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Essays in international trade Pupato, German Pablo 2011

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Essays in International Trade  by Germán Pablo Pupato B.A., Universidad de San Andrés, 2001 M.A., Universidad de San Andrés, 2005  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  Doctor of Philosophy in THE FACULTY OF GRADUATE STUDIES (Economics)  The University Of British Columbia (Vancouver) March 2011 c Germán Pablo Pupato, 2011  Abstract This dissertation consists of three chapters in the eld of international trade. The rst two, jointly written with Matilde Bombardini and Giovanni Gallipoli, explore the role of skill dispersion as a source of comparative advantage. The rst chapter presents a tractable multi-country, multi-sector model of trade with search frictions in which comparative advantage derives from (i) cross-sectoral differences in the substitutability of workers' skills and (ii) cross-country differences in the dispersion of skills in the working population. We provide conditions under which higher skill dispersion triggers specialization in sectors characterized by higher substitutability among workers' skills. The second chapter explores the empirical relevance of skill dispersion as a determinant of the pattern of trade across industries. The analysis relies on microdata from the International Adult Literacy Survey to construct measures of skill dispersion. Results indicate that the latter has a signi cant effect on the pattern of trade across industries, of a magnitude comparable to the aggregate endowments of human and physical capital. The result is robust to the controls for other proximate causes of comparative advantage, such as institutional quality and exibility of labour markets. The third chapter offers a relatively unconventional approach to the empirical analysis of the factors that determine export decisions at the rm level, by explorii  ing whether the characteristics of rms geographically located close to each other play a role in shaping their individual entry decisions. In particular, I develop an empirical framework to study whether export participation decisions of individual rms are in uenced by non-market interactions (e.g. learning or imitation) with rms that belong to a common reference group. The main testable hypothesis is that, in the presence of entry costs, group composition affects the degree of state dependence of individual export decisions. This proposition is tested by applying a dynamic panel data estimator to a data set of Argentine manufacturing rms. The ndings show that group composition in uences individual export decisions. Most of this effect is channelled through entry costs. Firms bene t from proximity to productive rms but not from proximity to other exporters.  iii  Table of Contents Abstract  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ii  Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  iv  List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  viii  List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ix  Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  x  Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xi  1  . . . . .  1  1.1  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  1  1.2  Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6  1.2.1  Preferences . . . . . . . . . . . . . . . . . . . . . . . . .  6  1.2.2  Production . . . . . . . . . . . . . . . . . . . . . . . . .  7  1.2.3  Labour Market . . . . . . . . . . . . . . . . . . . . . . .  8  1.3  Skill Dispersion as Comparative Advantage . . . . . . . . . . . .  10  1.4  The Firm's Problem and Bargaining . . . . . . . . . . . . . . . .  12  1.5  Entry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  15  1.6  Trade Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  16  Skill Dispersion and Trade with Labour Market Frictions  iv  2  1.7  Multi-Country Extension . . . . . . . . . . . . . . . . . . . . . .  16  1.8  Wage Distribution and Complementarity . . . . . . . . . . . . . .  17  1.9  Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  19  Skill Dispersion and Trade: an Empirical Analysis . . . . . . . . . .  21  2.1  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  22  2.2  Estimation Framework . . . . . . . . . . . . . . . . . . . . . . .  25  2.2.1  Skill Substitutability I: Residual Wage Dispersion Rankings 28  2.2.2  Skill Substitutability II: O*NET Rankings . . . . . . . . .  28  Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  29  2.3.1  Skill Dispersion . . . . . . . . . . . . . . . . . . . . . . .  29  2.3.2  Substitutability . . . . . . . . . . . . . . . . . . . . . . .  31  Baseline Results . . . . . . . . . . . . . . . . . . . . . . . . . . .  35  2.4.1  Substitutability Proxied by Wage Dispersion Rankings . .  36  2.4.2  Substitutability Proxied by O*NET Rankings . . . . . . .  37  Identi cation and Robustness . . . . . . . . . . . . . . . . . . . .  38  2.5.1  The Extensive Margin of Trade: Selection . . . . . . . . .  38  2.5.2  Omitted Determinants of Comparative Advantage . . . . .  40  2.5.3  Reverse Causality . . . . . . . . . . . . . . . . . . . . . .  42  Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  44  Non-Market Interactions and Entry into Export Markets . . . . . .  46  3.1  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  47  3.2  A Model of Entry into Export Markets with Sunk Costs . . . . . .  51  3.3  Export Decisions in Argentina During the 1990s . . . . . . . . . .  56  3.3.1  56  2.3  2.4  2.5  2.6 3  Exporters and Non-exporters . . . . . . . . . . . . . . . .  v  3.3.2  Transitions In and Out of Exporting and the Persistence of Entry Decisions . . . . . . . . . . . . . . . . . . . . . . .  57  Why do Firms Behave Similarly? . . . . . . . . . . . . . . . . . .  58  3.4.1  A Look at the Raw Data . . . . . . . . . . . . . . . . . .  58  3.4.2  Three Challenges for the Empirical Analysis . . . . . . .  61  Econometric Analysis . . . . . . . . . . . . . . . . . . . . . . . .  63  3.5.1  A Linear Speci cation . . . . . . . . . . . . . . . . . . .  63  3.5.2  Identi cation . . . . . . . . . . . . . . . . . . . . . . . .  68  3.5.3  Estimation Framework . . . . . . . . . . . . . . . . . . .  72  3.6  Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . .  76  3.7  Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  80  Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  82  3.4  3.5  Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 A Appendix to Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . 114 A.1 Suf cient Conditions for Property 1 . . . . . . . . . . . . . . . . 114 A.2 Output, Prices and Revenues . . . . . . . . . . . . . . . . . . . . 117 A.3 Mass of Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 A.4 Proof of Proposition 1 . . . . . . . . . . . . . . . . . . . . . . . . 121 A.5 Proof of Proposition 2 . . . . . . . . . . . . . . . . . . . . . . . . 122 A.6 Proof of Proposition 3 . . . . . . . . . . . . . . . . . . . . . . . . 122 A.7 Derivation of the Shapley Value . . . . . . . . . . . . . . . . . . 123 A.8 Proof of Proposition 4 . . . . . . . . . . . . . . . . . . . . . . . . 124 B Appendix to Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . 128 vi  B.1 Main Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 B.1.1  Measuring Skill Dispersion  . . . . . . . . . . . . . . . . 128  B.1.2  Measuring Wage Dispersion . . . . . . . . . . . . . . . . 129  B.2 Additional Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 B.3 Additional Results . . . . . . . . . . . . . . . . . . . . . . . . . 133 C Appendix to Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . 135 C.1 Data Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135  vii  List of Tables Table 1  Summary Statistics - IALS Log-Scores . . . . . . . . . .  83  Table 2  Substitutability Rankings . . . . . . . . . . . . . . . . .  84  Table 3  Correlations of Substitutability Proxies . . . . . . . . . .  85  Table 4  Estimates Using Residual Wage Dispersion Rankings and Residual Score Dispersion . . . . . . . . . . . . . . . .  Table 5  86  Estimates using O*NET Rankings and Residual Score Dispersion (St Dev) . . . . . . . . . . . . . . . . . . . .  87  Table 6  Estimates - Selection and Other Controls . . . . . . . . .  88  Table 7  Estimates - First Stages . . . . . . . . . . . . . . . . . .  89  Table 8  Additional Variables . . . . . . . . . . . . . . . . . . . .  90  Table 9  Descriptive Statistics - Mean and S.D. (in italics) . . . .  91  Table 10  Geographical Distribution of Firms and Exporters . . . .  92  Table 11  Persistence in Export Decisions . . . . . . . . . . . . . .  93  Table 12  Correlations between Individual and Group Behaviour .  94  Table 13  Dynamic Panel Data Estimation - Main Results . . . . .  96  Table 14  Dynamic Panel Data Estimation - Sensitivity Analysis . .  98  Table 15  Normalized Raw Scores and Wage Rankings . . . . . . .  99  Table 16  Non-Normalized Interactions . . . . . . . . . . . . . . . 100  viii  List of Figures Figure 1  Mean and Standard Deviation - IALS scores . . . . . . . 102  Figure 2  Industry Rankings by Standard Deviation of Residual Wages . . . . . . . . . . . . . . . . . . . . . . . . . . . 103  Figure 3  Transitions In and Out of Exporting . . . . . . . . . . . 104  Figure 4  Individual and Group Export Decisions . . . . . . . . . 105  Figure 5  Individual and Group Export Decisions, by Export Status 106  ix  Acknowledgments I am deeply indebted to Matilde Bombardini and Giovanni Gallipoli, for their unconditional support during the last three years. They have generously shared with me countless hours of their time for guidance, advice and discussions that, I hope, will help me get closer to their research standards. Special thanks to Matilde for kindly inviting me to spend a few weeks at the University of Chicago in October 2009. I am grateful to David Green and Keith Head for their insight at various stages of my work. Every discussion with them is necessarily quality time and an opportunity to learn something new. Brian Copeland, Mukesh Eswaran, Patrick Francois, Atsushi Inoue, Ashok Kotwal, Thomas Lemieux, Vadim Marmer, Nathan Nunn and Francesco Trebbi provided helpful comments and friendly advice. Mauricio Drelichman was always ready to offer support, honest advice and solid BBQ skills since day 1 at UBC. Thank you Mauricio! I would like to acknowledge the contribution of my peers to enhancing my graduate experience, specially during the earlier and certainly tougher years of the Ph.D.: Jonathan Goyette, Jian Mardukhi, Maryam Saaedi, Ali Shourideh, Cristian Troncoso-Valverde and, in particular, my good friend Marcos Agurto. Last, but surely not least, Flor, Diego, Nelly and Guillermo for their unconditional love. Nothing else matters. x  Dedicated to my mentor and friend, Daniel Chudnovsky  xi  Chapter 1  Skill Dispersion and Trade with Labour Market Frictions Synopsis. This chapter develops a tractable multi-country, multisector model of international trade with search frictions in the labour market. Comparative advantage derives from (i) cross-sectoral differences in the substitutability of workers' skills and (ii) cross-country differences in the dispersion of skills in the working population. We establish the conditions under which higher skill dispersion triggers specialization in sectors characterized by higher substitutability of skills across workers.  1.1  Introduction  One of the mainstays of the theory of comparative advantage is that countries' factor endowments determine the pattern of trade. In this chapter we study an alternative, but closely related, source of comparative advantage: the dispersion of 1  skills (or human capital) in the working population.1 Why would the distribution of skills matter for specialization and trade? We argue that industries vary in the degree of complementarity among the skills of workers employed in the production process. In some industries, such as aerospace or engine manufacturing, production requires completing a long sequence of tasks and poor performance at any single stage greatly reduces the value of output. These are industries with high skill complementarity (or O-Ring, as in Kremer, 1993), where teamwork is crucial. Ef ciency is higher when workers of similar skills are employed in every stage of production. On the contrary, in other industries, such as apparel, teamwork is relatively less important, workers' skills are more easily substitutable and therefore poor performance in some task can be mitigated by superior performance in others. In this chapter, we investigate theoretically whether countries with greater skill dispersion specialize in sectors characterized by higher substitutability of skills across tasks. The model features monopolistic competition, a single factor of production (skills), many countries and many sectors. Countries only differ in terms of the distribution of skills in the labour force. Sectors only differ in terms of the degree of skill substitutability in the production process. Importantly, we introduce search frictions in the labour market - as in Helpman and Itskhoki (2009a) and Helpman et al. (2008a; 2008b)- and focus on skills that are not observable ex-ante (i.e. before workers are hired).2 The latter modelling choice re ects the fact that observable characteristics of workers, including age 1 Human  capital is determined by many factors, among which formal education, family upbringing, underlying ability and on-the-job training. Throughout this chapter we refer to human capital or skills, terms that we use interchangeably, as a set of attributes that are of productive use in the workplace. 2 The unobservability of skills could also be broadly interpreted as a `friction'. However, in Chapters 1 and 2 of this dissertation, this term will exclusively be used to refer to the cost that rms incur when searching for workers, which is in line with its usage in the search and matching literature.  2  and education, account for a minor share of the total variation in work-related literacy scores within countries (see chapter 2, section 2.3.1). It is also consistent with evidence suggesting that rms only gradually learn the skills of their workers (see for example Altonji and Pierret, 2001 and Altonji, 2005). In this context, the model is best interpreted as a mechanism that illustrates how the dispersion of skills among workers with otherwise identical observable characteristics affects comparative advantage. In the rest of chapter 1 and chapter 2 we often refer to such skills as `residual' skills. One immediate advantage of our assumptions is that they allow the model to remain tractable in a setting with many countries and many sectors. Essentially, ex-ante unobservability and search frictions imply that rms in our model hire by randomly sampling workers from the endowment of the economy. As a result, rms and industries inherit the skill distribution of the economy -i.e. the distribution of skills of the workers employed in every rm is identical to the distribution of skills in the country.3 We show that this mechanism generates differences in output per worker across industries and countries that determine the pattern of international trade. In particular, the central result of the chapter establishes the conditions under which countries with a high dispersion of skills in the labour force will be relatively more productive and therefore export relatively more in sectors where skills are more easily substitutable across tasks. Our theoretical framework provides a useful guide to derive an appropriate econometric speci cation to test its main result empirically, a task pursued in chapter 2. In addition, it delivers a direct link between the unobservable degree of com3 Random  matching is consistent with recent international evidence (see Iranzo et al., 2008, and Lazear and Shaw, 2008) suggesting that most of the observed dispersion of wages occurs within, rather than between, rms.  3  plementarity and the observable dispersion of residual wages within industries. In particular, we also show that, in the presence of random matching on residual skills, residual wage distributions at the industry level uniquely re ect the degree of complementarity among skills. Industries with higher complementarity are characterized by more compressed wage distributions because, for example, workers with higher than average skills contribute to surplus relatively less, a fact re ected in their wage. This paper is related to a recent theoretical literature that has studied how skill distributions may in uence the pattern of trade. The hypothesis that skill dispersion may lead to specialization was rst put forth by Grossman and Maggi (2000) -henceforth GM- which is a useful point of reference, since their modelling assumptions complement those of this chapter. In particular, GM focused on the case of fully observable skills and competitive labour markets. In a two-country, twosector model, they show that when both production functions only differ in the degree of complementarity in skills, there is positive assortative matching of workers in every industry. As a result, skill diversity does not generate comparative advantage and there is no trade. They also show that comparative advantage emerges only if there are two sectors, one with supermodular and submodular production functions.4 These set of results motivate the emphasis on ex-ante unobservability and frictions in the labour market in this chapter.5 4 Trade  emerges only conditional on the existence of a supermodular sector, where workers of identical abilities are paired together, i.e. self-matching prevails, and of a submodular sector, where the most skilled workers are paired with the least skilled co-workers, i.e. cross-matching prevails. Supermodularity implies that the marginal product of any worker is increasing in the ability of the co-worker. Submodularity of the production function implies the opposite. In GM, the country with more dispersed skill distribution specializes in the submodular sector. 5 We expand on an element introduced by GM, who consider imperfect observability of skills. At the end of the paper the authors “note in passing that, with imperfect matching, trade would take place between two countries with different educational processes even if tasks were complementary in all production activities”, i.e. all production functions were super-modular, which is the case we consider. We extend this model to many countries and sectors, and derive sharp predictions for the pattern of trade.  4  Ohnsorge and Tre er (2007) propose a model with two-dimensional worker heterogeneity and show that, when each worker represents a bundle of two skills, the correlation of the two in the population determines comparative advantage. Grossman (2004) starts from the premise that, in some sectors, incomplete contracts make it dif cult to tie remuneration to an individual worker's output. In a country with high skill dispersion highly skilled individuals prefer to sort into sectors where individual performance is easier to measure, rather than working in an industry where the common wage is dragged down by workers with relatively low skills. This type of endogenous sorting results in comparative advantage. Finally, in Bougheas and Riezman (2007) comparative advantage emerges from differential returns to skills across sectors. This chapter also contributes to the large and established literature on factor endowments and comparative advantage, a topic which still receives a great deal of attention. For example, in a recent contribution to this literature, Costinot and Vogel (2009) build a model with a continuum of sectors and a continuum of skill levels and investigate the effect of trade on wage inequality in a rich framework. The paper begins with the analysis of the two-country case. Countries, Home and Foreign, are characterized by different skill distributions. They may also vary in size, but are otherwise identical. The next section introduces the model with a description of consumer preferences, production technologies and the labor market. Section 3 discusses of how different skill distributions generate productivity differences across countries and industries, the source of comparative advantage in the model. Sections 1.4 and 1.5 study the optimization problem of individual rms and the general equilibrium (entry). The following two sections analyze the implications for the pattern of international trade in the two-country and multi-country versions of the model. Section 1.8 characterizes the link between skill complementarity and wage inequality, which is extensively used in BGP. Section 1.9 provides 5  some concluding remarks.  1.2  Setup  1.2.1  Preferences  Countries are denoted with a subscript c where c 2 fH; Fg, which is dropped when it does not create ambiguity. Each country c is populated by a measure Lc of individuals. Utility of the representative consumer depends on the consumption of a homogeneous good Q (0) and a continuum of differentiated goods Q (i) with i 2 I. The utility function U is Cobb Douglas: logU = α (0) log Q (0) + with 0 < α (i) < 1 and α (0) +  R  i2I α (i) di  Z  i2I  α (i) log Q (i) di  = 1. The aggregate Q (i) is the con-  sumption index over the set Ω (i) of available varieties of product i and preferences exhibit a constant elasticity of substitution σ across varieties of good i.6 Under these preferences, demand for a given variety ω is represented by the following equation: d (ω; i) =  p (ω; i)  σ  α (i) E  1 σ  P (i)  (1.1)  where E is total expenditure, p (ω; i) is the price of variety ω of i, and P (i) is the ideal CES price index of aggregate Q (i). 6 More  speci cally: Q (i) =  Z  q(ω; i)  σ 1 σ  dω  σ σ 1  ω2Ω(i)  where q(ω; i) is the quantity consumed of variety ω of good i.  6  with σ > 1:  1.2.2  Production  Good Q (0) is produced under constant returns to scale by perfectly competitive rms. The technology is such that one unit of labour produces one unit of output. We choose Q (0) as our numeraire and we assume that all countries produce the numeraire good in positive quantity, which implies that the wage in sector 0, w (0), is equal to one. Each differentiated sector i is populated by a continuum of identical rms, each producing a different variety ω. The market is characterized by monopolistic competition among rms, with free entry and a xed cost of production f . Total output y depends on the skill level of each worker hired a, the measure of workers hired h and the distribution of skills across workers g˜ (a).7 The distribution of skills matters for production because we assume that different levels of skills are not perfectly substitutable.8 In particular, the production function of a representative rm in a sector depends on the degree of complementarity λ among workers' skills in that sector and takes the following form:  y=  Z  a hg˜ (a) da λ  1 λ  with  1  σ σ  <λ <1  (1.2)  The parameter λ measures the degree of skill complementarity, since the elasticity of substitution among skills levels, for a xed mass of workers h, is given by  1 1 λ,  which increases with λ . The larger λ , the more substitutable workers of different skill levels are.9 The key assumption in this model is that each sector i is charac7 For simplicity we only model `residual' skills and work under the assumption that other observable characteristics are accounted for. In this sense we do allow for selection on observables, but we do not model it explicitly. In Chapter 2 we carefully control for such selection. 8 One possible interpretation is that the skill of each worker is a differentiated input in the production process. An alternative interpretation, along the lines of the paper by Takii and Tanaka (2009), is that each worker produces a differentiated intermediate good, in quantity proportional to her skills, and intermediate inputs are aggregated by a CES production function. 9 For a xed h, this production function is analogous to that in Grossman and Maggi (2000), p.  7  terized by a different value of λ in production, and therefore by a different degree of complementarity among workers' skill levels. Since λ is the only characteristic that differentiates sectors, in the remainder of the theoretical section we drop the index i and index sectors by their parameter λ . Two properties of this production function are worth discussing in detail. First, for given mass of workers h, the function is homogeneous of degree one in the skills of workers. This property stresses the relative importance of the shape, rather than location, of the distribution of skills. Second, the production function features increasing returns to the mass of workers, given the distribution of skills.10 In particular, λ also represents the extent of increasing returns to scale (as well as the degree of complementarity), but this feature plays no substantial role in the model.11 We restrict the range of λ to guarantee that the rm's maximization problem is concave, as described in section 1.4.  1.2.3  Labour Market  We introduce labour market frictions in the spirit of Helpman and Itskhoki (2009a), although for simplicity we assume that there are no frictions in sector 0. Workers are characterized by different levels of skills and skill is a continuous variable distributed in the workers' population of country c according to a density function g (a; c). The interaction between rms and workers in the labour market has the 1261. 10 This  1  is easily seen by rewriting the production function as y = h λ  11 We  R λ a g˜ (a) da  1 λ  .  should note that it is not possible to obtain both constant returns to mass of workers and ability without confounding the quantity and quality of workers, as for example in a production 1 λ  R  function of the following type: y = (ahg˜ (a))λ da . We give priority to maintaining constant returns to ability because we do not want to confound the degree of complementarity with differential returns to aggregate ability in different sectors. Grossman and Maggi (2000) discuss this as another case in which the distribution of ability matters and Bougheas and Riezman (2007) explicitly model this aspect in a different framework.  8  following timing. First, workers choose whether to look for jobs in the homogeneous sector or in one of the differentiated good sectors. Second, rms in each differentiated sectors pay a cost bh to randomly sample a mass h of workers from the population of workers searching for a job in that sector. The search cost b depends on labour market conditions, as described further below. Third, production takes place. Umatched workers remain unemployed. Fourth, each rm and its employees bargain over the split of revenues into pro t.and wages. Regarding information sets, we follow Helpman and Itskhoki (2009a) and Helpman et al. (2008a) in assuming that individual skills are match-speci c and therefore cannot be observed when rms and workers are matched. That is, workers cannot condition their job search on their own skills and rms cannot condition their hiring decisions on skill levels. Individual skills are revealed to all parties only at the production stage. These assumptions on the observability of skills are consistent with the empirical literature in labour economics.12 As a result the initial distribution of residual skills in the worker population is inherited by the mass of workers looking for a job in each sector. Moreover, by de nition, workers' residual skills are not observable to the rm when hiring. The combination of these assumptions yields no sorting between workers and rms. It's worth noticing that if we allowed skills to be partially observable in our model we would obtain that rms only hire workers of identical observable skills. Therefore we can interpret our case of unobservable skills as a residual of overall skills, once the observable component has been accounted for. This has implications for the empirical analysis in the next chapter where, for consistency with the theory, our measure of skill dispersion will be purged of observable individual characteristics. 