil, China, India, Indonesia, Japan, Mexico, Nigeria, Pakistan, the Russian Federation and the United States) countries that have a population bigger than 100 million in 2013. For these countries, the second largest business city is also included (population-weighted average). The main goal of this data is to promote economies to use more efficient regulations.

In this section, the reader will observe a detail description of the variables used in the model. I will use the GDP per capita as dependent variable and the rest of the variables as explanatory variables. Trade Volume variable is the sum of import and exports over GDP and it was obtained from World Bank national accounts data, and OECD National Accounts data files. On the other hand, Trade Restrictions are: time to export and time to import both of them obtained from World Bank, Doing Business project. Time to export/import is the time necessary in calendar days required to export/import goods. From the moment the action of trade is initiated until it is completed (the time will be affected for legal procedure, additional costs and so on). These variables assume not wasting time and procedures without delay, for instance time during unloading of the cargo.

On the other hand, Physical Capital is divided in two groups: the Public Investment which will be represented by the general government final consumption expenditure (% of GDP) and the Private Investment will be gross fixed capital formation, private sector (% of GDP). The public investment includes all government current expenditures in goods and services such as national defense and security excluding government military expenditures while private investment consider all gross outlays by the private industry even though private nonprofit agencies. Both variables are obtained from World Bank national accounts data, and OECD National Accounts data files.

Moreover, School enrollment, secondary (% gross) will be used as a proxy for Human Capital variable. This variable is the ratio of total enrollment in secondary level regardless of age. This category requires the successful of basic education that began at the primary level. The data was obtained from the United Nations Educational, Scientific, and Cultural Organization (UNESCO) Institute for Statistics. In addition to that, considering Macroeconomic features the model will include change in active population by taking into account total labor force growth, this variable include people ages 15 and older, people employed and unemployed. The data is obtained from the International Labour Organization, using World Bank population estimates.

In this dissertation, I will use as proxy of Labor Market Flexibility an indicator related to redundancy rules. This indicator will tell us if there are restrictions before an employer can consider a worker redundant. It will be a dummy variable which will take the value of 1 for employers who can consider a worker redundant without problem and 0 otherwise. Annex A1 presents a complete description of each variable used.

Considering the above data description, for the empirical analysis and trying to determine the relationship between trade openness and economic growth given the degree of labor market flexibility, I will finally work with an unbalanced panel data for 14 Latin American countries over the period 2005-2012. They are: Antigua and Barbuda, Belize, Bolivia, Brazil, Ecuador, El Salvador, Guatemala, Guyana, Honduras, Mexico, Nicaragua, Paraguay, Peru, and Uruguay, the rest of the countries were excluded due to lack of information.

By using the above mentioned sample, here, the reader will find a brief descriptive statistic about some economic indicators of these countries. For instance, on average the degree of trade openness volume for Latin American Countries ranges between 40% and 80%. It can also be observed the existence of big differences in the level of trade openness between LAC. On the other hand, the average GDP for LAC is about 3.7%.

Graph1 and 2 support the statement.

Source: World Data Bank By taking into account a labor market flexibility indicator related to redundancy rules "Is legal to terminate the employment contract of a worker due to redundancy rules".

In countries where the labor laws allow employers to fire workers due to reduncy rules the economic growth ranges between 1% and 8% while for the rest of countries the range is lower between 2% and 5%. On average the growth rate for LAC under a framework of this restriction is lower than without it (3.6 % and 3.8% respectively).

One possible reason behind this, it is the ability of flowing of resources to the most productive sectors [START_REF] Bolaky | Trade, Regulations, and Growth[END_REF]) See Graph3. Figure3: Density function of GDP growth (annual %) for LAC according to redundancy rules (Is it legal for an employer to terminate the employment contract of a worker due to redundancy rules?) over the period 2005-2012.

According to the above statements, it seems that a complementary policy related to labor market flexibility may affect the impact of trade openness on economic growth. In the next section, the reader will find an empirical analysis about the relationship between trade openness and economic growth given the degree of labor market flexibility for Latin American Countries.

Empirical Analysis The Impact of Trade on Economic Growth

Estimation results based on the system GMM estimates of Eq. ( 1) are presented in Table 1. Since the level of strength in the relationship between trade openness and economic growth may depend on the data used cross section or panel data. [START_REF] Harrison | Openness and Growth: A Time-Series, Cross-Country Analysis for Developing Countries[END_REF]. The empirical analysis was made by using the data as it will be dealing with a pooled data and a panel data.