12 For  example, Altonji and Pierret (2001) nd that as employers learn about worker productivity the wage equation coef cients on easily observed characteristics, such as education, fall relative to the coef cients on hard-to-observe correlates of worker productivity.  9  Although the distribution of workers' skills g˜ (a) could potentially be sector speci c, random matching implies that every rm, in every sector λ , in country c inherits the residual skill distribution in the general population:13 g˜ (a) = g (a; c)  1.3  Skill Dispersion as Comparative Advantage  Given that rms and workers match randomly with respect to unobservable skills, in this section we discuss how different skill distributions across countries generate comparative advantage. To facilitate the discussion we rewrite the production 1  function in (1.2) as y = h λ A (λ ; c) where A (λ ; c) is de ned as:  A (λ ; c) =  Z  a g(a; c)da λ  1 λ  We loosely refer to A (λ ; c) as `productivity', although clearly this is not the result of countries having access to different technologies. The magnitude of A (λ ; c) depends on a combination of a country-speci c skill distribution and a sector-speci c level of complementarity across skills. We are interested in how the pattern of comparative advantage, i.e. the relative A's, are affected by the distribution of skills. The general idea we explore is whether countries with lower dispersion in the distribution of skills have a comparative advantage in sectors with high degree of complementarity, i.e. where it is relatively more important to employ workers with 13 We do not allow rms to screen workers as in Helpman et al. (2008a). We note that, contrary to the case described by Helpman et al. (2008a), with our choice of production function, rms would not want to screen workers even if the technology to screen were available, because the marginal product of an additional worker is always positive. This is the case in the static problem we are analyzing. In a dynamic framework we would expect rms to lay off unproductive workers and replace them with potentially more productive ones.  10  similar skills. Since the A's exhibit constant returns to skills, a proportional increase in the skills of all workers increases the A by the same proportion and does not affect comparative advantage. We concentrate on comparing A's across countries that have the same average skills and different dispersion.14 Without loss of generality countries are ordered so that, if c < c0 , then country c0 is characterized by a skill distribution g (a; c0 ) that is a mean-preserving spread of the skill distribution g (a; c) in country c. We state a general condition, Property 1, for a speci c pattern of comparative advantage to emerge as a result of differences in the distribution of skills. Property 1 A (λ ; c) is log-supermodular in λ and c, i.e. for λ < λ 0 and c < c0 : 0 A (λ ; c0 ) A λ ; c0 < A (λ ; c) A λ 0; c  (1.3)  Property 1 states that rms in countries with high skill dispersion will be relatively more productive in low complementarity sectors. As GM suggest,15 a general result of this type cannot be established for arbitrary skill distributions. However, since our goal is to derive testable implications of this theory, we are mainly interested in verifying the chapter relevance of Property 1 by employing the distributions of IALS scores observed in the data. Speci cally, we construct A (λ ; c) replacing g (a; c) with the empirical distribution of scores for 19 countries that participated in the IALS. For a grid of 100 λ 's in the [0; 1] interval, we calculate the ratio  A(λ ;c0 ) A(λ ;c)  where country c0 has higher skill  dispersion (coef cient of variation of scores) than country c. We then nd that, averaging across country pairs,  A(λ ;c0 ) A(λ ;c)  is increasing in λ for 97% of the grid points.  Similar results hold if countries are ranked according to alternative measures of 14 Note  that changes in the average ability that are not the result of a multiplicative change in all abilities will affect the pattern of comparative advantage. 15 See p.1271.  11  scores dispersion. This evidence suggests that Property 1 provides a reasonable approximation to the patterns of comparative advantage due to differences in skill dispersion. As an alternative approach, In the Appendix, we offer two alternative analytical approaches to studying this problem. First, we show that Property 1 can be established for any distribution if we place a lower bound on λ . Second, we perform comparative statics exercises that do not restrict the range of λ and verify Property 1 for speci c parametric skill distributions (Pareto, lognormal, uniform, triangular, gamma, beta and inverse Gaussian).  1.4  The Firm's Problem and Bargaining  This section analyzes the problem of a representative Home rm in a given sector. Analogous expressions can be derived for a Foreign rm. Firms can sell in the domestic market or export, facing a transport cost. The transport cost τ is of the iceberg type, so that rms have to ship τ > 1 units of good in order for one unit to arrive. We denote by xcc0 a variable x originating in market c and destined for market c0 . We drop the sector index to simplify notation. A Home rm must decide how much to produce for the Home and Foreign market and, since it maximizes pro ts, it equates marginal revenues across the two markets. This allows us to write total revenues of a Home rm rH as a function of total output: σ 1  rH = yHσ ΓH where yH = yHH +yHF , ΓH = BσH + BσF τ 1 16 Total  σ  1 σ σ 1  σ 1  (1.4)  σ σ revenues are given by rH = BH yHH + BF yHF τ  yHH yHF  BH BF  across markets, which implies = similarly to Helpman and Itskhoki (2009a).  σ  τσ 1  12  1  and Bc = Pc Qcσ for c = H; F.16 The 1 σ σ  . The equality of marginal revenues  and some algebraic manipulation lead to (1.4),  rm must then simply choose the total amount of output to produce and therefore how many workers to employ. In this decision it takes into account how much workers are paid. Because of the presence of search frictions, once workers are hired they are not interchangeable with outside workers and we assume that the rm and all workers employed engage in bargaining to share the surplus created. We assume that the intra- rm bargaining is of the type described by Stole and Zwiebel (1996), with the workers having unemployment as outside option, which we assume yields a payoff of zero. Stole and Zwiebel show that the bargaining solution yields payoffs that correspond to the Shapley value. We discuss wages in the following section, while here we show that the bargaining outcome for a rm with revenues r is given by sr, where: s=  σλ σ (1 + λ )  1  (1.5)  :  Given the expression for total revenues in (1.4), the rm static problem17 reduces to choosing how many workers to hire (h) to maximize pro ts π: h i σσ 1 1 max π = s A (λ ; H) h λ ΓH h  bh  f:  (1.6)  This is a concave problem because of the restriction placed on λ in (1.2). Since this is a standard problem we refer to the Appendix for details of the derivation, and report here the main results. The total output produced by a Home rm is given by: yH = A (λ ; H) φ where φ (λ ) =  h  f (σ 1) b(1+(λ 1)σ )  i1 λ  . Intuitively, output is increasing in productivity A,  the size of the xed cost f , and the elasticity of demand σ , while it decreases with 17 For  a dynamic extension of this type of framework see Helpman and Itskhoki (2009b).  13  the hiring cost b.18 We assume that differences in productivity between Home and Foreign rms in a given sector are not too large, that is: 1 τ  A (λ ; H) A (λ ; F)  (1.7)  τ 8λ  otherwise the amount produced is zero. Under condition (1.7) we can derive how much output is produced for the domestic and export market, yHH and yHF respectively (see Appendix). As standard with iso-elastic demand, the producer price is constant across markets and for a Home rm is equal to pH =  γ φ AH  where  γ (λ ) = f σσ λλ +σσ +11 . The consumer price in the export market is the producer price multiplied by τ: pHF =  γτ φ AH  (1.8)  In the Appendix we derive revenues accruing to rms in all markets. We focus attention here on the relative revenues (i.e. value of output sold) of a Home and Foreign rm in a given market, for example Foreign: rHF =ρ rFF  A (λ ; H) A (λ ; F)  σ 1  (1.9)  Intuitively, relative revenues increase in relative productivity, as predicted by comparative advantage. In the next section we solve for the mass of rms, which is the nal step in the determination of trade ows. 18 The hiring cost depends on tightness of the labor market x, and is assumed to take the same form as in Helpman and Itskhoki (2009a) and Helpman et al. (2008a): b = δ 0 xδ 1 . We refer to these papers for a discussion. We similarly obtain that in equilibrium the hiring cost is constant across sectors, i.e. 1 1+δ 1  b = δ0  .  14  1.5  Entry  In Section 1.4 we derived the amount of output sold by each rm in the domestic and export market. In order to determine trade ows we need to calculate the equilibrium mass of rms. Here we characterize entry while details of the derivation are presented in the Appendix. We remark that, similarly to other models of monopolistic competition with trade costs (Helpman and Krugman, 1985), the presence of a home-market effect requires that we restrict the degree of asymmetry in country sizes to prevent all rms from locating in one country. De ne relative population in Home as η  LH LF .  We impose throughout the restrictions that η low < η < η up .  If the condition is violated for some industries, we expect to observe no production and no exports.19 If the condition is satis ed, then the following proposition establishes a link between comparative advantage and equilibrium entry. Proposition 1 Under the condition that country sizes are suf ciently similar, i.e. η low < η < η up , the equilibrium mass of rms in country H relative to country F in sector λ 0 is higher than in sector λ if and only if country H has a comparative advantage in sector λ 0 , i.e. 0 0 A (λ ; H) A λ ; H MH (λ ) MH λ () < < A (λ ; F) MF (λ ) A λ 0; F MF λ 0 19 As  equations (A-19) and (A-20) establish, the conditions for a positive mass of rms depend on size, but also on comparative advantage. If a country is relatively more productive it can afford to be smaller in size and still have a positive mass of rms. In this sense our model also predicts an extensive margin of trade (whether we observe or not trade between two countries) based on comparative advantage, albeit a very stark one. Differently from models with heterogeneous rms, e.g. Helpman et al. (2008c), in this setup the assumption of identical rms implies that either rms exist and export or they do neither.  15  1.6  Trade Flows  In this model trade ows are completely determined by the amount sold in the export market by each rm and by the number of rms. Therefore, we now use the results in sections 1.4 and 1.5 to show that the value of exports is relatively higher in comparative advantage industries. In turn, as shown in section 1.3, the latter is determined by a combination of sector characteristics (the degree of complementarity λ ) and country characteristics (the dispersion of skills in the population). The following proposition summarizes the previous discussion and represents the main result of this section. We denote the value of total sales by rms from country c in market c0 , as Xcc0 . Relative total sales of good λ by Home and Foreign rms in a given market, for example Foreign, are then equal to: XHF (λ ) rHF (λ ) MH (λ ) = XFF (λ ) rFF (λ ) MF (λ )  (1.10)  Proposition 2 Under Property 1, a country with relatively higher dispersion of skills has a comparative advantage, and therefore exports relatively more to any destination, in sectors with high degree of substitutability λ .  1.7  Multi-Country Extension  The goal of this section is to generalize the model to many countries and provide the conditions under which the main result of the two-country model holds, i.e. countries with relatively higher dispersion of skills have a comparative advantage, and therefore export relatively more, in sectors where the dispersion of wages is higher. This result provides a foundation for the empirical analysis of skill dispersion and comparative advantage, carried out in the next chapter.  16  Without loss of generality we consider three countries, so that c 2 fH; F; Gg. Following HMR, we allow transport costs to be country-pair speci c and asymmetric, i.e. τ HF 6= τ FH . We x as destination market country F and express the value of exports of good λ by country H relative to country G as follows: XHF (λ ) rHF (λ ) MH (λ ) = XGF (λ ) rGF (λ ) MG (λ ) While the determination of relative revenues of individual rms rHF =rGF is straightforward, the equilibrium mass of rms can be computed, but not easily characterized, with more than two asymmetric countries. This is a known problem in the home-market effect literature.20 Therefore in the following proposition we limit ourselves to imposing that the relative mass of rms be non-decreasing in relative productivity. This is reasonable if we believe that, in equilibrium, entry is relatively higher in sectors where a country has a comparative advantage. H (λ ) Proposition 3 Under Property 1, if the relative mass of rms M MG (λ ) is non-decreasing  in relative productivity  A(λ ;H) A(λ ;G)  then a country with relatively higher dispersion of  skills has a comparative advantage, and therefore exports relatively more to any destination, in sectors with higher degree of substitutability λ .  1.8  Wage Distribution and Complementarity  As a bridge to the empirical analysis in the next chapter, this section discusses how the model provides a proxy for the degree of complementarity, which is not directly observable and for which we have no available estimates. In particular, this section establishes the existence of a one-to-one link between the degree of 20 Behrens  et al. (2009) show that the home-market effect intuition does not easily generalize to the case of more than two countries. Our case of multiple countries with productivity differences further complicates the problem and is beyond the scope of this chapter.  17  complementarity and the dispersion of wages in sector, which can be measured in the data. As discussed above, we assume that at the bargaining and production stage workers' skills are revealed, so that workers of different skills receive different wages as a result of intra- rm bargaining. Although the assumption that skill is perfectly revealed only at the production and bargaining stage is stark, we believe it captures some realistic features of the hiring process, where workers' skills in particular tasks are dif cult to assess until they start working. Moreover, even if skills were partially revealed at the production stage, as long as the portion revealed were constant across sectors, this would not substantially change the implications discussed below. Section A.7 in the appendix provides the derivation of the Shapley value for a worker of skill a. Since the average wage also differs across sectors, we normalize the wage of a worker of skill a in sector λ by the average wage in the sector. e λ) = The normalized wage is w(a;  aλ , E (aλ )  which re ects the marginal product of a  worker of skill a when added to the production team and depends on λ . The higher the substitutability across workers the larger the marginal product of a worker with high skills. In contrast, if λ is low, i.e. complementarity is high, a worker of high skills has a relatively lower marginal product because her skills are very different from the average skills of her team-mates. An implication of this wage structure is that workers with identical skills, but employed in different sectors, generally receive different wages, as returns to skills vary across industries.21 Keeping in mind that the distribution of skills is the same in every industry, the distribution of wages within a sector depends, in our framework, exclusively on technological factors that determine the marginal product of workers with different 21 The  point is made by Heckman and Scheinkman (1987), who show that returns to unobservable characteristics are different across sectors.  18  skills. It therefore does not re ect compositional differences across sectors. The following proposition establishes that the existence of a one-to-one correspondence between the degree of complementarity and several common measures of wage dispersion. Proposition 4 For any non-degenerate distribution of skills g (a; c), the following three measures of dispersion of sectoral wages are strictly increasing in the degree of substitutability of workers' skills, λ : (i) the Coef cient of Variation; (ii) the Gini Coef cient and (iii) the Inter-Percentile Ratio22 Proposition 4 establishes that the more complementary workers are, the more compressed the wage distribution is. The intuition follows from our discussion of normalized wages.  1.9  Conclusions  Relative differences in the distribution of production factors are central to the classical theory of international trade. The Heckscher-Ohlin-Samuelson factor proportion model stresses the idea that differences in factor endowments play a major role in predicting trade ows. Comparative advantage is associated with relatively abundant factors of production: the aggregate endowment of some important factor can be a driving force in determining international specialization. In this chapter we push this idea further and argue that the entire distribution of a productive factor, and not just its aggregate endowment, can help in understanding the pattern of trade. 22 The  Interpercentile-Ratio, IPRk j , is de ned as IPRk j =  wk wj ,  where wk (w j ) is the wage of the  worker at the kth ( jth ) percentile of the sectoral wage distribution and j < k.  19  We develop a theoretical framework where, because of frictions in the labor market and ex-ante unobservable skills, workers and rms are randomly matched. The skill distribution matters differently across industries because some of them are more capable of substituting skills across production tasks than others. All sectors inherit the distribution of residual skills in the country's population and, as a result, rms in sectors with higher complementarity are relatively more productive in countries with lower skill dispersion. Our model provides an observable proxy for the otherwise unobservable degree of complementarity among workers' skills, that is the dispersion of residual wages at the industry level. This result is exploited in the empirical evaluation of this theory, pursued in the next chapter of this dissertation. Finally, the theoretical framework developed in this chapter has implications for the impact of trade on overall wage inequality. Our model, taken at face value, implies that a more disperse skill distribution does not just have a direct effect on the income distribution, but also an indirect effect, as countries with higher skill dispersion specialize in sectors with higher residual wage dispersion. Thus, specialization patterns (and, more generally, industry composition) can reinforce or attenuate the effect of the initial skill distribution on wage inequality. Although beyond the scope of this study, the model suggests an interesting link between trade and residual wage inequality that remains to be explored in future research.  20  Chapter 2  Skill Dispersion and Trade: an Empirical Analysis Synopsis. While there is substantial empirical evidence that a country's aggregate endowment of skills is an important source of comparative advantage, this chapter investigates whether the distribution of skills in the labour force plays a role in explaining the pattern of international trade ows of manufacturing goods. In particular, using microdata from the International Adult Literacy Survey to construct measures of skill dispersion, we nd that countries with high skill dispersion export relatively more in industries where skills are more easily substitutable across workers. The magnitude of the estimated effect is comparable to that of aggregate endowments of human and physical capital. The result is robust to controlling for alternative sources of comparative advantage and proxies of skill substitutability.  21  2.1  Introduction  Numerous empirical studies of the Heckscher-Ohlin-Samuelson factor proportion theory identify quantities such as the stocks of human and physical capital of countries as primary sources of comparative advantage.1 In this chapter we provide evidence supporting an alternative, and empirically sizeable, source of comparative advantage: the dispersion of skills (human capital) in the working population.2 We present empirical evidence that diversity is in fact a strong determinant of specialization, a novel nding to the best of our knowledge. A rst glance at the data reveals that cross-country differences in skill dispersion are larger than differences in the average skills of workers. We use the distribution of scores in the International Adult Literacy Survey (IALS), an internationally comparable measure of work-related literacy, as a proxy for the distribution of skills. The coef cient of variation of the standard deviation of scores is 1.64 times larger than that of the average scores. Figure B.1 reports the mean and standard deviation of IALS scores during 1994-1998. The reasons why countries at similar stages of development differ in their skill distribution are beyond the scope of this study;3 such differences may be due to the degree of centralization in the education system and curricular control (Stevenson and Baker, 1991), the existence of elite schools, sorting and segregation,4 early 1 Among  others, Romalis (2004), testing the predictions of the theory about commodity trade, and Bowen et al. (1987), Tre er (1993), Tre er (1995), and Davis and Weinstein (2001), testing the factor content predictions of the theory. 2 As in chapter 1, we use the terms human capital or skills interchangeably, to refer to a set of individual attributes that are of productive use in the workplace. 3 What is not beyond the scope of this study is a discussion of how the endogeneity of skill dispersion might affect our empirical results. See Section 2.5. 4 The existence of peer effects, as documented for example by Hanushek et al. (2003) and Hoxby and Building (2000), implies that segregation and sorting might result in even higher inequality of educational outcomes. An example of this ampli cation mechanism is provided by Friesen and Krauth (2007).  22  tracking,5 local school nancing (Benabou, 1996) and the share of private and public schools (Takii and Tanaka, 2009).6 The objective of this study is to evaluate the main prediction of the theory presented in chapter 1: countries with more dispersed skill distributions specialize, and therefore export relatively more, in sectors with lower complementarity of skills in production. In order to achieve this goal, we adapt the empirical approach of Helpman et al. (2008c), henceforth HMR, to account for industry-level bilateral trade ows and augment it with our key variable of interest. We show that the interaction of the exporter's skill dispersion with sectoral measures of skill substitutability is a signi cant and economically large determinant of exports, after controlling for a variety of bilateral trade barriers, exporter and importer-industry xed effects (as dictated by the theory). We also include determinants of comparative advantage based on aggregate factor endowments as in Romalis (2004) and check that the result is not due to a correlation of country-level skill dispersion with institutional variables, like labor law rigidity and judicial quality, that have been found to in uence trade ows in recent research. Since the degree of substitutability across workers' skills is not directly observable, we take two distinct approaches to its measurement. First, we exploit the structure of the model presented in chapter 1, which delivers a direct link between the unobservable degree of complementarity and the observable dispersion of residual wages within industries. In view of substantial evidence linking rm size and wages (e.g. Oi and Idson, 1999), we are careful to lter out sector-speci c rm heterogeneity from our wage dispersion measures. In order to mimic random 5 Tracking refers to the practice of grouping students in different schools according to their ability.  Woessmann et al. (2006) show that when grouping happens before age 10, inequality in education outcomes increases at the country level. 6 James (1993) argues that the mix of public and private educational services is due, for example, to the degree of religious heterogeneity within a country.  23  matching we also purge wages of the effect of self-selection of workers into industries. As with IALS scores, in order to bring the empirical analysis in line with the theoretical focus on unobservable skills, we purge individual workers' wages (from the US Census) of the component explained by observable characteristics, to obtain residual wages. Second, we use an alternative set of measures of the degree of skills substitutability. These measures are based on survey data available from the Occupational Information Network (O*NET), which allow us to quantify cross-industry variation in the degree of teamwork, communication and interdependence between co-workers' labor inputs. These measures are not motivated by, and are independent of, the theory in chapter 1 and provide a direct and intuitive way to proxy for complementarity. Our ndings relate to recent work emphasizing less traditional sources of comparative advantage. In this literature the endowment of a country, interpreted in a broad sense, includes institutional features, such as the ability to enforce contracts (Levchenko, 2007, and Nunn, 2007), the quality of the nancial system (Manova, 2008a; 2008b) and the extent of labor market frictions (Helpman and Itskhoki, 2009a, Cuat and Melitz, 2007, Tang, 2008). We view our contribution as related to this `institutional endowment' view of comparative advantage because human capital dispersion in a country is to a large extent the result of the prevailing educational system and social make-up. The latter, in turn, can be considered, if not immutable, a slow-moving attribute of a country.7 Next we present the estimation framework. Section 2.3 describes the data and section 2.4 reports baseline results. Finally, section 2.5 discusses identi cation and provides robustness checks. The chapter ends with some concluding remarks. 7 Glaeser  et al. (2004) show that education is signi cantly more persistent than several other institutional features, such as the form of government.  