Column 1 shows the results of the OLS estimation, here we observe that trade openness volume has a negative and significant impact on economic growth for LAC. However, since the interaction term between labor market flexibility indicator and trade openness volume was included in the equation the negative sign of the coefficient of trade openness volume (-0.58) should not be interpreted as a pure effect of trad e on econom ic grow th. H ere, LAC where the labor law allows employers to fire workers due to reduncy rules get a more negative impact of trade on economic growth (-0.58-0.32). However, the impact is not statistically significant. On the other hand, if we consider trade restrictions variables we observe that an increase of one percent in the time required to import may decrease the economic growth about 0.7%. Other variables, such us public and private investment, education enrollment and labor force growth were included to improve the robustness of results. We observe a positive and significant relationship between private investment, human capital and economic growth. However, according to the related literature mention in section 2 and by using Haussman test, the OLS estimation results should be interpreted with caution due to an endogeneity problem generated by simultaneity between trade openness volume and GDP per capita, which implies that the coefficients of this estimation will be biased.

Column2 shows the results of GMM estimation as it will be dealing with a pooled data.

Here again, we observe a negative and significant impact of trade volume on economic growth for LAC. But now the coefficient of the interaction term between trade openness volume and labor market indicator becomes positive (0.32), which implies that complementary policies such as labor flexibility may reduce the negative impact of trade openness volume on economic growth (-1.50+0.32). In other words, since I am doing the GMM estimation as it will be dealing with a pooled data. It may be inferred that the degree of labor market flexibility might decrease the negative effect of trade on economic growth in the short run. However, these results are not statistically significant.

Other variables such as private investment and human capital are positive and statistically significant related to economic growth. For instance, an increase of one percent in the secondary school enrollment will generate an increase of 1.23% on economic growth. During the analysis, population density4 was used to control for endogeneity. On the other hand, considering the Eq. ( 1) and using an unbalanced panel data over the period 2005-2012 described in the previous section, Column3 shows the results of GMM estimation. Here, one of the most important results is that the pure effect of trade openness volume is positive and statistically significant related to economic growth (0.08), which suggests that the negative effect of trade openness volume on economic growth for LAC might become positive in a longer time period analysis. Moreover, I find the interaction term between trade openness volume and labor market flexibility indicator to be positive and statistically significant associated to economic growth, meaning that an increase of one percent of trade openness volume for LAC where it is legal to terminate the employment contract of a worker due to redundancy rules will generate an increase of 0.11 % (0.08%+0.03%) on economic growth under a longer time period framework. These findings suggest that reforms related to labor market such as redundancy rules have both direct and indirect benefits, making countries to take greater advantage of trade openness, supporting some empirical studies [START_REF] Bolaky | Trade, Regulations, and Growth[END_REF], and Chang, Kaltani, Norman V. Loayza, ( 2009)). In other words, in the long run LAC that increase the degree of trade openness with complementary policies such as more labor market flexibility are able to enjoy greater benefits from trade than LAC where it is forbidden to terminate the employment contract of a worker due to redundancy rules. Trade restrictions such as time required to export and to import have a negative effect on economic growth but not statistically significant. Other variables such as private investment and labor force growth are still positive related to economic growth for LAC but their relationship becomes weaker and in some cases not statistically significant.

Table1

According to Column3, both the strength and direction of relationship between trade openness volume and economic growth is conditioned to the degree of labor market flexibility. Here, we observe that in the long run LAC that introduces more trade openness together with complementary labor policies such as less difficulty to terminate the employment contract of a worker due to redundancy rules are able to overcome the negative effect of trade on economic growth observed in the short run. One possible explanation for this, it is that trade openness in LAC where employers can terminate the employment contract due to redundancy rules such as Honduras, Mexico, Paraguay and Brazil can adapt the kind of employees to changing environments observed in international markets, making them able to enjoy benefits from trade in the long run.

Conclusions and Recommendations

In this study the relationship between trade openness and economic growth for Latin American Countries by taking into account the Labor market flexibility of each country is investigated. For this purpose, I run several non-linear growth regressions, relying on the system GMM estimator. Econometric results show that in LAC growth effect of trade openness is conditioned by the degree of labor market flexibility under a long time framework. Trade openness encourages the growth of LAC where there is less rigidity in the labor market related to redundancy rules, therefore contributing to more flexible labor market policies make LAC to enjoy greater benefits from trade openness. All else equal, empirical results show that trade openness volume is likely to benefit more LAC where it is legal to terminate the employment contract of a worker due to redundancy than those where it is forbidden.