24  2.2  Estimation Framework  In this section, we build on the theory developed in chapter 1 in order to derive an econometric speci cation to evaluate its main predictions. As a rst step to design an empirical test of Proposition 3, we express the value of total exports of good i from exporter H to importer F as the product of the quantity demanded of an individual variety of i from equation (1.1), the price and the mass of rms/varieties: XHF (i) = dHF (i) pHF (i) MH (i) =  [pHF (i)]1  σ  α (i) EF  1 σ  [PF (i)]  MH (i)  (2.1)  The price of a variety produced by a Home rm and sold in Foreign, pHF (i), depends positively on transport costs and negatively on productivity, as shown in the Appendix: pHF (i) =  γ (i) τ HF : φ (i) A (i; H)  (2.2)  Once we substitute (2.2) in (2.1) and we take the natural logarithm, we obtain the following expression for the value of (log) exports: log XHF (i) = (σ  1) log A (i; H) + log MH (i)  + log α (i) + log EF  (σ  (σ  1) log τ HF  1) PF (i) + (σ  1) log  (2.3) φ (i) γ (i)  where A (i; H) captures comparative advantage of the exporting country, MH (i) the mass of rms in the exporting country, τ HF transport costs between the two countries, PF (i) an industry-importer speci c price index, EF the importing country total expenditure and φ (i), γ (i) and α (i) industry-speci c constants. Since we consider a discrete number of industries, in the remainder of this section we use subscript i to index variables that vary across industries. An ideal test of Proposition 3 would require quantifying the effect of a mean25  preserving spread in the distribution of residual skills in country H on its relative exports to country F, as a function of the elasticity of substitution in each sector i. These effects operate through AHi in equation 2.3. Although MHi is not observable, the model shows it is also a function of AHi . Therefore, in order to derive an estimation equation for log XHFi , we assume that (σ  1) log AHi + log MHi can  be written as an additive function of industry characteristics (δ i ), exporter characteristics (δ H ), an interaction between a measure of skill substitutability in industry i (Substiti ) and a measure of skill dispersion in country H (SkillDispH ), plus other unobservable determinants of comparative advantage in country H (ν Hi ), that is, (σ  1) log AHi + log MHi = β Substiti  SkillDispH + δ i + δ H + ν Hi .8  Transport costs are allowed to depend linearly on a vector of observable countrypair bilateral trade barriers (dHF ) and unmeasured i.i.d. trade frictions (uHF ).9 A set of industry-importer speci c xed effects (δ Fi ) controls non-parametrically for the price index PFi , industry constants  φi γi  and δ i . Finally, let η HFi capture mea-  surement errors in trade ows and the effect of other unobserved determinants of XHFi . With this speci cation, the estimation equation for exports takes the following form: log XHFi = β Substiti  SkillDispH + γdHF + δ H + δ Fi + ε HFi  8 Note  (2.4)  that AHi may also depend on the mean and other moments of the skill distribution of country H and these could potentially have different effect on productivity in different industries, a possibility that we explicitly consider in the empirical analysis of trade ows. These effects are summarized by ν Hi . 9 Alternatively, transport costs could have been captured non-parametrically by the inclusion of exporter-importer xed effects. Note that in this case our interaction of interest would still be identied since it varies at the exporter-industry level. However, for comparability with previous studies, we do not pursue this empirical strategy here. Also, we do not treat unmeasured trade frictions uHF as a random effect when estimating β , since that would require assuming stronger exogeneity conditions than needed. However, we account for the presence of uHF as a cluster effect in the computation of the standard errors.  26  where ε HFi = ν Hi + uHF + η HFi . The variable of interest is Substiti  SkillDispH and estimation of its coef cient  β allows us to test Proposition 3. To see why, assume that equation (2.4) correctly speci es a model for the conditional expectation of log XHFi , so that E [ε HFi jSubstiti  SkillDispH ; dHF ; δ H ; δ Fi ] = 0  Then, for any two countries H and G exporting to F, and any two industries i and j, equation (2.4) implies: E log  XHFi XGFi  where ∆HG SkillDisp  log  XHF j XGF j  SkillDispH  = β ∆i j Substit  ∆HG SkillDisp  (2.5)  SkillDispG and ∆i j Substit is similarly de-  ned. According to (2.5), Proposition 3 implies β > 0. A dif culty in implementing this test of the theory comes from the fact that the elasticity of substitution of individuals' skills at the industry level, Substiti , is not observable in the data and we are not aware of any estimates of the elasticity of substitution for a ne disaggregation of skills. Therefore we take two different approaches to proxy for the elasticity of substitution of workers skills, Substiti . The rst is based on a theoretically-founded link between complementarity and residual wage dispersion (chapter 1, section 1.8). The second approach is to construct proxies for complementarity available from occupation-level data. Although these two approaches do not identify the elasticity of substitution, Substiti , they allow us to rank industries in order of increasing Substiti .  27  2.2.1  Skill Substitutability I: Residual Wage Dispersion Rankings  While we now discuss a heuristic explanation of the link between complementarity and (residual) wage dispersion, section A.8 of the appendix provides the formal proof of the result. Consistent with empirical evidence, e.g. Altonji and Pierret (2001), suggesting that rms only gradually learn about worker skills, we posit that at least part of the unobservable skills at the time of hiring are revealed to rm and worker once production begins and bargaining takes place. Hence workers of different skills receive different wages. Since our model predicts that each sector inherits the same distribution of unobservable skills, the distribution of residual wages only re ects technological differences across sectors. In particular, the degree of complementarity affects the wage of workers that are far from the average. For example, in a sector with high complementarity, a worker with high skill has a lower marginal product because her skills are very different from the average, compared with a sector with high substitutability, where high skills yield a high marginal product and high wage. Therefore sectors with low complementarity (high substitutability) have a more dispersed wage distribution. Although we do not rely on the model to structurally recover the actual value of Substiti , we use its unambiguous prediction of a monotonic relationship between Substiti and wage dispersion to identify a ranking of industries in terms of Substiti .  2.2.2  Skill Substitutability II: O*NET Rankings  In our second approach we construct proxies for complementarity using occupationlevel data from O*NET. As described in section 2.3.2, this database rates industries in three dimensions which are closely associated to skill complementarity: i) Teamwork: team production can naturally be thought of as a particular type of O-Ring 28  production process (Kremer, 1993), in which the quality of nal output critically depends on the successful completion of a given number of complementary tasks. (ii) Impact on co-worker output: a closely related way of characterizing complementarity is to quantify the extent to which a worker's actions impact the performance of co-workers; a higher impact implies a higher degree of complementarity. (iii) Communication/Contact: communication and contact intensity are linked to the importance of coordinating tasks to achieve, for example, a given level of output quality; if co-workers have no need for communication or contact with each other, they are likely to have independent contributions to the nal outcome. As for wage dispersion, and because we do not know the exact mapping between the O*NET variables and Substiti , we simply rely on O*NET to identify a ranking of industries in terms of Substiti .10  2.3  Data  Before presenting the estimation results we describe the measurement of two key explanatory variables in the empirical analysis, skill dispersion at the country level and skill substitutability at the industry level. A detailed discussion of all data can be found in the Appendix.  2.3.1  Skill Dispersion  We use test scores from the 1994-1998 International Adult Literacy Survey (IALS) to approximate the skill distribution within a country. Collaborators in this household survey administered a common test of work-related literacy skills to a large sample of adults between the ages of 16 and 65 in 19 countries. The IALS fo10 With  both wage dispersion and O*NET, regression results are qualitatively unchanged if we employ the value of the proxies instead of their ranking.  29  cuses on literacy skills that are needed for everyday tasks (e.g. working out a tip, calculating interest on a loan and extracting information), across three different dimensions of literacy: quantitative, prose and document literacy. We combine the results of these three tests into a single average score for each individual, measured on a scale from 0 to 500. The skill distribution is proxied by the distribution of log-scores of individuals participating in the labor market and living in the same country. To ensure consistency with the theoretical assumption of imperfect skill observability, we construct a measure of residual scores dispersion within countries. For an individual k participating in the labor market of country H, we obtain the estimated residual εd kH from the following regression:  log(skH ) = XkH β H + ε kH  (2.6)  where skH is the IALS score of k and XkH is a vector of individual demographic information from the IALS questionnaire. The residual εd kH is then used to compute  the skill dispersion measures used for the estimation of trade ows. Analyzing the  R-squared of these country-by-country regressions, we nd that the variation in residual scores εd kH accounts for a minimum of 46% of the observed variation in  log-scores in Canada, for a maximum of 83% in Germany and for 70% in Finland, the median country in the sample.  Table 1 ranks 19 countries according to the coef cient of variation (CV) of IALS scores, and also reports their rank by mean, standard deviation (St Dev) and standard deviation of residual IALS (St Dev Res). The gures show different dispersion in countries at similar stages of development: for example, we observe a more spread distribution of skills in the US, UK and Canada, than in Sweden, the  30  Netherlands and Germany.11  2.3.2  Substitutability  In this section we describe the construction of the two rankings of skill substitutability at the industry level, based on residual wage dispersion and O*NET indices.  Residual Wage Dispersion  We use the 5% Public Use Microdata Sample (PUMS)  les of the 2000 Census of Population in the United States to construct industryspeci c measures of wage dispersion to identify a ranking of industries in terms of the unobserved elasticity of substitution. An advantage of our approach is that we can match individual wage observations to a detailed industry classi cation, accounting for the entire manufacturing sector12 . This procedure results in 63 industries for which both wage dispersion and international trade ows can be computed, at a level of aggregation between the 3 and 4 digit levels of the 1997 North American Industry Classi cation System (NAICS). As with IALS scores, we focus on residual wage dispersion. We start by removing variation in wages driven by individual characteristics on which rms can typically condition employment decisions. We also adapt the correction method proposed in Dahl (2002) to address the possibly non-random selection of workers into multiple industries. In essence, this procedure controls for selection effects using differences in the probabilities of being observed in a given industry due to 11 Brown et al. (2007) report similar variation in skill distributions in a comprehensive study using IALS, the 1995, 1999 and 2003 Trends in International Maths and Science Study (TIMSS), the 2000 and 2003 Programme for International Student Assessment (PISA) and the 2001 Progress in International Reading Literacy Study (PIRLS). 12 This is not feasible for IALS data, since individual observations are assigned a broad sectoral classi cation (e.g. agriculture, mining, manufacturing, construction, etc), while international trade data is available only for manufacturing industries.  31  exogenous variation, such as the state of birth of two people who are otherwise similar in terms of education, experience, household structure, race and gender. Details are provided in the Appendix. For an individual k employed in industry i, we obtain the estimated residual ξcki  from the following regression:  log(wki ) = Zki β i + ξ ki  (2.7)  where wki is the weekly wage of k and Zki is a vector of observable characteristics (age, gender, etc.). Note that we run these regressions separately for each industry to allow for differences in the return to observable characteristics across industries.13 Several studies have shown that rm size affects workers' wages.14 This implies that wage dispersion might also re ect variation in the distribution of rm size across different industries. Although the model does not incorporate rm heterogeneity, we purge residual wage dispersion of the effect of rm heterogeneity in order to isolate the degree of complementarity. Since the Census does not provide the size of the establishment at which individual workers are employed, we regress measures of dispersion of ξcki on the coef cient of variation of rm size within in-  dustry i, FirmDispi . The residuals from this regression are employed to construct  WageDispi , a ranking of industries in table 2, where we report the top and bottom 5. For example, in terms of the standard deviation of residual wages, the three lowest ranked sectors are railroad, ship building and aerospace. The three highest ranked are apparel accessories, bakeries and cut and sew apparel. The use of U.S. estimates as proxies for within-industry wage dispersion (and 13 Regression 14 See  results are available upon request. Oi and Idson (1999).  32  skill substitutability) in other countries is warranted if they have access to similar production technologies.15 Equal access to technology implies that the elasticity of substitution in any given industry will be constant across countries. As a result, the ranking of industries according to wage dispersion will be the same within each country, a hypothesis that is not easy to verify due to the scarcity of publicly available microdata with similar sector classi cation. However, we do perform this exercise for the U.S. and Canada. We compute the sectoral dispersion of wage residuals in Canada to verify whether the ranking is similar to the one prevailing in the US.16 To maximize comparability, we are careful to control for the same set of observable characteristics of workers in both countries when computing the residuals, use similar sampling criteria and the same industry classi cation. Figure B.2 shows industry rankings in terms of the standard deviation of the wage residuals in the two countries. The positive slope of the tted line is signi cant at the 1% level. Clearly, the sectoral ranking of residual dispersion in the US is strongly correlated to the one observed in Canada. Sectors like computers and clothing exhibit higher dispersion in both countries, compared to sectors like machinery and paper manufacturing. Although purging composition effects from the residuals by accounting for worker self-selection and rm size makes WageDispi a reasonable proxy for skill substitutability, it is not impossible to think about alternative deteminants of wage rankings. One such example is variation in unionization rates across industries. However, WageDispi will remain a valid proxy unless the correlation between 15 The  assumption that industry-speci c characteristics computed for the United States also apply to industries in other countries is not an unusual one in the recent empirical trade literature on comparative advantage. Examples include the measurement of nancial vulnerability (Manova, 2008b), the importance of relationship-speci c investment (Nunn, 2007), rm-speci c skill intensity (Tang, 2008) and the variance of rm-speci c shocks (Cuat and Melitz, 2007). 16 We use the Canadian Labor Force Survey data for May 2000. Details of this exercise are available upon request.  33  unionization rates and skill substitutability is suf ciently large to affect industry rankings. Also notice that WageDispi is robust to cross-country variation in labour market institutions that affect all manufacturing industries to a similar degree, such as miminum wage regulations. If, say, the minimum wage in the US is lower than in Germany, any given industry in the US will display higher wage dispersion than its counterpart in Germany. However, industry rankings are unlikely to be affected.  O*NET Measures of Complementarity  Sponsored by the Employment and Train-  ing Administration of the United States Department of Labor, O*NET provides detailed information on job requirements and worker attributes for 965 occupations in the U.S. Information on 277 descriptors including abilities, work styles, work context, interests, experience and training, is annually updated by ongoing surveys of each occupation's worker population and occupational experts. As anticipated in section 2.2, our complementarity rankings are based on four selected O*NET (Version 12.0) questions capturing different aspects of skill complementarity: (1) Teamwork: How important are interactions that require you to work with or contribute to a work group or team to perform your current job?17 (2) Impact: How do the decisions an employee makes impact the results of coworkers, clients or the company? (3) Communication: How important is communicating with supervisors, peers or subordinates to the performance of your current job? (4) Contact: How much contact with others (by telephone, face-to-face, or otherwise) is required to perform your current job? Respondents were asked to rate these questions on a scale from 1 to 5. The O*NET database provides average scores for each occupation. In constructing industry-level proxies of complementarity, O*NET scores were 17 An  alternative measure of teamwork can be obtained from the Detailed Work Activities (a supplemental le to O*NET). Reported results are qualitatively unchanged when this measure is used.  34  matched to the 2000 Census microdata.18 In this way, because occupational structures vary across industries, we obtain a different distribution of scores for each industry. Using the median score for each industry we generate O NETi , a ranking of sectors in terms of substitutability.19 Industries with higher O NETi exhibit lower skill substitutability. Table 2 reports the ranking in terms of Contacti for the top and bottom 5 industries as ranked according to residual wage dispersion (other O*NET variables produce similar rankings). The table shows that among the lowest ranked sectors in terms of wage dispersion appear the top ranked sectors in terms of O*NET measures. These are the low substitutability sectors. Similarly, among the highest ranked sectors in terms of WageDispi we nd the bottom O NETi sectors (those sectors with high substitutability). This re ects the fact that, as shown in table 3, O NETi and WageDispi are inversely correlated. Although weakly signi cant, correlation signs among substitutability rankings are consistent with the expected pattern.  2.4  Baseline Results  This section discusses results of the empirical analysis of trade ows using speci cation (2.4). The dependent variable in tables 4 to 6 is the log of exports from country H to country F in industry i. Our data set contains the value of exports in year 2000 from 19 exporters to 145 importers in 63 industries. We rst report results when Substiti is proxied by a wage dispersion ranking WageDispi and later show similar quantitative ndings when we utilize survey-based complementarity rankings from O*NET. 18 This is possible since the occupational classi cations in both O*NET and the Census are based on the Standard Occupational Classi cation. 19 The results reported in the empirical section are robust to reweighting by hours worked and to using mean scores instead of medians as complementarity proxies.  35  2.4.1  Substitutability Proxied by Wage Dispersion Rankings  Table 4 reports estimates of the impact of skill dispersion as proxied by the dispersion of residual IALS test scores (de ned in section 2.3.1): we identify this effect through an interaction with residual wage dispersion rankings (de ned in section 2.3.2). For comparability, all tables report standardized coef cients of the explanatory variables.20 The measures of dispersion employed in table 4 are: the standard deviation in columns (1) and (4), the 95-5 interpercentile range in columns (2) and (5), and the Gini mean difference in columns (3) and (6). Columns (1)-(3) add exporter, importer and industry dummies to our variables of interest; columns (4)(6) include theoretically consistent exporter and importer-industry dummies, along with a vector of bilateral trade barriers described in the Appendix. We nd that WageDispi  SkillDispH has a positive and signi cant effect on exports. We note  that the magnitudes of the coef cient are stable across speci cations and measures of dispersion. The standardized coef cient of WageDispi  SkillDispH varies be-  tween 1:4% and 1:9% in the six speci cations. We employ the estimated coef cients to gauge the economic magnitude of this source of comparative advantage. Our baseline estimate is 0.017 (column 4, table 4). Consider two countries, the US and Sweden, and two industries, `computers' and `plastics'. These countries and industries are chosen because the skill dispersion in the US is (approximately) one standard deviation higher than Sweden's and WageDispcomputers is one standard deviation higher than WageDisp plastics . Since the standard deviation of log exports is 2:204 (table 8), the relative ratios of US and Sweden's exports (to an average importer F) in the two sectors are given by 20 When  a regressor is the product of two variables, the latter are standardized before computing the interaction.  36  e0:017  2:204 ,  that is: XUS;F (computers) XSW EDEN;F (computers) = = 1:038 XUS;F (plastics) XSW EDEN;F (plastics)  This implies that all else constant, averaging across destination markets, the relative exports of computers to plastics in the US are 3:8% higher than in Sweden (this gure varies between 3:1% and 4:3% depending on the estimate used from table 4). To put the result in perspective, section 2.5 compares this effect against those of other sources of comparative advantage that have been studied in the literature. Section B.3 in the Appendix shows that similar results are obtained if raw wages and raw scores are employed in building measures of dispersion, that is wages and scores before we lter out the effect of observables.  2.4.2  Substitutability Proxied by O*NET Rankings  Next, we report estimates of the effect of skill dispersion on trade ows using four alternatives measures of skill complementarity constructed from the O*NET database. Table 5 replicates the structure of columns (4)-(6) of table 4, in terms of the set of xed effects included and trade barriers used as controls. The variable of interest is the interaction of SkillDispH (measured by the standard deviation of residual scores) and the corresponding O*NET ranking: Teamworki , Impacti , Communici and Contacti . Note that since O*NET rankings are proxying for complementarity, the expected sign of the interaction is negative (i.e. countries with a higher skill dispersion export relatively less in industries with high skill complementarity). This is con rmed in every speci cation of table 5 at the 1% signi cance level. The estimates of the effect of skill dispersion are quantitatively very similar to the ones generated using WageDispi . In unreported regressions we check that  37  these results are qualitatively unchanged if (i) SkillDispH is measured as either the 95-5 interpercentile range or the Gini mean difference of residual scores; (ii) importer-industry xed effects are replaced by importer and industry xed effects; (iii) trade barriers are not included in the estimation and (iv) O*NET rankings are computed using the mean score of occupations in the industry rather than the median.  2.5  Identi cation and Robustness  In this section we discuss some potential issues related to the identi cation of the effects quanti ed in tables 4 and 5. For parsimony we present our robustness analysis using residual wage dispersion rankings to proxy for substitutability. All the results presented below also hold when using the O*NET rankings.21  2.5.1  The Extensive Margin of Trade: Selection  Tables 4 and 5 report estimation results which do not take into account the fact that a substantial fraction of bilateral trade ows are zero and that trade ows reect both an intensive margin (the amount exported by each rm) and an extensive margin (the number of rms exporting, possibly zero). The estimation of (2.4) requires excluding observations for countries which do not trade in speci c industries. These amount to 66.5% of the sample (table 8). As discussed in HMR, selection of trading partners induces a negative correlation between observed and unobserved trade barriers (dHF and uHF ) that might bias OLS estimates in (2.4), including β . In order to correct for selection bias, we implement a two-step estimation pro21 Estimation  results are available from the authors.  38  cedure: in the rst step we account for the discrete export decision using a linear probability model and obtain the predicted probabilities of observing positive exports, ϕd HFi ; in the second stage, equation (2.4) is estimated including a exible  22 polynomial of degree four in ϕd HFi to control for selection bias. For identi cation  not to rely on the non-linearity of ϕd HFi one needs to identify a source of varia-  tion which affects the discrete choice of engaging in exports without changing the  intensity of trade ows. HMR argue that cross-country variation in start-up regulation costs likely relates to the decision to export, and it has no bearing on the intensive margin. The economic rationale lies in the fact that start-up costs in the exporting country, as well as in the importing one, affect xed rather than variable costs of trade. Different forces can be at work and the nature and strength of this effect may depend on characteristics of both exporting and importing countries. For example, HMR nd that start-up regulation costs are an effective predictor of the extensive export decision and that the interaction between home and foreign regulation costs has a negative gradient on the likelihood to export. On the other hand, De Groot et al. (2004) show that differences in institutional factors, including differences in regulation and red tape, have large effects on trade ows; their work unveils an alternative channel through which regulation can affect trade, and stresses the importance of `similarity' in institutional frameworks. An analysis of the rst-stage bilateral export decisions (see table 7) uncovers strong effects of regulation costs. We use exporter-importer interactions of three proxies of regulation costs: the number of days (RegDaysH of legal procedures (RegProcH  RegDaysF ), number  RegProcF ) and relative cost, as a percentage of  22 We  favor using a linear probability model in the rst stage since its two most common alternatives, probit and logit models, suffer different problems in the current application. The probit model with xed effects yields inconsistent estimates. In turn, estimating a xed effects logit becomes computationally very costly due to the large number of xed effects required by our speci cation of equation (2.4).  39  GDP per capita (RegProcH  RegProcF ), for an entrepreneur to start operating a  business.23 We nd that these proxies are signi cant predictors of selection into exporting.  24  In table 6 we report the second stage obtained using the selection correction. To facilitate comparison, column (1) of table 6 is identical to column (4) of table 4, which is the baseline result using WageDispi , i.e. we employ only one of the three measures of dispersion, the standard deviation.25 Columns (2)-(6) report the second stage of the selection-corrected estimation. Column (2) documents the robustness of the effect associated to the interaction WageDispi  SkillDispH : the  standardized coef cient is essentially unchanged at 0:016.  2.5.2  Omitted Determinants of Comparative Advantage  A second potential source of bias is due to the omission of other determinants of comparative advantage, possibly correlated to our variable of interest. Suppose that the true model includes an additional term ni ZH . If WageDispi is correlated with ni and SkillDispH is correlated with ZH , the OLS estimate of β in equation (2.4) will be inconsistent. As an example, industries with lower dispersion of wages tend to be capital intensive. Similarly, exporters with low skill dispersion tend to be relatively abundant in aggregate physical capital.26 In this case, comparative advantage 23 To  test the overidentifying restrictions we performed a Hausman test comparing second stage estimates using all three instruments to the corresponding estimates using only a subset of them. We tested all possible combinations of exclusion restrictions and in no case could we reject the null hypothesis that they are valid and, therefore, estimates with different restrictions only differ as a result of sampling error. 24 In fact, as might be expected, we nd that regulatory costs tend to have a direct negative effect on export choices, but also that relative differences across countries do matter, and can lead to positive interaction effects. Additional details available from the authors. 25 The same qualitative results emerge if we employ the other two measures of dispersion. 26 In our dataset, the correlation between the coef cient of dispersion of residual wages and physical capital intensity across industries is -0.511. In turn, the correlation between the standard deviation of residual IALS scores and physical capital abundance across exporters is -0.524.  40  driven by skill dispersion is correlated with comparative advantage deriving from standard factor proportions theory. Columns (3) to (5) of table 6 show that the estimated effect of the interaction WageDispi  SkillDispH is robust to a number of controls for other potential  determinants of comparative advantage. Column (3) introduces controls for standard Heckscher-Ohlin sources of comparative advantage: the interaction of factor endowment of a country (in particular, human capital SkillEndowH and physical capital KEndowH ) and factor intensity of the sector (human capital SkillIntensi and physical capital KIntensi ), as in Romalis (2004). Since their 95% con dence intervals overlap, we conclude that the impact of our variable of interest WageDispi  SkillDispH on trade ows is quantitatively similar to the effect of  interactions SkillIntensi  SkillEndowH and KIntensi  KEndowH . In column  (4) we control for the interaction between WageDispi and institutional features of countries that might be correlated with SkillDispH . Our concern is that, to the extent that WageDispi displays a similar pattern to other characteristics of sectors that make them bene t from those institutional features, our interaction of interest could be capturing alternative channels that have been found empirically relevant in the literature. In particular, we interact WageDispi with LaborRigidH (a measure of labor law rigidity in country H) and with JudicQualH (a measure of judicial quality). These alternative controls do not substantially affect the magnitude of our variable of interest. In column (5) we introduce the share of individual wages that are top-coded within an industry, TopCodei , interacted with SkillDispH , to show that our result is not driven by the fact that some sectors rely on `superstars' (those sectors that have a high share of top-coded wages). This suggests that more than one aspect of the dispersion of the distribution of wages is driving the result, and that the overall shape of the distribution seems to be better captured by broader measures of dispersion. 41  2.5.3  Reverse Causality  Finally, WageDispi and SkillDispH might be partly in uenced by the pattern of international trade, potentially resulting in reverse causality. We explore this possibility by examining the relationship between each of these two variables and the error term ε HFi . The orthogonality condition needed for consistent estimation of β in equation (2.4) is: E (WageDisps  SkillDispc  ε HFi ) = 0 8s; c  (2.8)  By the Law of Iterated Expectations, a suf cient condition to obtain identi cation is: E (WageDisps  ε HFi jSkillDispc ) = 0 8s; c  (2.9)  which requires that, for every exporter in our sample, within-industry wage dispersion be uncorrelated with unobserved determinants of trade. For example, a violation of (2.9) would arise if ε HFi contained the unobserved share of exporting rms in a given sector in H and the proportion of exporters varied across industries and importers. In a model with heterogeneous rms, Helpman et al. (2008a) show that within-industry wage dispersion is a function of the proportion of rms exporting in the industry since, on average, exporters pay higher wages than nonexporters.27 However, as shown in HMR, the correction for self-selection into the export market discussed in section 2.5.1 effectively removes this potential bias. Furthermore, since we measure wage dispersion at the industry level using U.S. data, we can check the robustness of our estimates by removing the U.S. from our set of exporters. To the extent that the U.S. wage structure is not signi cantly affected by bilateral trade ows between other countries, this procedure 27 Exporters do pay higher wages. See, for example, Bernard et al. (1995) and Bernard and Jensen (1997).  42  substantially decreases the likelihood of feedback effects running from trade ows to WageDisps . Column (6) in table 6 shows that, also in this case, the coef cient of our interaction of interest maintains the same magnitude and signi cance. An alternative suf cient condition that guarantees (2.8), and therefore identi cation of β , is E (SkillDispc  ε HFi jWageDisps ) = 0 8s; c  which means that, for every sector, skill dispersion in every exporting country is uncorrelated with the error term ε HFi . This condition is satis ed if unobserved exporting opportunities captured in ε HFi are not signi cantly related to the dispersion, and overall distribution, of residual skills in a country. There are several reasons to believe that this is plausible. First, the unobserved exporting opportunities ε HFi must occur at levels other than exporter or importer-industry, which are already captured by our set of dummies. Moreover, since our skill dispersion measures pre-date trade ows by several years, the link between ε HFi and SkillDispc introduces bias only if: (i) ε HFi is a highly persistent shock to exporting opportunities which is not captured by our dummies and also affects the long-term, `residual' skill distribution, and (ii) the skill distribution reacts very quickly in response to export shocks. In this respect Glaeser et al. (2004) show that the education system is a slow-changing characteristic of a country. However, skill dispersion is not only the product of the formal education system, but may change after school through on-the-job training. A number of chapters have established the relatively limited impact of on-the-job training on the overall level of human capital.28 Nevertheless, we explicitly account for the possibility that re-training is triggered by exporting opportunities through the inclusion, in the derivation of residual skills, of a control 28 See  discussion in Carneiro and Heckman (2003) and Adda et al. (2006).  43  for whether a worker was re-trained in the previous year.  2.6  Conclusions  This chapter explores the empirical relevance of skill dispersion as a determinant of the pattern of trade across industries. The analysis relies on microdata to construct measures of skill dispersion in the labour force for a set of countries that participated in the IALS. The evidence indicates that exporters with higher residual skill dispersion specialize in low complementarity sectors. The result is robust to a variety of controls for alternative sources of comparative and is also quantitatively large: in fact we nd that the magnitude of the effect of skill dispersion on trade ows is comparable to that of the aggregate endowment of human capital. Two alternative measures of skill substitutability produce results that are qualitatively and quantitatively very similar. Building on the theory developed in chapter 1, the analysis focuses on the impact of residual skill dispersion: in the model this means analyzing unobservable skills; in the empirical analysis it translates into purging skills and wages of all characteristics that are observable to the econometrician. To the extent that a substantial component of residual wages and skills is observed by rms and workers, but unobservable to the econometrician, two remarks about the interpretation of our evidence are in order. First, the empirical results are not necessarily inconsistent with a model of observable skills as in GM: we nd that countries with high skill dispersion specialize in sectors with high wage dispersion. In our model wage dispersion only re ects the degree of complementarity, and not compositional effects. Conversely, in GM, any differences in the sectoral wage distribution is due exclusively to industries employing workers of different skills: the supermodular sector employs similar 44  workers, the submodular sector employes workers at the tails of the skill distribution. We expect that a multi-country, multi-sector extension of GM could be consistent with the empirical evidence that this chapter presents. We are not aware of such an extension and we believe it would be non-trivial.29 Second, we hypothesize that a Heckscher-Ohlin-Samuelson model of factor proportions with a large number of factors and different factor intensities across sectors would potentially yield testable implications similar to our model. Our results indicate that such a model should encompass a much ner level of disaggregation of factors than Heckscher-Ohlin-Samuelson-type models and their empirical tests have employed so far.30  29 As  previously noted, trade does not emerge in GM with supermodular sectors and observable skills. Therefore such an extension with n sectors would have to feature n 1 submodular industries, that exhibit different degrees of submodularity. 30 Tests of the factor proportions theory typically involve a dichotomous classi cation of workers into production and non-production, or college and non-college educated.  45  Chapter 3  Non-Market Interactions and Entry into Export Markets Synopsis. Previous research suggests that rms that penetrate foreign markets reduce entry costs for other potential exporters, generating export spillovers. This chapter continues this line of research by developing a general empirical framework to study whether export participation decisions at the rm level are in uenced by the characteristics of rms that belong to a common reference group (de ned by industry and geographical region). It is shown that, in the presence of entry costs, group composition affects the degree of state dependence of individual export decisions, thus making its impact contingent on export status. I test this idea applying the dynamic panel data estimator introduced by Blundell and Bond (1998) to a data set of Argentine manufacturing rms. Group composition in uences individual export decisions and most of this effect is channeled through entry costs. However, these non-market interactions are not driven by 46  export spillovers, but by average rm size at the group level.  3.1  Introduction  What explains the export behaviour of rms? Most of the research at the micro level has centered on analyzing which characteristics of a rm affect its propensity to export, including productivity (Bernard et al., 1995) and export status, i.e. past export experience (Roberts and Tybout, 1997). However, a number of studies have taken a different approach by focusing on whether the characteristics of rms located close to each other play a role in shaping individual entry decisions. Intuitively, proximity among rms could in uence individual export decisions if it enables interactions such as learning or imitation.1 The literature on export spillovers searches for a speci c learning interaction generated by exporters and in uencing the export decisions of rms belonging to the same reference group. The reference group describes the space of interaction (i.e. who interacts with whom) and is usually de ned in terms of product similarity and geographical proximity. In particular, these studies suggest that rms that penetrate foreign markets reduce entry costs for other potential exporters in the same industry and region, either through learning effects or by establishing commercial linkages. However, a recent survey, Greenaway and Kneller (2007, p. 143) concludes that the evidence of export spillovers is "somewhat mixed". The objective of this chapter is to re-examine the role of group composition (i.e. variation in the characteristics of the reference group) as a determinant of export decisions while addressing three methodological issues that, to the best of my knowledge, have been overlooked in previous research: 1 Note that, in principle, learning does not require rms to cooperate actively; the observation of the actions of competitors could potentially reveal information that facilitates entry to export markets. Aitken et al. (1997, p. 104) provide an example.  47  (i) Nine out of the eleven chapters surveyed in Greenaway and Kneller (2007, table 2) apply static estimation frameworks to analyze entry decisions. Modeling the rm's export decision in the presence of entry costs as in Bernard and Jensen (2004), I illustrate the well-known result (Roberts and Tybout, 1997) that a static approach is incompatible with the existence of entry costs in export markets, resulting in misspeci ed empirical models and complicating the interpretation of the results. (ii) The remaining two studies reviewed in that survey, Clerides et al. (1998) and Bernard and Jensen (2004) apply dynamic frameworks and nd weak evidence of export spillovers.2 However, a maintained assumption in these studies (and, in general, in the export spillovers literature) is that, once differences in productivity across rms and prior export experience have been controlled for, the in uence of group composition on export decisions is the same for every rm belonging to the reference group. A second goal of this chapter is to show that this assumption is inappropriate for testing whether exporter concentration reduces entry costs in export markets. On the contrary, if group composition affects entry costs, its impact on individual decisions should depend on the rm's export status. The intuition behind this result is that any effect of group composition on entry costs should only in uence the decision of rms considering whether to start exporting or not, and be irrelevant in the export decision of rms with recent experience in export markets (since, by de nition, the latter have already incurred entry costs). (iii) As mentioned, the literature on export spillovers has exclusively focused on whether individual export decisions are driven by the concentration of exporters 2 Clerides et al (1998) examine the role of exporter concentration within regions and industries on  the export decision of Colombian plants. They nd only weakly signi cant evidence that the presence of other exporters makes it easier for domestically oriented rms to break into foreign markets, but nd no spillovers reducing marginal costs of exporters. Using a panel of U.S manufacturing rms, Bernard and Jensen (2004) nd signi cant entry costs to foreign markets but negligible market access spillovers from export activity of rms in the same industry or region.  48  in the reference group. However, interactions could be related to other features of group composition. Therefore, a third objective of this chapter is to provide a general framework to account for alternative sources of non-market interactions. As an example, instead of learning from other exporters, a rm considering entry could plausibly learn from the R&D investment of rms in its reference group (perhaps, by learning new ways to upgrade its products, making them more appealing to foreign consumers). Another alternative is for rms to become more productive (and, as a result, more prone to exporting) by tapping into a group-speci c stock of innovations that have already been made by past innovators in the group. The idea of rms catching up to a technological frontier is applied by Aghion and Howitt (2006) to study the role of technological spillovers in explaining growth rates across countries, but it can also be used to think about the transfer of knowledge within rms belonging to the same group. In general, sorting out which features of group composition generate interactions on individual behaviour is likely to have policy implications. As an example, if rms learn from exporters (as suggested in the spillovers literature), government support to any single exporter will generate an indirect bene t for other rms considering entry to export markets. But if rms learn how to export as a result of the R&D investment of other rms located nearby, then resources allocated to export promotion may end up being socially more productive if redirected to R&D support programs. Overall, exploring the link between individual export decisions and group outcomes is appealing for a number of reasons. First, from a general perspective, because it is in line with a relatively recent and growing interest among economists of various elds in understanding how social factors beyond the marketplace affect individual decisions and outcomes.3 Second, because it may provide a better 3 The study of social interactions in economic decision making is also referred to as the new social  49  foundation for evaluating speci c policy issues, such as the case of government support to exporters. As shown in Melitz (2003), access to export markets leads to inter- rm resource reallocation towards the more productive rms, contributing to welfare gains from trade liberalization. If entry decisions at the rm level are in uenced by non-market interactions, then there is likely to be a positive role for government intervention in, for example, coordinating or promoting entry to export markets. The rm-level data used for empirical analysis in this chapter is a representative sample of manufacturing rms in Argentina between 1992 and 2001. Argentina has substantially increased its openness to foreign trade during the 1990s and entry into foreign markets has since been seen as a critical issue for the long run success of this policy. Therefore, these data provide an interesting and relevant ground for analyzing entry into export markets. The econometric approach relies on the GMM dynamic panel data estimator developed by Blundell and Bond (1998) in order to deal with unobserved heterogeneity and the dynamic effects generated by entry costs into export markets. This approach is also convenient for dealing with the potential endogeneity of group composition, including the re ection problem that arises in the identi cation of the effect of group behaviour on individual export decisions (Manski, 1993). Brie y, the results indicate that variation in group composition plays an important role in the determination of individual export decisions, after controlling for the effect of the rm-level determinants usually emphasized in the empirical micro literature (past export experience and rm heterogeneity). As suggested by the export spillovers literature, most of this effect is channeled through its in uence economics (Durlauf and Young (2001, p.1)). Soetevent (2006) is a recent survey of the empirical literature on social interactions, including neighborhood effects, substance use among teenagers and peer effects among university roommates  50  on entry costs and is, therefore, contingent on export status. However, group composition effects are not driven by the concentration of exporters, but by average rm size in the group. Furthermore, the bene t (in terms of increased likelihood of exporting) of belonging to a group characterized by a higher average rm size is larger for small rms than for large rms. If average rm size at the group level is viewed as proxying for a group-speci c stock of past innovations or technological frontier, a possible interpretation of the result is that non-market interactions lead to a "backwardness advantage" -Gerschenkron (1965)- that, ceteris paribus, increases the likelihood of exporting in smaller rms. The outline of the chapter is as follows. The next section presents a model of entry into export markets with sunk costs in order to characterize export decisions at the rm level and to illustrate different channels through which non-market interactions could exert their in uence on individual behaviour. Section 3.3 describes the data set and presents descriptive statistics of the export decisions of manufacturing rms during the 1990s in Argentina. Section 3.4 offers a preliminary exploration of the links between individual export behaviour and group composition that can be found the raw data. Section 3.5 begins with a discussion on the identi cation of non-market interactions and then sets up the econometric model to formally analyze the determinants of export decisions. Section 3.6 presents the estimation results and section 3.7 concludes.  3.2  A Model of Entry into Export Markets with Sunk Costs  In order to examine whether group composition generates non-market interactions that reduce entry costs to potential exporters, it is crucial to apply an empirical framework designed to identify the effects of entry costs on export participation de51  cision at the rm level. In this section, I present a simple model of export decisions that explicitly incorporates the role of entry costs in export markets, a modi ed version of the models in Roberts and Tybout (1997) and Bernard and Jensen (2004).4 As an additional feature, group composition is introduced into the analysis in a stark way with the goal of illustrating its potential impact on export decisions. The model provides a useful framework that will guide the speci cation and interpretation of the empirical analysis in sections 3.4 and 3.5. As shown below, a consequence of the existence of entry costs is that the export decision of a rm will exhibit state dependence. This implies that a proper econometric evaluation of the in uence of group composition on entry costs requires modelling export decisions in a dynamic framework. An additional feature of the model is that it explicitly separates the role of pro t heterogeneity and entry costs. This is convenient to allow for different channels through which non-market interactions could in uence individual entry decisions. In particular, the model also shows that the in uence of group composition on individual export decisions is contingent on export status, a result that plays a central role in the empirical analysis. Consider a rm i that in any given period τ can earn pro ts by selling in the domestic (d) and/or export ( f ) markets. Let this rm belong to a reference group g 2 G, where g indexes a speci c industry and geographical location where the rm carries out its production activities in the domestic market. G is the nite set of all groups producing in this market. Assume that the rm's pro t function is separable by letting π kg;τ represent the pro t obtained by selling in market k = fd; f g in period  τ.5  Let the per-period, xed costs of being an exporter (e.g. dealing with cus4 The  description of the model closely follows that in Clerides et al (1998). t separability can be derived from a model of monopolistically competitive rms that can price discriminate between foreign and domestic buyers, and produce at constant marginal costs –see Clerides et al (1998). 5 Pro  52  toms and intermediaries) be Mg;τ . Then, the rm will earn positive pro ts from f exporting in τ whenever π g;τ  Mg;τ . Accordingly, if there were no start-up costs  associated with becoming an exporter (and no learning-by-exporting effects) rms would simply participate in foreign markets whenever this condition was satis ed. However, as noted in Bernard and Jensen (2004), the existence of an entry cost (denoted by λ g;τ ) makes the rm's entry decision forward-looking and opens up the possibility that rms export today in anticipation of cost reductions, or foreign demand increases, later on. In particular, it may be optimal to keep exporting f even if π g;τ < Mg;τ since, by remaining in the export market, the rm avoids future  re-entry costs. Perhaps the simplest possible way to introduce non-market interactions in this framework is to model λ , M and π k as functions of a group-speci c vector Sg;τ that summarizes characteristics of group g that are thought to generate externalities. As a result, λ g;τ  λ (Sg;τ ), Mg;τ  M(Sg;τ ) and π kg;τ  π k (zkg;τ ; Sg;τ ) where, in addi-  tion, zkg;τ captures both individual characteristics of the rm and usual exogenous demand shifters in k (income level, exchange rates and goods' prices). These functions provide a reduced-form link between individual export decisions and group composition through different channels; i.e. through their in uence on marginal, xed and entry costs of exporting. In empirical studies, Sg;τ is usually a measure of the concentration of exporters in group g, period τ. In general, non-market interactions could be generated by export decisions or by other exogenous characteristics of rms belonging to reference group g (such as the proportion of foreign rms in g). An implicit assumption in this formulation is that rms interact only with rms belonging to the same group. I also assume throughout this section that the number of rms belonging to each group g 2 G is large so that, when solving their export decision problem, rms can ignore the impact of their decision on the vector of non-market interactions Sg;τ . 