According to these findings the decision to open their economy is not enough as a tool to promote economic growth in LAC. Complementary policies such as labor market flexibility are required to enjoy greater benefits from trade openness. In other words, both trade openness and labor market policies should be considered to promote benefits from trade.

The present research shows that while trade openness may potentially reduce growth in the short run; it is likely to boost growth for LAC in the long run and this positive effect can increase under a framework of complementary labor policies that allow employers to fire workers due to redundancy rules. These findings have serious policy implications considering the rapid trade liberalization observed in the LAC region during the last decades. Thus the present thesis provides evidence in favor of trade openness and complementary labor reforms to promote economic growth for Latin American Countries, contributing to the debate about the gains from trade openness in developing countries.

On the other hand, as discussed in previous sections, the empirical evidence about the impact of trade openness on economic growth is not conclusive, failing to reveal undisputed beneficial effect, which contributes to a lively academic and political debate about whether trade liberalization is good or not for developing countries. In this sense, the present analysis can be improved by using a longer time period, incorporating other proxy's variables of trade openness based on tariffs and non-tariff Barriers, and including a better proxy of human capital such as net school enrollment in the tertiary level which will help to inspect robustness of results. Other labor market indicators such as doing business are required in the analysis to inspect for trade benefits on growth considering labor market policies, which were not included due to the lack of information. This suggests the importance of future researches that develop better and more unified proxies of labor market behavior, contributing to the ongoing debate about trade benefits for developing countries.

Annexs

Annex1

Indicator Name Definition

GDP per capita (2005 U.S. dollars).

"GDP per capita is gross domestic product divided by midyear population. GDP is the sum of gross value added by all resident producers in the economy plus any product taxes and minus any subsidies not included in the value of the products. It is calculated without making deductions for depreciation of fabricated assets or for depletion and degradation of natural resources. Data are in constant 2005 U.S. dollars."

Trade Measures Trade (% of GDP)

"Trade is the sum of exports and imports of goods and services measured as a share of gross domestic product." Time to export /import(days)

"Time to export is the time necessary to comply with all procedures required to export goods. Time is recorded in calendar days. The time calculation for a procedure starts from the moment it is initiated and runs until it is completed. If a procedure can be accelerated for an additional cost, the fastest legal procedure is chosen. It is assumed that neither the exporter nor the importer wastes time and that each commits to completing each remaining procedure without delay.

Procedures that can be completed in parallel are measured as simultaneous. The waiting time between procedures--for example, during unloading of the cargo--is included in the measure."

"Time to import is the time necessary to comply with all procedures required to import goods. Time is recorded in calendar days. The time calculation for a procedure starts from the moment it is initiated and runs until it is completed. If a procedure can be accelerated for an additional cost, the fastest legal procedure is chosen. It is assumed that neither the exporter nor the importer wastes time and that each commits to completing each remaining procedure without delay. Procedures that can be completed in parallel are measured as simultaneous. The waiting time between procedures--for example, during unloading of the cargo--is included in the measure." "Net enrollment rate is the ratio of children of official school age who are enrolled in school to the population of the corresponding official school age. Primary education provides children with basic reading, writing, and mathematics skills along with an elementary understanding of such subjects as history, geography, natural science, social science, art, and music."

Source

Macroeconomic and Geographical Features

Labor force participation rate, total "Total labor force comprises people ages 15 and older who meet the International Labour Organization definition of the economically active population: all people who supply labor for the production of goods and services during a specified period. It includes both the employed and the unemployed. While national practices vary in the treatment of such groups as the armed forces and seasonal or parttime workers, in general the labor force includes the armed forces, the unemployed, and first-time job-seekers (…)."

Population density "Population density is midyear population divided by land area in square kilometers. Population is based on the de facto definition of population, which counts all residents regardless of legal status or citizenship--except for refugees not permanently settled in the country of asylum, who are generally considered part of the population of their country of origin. Land area is a country's total area, (...)."

Content 1 .