53  In other words, rms take Sg;τ as given, although some of its components could be endogenous variables determined in the general equilibrium -for example, if Sg;τ contains the average export decision of rms in group g. For the purposes of this chapter, however, I will only study the partial equilibrium of this model. Letting yτ be a binary indicator equal to one if the rm decides to export in τ, assume that in an initial period t the rm chooses a sequence of export participation decisions fyt+τ g∞ τ=0 in order to maximize the expected value of future discounted pro ts: Vt (yt  1 ; zg;t ; Sg;t )  max∞ Et  fyt+τ gτ=0  ∞  f ∑ δ τ fyt+τ [π g;t+τ  Mg;t+τ  (1  yt+τ  1 )λ g;t+τ ]  τ=0  + π dg;t+τ g  where Et is an expectations operator conditioned on the set of information available at time t and δ is the one-period discount rate. This formulation implies that producers who exit the market and re-enter face the same start-up costs as producers who never exported.6 Note that the entry cost, λ g;t+τ , is incurred if and only if the rm decides to start exporting in t + τ without recent export experience -i.e. if and only if yt+τ = 1 and yt+τ  1  = 0. The rm's problem can equivalently be viewed as  choosing yt to satisfy Bellman's equation: Vt (yt  1 ; zg;t ; Sg;t )  =  f max fyt [π g;t  yt 2f0;1g  Mg;t  (1  yt  d 1 )λ g;t ] + π g;t  + δ Et (Vt+1 (yt ; zg;t+1 ; Sg;t+1 )g  After evaluating the right-hand side of this equation at yt = 0 and yt = 1, comparing the resulting expressions and recognizing that ht and λ g;t are functionally 6 This  will be assumed in the empirical analysis of this chapter. However, it can be generalized by allowing start-up costs to depend upon previous exporting experience –see Roberts and Tybout (1997).  54  dependent on Sg;t , the rm's export decision in period t can be written as yt = 1[ht (zg;t ; Sg;t )  [1  yt  1 ]λ g;t (Sg;t )  0]  (3.1)  where 1[:] denotes an indicator function equals 1 if the expression is true and zero otherwise, and ht (zg;t ; Sg;t )  f π g;t  Mg;t + δ [Et (Vt+1 (yt = 1; zg;t+1 ; Sg;t+1 )  (3.2)  Et (Vt+1 (yt = 0; zg;t+1 ; Sg;t+1 )] Equation (3.1) implies that incumbent exporters continue exporting whenever current net operating pro ts from exports plus the expected discounted payoff from remaining an exporter (which includes avoiding the entry cost next period) is positive, and non-exporters begin exporting whenever this sum, net of entry costs, is positive. Therefore, the existence of sunk costs (λ g;t > 0) generates statedependence, introducing a dynamic component in the export decision of the rm. Equation (3.1) suggests two distinct channels through which non-market interactions may in uence entry decisions. Firstly, through net pro ts ht . This effect would arise if, for example, the presence of other exporters in the same group g increases the availability of specialized capital and labour inputs, lowering the rm's marginal cost of production. I'll refer to this channel as a productivity spillover. A second channel of externalities operates on the sunk cost of access to export markets, generating an entry cost spillover. This result bears important implications for the empirical analysis of nonmarket interactions and entry to export markets. First, it shows that in order to conduct a proper evaluation of the existence of entry cost spillovers it is necessary to identify the degree of state dependence on individual export decisions. Second,  55  as opposed to productivity spillovers, only the decisions of rms with no prior export experience can be in uenced by entry cost spillovers -since only these rms need to incur the sunk cost to export in period t. In other words, the in uence of group composition Sg;t on individual export decisions is contingent on export status. These two observations play an important role in the empirical analysis of this chapter.  3.3  Export Decisions in Argentina During the 1990s  The data set used in the empirical analysis comes from a variety of sources that are described in detail in the appendix, section C.1. Brie y, the rm-level data is a random sample of manufacturing rms in Argentina, collected during two Innovation Surveys carried out by I.N.D.E.C. (Argentina's National Statistical Agency). The rst survey provides information on 1639 rms in 1992 and 1996, while the second survey collected information on 1688 rms in 1998 and 2001 (Bisang and Lugones 1998, 2003). The rest of this section presents summary statistics of exporters and non-exporters, and documents the persistence of entry decisions in the data.  3.3.1  Exporters and Non-exporters  Table 9 summarizes the characteristics of exporters and non-exporters in the Argentine manufacturing industry after pooling all observations for 1992, 1996, 1998 and 2001. Exporters comprise slightly more that half of the observations in the sample (53%). In line with previous research, exporters are clearly larger and better performing rms, invest more heavily in capital and R&D, and demand relatively more skilled employees than non-exporters. The presence of foreign rms among exporters is substantially larger as well.  56  Table 10 shows the distribution of rms and exporters across provinces in Argentina. The activity of rms is highly concentrated in the three most populated provinces, Buenos Aires, Cordoba and Santa Fe. These provinces account for 64% of the country's population in 2001, over 85% of the observations and almost 90% of the exporters in the data set.  3.3.2  Transitions In and Out of Exporting and the Persistence of Entry Decisions  Figure B.3 shows the magnitude of the ows in and out of exporting that occurred in the manufacturing industry during the 1990s. While most of the rms where non-exporters in 1992, the reverse occurred later in the sample. The number of exporters peaked in 1996, driven by both high entry and very low exit rates. The reduction in the number of exporters in 1998 comes more from a rise in exits than a decline in entry. On average, 15.6% of exporters were entrants in any given year (i.e. they were non-exporters in the previous sample year). Similarly, 12.1% of non-exporters were, on average, previous exporters. The degree of variation in export decisions displayed in this sample is similar to that reported in Bernard and Jensen (2004, p. 563) for U.S. manufacturing rms during 1984-1992 -their average entry and exit rates are 13.9% and 12.6%, respectively. Though a substantial number of rms enter and exit the export market each year and exporting became more prevalent over time, there is still a large degree of persistence in the export status of individual plants. Columns (1) and (2) of table 11 report the fractions of exporters and non-exporters in 1992 who were exporters in subsequent years. Among plants that exported in 1992, 84% were exporting in 2001. Non-exporters show a smaller persistence: 68% remained with the same export status in 2001. Columns (3) and (4) of table 11 report the predicted rates of  57  persistence if exits and entrants were chosen randomly according to the calculated annual transition rates. At all horizons, the predicted persistence is substantially lower than that observed in the sample. From this we conclude that there is a high degree of reentry by former exporters, that is, they have a higher probability of reentering export markets. Similarly, former non-exporters have a higher probability to continue producing exclusively for the domestic market. This is consistent with the predictions of the export decision model presented in section 3.2. The empirical analysis intends to examine whether this persistence in exporting results from rm heterogeneity or from sunk costs, and the extent to which these sources of persistence are affected by the characteristics of reference groups.  3.4 3.4.1  Why do Firms Behave Similarly? A Look at the Raw Data  I now turn to exploring the link between individual entry decisions and group export behaviour in the raw data. To characterize the latter, I'll measure the concentration of exporters in reference group g by Y(  i)gt ,  the proportion of exporters in  group g and year t excluding rm i, Y(  i)gt  (  ∑  y jgt )=(Ng  1)  j2g; j6=i  where Ng is the number of rms in g.7 Alternatively, Y(  i)gt  can be interpreted as  the average export decision in group g. How are groups de ned? In this chapter, I follow the usual practice in the literature and assume that non-market interactions operate within groups of rms that produce similar products and are located close 7Y ( i)gt  0 if Ng = 1  58  to each other. Product similarity is measured at the 3-digit ISIC level of aggregation and geographical locations are de ned by provincial boundaries.8 A starting point in the analysis is the observation that a rm's decision to enter export markets is positively correlated with the decisions of rms belonging to the same group. Column (1) in table 12 shows the results of the linear projection of individual entry decisions on group behaviour, obtained by means of an OLS estimation of equation 3.3, yigt = δ t + β yY(  i)gt  + uigt  (3.3)  where δ t is a time-varying intercept common to all groups and uigt captures variation in export decisions that is orthogonal to Y( positive correlation between yigt and Y( this regression against Y(  i)gt .  i)gt .  The results indicate a strong  Figure B.4 plots the tted values of  i)gt .  The nding that members of the same group tend to behave similarly is an empirical regularity observed in different contexts in the social sciences.9 As mentioned, a maintained assumption in the export spillovers literature is that the in uence of group composition on export decisions is the same for every rm belonging to a given group. However, the analysis presented in section 3.2 showed that it is inappropriate for testing whether exporter concentration reduces entry costs in export markets. If group composition affects entry costs, its impact should depend on a rm's export status. The intuition behind this result is that any effect of group composition on entry costs should only in uence the decision of rms considering 8 The  ndings of this section are robust to changing the level of industry aggregation to 2 and 4 digits of ISIC. 9 Researchers have hypothesized that this observation could be driven by interactions in which the propensity of an agent to behave in some ways varies positively with the prevalence of this behaviour in the group. As noted in Manski (2000), according to the context, these interactions may be alternatively called "peer in uences", "neighborhood effects" or "herd behaviour", among others.  59  whether to start exporting or not, and be irrelevant in the export decision of rms with recent experience in export markets. In other words, we should expect the correlation illustrated in gure B.4 to be contingent on export status. As a rst step towards analyzing this hypothesis more formally, it is interesting to verify if it can be observed in the raw data. This requires introducing yigt  1,  export status, in equation 3.3 and allowing its coef cient λ gt to depend on the average export decision in group g; that is, λ gt = λ 0 + λ yY( In this way, the effect of Y(  i)gt  i)gt  on yigt can now operate through a direct and an  indirect channel, captured by λ y and β y , respectively. Substituting λ gt in equation 3.3 yields, yigt = α t + λ 0 yigt  1 + λ y yigt 1Y( i)gt  + β yY(  i)gt  + uigt  (3.4)  The results of the OLS estimation of equation 3.4 are presented in column (2) of table 12. The coef cient of interest, λ y , is negative and highly signi cant. This has two main implications. First, consistent with the analysis in section 3.2, the correlation illustrated in gure B.4 is contingent on export status. In particular, a higher concentration of exporters is correlated with a smaller in uence of export status on export decisions. This is illustrated in gure B.5, a plot of the tted values of this regression against Y(  i)gt ,  contingent on export status. The vertical  distance between the tted lines illustrates how the persistence of export decisions at the rm level, λ gt , decreases with export concentration. Second, a negative sign of λ y together with the fact that β y is positive and signi cant also implies that the export decision of rms considering whether to start exporting in period t is  60  more sensitive to changes in export concentration than the decision of rms that exported in period t  1.10 Note in gure B.5 that the tted line for t  1 exporters  is almost at. In fact, a Wald test of λ y + β y = 0 in equation 3.4 cannot be rejected at conventional signi cance levels.11  3.4.2  Three Challenges for the Empirical Analysis  Overall, a simple examination of the raw data points to the importance of allowing the in uence of group behaviour to be contingent on export status and, as a consequence, to operate indirectly through its effect on the degree of persistence in export decisions. The literature on export spillovers, on the other hand, has focused on studying the uncontingent effect (i.e. independent of export status), albeit after controlling for export status as in Clerides et al. (1998) and Bernard and Jensen (2004). The primary objective of the empirical analysis is to assess whether the geographical concentration of exporters in the same industry generates non-market interactions on individual export decisions. Are the correlations between individual and group behaviour shown in gures B.4 and B.5 evidence of this hypothesis? Not necessarily. An appropriate test of this hypothesis has to meet three basic challenges. First, it must disentangle persistence in export decisions due to state dependence (export status) from persistence due to unobserved heterogeneity in rm characteristics.12 The analysis in section 3.2 implies that entry costs generate state dependence. The econometric analysis thus needs to isolate this source of persis10 This 11 The  follows because  ∂ yigt ∂Y( i)gt  = β y + λ y yigt  1  in equation 3.4.  p-value for this hypothesis is 0.1541. 12 In a series of papers, Heckman (1978, 1981b, 1981a) discusses these two sources of serial persistence.  61  tence as a prior condition to evaluating the relevance of export spillovers on entry costs. A second task is to isolate an exogenous source of variation in group export propensity (and, in general, in group composition). Although export spillovers within provinces would generate feedback loops in export decisions that stimulate the agglomeration of exporters such as in gures B.4 and B.5, other alternative mechanisms could be at work. A most natural alternative is to imagine that some provinces provide rms with institutional and economic environments that are more conducive to exporting than others. This could be driving the agglomeration of rms described in table 10. In this story, the geographical characteristics of provinces and the quality of both local public goods and provincial governments are likely to play key roles. Alternatively, the co-movement of export decisions could be simply re ecting rms adjusting to changes in fundamentals across industries, such as export prices or transport costs. These issues are discussed in detail in section 3.5.2. Conditional on the previous two, a nal task of the empirical analysis is to identify the source of non-market interactions. The concentration of exporters may still be driven by non-market interactions, but of a different kind than suggested in the export spillovers literature. Exporter agglomeration may be related to features of group composition other than export propensity. Instead of learning from other exporters, a rm considering entry could plausibly learn from the R&D investment of rms in the same group (perhaps, by learning new ways to upgrade its products, making them more appealing to foreign consumers). Another plausible alternative is for rms to become more productive (and, as a result, more prone to exporting) by tapping into a stock of innovations that have already been made by past innovators belonging to a given group, catching up to a group-speci c technological frontier. There is no reason to rule out these possibilities a priori and, 62  as suggested in the introduction, sorting out which features of group composition generate interactions on individual behaviour is likely to have policy implications. As a summary of this section, stripped to its basics, the correlations shown in gures B.4 and B.5 could be driven by (Manski (2000)): a) Endogenous interactions, wherein the export propensity of a rm varies with the export propensity at the group level -the export spillovers hypothesis. b) Exogenous interactions, wherein the export propensity of a rm varies with other exogenous characteristics of group composition. c) Correlated effects, wherein rms in the same group tend to behave similarly because the have similar individual characteristics or face similar institutional environments (including market fundamentals). Notice that while endogenous and exogenous effects represent genuine nonmarket interactions between rms of the same group, correlated effects operate entirely at the individual level and, therefore, should not be regarded as any form of interaction.  3.5  Econometric Analysis  In this section, I start by presenting the econometric framework for analyzing export decisions at the rm level. I then turn to a discussion of the identi cation of non-market interactions that leads to the empirical strategy used in this chapter.  3.5.1  A Linear Speci cation  As a rst step in setting up the econometric model, I follow Bernard and Jensen (2004) and Bernard and Jensen (2004) and express yt in equation 3.2 as a reduced linear form of observable rm and group-speci c (including group composition)  63  characteristics and unobservable idiosyncratic rm effects. Furthermore, as shown in section 3.2, if non-market interactions in uence entry costs λ gt , its effect on individual entry decisions is contingent on the export status of a rm. Therefore, I allow λ gt to depend linearly on group composition. As a result, the rm's export decision in equation 3.1 can be expressed as yigt = 1[λ gt yigt  1 + zigt  T  η + Sgt T β + xgt T γ + δ t + uigt ]  0  (3.5)  for t = 1; :::; T; where λ gt (Sgt ) = λ 0 + Sgt T λ 1  (3.6)  As in previous sections, reference groups g 2 G are de ned by product similarity and geographical proximity. Therefore, G  f(industry; location)g, where  industry is de ned by 3-digit industries of the ISIC classi cation and location is de ned by Argentine provinces. Since the Innovation Surveys provide data on export decisions for 1992, 1996, 1998 and 2001, then T = 3 for the model in equation 3.5. Using the notation in section 3.2, yigt is the export decision of rm i, in group g 2 G and period t; (zigt ; uigt ) are rm-speci c attributes that directly affect yigt ; xgt are attributes characterizing group g in period t; δ t controls for aggregate time effects; Sgt describes the composition of the set of rms in group g during period t. In particular, as mentioned in the previous section, non-market interactions arising from group composition Sgt can comprise both endogenous and exogenous effects. While endogenous effects are generated by the export decisions of rms belonging to group g, exogenous effects are generated by the predetermined characteristics zigt of these rms. In order to capture these features of group composition explic-  64  itly, I de ne13 Sgt Also, let β  [β y ; β z ]T and λ 1  [E(ygt jg); E(zgt jg)]T [λ y ; λ z ]T be the coef cients of [E(ygt jg); E(zgt jg)]  in equations 3.5 and 3.6, respectively. The unobserved term, uigt , is assumed to have the following structure: uigt = α i + ε igt  (3.7)  where α i captures time invariant unobserved characteristics of the rm, including geographical location and industry effects (since these two characteristics are time invariant in the data set used in this chapter). Geographical effects that could in uence export decisions include the institutional environment and accessibility to major markets. Industry effects include factor endowments and other time-invariant determinants of comparative advantage. ε igt is an error term that I'll describe in detail below. In this setup, λ y 6= 0 implies that exporter concentration in group g affects entry costs for rms with no prior export experience, thus generating entry cost spillovers. If β y 6= 0, exporter concentration affects export decisions independently of export status; in light of equation 3.1, this is interpreted as a spillover on productivity. Both λ y and β y thus capture endogenous interactions. λ z and β z have similar interpretations, but they measure the effect of exogenous interactions on export decisions. If γ 6= 0 in equation 3.5, the model expresses correlated effects: rms in group g tend to behave similarly because they face similar institutional 13 The use of expected average choice rather than the realized average choice is made for analytical convenience. As noted in Blume and Durlauf (2006), the assumption makes most sense for larger groups where the behaviors of the rest of group are not directly observable. The assumption that individuals react to expected rather than actual behaviors is not critical for the identi cation analysis I describe below.  65  environments and market fundamentals.14 The speci cation of (zigt ; xgt ; Sgt ) for the empirical analysis of manufacturing rms in Argentina is the following: zigt includes: rm size (log of total number of employees), output per worker (log of total sales of goods produced by the rm per employee), foreign ownership dummy (equal to 1 if the majority of the rm's shares are held by nonArgentine residents), skilled labour (proportion of employees with completed college or higher education) and R&D intensity (share of R&D expenditures in total sales). xgt includes industry and location time-varying controls. Industry controls: producer price index in ISIC industry, export price index in ISIC industry, total exports in ISIC industry. Location controls: province population, share of public employees in province population and provincial government's per capita expenditure in education, health and infrastructure services.15 Regarding group composition, E(ygt jg) and E(zgt jg) are estimated non-parametrically using sample data by Y(  i)gt  (∑ j2g; j6=i y jgt )=(Ng  1) and Z(  i)gt  (∑ j2g; j6=i z jgt )=(Ng  1) (3.8)  respectively, where Ng is the number of rms in g.16 Excluding rm i's decision (yigt ) or characteristic (zigt ) does not affect the consistency of Y(  i)gt  or Z(  i)gt  and  avoids a mechanic positive correlation between individual and group outcomes. Equations 3.5 through 3.7 de ne a dynamic binary choice decision model with unobserved heterogeneity that characterizes export decisions in the presence of 14 Actually,  γ captures correlated effects arising from group characteristics that change over time. Time-invariant correlated effects are, in turn, captured by α i . 15 See section C.1 for details on data sources. 16Y 0 and Z( i)gt 0 if Ng = 1 ( i)gt  66  entry costs and non-market interactions. There are several potential estimation strategies for this type of models. A rst decision is whether to use a linear or nonlinear estimation framework to model export decisions. Linear probability models are robust to arbitrary correlation between the unobserved heterogeneity α i and the regressors, and can be used to eliminate the incidental parameters associated with the unobserved heterogeneity in xed effects probit models. Random effects probit models, which parameterize the distributions of α i and ε igt , rely more strongly on the functional form assumptions made, are computationally more demanding and require dealing with the problem of specifying the initial conditions of the dynamic process.17 For these reasons, the estimation approach in this chapter is to use a linear probability model.18 Substituting equations 3.6 and 3.7 into a linear probability model speci cation of equation 3.5 yields the estimating equation for the econometric analysis of this chapter: yigt  = λ 0 yigt  1 + yigt 1 [E(ygt jg)  E(zgt jg)]T λ 1 + zigt T η  (3.9)  +[E(ygt jg) E(zgt jg)]T β + xgt T γ + α i + δ t + ε igt It will be useful to write this equation in a compact way. Letting ψ  (λ 0 ; λ 1 ; η; β ; γ)T  and Wigt denote the vector of explanatory variables, Wigt  (yigt  1 ; yigt 1 E(ygt jg); yigt 1 E(zgt jg); zigt ; E(ygt jg); E(zgt jg); xgt ; δ t )  17 For  example, implementing Heckman (1981c) would rst require assuming a density of the initial condition yig0 for given covariates and α i and then specifying the conditional density of α i given the covariates. Misspeci cation of of these densities generally results in inconsistent estimates of the parameters of interest. Wooldridge (2005) suggests an alternative quasi maximum likelihood approach that avoids specifying a density for the initial conditions but still requires restricting the distribution of the unobserved heterogeneity. 18 Bernard and Jensen (2004) also rely on linear probability models in their econometric analysis.  67  equation 3.9 can be reformulated as yigt = Wigt T ψ + α i + ε igt  3.5.2  (3.10)  Identi cation  Next, I study the identi cation of non-market interactions in equation 3.9. Although most of the discussion is centered on dealing with the endogeneity of export status and group composition, it is essential to begin with a comment on what the causal effect of interest is. An important point to acknowledge is that, in general, group composition may in uence individual export decisions directly through nonmarket interactions such as learning or imitation processes, or indirectly through its effect on market prices in the general equilibrium. While the direct channel is emphasized in the spillovers and social interactions literatures, Melitz (2003) provides an example of the indirect channel by showing how average rm productivity within industry determine aggregate price and income indices that, in turn, affect entry into export markets in the general equilibrium.19 Since the objective of this chapter is to learn whether group composition generates non-market interactions that in uence individual export decisions, the focus is to isolate the effect of the direct channel. Therefore, even if the variation in group composition were completely exogenous in my sample it would be necessary to control for market prices as a necessary step in interpreting the correlation between export decisions and group composition as evidence of non-market interactions. This motivates the inclusion of domestic and export prices and aggregate expenditure at the industry level controls in vector xgt in the empirical analysis (see page 66). The causes of the endogeneity of group composition in equation 3.9 can be 19 See  Melitz (2003, p. 1700).  68  grouped into two broad categories (see Mof tt, 2001):20 (i) the simultaneity problem (ii) the correlated unobservables problem The simultaneity problem complicates the identi cation of non-market interactions because group composition is itself determined by the behaviour of group members. Hence, data on outcomes do not necessarily reveal whether group behaviour actually affects individual behaviour, or group behaviour is simply the aggregation of individual behaviour. This problem was formally analyzed in Manski (1993), and has since been also known as the `re ection problem'. To illustrate Manski's argument, consider a version of equation 3.9 where, for the sake of the argument, there are no spillovers on entry costs; i.e. λ 1 = 0, yigt = λ 0 yigt  1 + zigt  T  T η + β y E(ygt jg) + E(zgt jg)T β z + xgt γ + α i + δ t + ε igt (3.11)  Assume, for the moment, that 3.11 represents a structural equation for yigt , so that E[ε igt jyigt  1 ; zigt ; xgt ; α i ; g]  =0  It follows that, for a given g 2 G, the mean regression of yigt on (yigt  1 ; zigt ; xigt ; α i )  has the linear form E(yigt jyigt  1 ; zigt ; xgt ; α i ; g)  = λ 0 yigt  1 + zigt  T  η + β y E(ygt jg) + E(zgt jg)T β z  +xgt T γ + α i + δ t Integrating this expression with respect to (yigt  1 ; zigt ; xgt )  reveals that E(yigt jg)  20 Actually, Mof tt (2001) adds a third category, the endogenous group membership problem, which arises from the self-selection of rms into groups due to factors that are also correlated with the dependent variable. However, endogenous membership can be considered as a particular case of the correlated unobservables problem -see Mof tt (2001, p. 65).  