 1 Introduction .......................................................... 2. Related Literature................................................. 3. Empirical Framework ........................................ 4. Data Description ................................................ 5. Empirical Analysis ............................................. 6. Conclusions and Recommendations .................. 7. Annexs ............................................................... 8. References ..........................................................

  inequality hurt human capital accumulation through a reduction in education opportunities for individuals in the bottom of the income distribution, which lower social mobility and skills development (Focus on Inequality and Growth OECD 2004). Income inequality will affect growth and its sustainability (Causes and Consequences of Income Inequality: A Global Perspective Dabla-Norris, Kochhar, Suphaphiphat, Ricka, Tsounta IMF, 2015). Nowadays, the effectiveness of world trade agreements for developing countries is highly debated in both the academic and political field because of different issues such as outsourcing and the physical location of firms, human skills, macroeconomic and political environment. That is why there are many empirical researches to figure out the Relationship between Trade openness and Economic growth. For instance, Harrison (1996) found a positive correlation between trade openness and economic growth but not strong in all cases. The level of strength in the relationship depends on the dataset used cross-section or panel data. Author uses a general production function in which GDP depends on, capital stock, primary and secondary education, population, labor force, technological change and arable land for each country. Then the openness trade variable is included in the production function to test their impact on technological change-growth in output after controlling for increase in resource used. Trade openness variables used are: an annual index of trade liberalization based on exchange rate and commercial policies, an index of trade liberalization based on tariffs and nontariff barriers, a black-market premium and the Dollar index. The results of this research suggest that all the different measures except trade shares exhibit a negative relationship between trade and economic growth (due to more distortions) while trade share have a positive relationship with economic growth.

  welfare for Developed Countries (DC) is positive because of static and dynamic gains while for Least Developed Countries (LDC) the effect is ambiguous. Moreover, by using a three-equation system, a panel data from 100 developed and developing countries between 1970 and 1997, and considering two groups of measure of trade openness: trade volumes and trade restrictions, Halit Yanikkaya (2003) found a positive relationship between trade restrictions and economic growth which implies that under certain macroeconomic conditions, developing countries can benefit from trade 1 "Whose sign is adjusted so that a high value means a more open regime" Luca Antonio Ricci, and Roberto Rigobon

  conclusive and promises more that it can really give us because of several econometric problems. One of the potential problems in determining the relationship between trade openness and growth is the simultaneity, which means that trade openness variables are linked to the level of income. For instance, trade share is a function of GDP which will generate endogeneity problems and for consequence biased results[START_REF] Ha | Once Again, is Openness Good for Growth?[END_REF]. Another problem is the accuracy of the trade openness indicators, for instance "trade volume" might be a function of other variables like quality of institutions, health conditions, geographic, availability of natural resources size and so on(Rodriguez and Rodrik , 2004). By using a set of data of 140 countries[START_REF] Rigobon | Rule of Law, Democracy, Openness and Income: Estimating the Interrelationships[END_REF] showed that including variables like quality of institutions measured by the rule of law and property rights makes the relationship between trade and economic growth disappear. Moreover, open economies can induce government authorities to increase public expenditure devoted for exporters in case of foreign shocks which may reduce economic growth(Rodrik, 1998). According to these results, trade openness indicators are not robust to the inclusion of macroeconomic variables.

Figure1:Figure2:

  Figure1: Density function of GDP growth (annual %) for Latin American Countries over the period2005- 2012

  annual %) [NY.GDP.MKTP.KD.ZG] No

  These last are divided in six categories: Trade Openness

	measures, Physical and Human Capital Proxies, Macroeconomic features, Labor
	Market Flexibility Indicator, and Interaction Term between Labor Indicator and Trade
	Openness Volume.

The dependent variable, state GDP per capita, was obtained from World Bank national accounts data, and OECD National Accounts data files. The series are expressed in constant currency (2005 U.S. dollars). The measure of Trade Openness which is one of the variables of interest is divided in two groups: Trade Volume and Trade Restrictions.

  Robust standard errors in parentheses. Column 3 shows the GMM estimation considering an unbalanced panel data over the period 2005-2012, where lags of trade openness volume were included as instrument variables to control for endogeneity. (* p<.1; ** p<.05; *** p<.001). During the analysis, to examine the validity of the instruments the Sargan test was used. ** Is legal to terminate the employment contract of a worker due to redundancy rules?