69  solves the following equilibrium equation in every period t = 1; :::; T E(ygt jg) = λ 0 E(ygt  T T 1 jg) + β y E(ygt jg) + E(zgt jg) (β z + η) + xgt γ  + E(αjg) + δ t  Therefore, assuming β y 6= 1, E(ygt jg) =  λ0 E(ygt (1 β y ) +  T 1 jg) + E(zgt jg)  (β z + η) γ + xgt T 1 βy 1 βy  E(αjg) δt + 1 βy 1 βy  Therefore, E(ygt jg) is a linear function of [E(ygt  1 jg); E(zgt jg); xgt ; dt ; dg ],  where  dt and dg denote time-varying and group-speci c intercepts. Identi cation of nonmarket interactions in equation 3.11 is not possible if either λ 0 = 0 or E(ygt  1 jg)  is included as an additional explanatory variable, since in these cases E(ygt jg) becomes perfectly collinear to the rest of the explanatory variables in equation 3.11. When λ 0 = 0, the model becomes a static linear case similar to that analyzed in Manski (1993).21 The last observation suggests that the existence of dynamic effects, in this case arising from the presence of entry costs, may help to mitigate the simultaneity problem. However, this will be true as long as E(ygt from equation 3.11. Intuitively, if excluded, E(ygt  1 jg)  1 jg)  is (correctly) excluded  acts as an instrument for  E(ygt jg) breaking the re ection in the same way as exclusion restrictions are used to solve standard simultaneous equations in econometrics. This idea is formalized in the next section. Brie y, the identifying restriction is that individual export decisions are not directly in uenced by E(ygt  1 jg);  that is, yigt  1  does not generate  non-market interactions in period t once E(ygt jg) has been controlled for.22 The 21 Manski  (1993) considers the case with no unobserved heterogeneity; i.e. α i = 0. noted by Mof tt (2001), this example shows that there might be a larger class of exclusion restrictions consisting of characteristics of rms that can be argued on some basis to not have a direct 22 As  70  assumption becomes more plausible if the value of non-market interactions depreciates rapidly over time. This appears to be a reasonable approximation to the case I study in this chapter, considering that the average time gap between the available data points (1992, 1996, 1998 and 2001) is 3 years and the fact that, during the 1990s, manufacturing rms in Argentina were in the midst of a radical process of structural change and adjustment to increased competition stemming from trade liberalization and a reduction of government intervention in the economy. In turn, the problem of correlated unobservables arises if there is some individual or group-speci c component of the error term ε igt that is correlated with the explanatory variables in equation 3.9. Thus, it is equivalent to a standard omitted variable problem in econometrics. The unobservables may arise from unobserved product attributes or managerial ability at the rm level or may represent group effects. As mentioned in section 3.3, some provinces are likely to provide rms with institutional and economic environments that are more conducive to exporting than others. Alternatively, the co-movement of export decisions could simply re ect rms adjusting to changes in fundamentals across industries, such as export prices or transport costs, or other idiosyncratic shocks to comparative advantage. In these cases, unobservable determinants of the export decision are also correlated with zigt , E(ygt jg) or E(zgt jg). The empirical strategy for dealing with correlated unobservables in this chapter is the following. First, I will use an estimator that allows for arbitrary correlation between time-invariant unobservables (α i ) and the explanatory variables. This feature covers some important cases mentioned above such as geographic and, to the extent they remain roughly constant over time, industry effects and managerial ability. Second, I will control for several sources of time-varying correlated unobservables, including local government performance and demand shocks at the in uence on others.  71  industry level (see details in page 3.5.1). Finally, in order to deal with any residual correlation in the error term ε igt , I will use an instrumental variables strategy similar to the one outlined in the context of the simultaneity problem. Next, I turn to describing this approach.  3.5.3  Estimation Framework  Consistent estimation of the parameters in equation 3.9 requires dealing with the presence of a lagged dependent variable (export status) as a regressor and, as analyzed previously, with the endogeneity of group composition. It is well known that OLS and standard panel data estimators yield inconsistent estimates in the presence of a lagged dependent variable and unobserved heterogeneity -see Cameron and Trivedi (2005, p. 764). The consistency of OLS estimators depends on the assumption that rm heterogeneity α i is uncorrelated with the regressors in Wigt . This assumption is violated by equation 3.9, due to the presence of export status yigt  1  as an explanatory variable. Thus, a rst  step in obtaining consistent estimates is to eliminate α i . The `within' panel data (or xed-effects) estimator transforms equation 3.9 to express the original observations as deviations from their rm-speci c means. OLS is then used on the transformed equation. Consistent estimation requires the right-hand side variables of equation 3.9 to be strictly exogenous.23 That is, strict exogeneity requires E(ε igt jWig1 ; :::;WigT ; α i ) = 0. This implies E(Wigs :ε igt ) = 0 for s;t = 1; :::; T and g 2 G, an assumption that is violated in equation 3.10 since yigt 2 Wigt+1 . In general, strict exogeneity rules out feedback effects from the dependent variable yigt to future values of Wigt . In the context of this chapter, this is not only incompatible with the existence of entry costs in export markets, but it also rules out 23 The random effects estimator also requires strict exogeneity in order to achieve consistency. These results are shown in Wooldridge (2002, chapter 10).  72  other phenomena of interest such learning by exporting, which involves the effect of exporting activity on future rm productivity.24 In other words, in the presence of either entry costs or learning by exporting effects, the xed-effects estimator is inconsistent. An alternative GMM-based approach can be applied by rst removing unobserved rm heterogeneity α i and then searching for instrumental variables. I start by relaxing strict exogeneity and introducing a set of sequential moment conditions E(ε igt jWigt ;Wigt  1 ; :::;Wig1 ; α i )  = 0, for t = 1; :::; T  (3.12)  That is, the explanatory variables in equation 3.10 are sequentially exogenous in the sense of being uncorrelated with current and future values of ε igt . However, no restriction is imposed on their correlation with past values of ε igt . Below, I explain how to treat endogenous regressors, such as group composition, that are likely to be contemporaneously correlated with ε igt . Given the model in equation 3.10, assumption 3.12 is equivalent to E(yigt jWigt ;Wigt  1 ; :::;Wig1 ; α i )  T = E(yigt jWigt ; α i ) = Wigt ψ + α i , for t = 1; :::; T  (3.13) The rst equality makes it clear what sequential exogeneity implies about the explanatory variables: after Wigt and α i have been controlled for, no past values of Wigt affect the expected value of yigt . In other words, under sequential exogeneity, the model in equation 3.10 is assumed to be dynamically complete conditional on α i . It means that one lag of yigt is suf cient to capture the dynamics in the condi24 The empirical relevance of learning by exporting is far from being settled. Clerides et al (1998), Bernard and Bradford Jensen (1999), Isgut (2001) and Delgado et al. (2002) are rm level studies that do not nd evidence of learning by exporting. An exception is Van Biesebroeck (2005), who nds that past export experience has a causal effect on the performance in a panel of sub-Saharan African rms.  73  tional expectation of export decisions; neither further lags of yigt nor lags of other components of Wigt are important once Wigt and α i have been controlled for. The second equality is an implication of equation 3.10. First differencing equation 3.10 to remove unobserved rm heterogeneity α i gives ∆yigt = ∆Wigt T ψ + ∆ε igt  (3.14)  Note that ∆Wigt is necessarily endogenous in this equation since, in any period t, ∆yigt  1  = yigt  1  yigt  2  2 ∆Wigt is correlated with ∆ε igt = ε igt  ε igt  1.  Group  composition is also likely to be endogenous for the reasons given in the previous section. Next, note that sequential exogeneity implies E(Wigs ε igt ) = 0, for s = 1; :::;t and t = 1; :::; T . Therefore, E(Wigs ∆ε igt ) = 0, for s = 1; :::;t 0 This implies that, in period t, Wigt  1  1  (3.15)  can be used as potential instruments for ∆Wigt  in equation 3.14, where 0 Wigt  (Wig0 ;Wig1 ; :::;Wigt )  The moment conditions in equation 3.15 form the basis of the Arellano and Bond (1991) GMM `difference estimator' for dynamic panel data, that uses lagged levels 0 of the explanatory variables Wigt  1  as instruments in the estimation of equation  3.14. A convenient feature of this framework is that it can easily accommodate for endogenous regressors. If some component of Wigt , such as group composition,  74  is presumed to be correlated with unobservables in uencing export decisions in 0 period t, then Wigt  2  0 can be used in place of Wigt  1  as an instrument for Wigt .  The difference estimator has the statistical shortcoming that if the regressors in equation 3.9 are persistent, then lagged levels of Wigt are weak instruments, that is, they are not highly correlated with the regressors, and so the estimated coef cients may be biased. This problem is particularly serious the shorter the length of the panel is (that is, the smaller T is), see Baltagi (2005). To overcome these problems, Arellano and Bover (1995) and Blundell and Bond (1998) developed a `systems estimator' that combines the differenced model in 3.14 with the levels model in equation 3.10. In order to be able to use lagged differences of the variables on the right-hand side of equation 3.14 as valid instruments for the regression in levels, the following identifying assumptions are introduced: E(∆Wigt α i ) = 0  (3.16)  which imply that there is no correlation between the differences of the regressors and the country-speci c effect; in other words, the rm-speci c effect and the regressors are still allowed to be arbitrarily correlated, but this correlation should be constant over time. Given 3.16, the following moment conditions can be added to those speci ed above in equation 3.1525 : E(∆Wigt ε igt ) = 0  (3.17)  Endogenous regressors can be treated in a similar way as in the difference estimator, by using ∆Wigt  1  as an instrument for Wigt .  In a nutshell, where Arellano and Bond (1991) instrument differences with lev25 Using  3.7 and 3.16, we have E(∆Wigt uigt ) = E(∆Wigt (α i + ε igt )) = E(∆Wigt ε igt ) = 0  75  els, Blundell and Bond (1998) suggest instrumenting levels with differences. The Blundell-Bond estimator stacks the data for the levels and the difference equations (numbers 3.10 and 3.14, respectively) and estimates them simultaneously in a GMM framework using the moment conditions in 3.15 and 3.17. Further details can be found in Roodman and Floor (2006).  3.6  Estimation Results  Table 13 reports the estimation results of different speci cations of equation 3.9, using Blundell and Bond's (1998) GMM system estimator for dynamic panel data.26 Every speci cation uses instruments for export status and group composition as explained above, two-period and deeper level lags in the difference equation and oneperiod and deeper difference lags in the levels equation. Although not reported, all estimations include time dummies, export prices, and total industry exports. Industries are de ned at the 3-digit ISIC level, but the results are qualitatively robust to changes in the level of aggregation. The rst two columns present an endogenous interactions model that borrows two distinctive features from usual speci cations found in the spillovers literature. First, I assume that the impact of average export intensity at the group level is the same for every rm belonging to a given group -i.e. it is not contingent on export status. However, I do control for export status -as in Clerides et al. (1998) and Bernard and Jensen (2004). Second, I do not consider the in uence of other features of group composition (exogenous interactions). In terms of the notation in equation 3.9, I assume λ 1  [λ y ; λ z ]T = [0; 0]T and β  [β y ; β z ]T = [β y ; 0]T .  As in Clerides et al. (1998) and Bernard and Jensen (2004), the evidence on 26 All estimations were implemented in Stata 9.0, using the program `xtabond2'. A detailed description of this command can be found in Roodman (2006).  76  export spillovers is very weak. In column (1), the effect of export intensity on individual export decisions, β y , is statistically insigni cant. In line with the empirical literature that has analyzed the determinants of exporting at the micro level, export status and heterogeneity in rm characteristics (output per worker, rm size and R&D investment) are highly signi cant. In particular, the signi cance of export status provides evidence of the importance of entry costs in export markets.27 Column (2) repeats this speci cation, but instrumenting for rm-level characteristics. The results are qualitatively invariant to this modi cation -except in the case of R&D investment. Columns (3), (4) and (5) explore the consequences of introducing the interaction between export status and exporter concentration at the group level to allow for a contingent effect of the latter on export decisions. For the moment, I still rule out exogenous interactions (that is, [λ z ; β z ]T = [0; 0]T is maintained) and focus on the vector of endogenous interactions [λ y ; β y ]. These speci cations differ in terms of the inclusion of both location controls (see page 66) and IVs for rm-level controls. The results show that the coef cient of the interaction λ y is negative and becomes signi cant at the 5% level when location controls and IVs for rm-level controls are included. This implies that the in uence of export status declines in groups where the proportion of exporters is larger. In the context of the model of section 3.2, this is equivalent to stating that a higher export propensity at the group level reduces entry costs into export markets. The fact that β y is insigni cant in all three speci cations actually means that the proportion of exporters at the group level does not affect the export decisions of rms with export experience in period t  1. These results provide evidence supporting endogenous spillovers on entry 27 Actually,  the magnitude of the estimated coef cient for export status in these speci cations is very similar to the point estimate in Bernard and Jensen (2004, table 5, page 567).  77  costs and against endogenous spillovers on productivity. With respect to the in uence of rm characteristics, the results in columns (3) to (5) show that export status, output per worker and rm size remain signi cant determinants of export decisions. The binary indicator for foreign rms becomes highly signi cant in (4) and (5). In column (6), I allow for general group composition effects by allowing every individual characteristic of a rm to potentially generate exogenous interactions on the export decisions of other rms in the same group. These group variables are denoted with a subscript g in table 13 to distinguish them from rm-level controls. For example, Sizeg is the within-group average rm size. As in (3) to (5), the impact of group composition is allowed to be contingent on export status. The results change considerably when exogenous interactions are explicitly introduced in the analysis. Endogenous interactions from other exporters are no longer signi cant. Spillovers on entry costs are now driven by both average rm size and the share of foreign rms at the group level. Interestingly, there's no evidence of spillovers on productivity, which were also absent in previous specications. Therefore, the impact of group composition is channeled through entry costs rather than productivity. Note that the estimated coef cients of average rm size and the share of foreign rms have opposite signs. A negative sign in the coefcient of the interaction with export status λ z implies that larger average rm size generates positive spillovers on entry costs. On the other hand, a higher proportion of foreign rms at the group level generates negative spillovers on entry costs. The rst two columns in table 14 show that the results derived from the last speci cation in table 13 are largely robust to the level of industry aggregation -in columns (1) and (2) industries are de ned at 2 and 4 digits of the ISIC classi cation, respectively. So, why do export spillovers vanish when other features of group composition are controlled for? Columns (3) to (6) in table 14 examine the 78  sensitivity of endogenous interactions to the inclusion of average rm size and the share of foreign rms at the group level. Columns (3) and (4) show that if average rm size (Sizeg ) is excluded, endogenous spillovers reappear. This does not occur if only the share of foreign rms in the group is excluded -columns (5) and (6). Therefore, the positive effect of exporter concentration present in columns (4) and (5) of table 13 was actually driven by average rm size at the group level. As mentioned in the introduction, average rm size at the group level can be viewed as a proxy for a stock of past innovations or technological frontier,28 a group-speci c public good that rms can access to upgrade their products. In this interpretation, it becomes interesting to evaluate whether the intensity of the exogenous interactions generated by average rm size on export decisions increases in smaller rms. This hypothesis is reminiscent of Gerschenkron's (1965) `advantage of backwardness'. In the present context, the advantage for a smaller rm could arise from the fact that implementing innovations allows it to make larger quality improvements the further it has fallen behind the frontier.29 The thought experiment is the following: we would like to evaluate the effect of shifting the group's technological frontier while holding the size of the rm constant; that is, to evaluate an increase in the rm's `distance to the frontier'. Furthermore, we'd like to assess whether this effect is stronger in smaller rms. To implement this test, I augment speci cation (6) in table 13 by allowing the effect of average rm size to depend on the individual size of a rm. This requires a triple interaction between export status, Sizeg and Size. An additional interaction between Size and export status is also included to allow entry costs to vary with rm size. The last column of table 14 presents the estimation results. Smaller rms face higher entry costs 28 After  all, rm size can be naturally viewed as a measure of a rm's past success. and Howitt (2006) applly Gerschenkron's analysis to study the role of technological spillovers in explaining growth rates across countries. 29 Aghion  79  (signi cant at 5%) and the positive estimated coef cient of the interaction between export status, Size_G and Size suggests that the exogenous interactions on entry costs are weaker for larger rms. This result provides support for the advantage of backwardness hypothesis at the 10% level. Overall, the picture that emerges from tables 13 and 14 is that group composition plays an important role in the determination of individual export decisions, beyond the effect of the rm level determinants that have been usually emphasized in the micro literature (past export experience and rm heterogeneity). Group composition generates non-market interactions that in uence individual export decisions. As suggested by the export spillovers literature, most of this effect is channeled through its in uence on entry costs and is, therefore, contingent on export status. However, group composition effects are not driven by the average export propensity at the group level, but by average rm size and the share of foreign rms.  3.7  Conclusions  This chapter examined the role of group composition in shaping export decisions at the rm level. Particular attention was given to the hypothesis that exporters belonging to the same group reduce entry costs for other rms considering entry. Theory indicates that the in uence of group composition on entry costs changes the degree of state dependence of individual export decisions. A proper empirical evaluation of this implication required disentangling the effect of state dependence from other sources of persistence in export decisions and obtaining a source of exogenous variation in group composition. I used a dynamic panel data approach that relies on sequential moment conditions to achieve identication. It would be interesting to search for other identi cation strategies in order to provide more robust evidence on the ndings. Nevertheless, the methodological 80  contribution of the chapter is independent of the effectiveness of the identi cation strategy used. The results show that group composition in uences individual export decisions and that most of this effect is channeled through entry costs. This holds after controlling for the key determinants of export participation emphasized in recent research, past export experience and rm heterogeneity. Interestingly, these nonmarket interactions are not driven by export spillovers, but by other features of group composition, namely average rm size and the share of foreign rms at the group level. I have provided a tentative interpretation for the effect of average rm size as a proxy for a group-speci c technological frontier, in which non-market interactions generate a "backwardness advantage" that, ceteris paribus, increases the likelihood of exporting in smaller rms. In this story, rms become more productive (and, as a result, more prone to exporting) by tapping into the stock of innovations that have already been made by past innovators belonging to the same group. The results show that once this effect is controlled for, spillovers arising from exporters to other rms considering entry become statistically insigni cant. Of course, nothing in this interpretation rules out a mechanism where spillovers from exporters could still impact export decisions by generating a shift in the group-speci c technological frontier which, in my argument, was taken to be exogenously determined. These issues are beyond the scope of this paper and are left to future research.  81  Tables  82  Exporter  Mean Rank  St Dev Rank  St Dev Res Rank  Denmark Germany Netherlands Norway Finland Sweden Czech Republic Hungary Belgium New Zealand United Kingdom Ireland Switzerland Canada Italy United States Chile Slovenia Poland  3 6 4 2 5 1 7 15 8 10 11 14 13 9 16 12 19 17 18  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19  1 3 2 4 5 6 7 9 10 13 19 12 8 11 16 14 15 17 18  CV Rank 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19  5.671 5.654 5.666 5.684 5.666 5.717 5.636 5.546 5.632 5.597 5.595 5.569 5.573 5.628 5.499 5.587 5.355 5.446 5.415  0.150 0.162 0.167 0.171 0.181 0.184 0.190 0.204 0.221 0.240 0.262 0.266 0.269 0.274 0.285 0.289 0.302 0.314 0.333  Table 1: Summary Statistics - IALS Log-Scores  83  0.134 0.151 0.149 0.156 0.162 0.168 0.171 0.192 0.199 0.222 0.318 0.222 0.189 0.216 0.256 0.227 0.230 0.260 0.312  WageDispi St Dev Res Rank  O NETi Contacti Rank  Lowest Substiti Railroad rolling stock Ship and boat building Aircraft, aerospace products and parts Engines, turbines, and power trans. equipment Nonferrous metals, exc. aluminum  1 2 3 4 5  60 40 28 42 59  Highest Substiti Leather tanning and products, except footwear Seafood and other miscellaneous foods, n.e.c. Apparel accessories and other apparel Bakeries Cut and sew apparel  59 60 61 62 63  21 31 2 32 1  Table 2: Substitutability Rankings  84  WageDispi St DevRes  StDev Mean StDev Mean  1  St Dev Res  0.8497 0.000 -0.2061 0.1052 -0.1414 0.2689 -0.2414 0.0567 -0.1606 0.2087  Contacti Communici Impacti Teamworki  Contacti  O NETi Communici Impacti  Teamworki  1 -0.1756 0.1688 -0.0755 0.5565 -0.097 0.4496 -0.1666 0.1919  1 0.5818 0.000 0.668 0.000 0.7943 0.000  1 0.7467 0.000 0.614 0.000  1 0.7254 0.000  p-values in italics Table 3: Correlations of Substitutability Proxies  85  1  (1)  (2)  (3)  (4)  (5)  (6)  St Dev  95-5 IPR  Gini MD  St Dev  95-5 IPR  Gini MD  0.017** (0.003)  0.019** (0.004)  0.016** (0.004)  0.017** (0.003)  0.018** (0.004)  0.014** (0.004)  Trade Barriers  No  No  No  Yes  Yes  Yes  Exporter FE Importer FE Industry FE Importer-Industry FE  Yes Yes Yes No  Yes Yes Yes No  Yes Yes Yes No  Yes No No Yes  Yes No No Yes  Yes No No Yes  58124 0.54  58124 0.54  58124 0.54  58124 0.70  58124 0.70  58124 0.70  Measure of Dispersion  WageDispi  Observations R-squared  SkillDispH  The dependent variable is the natural logarithm of exports from country H to country F in industry i. Standardized beta coef cients are reported. † , * and ** indicate the coef cient is signi cant at the 10%, 5% and 1% levels. Bootstrap standard errors clustered by importerexporter pair in parenthesis (50 replications).  Table 4: Estimates Using Residual Wage Dispersion Rankings and Residual Score Dispersion  86  (1) O NETi = Teamworki  (2) O NETi = Impacti  (3) O NETi = Communici  (4) O NETi = Contacti  -0.016** (0.004)  -0.016** (0.004)  -0.016** (0.005)  -0.014** (0.003)  Trade Barriers  Yes  Yes  Yes  Yes  Exporter FE Imp-Ind FE  Yes Yes  Yes Yes  Yes Yes  Yes Yes  Observations R-squared  58124 0.70  58124 0.70  58124 0.70  58124 0.70  Measure of Complementarity  O NETi SkillDispH  Bootstrap standard errors clustered by importer-exporter pair in parenthesis (50 replications).  Table 5: Estimates using O*NET Rankings and Residual Score Dispersion (St Dev)  87  WageDispi KIntensi  SkillDispH  (2)  (3)  (4)  (5)  (6)  Baseline (St Dev)  HMR Selection  Heckscher Ohlin  Institution Controls  Top Coding  Without US  0.017** (0.003)  0.016** (0.004)  0.020** (0.005) 0.028** (0.008) 0.034** (0.005)  0.013** (0.005)  0.023** (0.005)  0.017** (0.003)  KEndowH  SkillIntensi  SkillEndowH  WageDispi  JudicQualH  WageDispi  LaborRigidH  TopCodei  (1)  -0.008* (0.004) -0.007† (0.004)  SkillDispH  -0.015* (0.007)  Trade Barriers  Yes  Yes  Yes  Yes  Yes  Yes  Exporter FE Importer-Industry FE  Yes Yes  Yes Yes  Yes Yes  Yes Yes  Yes Yes  Yes Yes  58124 0.69  52455 0.69  41301 0.73  51166 0.70  52455 0.70  48129 0.68  Observations R-squared  The dependent variable is the natural logarithm of exports from country H to country F in industry i. Standardized beta coef cients are reported. † , * and ** indicate the coef cient is signi cant at the 10%, 5% and 1% levels. Bootstrap standard errors clustered by importer-exporter pair in parenthesis (50 replications). Column (6) is the same speci cation of column (2) excluding the observations involving US as exporter. The regression includes a polynomial in the probability to export, obtained from the rst stage, which is signi cant and we do not report.  