	Table1-Impact of Trade Openness on Economic Growth for Latin American
	Countries by taking into account Labor Market Flexibility of each country
	( GMM estimator, 14 Latin American Countries; 2005-2012)
	Dependent Variable: GDP per capita
	, per capita income (constant 2005 USD)
	Independent variables	(1)OLS	(2) GMM	(3)GMM*
		-0.5772*	-1.4964**	0.0804**
		0.3205	0.7361	0.0359
		0.0691	0.4022	-0.0300
		0.4024	0.5047	0.0198
		-0.7090**	-0.8874**	-0.0092
		0.2971	0.3196	0.0344
		0.57178**	0.5423***	0.0157
		0.1688	0.1376	0.0147
		0.30727	0.7525	-0.1888**
		0.46117	0.6042	0.0662
		1.2083**	1.2342**	-0.0764
		0.4684	0.4421	0.1534
		-0.0201	0.0313	0.0078
		0.1091	0.1029	0.0100
	**	1.5592	-1.2299	-0.1965**
		1.6910	2.6113	0.0663
		-0.3201	0.3230	0.0366**
		0.38412	0.6118	0.0131
	Coefficient	4.6911**	7.3088**	1.9646**
		1.9954	2.8895	0.8217
	N. Observations	69	69	50
	R2	61%	56%
	Sargan test, p-level			0.57

* Notes:

: World Development Indicators -World Data Bank Physical and Human Capital

  General government final consumption expenditure (formerly general government consumption) includes all government current expenditures for purchases of goods and services (including compensation of employees). It also includes most expenditures on national defense and security, but excludes government military expenditures that are part of government capital formation."

	Gross fixed
	capital
	formation,	"Private investment covers gross outlays by the private sector
	private sector	(including private nonprofit agencies) on additions to its fixed
	(% of GDP)	domestic assets".
	General government final consumption expenditure (% of GDP) "School
	enrollment,
	secondary (%
	net)

In the BPAs agreements central banks guarantee to pay the respective foreign exporter for the export value in the case of default, which help to finance trade with non-dollar world.

In panel data, the original time-varying errors are serially uncorrelated, after the differencing process errors have serial correlation. However, the GMM allow us to work under serial correlation.

Source: World Data Bank

Annex 2 shows a table related to the validity of the instrument.

Acknowledgements

Source: Doing Business Project -World Bank Group.

Annex2

First

Labor Market Flexibility Indicators

Redundancy rules:"Is it legal for an employer to terminate the employment contract of a worker on the basis of redundancy?"


Maurice Oreilly
email: maurice.oreilly@dcu.ie

Statistical overview of CERME10

CERME evolves over time, and so it is of interest to gather and present some quantitative data on the number of participants and on the scientific output at CERME10.

The data for the table comes from two sources: the submissions made online (to the CERME10 website) by mid-December 2016, and the registration and attendance database for the congress. The final column shows the 768 (distinct) participants at CERME10, allocating each to exactly one TWG. Although over 80 participants were active in more than one TWG, care was taken to ensure that no participant was included more than once (by fine-tuning the 'Additional authors' column appropriately). This was facilitated by taking into account the TWG explicitly chosen by each participant at registration. The foreword states that there were 774 participants; this figure includes the six presenters at the plenary sessions.

Of the 565 submissions made in advance of CERMEcomprising 466 (long) papers and 99 posters (or short contributions)the attrition by the time these proceedings have been edited was only 20 (about 3.5%). This low figure underscores the observation mentioned in the foreword that "nobody was wandering in the corridors". Contributions to the proceedings as a proportion of the total number of participants was 0.71 (= 545/768), this figure varying from 0.56 (for TWG2) to 0.82 (for TWG16). Another indicator of the intensity of the work at CERME is the low number of participants (84) who did not contribute papersalthough they did contribute to the lively discussion! This was 10.9% of the total number of participants, with extremes ranging from 3.0% (for TWG10) to 20.0% (for TWG24). Yet another perspective on the hard work undertaken in the context of the congress is illustrated by the number (453) of 'long' papers as a proportion of all contributions: 83% overall, with a minimum of 71% (for TWG14) and an impressive maximum of 100% (for TWG2).

It has already been noted (in the foreword) that participants at CERME10 were drawn from 52 countries. It is part of the 'CERME spirit' to support academics who would normally have limited access to CERME (either from underrepresented or economically weak countries). This is made possible through the Graham Littler Fund which draws from those who can afford, in support of those who cannot. For CERME10, 46 participants were awarded grants totaling €21 100 (€12 300 for registration and €8 800 for travel and accommodation).

It is hoped that the data provided on these two pages helps quantify important aspects of CERME10, putting the scientific output in perspective. Submissions were made online by mid-December 2016, most of which are published in these proceedings (as either long or short contributions).

TWG

In each TWG, the number of submissions is augmented by 'Additional authors' indicating the number of participants at CERME10 who contributed to (long or short) papers. The 'Additional participants' attended CERME10 but were not authors of these papers.

The 'Total number of participants in each TWG' is then the sum of all the submissions along with the additional authors and participants.

Proceedings of CERME10