Table 6: Estimates - Selection and Other Controls  88  WageDispi  SkillDispH  RegCostsH  RegCostsF  RegDaysH  RegDaysF  RegProcH  RegProcF  KIntensi  (2)  (3)  (4)  (5)  HMR Selection  Heckscher Ohlin  Institution Controls  Top Coding  Without US  0.004** (0.001) 0.008** (0.003) 0.007* (0.003) 0.008** (0.003)  0.010** (0.001) 0.001 (0.004) 0.009† (0.005) 0.021** (0.005) 0.002† (0.001) -0.004* (0.001)  0.005** (0.001) 0.007* (0.003) 0.006 (0.004) 0.009** (0.003)  0.009** (0.001) 0.008** (0.003) 0.007* (0.003) 0.008** (0.003)  0.004** (0.001) 0.004† (0.002) 0.006* (0.002) 0.008** (0.003)  KEndowH  SkillIntensi  SkillEndowH  WageDispi  JudicQualH  WageDispi  LaborRigidH  TopCodei  (1)  0.002† (0.001) -0.003* (0.001)  SkillDispH  -0.012** (0.002)  Trade Barriers  Yes  Yes  Yes  Yes  Yes  Exporter FE Importer-Industry FE  Yes Yes  Yes Yes  Yes Yes  Yes Yes  Yes Yes  132867 0.58  94794 0.59  125874 0.58  132867 0.58  124740 0.58  Observations R-squared  Columns (1)-(5) report the rst stage estimation results corresponding to Columns (2)-(6) of Table 6. The dependent variable equals one if exports from country H to country F in industry i are positive, zero otherwise. Standardized coef cients reported. † , * and ** indicate statistical signi cance at 10%, 5% and 1%. Bootstrap s.e. clustered by importer-exporter pair in parenthesis (50 replications).  Table 7: Estimates - First Stages  89  Variable  Obs  Mean  Std. Dev  Min  Max  Exports dummy Exports volume (XHFi ) Language Legal Religion Land Border Currency Union Distance FTA Colonial Ties Gatt / WTO Island Landlock RegProcF RegDaysF RegCostsF RegProcH RegDaysH RegCostsH SkillEndowH JudicQualH LaborRigidH KEndowH SkillIntensi KIntensi TopCodei  173565 58124 2755 2755 2755 2755 2755 2755 2755 2755 2755 2755 2755 112 112 112 19 19 19 14 18 19 14 61 61 63  0.335 7.866 0.193 0.217 0.196 0.019 0.002 4.136 0.017 0.022 1.489 0.291 0.309 9.679 49.402 90.065 5.947 23.842 7.874 -3.435 0.832 0.473 -0.530 0.381 0.859 0.009  0.472 2.204 0.395 0.412 0.257 0.135 0.047 0.806 0.131 0.146 0.578 0.494 0.509 3.491 38.593 165.785 2.818 16.433 7.190 0.402 0.115 0.155 0.662 0.116 0.464 0.005  0 0 0 0 0 0 0 0.882 0 0 0 0 0 2 2 0 2 3 0 -4.522 0.615 0.205 -1.377 0.166 0.235 0.004  1 17.906 1 1 0.973 1 1 5.661 1 1 2 2 2 19 203 1268.4 10 61 22.9 -2.957 0.972 0.667 0.925 0.757 2.535 0.030  Table 8: Additional Variables  90  Sales (thousands of pesos) Labor Investment K (thousands of pesos) Skilled labor (share) Foreign Ownership (dummy) R&D (thousands of pesos) Observations  Non-exporters  Exporters  10652 26093 109 204 428 2182 0.043 0.077 0.052 0.222 17.30 118.27 1565  56221 157565 377 650 3501 34637 0.075 0.088 0.293 0.455 133.44 1069.63 1771  Pooled data for 1992, 1996, 1998, 2001  Table 9: Descriptive Statistics - Mean and S.D. (in italics)  91  Geographical distribution of rms and exporters - Pooled data  Province  Population in 2001  Buenos Aires Cordoba Santa Fe Mendoza Tucuman Entre Rios Salta Chaco Misiones Corrientes Santiago San Juan Rio Negro Formosa Neuquen Chubut San Luis Catamarca La Pampa La Rioja Tierra del Fuego ARGENTINA  Firms Number % in total  16,485,462 3,052,747 2,975,970 1,573,671 1,331,923 1,152,090 1,065,291 978,956 961,274 926,989 795,661 617,478 549,204 489,276 471,825 408,191 367,104 330,996 298,772 287,924 100,313 35,221,117  2,357 216 291 70 47 31 24 8 45 12 12 35 12 4 7 29 96 20 12 4 7 3,339  70.59 6.47 8.72 2.10 1.41 0.93 0.72 0.24 1.35 0.36 0.36 1.05 0.36 0.12 0.21 0.87 2.88 0.60 0.36 0.12 0.21 100.00  Number 1,364 79 143 43 13 13 5 4 28 3 0 10 2 0 0 14 41 2 2 0 5 1,771  Pooled data for 1992, 1996, 1998, 2001  Table 10: Geographical Distribution of Firms and Exporters  92  Exporters % in prov % in total 58 37 49 61 28 42 21 50 62 25 0 29 17 0 0 48 43 10 17 0 71 53  77.02 4.46 8.07 2.43 0.73 0.73 0.28 0.23 1.58 0.17 0.00 0.56 0.11 0.00 0.00 0.79 2.32 0.11 0.11 0.00 0.28 100.00  Fraction of 1992 plants with the same export status (%)  Actual Year 1996 1998 2001  (1) Exporters 0.97 0.82 0.84  (2) Non-Exporters 0.69 0.70 0.68  Expected (3) (4) Exporters Non-Exporters 0.97 0.69 0.76 0.60 0.72 0.53  Table 11: Persistence in Export Decisions  93  OLS estimation - Equations 3.3 and 3.4  (1)  (2)  0.338 (0.023)**  0.747 (0.022)** -0.095 (0.040)* 0.129 (0.032)**  Time dummies  Yes  Yes  Observations R-squared  3336 0.07  2444 0.52  Export Status (yigt  1)  Export Status * Exporter Concentration Exporter Concentration (Y(  i)gt )  The dependent variable (yigt ) is a dummy that equals 1 if rm i in group g exports in period t . Robust s.e. in parentheses. * and ** indicate signi cance at 5% and 1%, respectively.  Table 12: Correlations between Individual and Group Behaviour  94  Blundell and Bond (1998) estimator - Equation 3.9. (continues on next page) Dependent Var: Export decision yigt  (1)  (2)  (3)  (4)  (5)  (6)  Entry Cost Spillovers  yigt  1  yigt  Y(  1  i)gt  -0.294  -0.373  -0.416  -0.064  (0.189)  (0.201)†  (0.207)*  (0.280)  Output/workerg  -0.075 (0.056)  yigt  1  Investment Kg  -0.006 (0.008)  yigt  1  Skilledg  yigt  1  R&Dg  2.602 (1.810) -0.027 (0.281)  yigt  1  Foreigng  1.130 (0.490)*  yigt  1  Sizeg  -0.232 (0.096)*  Productivity Spillovers  Y(  i)gt  -0.006  0.053  0.158  0.235  0.279  0.174  (0.100)  (0.112)  (0.138)  (0.154)  (0.172)  (0.199)  Output/workerg  0.007 (0.006)  Investment Kg  -1.675 (1.462)  Skilledg  0.085 (0.233)  R&Dg  -0.022 (0.039)  Foreigng  -0.415 (0.281)  Sizeg  0.056 (0.065)  95  Blundell and Bond (1998) estimator - Equation 3.9. (continued) Dependent Var: Export decision yigt  (1)  (2)  (3)  (4)  (5)  (6)  Firm-level controls  yigt  1  Output/worker Size Foreign Investment K Skilled R&D  Observations  0.380  0.414  0.525  0.603  0.627  0.656  (0.042)**  (0.044)**  (0.107)**  (0.114)**  (0.117)**  (0.222)**  0.031  0.062  0.027  0.053  0.050  0.035  (0.015)*  (0.029)*  (0.015)†  (0.029)†  (0.030)†  (0.030)  0.119  0.062  0.117  0.059  0.058  0.076  (0.020)**  (0.026)*  (0.020)**  (0.026)*  (0.026)*  (0.027)**  0.036  0.104  0.044  0.128  0.136  0.163  (0.045)  (0.056)†  (0.045)  (0.056)*  (0.057)*  (0.059)**  -0.000  0.001  -0.000  0.001  0.001  0.001  (0.000)  (0.001)  (0.000)  (0.001)  (0.001)  (0.001)  0.323  0.046  0.339  0.079  0.102  0.092  (0.203)  (0.211)  (0.205)†  (0.206)  (0.208)  (0.220)  -0.005  0.003  -0.004  0.006  0.008  0.009  (0.002)*  (0.031)  (0.002)†  (0.032)  (0.033)  (0.030)  2440  2440  2440  2440  2440  2440  IV for rm-level controls  No  Yes  No  Yes  Yes  Yes  Location controls  No  No  No  No  Yes  Yes  Robust standard errors in parentheses, ** p<0.01, * p<0.05, † p<0.1. All regressions include rm xed-effects, time dummies, export prices and total exports in ISIC sector. Group variables are de ned by province and industry -at the 3-digit ISIC level.  Table 13: Dynamic Panel Data Estimation - Main Results  96  Blundell and Bond (1998) estimator - Equation 3.9. (continues on next page) Dependent Var: Export decision yigt (1)  (2)  (3)  (4)  (5)  (6)  (7)  -0.189  -0.045  -0.422  -0.457  0.060  0.128  0.020  (0.279)  (0.224)  (0.255)†  (0.241)†  (0.335)  (0.305)  (0.278)  -0.073  -0.094  0.037  0.029  -0.016  -0.020  -0.056  (0.055)  (0.053)†  (0.036)  (0.035)  (0.051)  (0.050)  (0.055)  Entry Cost Spillovers  yigt  1 *Ygt  yigt  1  yigt  1  Output / workerg Investment Kg  yigt  1  yigt  1 R&Dg  yigt  1  yigt yigt  1 1  Skilledg  Foreigng Sizeg  -0.006  0.000  -0.013  -0.014  -0.003  -0.003  -0.004  (0.007)  (0.008)  (0.008)†  (0.007)†  (0.007)  (0.007)  (0.008)  4.323  1.751  3.607  3.552  4.816  4.736  2.941  (2.409)†  (1.422)  (2.100)†  (2.003)†  (1.818)**  (1.619)**  (1.924)  0.739  -0.016  0.090  0.034  0.172  -0.019  -0.078  (0.518)  (0.159)  (0.336)  (0.299)  (0.331)  (0.288)  (0.285)  0.968  0.946  0.716  0.678  0.946  (0.454)*  (0.394)*  (0.546)  (0.478)  (0.495)†  -0.186  -0.249  -0.163  -0.161  -0.560  (0.093)*  (0.091)**  (0.092)†  (0.089)†  (0.222)*  Size  -0.467 (0.198)*  yigt  1  Sizeg  Size  0.077 (0.044)†  Productivity Spillovers  Ygt Output / workerg Investment Kg Skilledg R&Dg Foreigng Sizeg  0.371  0.145  0.244  0.445  0.006  0.028  0.126  (0.184)*  (0.163)  (0.170)  (0.212)*  (0.260)  (0.230)  (0.200)  -0.014  0.011  -0.057  -0.099  -0.013  -0.015  -0.008  (0.044)  (0.034)  (0.026)*  (0.034)**  (0.037)  (0.037)  (0.040)  0.004  0.002  0.010  0.011  0.003  0.003  0.005  (0.006)  (0.007)  (0.006)†  (0.006)†  (0.005)  (0.005)  (0.006)  -2.770  -0.464  -2.580  -2.401  -2.888  -3.143  -2.010  (1.758)  (1.090)  (1.537)†  (1.562)  (1.409)*  (1.352)*  (1.493)  -0.596  0.002  -0.002  0.047  -0.073  0.084  0.146  (0.413)  (0.145)  (0.266)  (0.245)  (0.276)  (0.241)  (0.239)  -0.309  -0.644  -0.236  -0.094  0.096  -0.393  (0.265)  (0.235)**  (0.298)  (0.286)  (0.186)  (0.285)  0.054  0.072  -0.103  0.070  0.055  0.206  (0.061)  (0.058)†  (0.064)  (0.067)  (0.164)  (0.069) Sizeg * Size  -0.034  97  (0.033)  Blundell and Bond (1998) estimator - Equation 3.9. (continued) Dependent Var: Export decision yigt  (1)  (2)  (3)  (4)  (5)  (6)  (7)  0.415  0.635  0.600  0.583  0.729  0.686  2.805  (0.318)  (0.173)**  (0.226)**  (0.226)*  (0.230)**  (0.222)**  (0.887)**  0.051  0.045  0.037  0.031  0.053  0.046  0.023  (0.032)  (0.030)  (0.031)  (0.031)  (0.033)  (0.032)  (0.030)  Firm-level controls  yigt  1  Output / worker Size Foreign Investment K Skilled R&D Observations  0.078  0.053  0.070  0.077  0.081  0.086  0.275  (0.027)**  (0.029)†  (0.027)**  (0.027)**  (0.025)**  (0.025)**  (0.152)  0.001  0.001  0.001  0.001  0.001  0.001  0.001  (0.001)  (0.001)  (0.001)  (0.001)  (0.001)  (0.001)  (0.001)  0.007  0.274  0.117  0.076  0.023  0.029  -0.009  (0.227)  (0.216)  (0.234)  (0.237)  (0.243)  (0.248)  (0.253)  0.185  0.256  0.154  0.157  0.165  0.145  0.204  (0.059)**  (0.076)**  (0.062)*  (0.060)**  (0.058)**  (0.056)**  (0.062)**  -0.036  0.023  0.015  0.007  0.013  0.012  -0.012  (0.042)  (0.030)  (0.030)  (0.030)  (0.031)  (0.030)  (0.028)  2440  2421  2440  2440  2440  2440  2440  IV for rm-level controls  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Location controls  Yes  Yes  Yes  Yes  Yes  Yes  Yes  Robust standard errors in parentheses, ** p<0.01, * p<0.05, † p<0.1. All regressions include rm xed effects, time, dummies, export prices and total exports in ISIC sector. Group variables are de ned at the 3-digit ISIC level. In columns(1) and (2), ISIC industries are de ned at 2 and 3 digits of aggregation, respectively. Columns (3) to (6) examine the sensitivity of the results column (7) of Table 13 by excluding average rm size and proportion of foreign rms at the group level. In column (7), entry time costs and spillovers are allowed to depend on rm size.  Table 14: Dynamic Panel Data Estimation - Sensitivity Analysis  98  (1)  (2)  (3)  (4)  (5)  (6)  St Dev Mean  95-5 IPR Mean  Gini RMD  St Dev Mean  95-5 IPR Mean  Gini RMD  0.013** (0.004)  0.009* (0.004)  0.010* (0.004)  0.015** (0.004)  0.010* (0.004)  0.010* (0.004)  Trade Barriers  No  No  No  Yes  Yes  Yes  Exporter FE Importer FE Industry FE Importer-Industry FE  Yes Yes Yes No  Yes Yes Yes No  Yes Yes Yes No  Yes No No Yes  Yes No No Yes  Yes No No Yes  58124 0.54  58124 0.54  58124 0.54  58124 0.70  58124 0.69  58124 0.69  Measure of Dispersion  WageDispi  SkillDispH  Observations R-squared  The dependent variable is the natural logarithm of exports from country H to country F in industry i. Standardized beta coef cients are reported. † , * and ** indicate the coef cient is signi cant at the 10%, 5% and 1% levels. Standard errors clustered by importer-exporter pair in parenthesis.  Table 15: Normalized Raw Scores and Wage Rankings  99  Measure of Dispersion  WageDispi  SkillDispH  (1)  (2)  (3)  (4)  (5)  (6)  St Dev  95-5 IPR  Gini MD  St Dev  95-5 IPR  Gini RMD  0.024** (0.006)  0.013* (0.006)  0.022** (0.008)  0.024** (0.006)  0.013* (0.006)  0.022** (0.008)  WageMeani  SkillMeanH  0.145** (0.007)  0.156** (0.007)  0.164** (0.009)  0.145** (0.007)  0.156** (0.007)  0.164** (0.009)  WageMeani  SkillDispH  0.075** (0.007)  0.090** (0.006)  0.093** (0.008)  0.753** (0.007)  0.090** (0.006)  0.093** (0.008)  WageDispi  SkillMeanH  0.023** (0.008)  0.011 (0.008)  0.025** (0.009)  0.023** (0.008)  0.011 (0.008)  0.025** (0.009)  Trade Barriers  Yes  Yes  Yes  Yes  Yes  Yes  Exporter FE Importer FE Industry FE Importer-Industry FE  Yes No No Yes  Yes No No Yes  Yes No No Yes  Yes No No Yes  Yes No No Yes  Yes No No Yes  58124 0.70  58124 0.70  58124 0.70  58124 0.70  58124 0.70  58124 0.70  Observations R-squared  The dependent variable is the natural logarithm of exports from country H to country F in industry i. Standardized beta coef cients are reported. † , * and ** indicate the coef cient is signi cant at the 10%, 5% and 1% levels. Standard errors clustered by importer-exporter pair in parenthesis.  Table 16: Non-Normalized Interactions  100  Figures  101  300  SWE  NOR DNK  FIN CZE  280  GER NLD  CAN  BEL  Mean IALS score 240 260  NZL CHE  USA UK  IRL HUN ITA SVN  220  POL  CHL  40  50 60 Standard Deviation IALS scores  Figure 1: Mean and Standard Deviation - IALS scores  102  70  20 18  pr tro  /co  Canada S.D. 8 10 12  14  16  pe  clo  thi ng  /le  ath sc  er  pr  ma  nu  fac  tur  int  ing  an  dr  ela  0  2  co  0  2  mp ute for/o edle /bce trov /ntoi cba c  4  co  od  utce txstil e  tra ns mi lls  po  od  em i ca lm an  pr  6  od  prno odnu -cmt  ufa  etfaa lblicri cma itneed ram l et  pli  eq  uip  me n  an ce ma ch ine  ry  ym eta lm  an  ufa  ct  t  ma nu  fac  tur  e  al  Intercept 3.82 (2.16) Slope 0.60 (0.20)  ctu rin g  8  rt  pa  ted  wo  ing  ch  pr  pe /pr r pla oduc man sti ufa t cs ctu fur an rin nit dr g ur ub ea be nd r re lat ele ed ce qu ip/ ap  4  6  mi  al  im ar  10 US S.D.  12  14  16  18  20  ®  Figure 2: Industry Rankings by Standard Deviation of Residual Wages  103  The number of exporters and non-exporters each year are represented by the bar graph (left-hand axis). 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Our rst approach yields a general result based on restrictions on the degree of complementarity and on the upper bound of the support of the skill distribution.1 Proposition A-1 Property 1 holds, i.e. a country c0 with a more dispersed skill distribution than country c has a comparative advantage in sectors with lower complementarity (higher λ ) under the following suf cient conditions: (i) Skill is bounded from above by amax (ii) The degree of complementarity is low enough: λ > λ where λ is de ned by the following condition log amax =  2λ 1  1 λ λ  Proof. By de nition of log-supermodularity we need to prove that, if g (a; c0 ) 1 Imposing  an upper bound on a is realistic because it means we do not admit the existence of in nitely productive workers.  114  is a mean-preserving spread of g (a; c) then: ∂ log A (λ ; c) ∂λ  ∂ log A (λ ; c0 ) : ∂λ  The partial derivative has the following expression: ∂ log A (λ ; c) 1 = ∂λ λ  R λ a log a g(a; c)da R  aλ g(a; c)da  1 λ  log 2  Z  aλ g(a; c)da  (A-1)  A mean-preserving spread of g (a; c) increases the second term of the right-hand side of (A-1) by de nition, since aλ is a concave function. A suf cient condition for the rst term of (A-1) to increase with a mean-preserving spread in g (a; c) is that k (a) = aλ log a is a convex function which is veri ed if its second derivative 1 with respect to a is positive for every value of a. i.e. log a < (12λ λ )λ . Since the right-hand side of this inequality is continuous and increasing in λ , it is equal to 1 zero for λ = 12 and limλ !1 (12λ λ )λ = ∞ then, if a is bounded above by amax , then ;c) 2λ 1 . If λ > λ then ∂ log∂A(λ λ (1 λ )λ increases with a mean preserving spread of g (a; c). In our second approach to studying Property 1 we relax the conditions on complementarity at the cost of concentrating on speci c distributions. We can only consider continuous distributions that are characterized by at least two parameters (in order to be able to consider mean-preserving increases in dispersion) and are de ned on a positive support.  there exists a value λ < 1 such that log amax =  Proposition A-2 If skills are distributed according to a Pareto or Log-normal distribution then, if country c and c0 are characterized by skill distributions g (a; c) and g (a; c0 ) such that g (a; c0 ) has equal mean and higher variance than g (a; c) and if λ < λ 0 then Property 1 holds, i.e. country c0 has a comparative advantage in λ 0 . (i) Pareto Distribution - Under the assumption that skills follow a Pareto distribution with mean µ and standard deviation σ , A takes the following expres-  115  sion:2 A=  µ2 + σ 2  σ µ  p  !1 p λ σ + µ2 + σ 2 p : σ + µ2 + σ 2 λ σ  µ2 + σ 2  Since A is twice differentiable in σ and λ , the result in Proposition 1.3 is 2 A equivalent to A being log-supermodular in λ and σ , that is ∂∂ σlog ∂ λ > 0. The expression for the cross partial derivative is the following: p σ µ2 + σ 2 σ ∂ 2 log A h i =p p ∂σ∂λ µ 2 + σ 2 σ (1 λ ) + µ 2 + σ 2  (A-2)  and λ < 1 so A is log-supermodular in λ and σ .  (ii) Log-Normal Distribution - If the distribution of skills a is lognormal on the support [0; ∞] with mean µ and standard deviation σ then A takes the following form: A=e  1 λ 2  log µ  log  σ2 +1 µ2  It is easy to show that under this distribution, A is log-supermodular since the following expression is always positive: ∂ 2 log A σ = 2 ∂σ∂λ µ +σ2 2 The  Pareto distribution is characterized by a shape parameter k and location parameter amin , i.e. amin k with amin > 0 and k > 2. We the cumulative distribution of ability is given by G (a) = 1 a could have written A as a function of those parameters: A = amin  1 λ  k k  λ  Since we are interested in a mean-preserving increase in variance, we express the A as a function of µ and σ , which are related to shape and location parameters according to the following equations: p µ2 + σ 2 σ µ2 + σ 2 amin = µ p 2 σ + µ +σ2 k = σ  116  While Proposition A-2 establishes an analytical result, we have also numerically computed the A's for the following distributions: uniform, triangular, gamma, beta and inverse Gaussian. For all these distributions, and for a wide range of parameters, we cannot nd a violation of the ranking in (1.3).3  A.2  Output, Prices and Revenues  In this section we provide details about the solution to the rm problem. Revenues (1.4) First, we show how to derive the expression for total revenues in (1.4). Total revenues of a rm in Home are given by: σ 1  σ 1  σ σ rH = BH yHH + BF yHF τ  1 σ σ  (A-3)  For a pro t-maximizing rm marginal revenues have to be equal across markets. Rearranging the equality of marginal revenue condition leads to the following: yHH = yHF  BH BF  σ  τσ  1  (A-4)  From (A-4) yHH can be expressed as a function of yHF and replaced in (A-3) to nd: 1 1 σ (A-5) rH = BF yHFσ τ σ (yHH + yHF ) From (A-5) and its analogous for yHH we can nd the two following equations: yHH yHF  = rH σ BσH (yHH + yHF )σ =  rH BσF σ  (yHH + yHF ) τ  3A  σ  (A-6) 1 σ  (A-7)  violation of the ranking can be engineered using a result by Ross (1981). The intuition is the following. Ross (1981) shows that, if we adopt the Arrow-Debreu de nition of risk aversion, then, starting from a given lottery, we might nd the counterintuitive result that a more risk-averse individual is willing to pay less than a less risk-averse individual to avoid an an increase in risk in the sense of a mean-preserving spread. We can view our A as the certainty equivalent of lottery g for an individual with Bernoulli utility u (a) = aλ , 0 < λ < 1. Individuals with lower λ are more risk averse in the Arrow-Pratt sense. In our case we can show, using the example proposed by Ross (1981) that, with a mean-preserving spread, the certainty equivalent of a more risk averse individual drops proportionately by less than for a less risk averse individual. Details are available from the authors.  117  Adding up (A-6) and (A-7) and rearranging them leads to the expression for revenues reported in (1.4): rH = (yHH + yHF )  σ 1 σ  BσH + BσF τ 1  σ  1 σ  Output and Prices The rst order condition of problem (1.6) can be written as a function of revenues rH as follows: σ 1 s rH = hH σλb This rst order condition, together with the zero pro t condition derived from free entry, implies: srH bhH f = 0 delivers total revenues and employment: rH  =  hH  =  f σλ s (σ λ σ + 1) f (σ 1) b (σ λ σ + 1)  Given the production function, the expression for total output follows: f (σ 1) yH = A (λ ; H) b (σ λ σ + 1)  1 λ  (A-8)  Next, we determine how output is divided across the domestic and export market. We employ (A-6) and (A-7) and their analogous for the Foreign rm to nd the relative output of rms selling in the same market: yHH yFH  =  yFF yHF  =  rH σ (yHH + yHF )σ rF σ (yFF + yFH )σ τ 1 rF σ (yFF + yFH )σ rH σ (yHH + yHF )σ τ 1  σ  σ  (A-9) (A-10)  The expressions above can be simpli ed using the fact that total revenues are constant in a given sector: rH = rF = r. Together with (A-8) and its foreign equivalent, (A-9) and (A-10) deliver the amount of output sold by a Foreign and a Home rm in every market. The amounts of output sold in the two markets by a Home rm 118  are given by:  where ρ = τ 1  σ,  yHH  =  yHF  =  " # A (λ ; H) σ 1 φ A (λ ; H) 1 ρ 1 ρ2 A (λ ; F) " # A (λ ; H) σ 1 φ ρA (λ ; H) ρ 1 ρ2 A (λ ; F)  (A-11) (A-12)  while the corresponding Foreign rm expressions are: " # φ A (λ ; F) A (λ ; H) 1 σ yFF = 1 ρ 1 ρ2 A (λ ; F) " # φ ρA (λ ; F) A (λ ; F) σ 1 yFH = ρ 1 ρ2 A (λ ; H)  (A-13) (A-14)  Finally we derive relative revenues for a Home and a Foreign rm in a given market σ 1 σ  1 σ  (1.9) by expressing it rst as a function of relative output rrHF = yyHF τ σ , and FF FF then replacing the expressions for yHF and yFF . Intuitively, relative revenues increase in relative productivity, as predicted by comparative advantage. As standard with iso-elastic demand, the producer price is constant across markets and for a Home rm is equal to pH = φ Aγ H where γ (λ ) = f σσ λλ +σσ +11 . The consumer price in the export market is the producer price multiplied by τ; i.e. pHF = φγτ AH .  A.3  Mass of Firms  Previously we derived the amount of output sold by each rm in the domestic and export market. In order to determine trade ows we need to calculate the equilibrium mass of rms for country c and sector λ , Mc (λ ). Having determined the revenues of a rm in each market, the mass of rms in each country has to be such that, total expenditure on good λ in a given country is equal to total revenues accruing to all rms operating in that market. The two equations below express  119  these equilibrium conditions for sector λ : α (λ ) LH  = MH (λ ) rHH (λ ) + MF (λ ) rFH (λ )  (A-15)  α (λ ) LF  = MF (λ ) rFF (λ ) + MH (λ ) rHF (λ )  (A-16)  It is convenient to rewrite conditions (A-15) and (A-16) as a function of output, rather than of revenues: αLH αLF  γ γ yHH + MF yFH ; φ A (λ ; H) φ A (λ ; F) γ γ = MF yFF + MH yHF : φ A (λ ; F) φ A (λ ; H) = MH  The solution to this linear system is given by the following expressions for MH and MF : MH MF  αφ (LH yFF LF yFH ) ; γ (yFF yHH yHF yFH ) αφ (LF yHH LH yHF ) = A (λ ; F) : γ (yFF yHH yHF yFH )  = A (λ ; H)  (A-17) (A-18)  First, we show that the denominator of MH and MF is always positive. De ne ;H) Home productivity advantage z (λ ) = A(λ A(λ ;F) . The denominator is positive if and  > yyHF , a condition we can rewrite as zσ ρ1 > zσ ρ and that is always only if yyHH FH FF satis ed since ρ < 1. We remark that, similarly to other models of monopolistic competition with trade costs (Helpman and Krugman, 1985), the presence of a home-market effect requires that we restrict the degree of asymmetry in country sizes to prevent all rms from locating in one country. De ne relative population in Home as η LLHF . The mass of Home rms MH is positive if and only if LH yFF LF yFH > 0. This condition places a lower bound on the relative population, since MH > 0 if and only if: ρ zσ1 1 ρ η> = η low (A-19) 1 zσρ 1 Equivalently, MF is positive if and only if LF yHH  120  LH yHF > 0, a condition that  places an upper bound on the relative population η, i.e. MF > 0 if and only if: η<  1 ρzσ 1 = η up ρ (zσ 1 ρ)  (A-20)  Both η low and η up are positive under the condition that we imposed in order to guarantee that a positive amount of output is produced for every market: ρ < zσ 1 < ρ1 . We impose throughout the restrictions that η low < η < η up . If the condition is violated for some industries, we expect to observe no production and no exports.4 If the condition is satis ed, then proposition 1 establishes a link between comparative advantage and equilibrium entry.  A.4  Proof of Proposition 1  H We de ne the mass of Home relative to Foreign rms in sector λ as m (λ ) M MF . We investigate how m changes with z, assuming that we are operating in the parameter space where η low < η < η up . We rewrite the relative mass of rms, using (A-17), (A-18), the expressions for Home rm outputs, (A-11) and (A-12), and the corresponding expressions for the Foreign rm:  m=  z1 zσ  (1 + η) ρ η + ρ2 1 (1 + η) ρ (1 + ηρ 2 ) σ  The rst derivative of m with respect to z takes the following form: ∂m 1 = σ +2 (σ ∂z z  1) (1 + η)  2z1+σ (1 + η) ρ + z2σ η + ρ 2 + z2 1 + ηρ 2 (ρzσ  1  ηρ 2 + ηρzσ  1  1)2  This derivative is positive if the numerator is positive and the numerator can be divided in two parts, which we show are both positive. The rst part, denoted by 4 As  equations (A-19) and (A-20) establish, the conditions for a positive mass of rms depend on size, but also on comparative advantage. If a country is relatively more productive it can afford to be smaller in size and still have a positive mass of rms. In this sense our model also predicts an extensive margin of trade (whether we observe or not trade between two countries) based on comparative advantage, albeit a very stark one. Differently from models with heterogeneous rms, e.g. Helpman et al. (2008c), in this setup the assumption of identical rms implies that either rms exist and export or they do neither.  121  ψ 1 is:  ψ 1 = z1+σ (1 + η) ρ + z2σ η + ρ 2 ;  while the second part denoted by ψ 2 is: ψ 2 = hz1+σ (1 + η) ρ + z2 1 + ηρ 2 : It is straightforward to show that ψ 1 > 0 if and only if η > η low and that ψ 2 > 0 if and only if η < η up , conditions we have imposed throughout.  A.5  Proof of Proposition 2  The result follows directly since we have proven that both components of relative MF (λ ) FH (λ ) sales (1.10), relative revenues per rm rrHH (λ ) and relative mass of rms MH (λ ) are  A(λ ;F) increasing in relative productivity A(λ ;H) (see (1.9) and Proposition 1) and relative productivity depends the degree of complementarity λ (proxied by the dispersion of wages according to Proposition 4) and the dispersion of skills according to the discussion in Section 1.3.  A.6  Proof of Proposition 3  Since the derivation is analogous to the two-country case we simply report the expression relative revenues:5 rHF = rGF  A (λ ; H) A (λ ; G)  σ 1  τ HF τ GF  1 σ  :  It follows that, if the relative mass of rms is non-decreasing in relative productivity, relative exports are higher in comparative advantage sectors, similarly to the two-country case in Proposition 5 Details  are available from the authors upon request.  122  A.7  Derivation of the Shapley Value  In this section we provide details on how to derive the share of revenues accruing to the rm and the wages paid to workers. Stole and Zwiebel (1996) have proved the equivalence of their bargaining solution to the Shapley value of the corresponding cooperative game not only for the case of identical workers, but also for the case of heterogeneous workers,6 therefore we calculate the Shapley value directly.7 The Shapley value of the rm is heuristically derived as its marginal contribution averaged over all possible orderings of employees and the rm itself. The case of heterogeneous employees is easy to handle under our assumption of a continuum of workers because no matter how the rm is ordered, it is preceded by a mass of workers whose skill distribution mirrors the overall skill distribution in the workers population, so the only variable we have to keep track of is the mass of workers preceding the rm, de ne it n, which varies from zero to h. As discussed in Acemoglu et al. (2007), since the rm is an essential input its marginal contribution is equal 1  to revenues when n workers are employed in production rH (n) = n λ A The Shapley value of the rm S f irm is therefore: S f irm =  Z h 1 0  h  1 λ  n A  σ 1 σ  σ 1 σ  ΓH .  ΓH dn = srH  where s is de ned by (1.5). As discussed in Acemoglu et al. (2007) the share of revenues accruing to the rm depends on the curvature of the revenue function, due to characteristics of the demand function (σ ) and the production function (λ ). In a similar fashion we calculate the Shapley value of a worker of skill a, by averaging its marginal contribution across all possible orderings. When a mass n of workers is employed, revenues of the rm are: r (n) = ΓH  Z  a n(a; c)da λ  a  σ 1 σλ  where n(a; c) = ng (a; c). The marginal contribution of a worker of skills a is given by the marginal revenue from an increase in the mass of workers of skill a, n (a; c), conditional on the rm being ordered before the worker (otherwise the marginal 6 See  their Theorems 8 and 9, p. 393.  7 The analogous of the Shapley value for a continuum of players is derived in Aumann and Shapley  (1974).  123  contribution is null): Z  σ 1 ∂ r (n) = ΓH ∂ n(a) σλ  a  ng(a)a ˜ da λ  σ 1 σλ  1  aλ  The Shapley value and wage of worker of skill a in industry λ is: 1 w(a; λ ) = h  Z h n ∂ r (n) o  h ∂ n(a)  dn = ΓH A (λ ; c)  σ 1 σλ σ  σ  σ 1 σ 1 h σλ 1+σλ  1 λ  a  Since the average wage also differs across sectors, we normalize wages by the ave λ) = erage wage in the sector E [w(a; λ )]. The normalized wage is denoted by w(a; w(a;λ ) E[w(a;λ )] and takes the following form: e λ) = w(a;  A.8  aλ E aλ  Proof of Proposition 4  We consider three measures of wage dispersion: (i) the Coef cient of Variation of wages w (a; λ ), directly related to the variance e λ ), Var (w(a; e λ )), which is given by: of the normalized wage w(a; e λ )) = Var (w(a;  E a2λ  E aλ  2  1;  (A-21)  (ii) the Gini Coef cient, de ned with respect to the Lorenz Curve for normalized wages at the sector level Λ (w; λ ), (iii) the Inter-Percentile Ratio IPRk j de ned as: IPRk j =  wk ; wj  where wk (w j ) is the wage of the worker at the kth ( jth ) percentile of the sectoral wage distribution and j < k. (i) Coef cient Of Variation 124  Since the variance of normalized wages is equal to the square of the coef cient of variation we prove the result for the former. We start by rewriting (A-21) in an explicit form, dropping the country index c to simplify notation: R 2λ a g˜ (a) da e λ )) = R Var (w(a; 2  aλ g˜ (a) da  1  (A-22)  The derivative of (A-22) with respect to λ is non-negative if an only if the following inequality is satis ed: Z ∞ 0  Z ∞ 0  a2λ log a g˜ (a) da a log a g˜ (a) da λ  Z ∞  Z  0  0 ∞  aλ g˜ (a) da  (A-23)  a2λ g˜ (a) da  (A-24)  The left-hand side of (A-23), which we denote by ΦL can be rewritten as: ΦL =  Z ∞Z ∞ 0  0  a2λ log a g˜ (a) bλ g˜ (b) dadb  We can divide the region of integration in two parts, delimited by the 45 degree line in the plane [0; ∞] [0; ∞]. It follows that ΦL can be rewritten as: ΦL =  Z ∞ Z a 0  0  0  a  Z ∞ Z ∞  bλ g˜ (b) db a2λ log a g˜ (a) da +  (A-25)  bλ g˜ (b) db a2λ log a g˜ (a) da  (A-26)  We change the order of integration in the second component of ΦL so that we can rewrite (A-25) it as: ΦL =  Z ∞ Z a 0  0  0  0  Z ∞ Z b  bλ g˜ (b) db a2λ log a g˜ (a) da +  (A-27)  a2λ log a g˜ (a) da bλ g˜ (b) db  (A-28)  Finally, a change of variable in the second component of (A-27) allows us to  125  express ΦL as: Z ∞ Z a  ΦL =  0  0  Z ∞ Z a 0  0  bλ g˜ (b) db a2λ log a g˜ (a) da + b2λ log b g˜ (b) db aλ g˜ (a) da  If the same decomposition is performed on the right-hand side of (A-23) we can rewrite the inequality as follows: Z ∞ Z a 0  0  aλ bλ  h  aλ  bλ (log a  which is always satis ed since aλ  i log b) g˜ (b) g˜ (a) db da  bλ (log a  log b)  0  0.  (ii) Gini Coef cient We proceed by deriving the Lorenz Curve for sectoral normalized wages and showing that increasing λ produces a downward shift in the curve at all points. This is a suf cient condition for the Gini coef cient to increase with an increase in λ . The Lorenz Curve Λ (w; λ ) of normalized wages in sector λ is given by the following expression: Rw λ a g˜ (a) da Λ (w; λ ) = R0∞ λ 0  a g˜ (a) da  ) is non-positive if and only if The rst derivative with respect to λ , ∂ Λ(w;λ ∂λ the following condition is satis ed 8w:  Z w 0  Z w 0  aλ log a g˜ (a) da aλ g˜ (a) da  Z ∞ 0  Z ∞ 0  bλ g˜ (b) db  bλ log b g˜ (b) da  The region of integration can be divided into two part on both sides of the  126  inequality, so that the inequality can be rewritten as follows:  Z  Z w Z w 0 w  0  Z  Z  0 ∞  w  bλ g˜ (b) db aλ log a g˜ (a) da  Z w Z w 0 w  0  Z  0 ∞  w  bλ g˜ (b) db aλ log a g˜ (a) da +  bλ log b g˜ (b) db aλ g˜ (a) da +  bλ log b g˜ (b) db aλ g˜ (a) da  Simplifying and factorizing leads to the following inequality: Z wZ ∞ 0  w  bλ aλ (log a  log b) g˜ (b) g˜ (a) dbda  0  which is always satis ed since the range of integration of a is [0; w] while the range of integration of b is [w; ∞]. (iii) Inter-Percentile Ratio It is straightforward to show that IPRk j increases with λ since for any percentile the ratio of wages is given by: IPRk j =  ak aj  λ  where ak (a j ) is the skill of the worker at the kth ( jth ) percentile.  127  Appendix B  Appendix to Chapter 2 B.1  Main Variables  B.1.1  Measuring Skill Dispersion  The IALS microdata used for this chapter was compiled by Statistics Canada using the original data sets collected between 1994 and 1998 in each of the participating countries. Tuijnman (2000) describes the three dimensions of literacy used to approximate skills. Prose literacy represents the knowledge and skills needed to understand and use information from texts including editorials, news stories, brochures and instruction manuals. Document literacy represents the knowledge and skills required to locate and use information contained in various formats, including job applications, payroll forms, transportation schedules, maps, tables and charts. Quantitative literacy represents the knowledge and skills required to apply arithmetic operations, either alone or sequentially, to numbers embedded in printed materials, such as balancing a chequebook, guring out a tip, completing an order form or determining the amount of interest on a loan from an advertisement. We employ the logarithm of scores (in conjunction with the log of wages) because the standard deviation of the logarithm of a random variable is scale invariant. When extracting residual scores in equation (2.6), using log-scores on the left-hand side is consistent with the common practice of obtaining residual wages from a regression of log-wages, as in equation (2.7). The results of the empirical analysis are qualitatively similar if we use levels instead of logs. 128  Only individuals participating in the labor market are included in the estimation of equation (2.7). These individuals were either: (i) employed or unemployed at some time in the 12 months previous to the survey or (ii) not searching for a job due to skill upgrading (school or work programs) or a temporary disability. The right-hand side vector XkH in equation (2.6) includes a number of observable individual characteristics. Education is among them: we include indicators for 7 levels of educational attainment as de ned by the International Standard Classication of Education (ISCED). The levels considered in IALS are: ISCED 0 Education preceding the rst level; ISCED 1 Education at the rst level; ISCED 2 Education at the second level, rst stage; ISCED 3 Education at the second level, second stage; ISCED 5 Education at the third level, rst stage (leads to an award not equivalent to a rst university degree); ISCED 6 Education at the third level, rst stage (leads to a rst university degree or equivalent; ISCED 7 Education at the third level, second stage (leads to a postgraduate university degree or equivalent); ISCED 9 Education not de nable by level. The vector XkH also includes 5 age intervals 16-25, 26-35, 36-45, 46-55 and 56-65, gender, immigrant status and participation in adult education or training programs 12 months prior to the survey date. The latter lters out the effect of skill upgrading on individual residual scores. As explained in section 2.5, this is an important issue for the identi cation of the effect of skill dispersion on trade ows as (unobserved) trade shocks might have an impact on aggregate skill dispersion by changing incentives for skill upgrading at the c d individual level. Residual scores εd kH are constructed as ε kH = log(skH ) XkH β H , c where β H is estimated by OLS. As a result of focusing on log-scores, the scale of measurement of IALS scores does not affect the standard deviation of εd kH or log(skH ). Also note that, since XkH in (2.6) contains a constant, the distribution of εd kH has the same (zero) mean in each country. For this reason, we do not normalize the standard deviation (or any inter-percentile range) by the mean in order to make cross-country comparisons of residual scores dispersion.  B.1.2  Measuring Wage Dispersion  Wage inequality measures are computed from a sample of full-time manufacturing workers, 16-65 years old, not living in group quarters, reporting positive wages  129  and industry af liation.1 Following Dahl (2002), individuals were considered as `full-time employed' if in 1999 they: (i) were not enrolled full time in school, (ii) worked for pay for at least ten weeks, and (iii) earned an annual salary of at least 2,000 dollars. We focus on the log of weekly wages, calculated by dividing wage and salary income by annual weeks worked. We use weekly wages as opposed to hourly wages, because it requires fewer assumptions to calculate it. In the 2000 Census, hours worked are reported as `usual hours'. Using this variable to convert weekly wages into hourly wages would almost certainly result in the introduction of a source of measurement error. Incomes for top-coded values are imputed by multiplying the top code value ($175,000) by 1.5.2 In equation (2.7), vector Zki includes indicators for 4 categories of educational attainment,3 a quartic polynomial in age, race and gender dummies (plus their interaction), Hispanic and immigrant dummies (plus their interaction) and state of residence dummies. Residual wages are constructed as ξcki = log(wki ) Zki βbi , where βbi is estimated by OLS. Correcting for self-selection into industries is important in estimating equation (2.7), as the assumption that workers do not selectively search for jobs according to comparative advantage or unobservable tastes is relevant for Proposition 4. In the presence of self-selection the distribution of residual wages in any given industry would re ect not only the degree of skill substitutability in production but also workers' skill composition. For this reason, we use a selection estimator proposed by Dahl (2002). In equation (2.7), correcting for self-selection is complicated by the fact that individuals could choose to search for a job in any of the 63 industries of the manufacturing sector, potentially making the error mean, i.e. E(ξ ki jk is observed in i), a function of the characteristics of all the alternatives. In this case, Dahl (2002) argues that under a speci c suf ciency assumption,4 the error mean is only a function of the probability that a person born in the same state as k would make the choice that k actually made (i.e. selecting into industry i), which can be estimated. The suf ciency assumption can be relaxed by including functions of additional selection probabilities; for this reason, Zki includes a cubic polynomial in 1 Manufacturing employment excludes workers in private non-pro t and government organizations. 2 Since top codes vary by state, we follow Beaudry et al. (2007) and impose a common top-code value of $175,000. 3 These are: (i) High school dropout, (ii) high school graduate, (iii) some college but no degree, (iv) college degree or higher. 4 See Dahl (2002), page 2378.  130  the estimated rst-best selection probability and in the highest predicted probability for k. Identi cation in this approach is based on the exclusion of state of birth by industry of employment interactions from equation (2.7). To estimate selection probabilities, we group individuals into cells de ned by state of birth5 and a vector of discrete characteristics: 4 categories of education attainment, 4 age intervals (16-30, 31-40, 41-50, 51-65), race, gender and 2 binary indicators of family status (family/non-family household and presence of own child 18 or younger in the household). As in Dahl (2002), for every individual k, we estimate his selection probability into each industry j using the proportion of individuals within k's cell that are observed working in j, denoted by pc k j . Individual k's estimated rst-best selection probability is pc and k's highest predicted ki probability is given by d pk j , where j is such that d pk j = maxf pc k j g 8 j. For the empirical analysis, the Census industry classi cation was matched to NAICS. It was not possible to match the trade data to Census codes directly, since the former is originally coded according to the Standard International Trade Classi cation (SITC rev.2). However, it is possible to use NAICS as a bridge between the two classi cations. We construct a one-to-one mapping between the Census classi cation and NAICS by re-coding two or more 4 digit NAICS codes into a single industry (which does not necessarily match a 3 digit level). This re-coding also involves cases where two Census codes map perfectly into two NAICS codes -although originally there was no one-to-one matching between them. Importantly, the resulting mapping (available upon request) exhausts all manufacturing sectors in NAICS. Finally, the trade data was matched to wage inequality data using a concordance between SITC rev. 2 and NAICS, available through the NBER online database.  B.2  Additional Data  In this Appendix we provide a description of additional data sources used in the empirical analysis. Descriptive statistics for each variable can be found in table 8. Bilateral export volumes at the industry level: From Feenstra et al. (2005), for the year 2000. Sector-level bilateral exports data are categorized at the 4-digit SITC (4-digit rev. 2) level. The mapping from SITC to NAICS required the concordance 5 As in Beaudry et al. (2007), we keep immigrants in the analysis by dividing the rest of the world  into 14 regions (or `states' of birth).  131  available at the NBER website.6 Bilateral trade barriers: From HMR. This is a set of exporter-importer speci c geographical, cultural and institutional variables. 1) Distance, the distance (in km.) between importer's and exporter's capitals (in logs). 2) Land border, a binary variable that equals one if and only if importer and exporter are neighbors that meet a common physical boundary. 3) Island, the number of countries in the pair that are islands. 4) Landlocked, the number of countries in the pair that have no coastline or direct access to sea. 5) Colonial ties, a binary variable that equals one if and only if the importing country ever colonized the exporting country or vice versa. 6) Legal system, a binary variable that equals one if and only if the importing and exporting countries share the same legal origin. 7) Common Language, a binary variable that equals one if and only if the exporting importing countries share a common language. 8) Religion, computed as (% Protestants in exporter % Protestants in importer)+(% Catholics in exporter % Catholics in importer)+(% Muslims in exporter % Muslims in importer). 9) FTA, a binary variable that equals one if exporting and importing countries belong to a common regional trade agreement, and zero otherwise. 10) GATT/WTO, the number of countries in the pair that belong to the GATT/WTO. Start-up regulation costs: From HMR. We use exporter-importer interactions of three proxies of regulation costs: the number of days (RegDaysH RegDaysF ), number of legal procedures (RegProcH RegProcF ) and relative cost as a percentage of GDP per capita (RegProcH RegProcF ), for an entrepreneur to start operating a business. Factor endowments: Physical capital endowment, KEndow, and human capital endowment, SkillEndow, are taken from Antweiler and Tre er (2002). A country's stock of physical capital is the log of the average capital stock per worker. The stock of human capital is the natural log of the ratio of workers that completed high school to those that did not. The measures used are from 1992, the closest year of which data are available. There's no data on factor endowments for four countries in our sample: Switzerland, Czech Republic, Hungary and Poland. Factor intensities: From Nunn (2007). Originally coded as 1997 I-O industries, the mapping to NAICS required a concordance available from the Bureau of Economic Analysis.7 Physical capital intensity, KIntens, is the total real capital stock divided by value added of the industry in the United States in 1996. Skill 6 http://www.nber.org/lipsey/sitc22naics97/  7 http://www.bea.gov/industry/xls/1997import_matrix.xls  132  intensity, SkillIntens, is the ratio of non-production worker wages to total wages at the industry level in the United States in 1996. There's no data on factor intensities for two industries: `Furniture and related products manufacturing' and `Sawmills and wood preservation'. Proportion of top-coded wages: From the 2000 Census of Population in the U.S. For each industry, TopCode is calculated as the proportion of workers earning a wage exceeding the top code value of $175,000. Firm size dispersion: From the 1997 Census of manufacturing in the U.S. For each industry, we calculate FirmDisp, the coef cient of variation in the average shipments per establishment across bins de ned by employment size. The employment bins de ned in the Census are: 1-4, 5-9, 10-19, 20-49, 50-99, 100-249, 250-499, 500-999, 1000-2499 and 2500 employees or more. Quality of the judicial system: From Nunn (2007) JudicQual is based on the “rule of law” measures originally from Kaufmann et al. (2003). Labor law rigidity: From Tang (2008) LaborRigid is an index that summarizes ring and employment contract adjustment costs combined with measures of the power of labor unions. These measures are originally from Botero et al. (2004).  B.3  Additional Results  Table 15 reports estimates of the impact of skill dispersion as proxied by the dispersion of (raw) test scores: we identify this effect through an interaction with a (raw) wage dispersion ranking.8 We show results based on three alternative measures of dispersion: the 95-5 interpercentile range divided by the average in column (1), the Gini relative mean difference (i.e. twice the Gini coef cient) in column (2) and the coef cient of variation in column (3).9 Columns (1)-(3) add exporter, importer and industry dummies to our variables of interest; columns (4)-(6) include theoretically consistent exporter and importer-industry dummies, along with a vector of bilateral trade barriers described above. 8 Raw  measures are not purged of the effect of observable characteristics. note that all three measures have a common structure in that the numerator is a measure of dispersion (the 95-5 interpercentile range, the standard deviation and the Gini mean difference) while the denominator is the average of the variable. Since we are using the logarithm of variables, the reason why we employ measures of dispersion divided by the average is not for rescaling, but rather to parsimoniously control for the effect that the interaction of the averages might have on trade ows. 9 We  133  In all speci cations the estimated interaction WageDispi SkillDispH shows a positive effect on exports, signi cant throughout at the 5% level. The reported coef cients imply that a one standard deviation increase in the value of the interaction raises log exports by anywhere between 3:5% and 6:5% standard deviations.10 Table 16 reproduces the structure of table 15 in terms of controls, but it separately reports the effect of the interaction WageDispi SkillDispH (where the measure of dispersion is not divided by the average), as well as those of the interaction of average scores and average wages, WageMeani SkillMeanH , and of the other two interactions, WageDispi SkillMeanH and WageMeani SkillDispH . The interaction of the averages is expected to capture standard factor proportions effects: on average, countries with more skilled workers specialize in sectors that employ skilled workers and have higher average wages. The interaction WageMeani SkillDispH is a exible way to control for possible bias, due to differences in sectoral average wages, in the estimated effect of our interaction of interest. The interaction WageDispi SkillMeanH plays a similar role.11 In general, columns (1)-(6) suggest that the coef cient of WageDispi SkillDispH is robust to the inclusion of all interactions: all estimates are similar to the ones in table 15 and, when trade barriers and importer industry dummies are included, signi cant at the 5% level. As for the other interactions, as expected WageMeani SkillMeanH has a strong and positive impact on trade ows. Moreover WageMeani SkillDispH is consistently positive, signi cant and large, while WageDispi SkillMeanH is positive, but not always signi cant, particularly in columns (1)-(3). We note that the magnitudes of the impact of our variable of interest are similar in tables 15 and 16 to the ones in tables 4 and 5, indicating a substantial degree of robustness in our results.  10 In  regressions we do not report, we interacted all three measures of dispersion for wages and scores with one another obtaining results qualitatively and quantitatively similar to columns (1)-(6). 11 This interaction relates to the theoretical prediction that increases in average skills not resulting from proportional changes also have an effect on comparative advantage. This effect depends on the degree of complementarity, approximated by WageDispi .  134  Appendix C  Appendix to Chapter 3 C.1  Data Sources  The data set used in the empirical analysis comes from a variety of sources. The rm-level data is comprised of manufacturing rms in Argentina, sampled in two Innovation Surveys carried out by I.N.D.E.C. (Argentina's National Statistical Agency). The rst survey provides information for 1639 rms in 1992 and 1996, while the second survey collected information for 1688 rms in 1998 and 2001 (Bisang and Lugones 1998, 2003). These samples were randomly drawn from the National Economic Census of 1993 and from the Input–Output Matrix survey of 1997, respectively. The surveys provide information on sales of goods produced in the rm, educational attainment of employees, investments in innovation activities (including R&D) and ownership for the years 1992, 1996, 1998, 2001. There is also information on the geographical location (i.e. Argentine provinces) and the industry to which rms belong (at a 4-digit ISIC level). I also use geographical data to account for differences in the institutional and economic environment in which rms carry out their activities and interact with each other. The data was collected by the Ministry of Economy and Production of Argentina, it is publicly available through the internet and includes population levels and several indicators of overall performance of the provincial economy and local government (see page 66).1 Finally, I constructed series of export prices for 4-digit ISIC industries using 1 http://www.mecon.gov.ar/hacienda/dncfp/index.html  135  the NBER-U.N. Trade Data compiled by Robert C. Feenstra.2 Since the latter was coded according to the SITC classi cation, the task also required matching SITC to ISIC industries. This was done with the help of a concordance provided by the O.E.C.D., available at Jon D. Haveman's website.3 Following Schott (2004), the unit value of an SITC product was computed by dividing import value by import quantity.4 Before moving on to the description of the data, it is important to point out that the empirical analysis in this chapter is restricted to the subset of rms that were sampled in both surveys, 827 rms. The reason is that the estimation of a dynamic model of export decisions that accounts for unobserved rm heterogeneity requires the availability of at least three data points (see section 3.5), while each survey provides only two. As described above, the importance of previous export experience and rm heterogeneity as determinants of entry in export markets is well documented in the recent empirical literature. However, restricting the analysis to a balanced panel may raise concerns of potential inferential biases due to ignoring both the attrition of rms from the First Survey and the appearance of a set of rms in the Second Survey that were not previously surveyed.5 This trade-off is attenuated in this study due to the fact that, by design, the set of rms sampled in each survey were randomly drawn from two different sources (as mentioned above), a situation which resembles that of rotating panels. As shown in see Wooldridge (2002, p. 569), in rotating panels where the decision to rotate units out of the panel is made randomly, the identifying conditions required for obtaining consistent panel data estimators are the same regardless of whether the selected or a full (unrestricted) sample are used in the estimation. Additionally, the empirical analysis in this chapter is robust to systematic selection based on time-invariant and other observable characteristics of rms.  2 The  data is available at http://cid.econ.ucdavis.edu/  3 http://www.macalester.edu/research/economics/PAGE/HAVEMAN/Trade.Resources  /TradeConcordances.html 4 For some years and products there are multiple country observations of value and quantity. In those cases, I follow Schott (2004) in de ning the unit value to be a value-weighted average of the observations. Availability of unit values ranges from 77 percent of product-country observations in 1972 to 84 percent of observations in 1994. 5 This issue appears to have received little attention in recent research. Clerides et al (1998) and Bernard and Jensen (2004) apply estimation methods that are similar to this paper, but using longer panels than in this study. However, both papers restrict their analyses to the set of rms sampled in every year, ignoring potential selection bias.  136  

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