Trade, Labor Markets and the Organization of Production within Firms

Trade, Labor Markets and the Organization of Production within Firms Dissertation zur Erlangung des Grades eines Doktors der Wirtschaftswissenschaft der Rechtsund Wirtschaftswissenschaftlichen Fakult¨ at der Universit¨ at Bayreuth Vorgelegt von Michael Koch aus Bamberg Dekan: Prof. Dr. Herbert Woratschek Erstberichterstatter: Prof. Dr. Hartmut Egger Zweitberichterstatter: Prof. Dr. Carsten Eckel Tag der m¨undlichen Pr¨ufung: 13.11.2013 F¨ur meine Eltern iv Acknowledgements I would like to thank all the people that helped and supported me while writing this theses. In particular I would like to thank my first supervisor Hartmut Egger for his insightful guidance and continuous encouragement. The numerous discussions and the pleasant atmosphere at his chair have strongly contributed to the success of my theses. I would also like to thank my second supervisor Carsten Eckel for his useful advice and comments on the different chapters in this thesis. My grateful thanks are also extended to my colleges at the department for law and economics at the University of Bayreuth, in particular Daniel Etzel, for inspiring conversations and helpful discussions during the last years. I would also like to extend my thanks to the Department of Economics at the University of Bergen for their hospitality during my research stay. In particular I would like to thank Frode Meland for inviting me to Bergen and his valuable and constructive suggestions. I would also like to thank Kjetil Gramstad, Inger Sommerfelt Ervik, Leroy Andersland and Hans-Martin Straume for the kindly stay in Bergen. Furthermore, I gratefully acknowledge the financial support by the Bavarian Graduate Program in Economics (BGPE). Finally, I would like to thank my father Karl-Ernst and my mother Christa for supporting me. Special thanks go to my partner Susan for her encouragement, the understanding and love during the past few years. v vi Abstract The main research question of this thesis is how globalization shapes the organization of production within firms, with a particular focus on the role of labor market imperfections in open economies. For that reason, I make use of three different models to investigate the interaction between firm organization and labor market imperfections in the process of globalization. Thereby, the organization of production is discussed from different perspectives: (i) the number of products a firm is willing to produce and (ii) the organization of labor within firms. In each chapter, I use a different approach to account for imperfections in factor markets. This allows a broad discussion on how labor market institutions affect the equilibrium outcome in closed and open economies, and how these imperfections affect a firm’s organization choice. After a short introduction in Chapter 1, Chapter 2 sets up a general oligopolistic equilibrium model with multi-product firms and union wage setting. In this model, two policy experiments are conducted. First, it is shown that deunionization induces a general decline in firm scale and scope, with the respective reduction being more pronounced in non-unionized industries. Second, the consequences of trade liberalization are studied, and it is shown that access to foreign markets lowers firm scope in all industries as well as the scope differential between unionized and non-unionized firms. Adjustments in firm scale turn out to be less clearcut and inter alia depend on the degree of product differentiation. Chapter 3 looks inside the firm and investigates how trade alters the matching of worker-specific abilities and task-specific skill requirements. The outcome of this matching process depends on how firms organize their recruitment process and how much they invest into the screening of applicants. In the open economy, the most productive firms start exporting. They increase their market share and therefore find it attractive to increase their screening investment, which improves the matching outcome. Things are different for non-exporters, whose market share shrinks in the open economy, lowering their incentive to invest for screening applicants. Due to this asymmetric response, access to trade raises the dispersion of productivity between heterogeneous producers, while at the same time increasing the average quality of worker-task matches and thus economy-wide labor productivity. Chapter 4 sets up a heterogeneous firms model, where production consists of a continuum of tasks and firms hire low-skilled and high-skilled workers for vii viii the performance of tasks, which differ in their complexity. How firms assign workers to tasks depends on factor prices for the two skill types and the productivity advantage of high-skilled workers in the performance of complex tasks. After characterizing the closed economy equilibrium with fully flexible wages, I show how firms adjust the assignment of workers top tasks in response to the introduction of a binding real minimum wage for low-skilled workers and migration of low-skilled or high-skilled workers. With a minimum wage, the opening up for trade reduces the range of tasks performed by high-skilled workers. It furthermore leads to a higher per-capita income of both skill types, which implies a higher welfare in the open than in the closed economy, while inequality between the two skill types increases. In an extension, I discuss how the firm-internal assignment of skills to tasks is affected by labor market linkages in open economies. Contents 1 Introduction 1 2 Labor Unions and Multi-Product Firms in Closed and Open Economies 5 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 MPFs and imperfect labor markets: The closed economy . . . . . . . . . . . . . . 7 2.2.1 Preferences and consumer demand . . . . . . . . . . . . . . . . . . . . . . 8 2.2.2 Technology, production, and profit maximization . . . . . . . . . . . . . . 9 2.2.3 Union wage setting and the labor market . . . . . . . . . . . . . . . . . . 10 2.2.4 The consequences of deunionization for firm-level variables . . . . . . . . 12 2.3 MPFs and labor market imperfection in an open economy . . . . . . . . . . . . . 14 2.4 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.5 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.5.1 Extension – Linear cost function . . . . . . . . . . . . . . . . . . . . . . . 25 2.5.2 Extension – Firm level unions . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.5.3 Program codes for simulation exercises . . . . . . . . . . . . . . . . . . . . 33 3 Trade and the Firm-Internal Allocation of Workers to Tasks 39 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.2 The closed economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.2.1 Model structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.2.2 Equilibrium in the closed economy . . . . . . . . . . . . . . . . . . . . . . 44 3.3 The open economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.3.1 Basic structure and preliminary insights . . . . . . . . . . . . . . . . . . . 46 3.3.2 The open economy equilibrium . . . . . . . . . . . . . . . . . . . . . . . . 48 3.4 A model variant with involuntary unemployment . . . . . . . . . . . . . . . . . . 51 3.5 A calibration exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.6 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4 Trade and the Firm-internal Assignment of Skills to Tasks 67 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.2 The closed economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.2.1 Model structure and firm-level analysis . . . . . . . . . . . . . . . . . . . . 71 4.2.2 General equilibrium with perfect labor markets . . . . . . . . . . . . . . . 75 4.2.3 Equilibrium with a minimum wage for low-skilled workers . . . . . . . . . 78 4.2.4 Comparative-static analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.3 The open economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 ix 2CHAPTER 1. INTRODUCTION the comparative-static experiments, the focus is on two specific research questions that have sparked considerable interest in academic circles and, at the same time, are relevant for policy makers who aim at introducing measures of deregulation in product and/or labor markets. The first question is how firms absorb changes in labor market institutions, and how institutional changes in certain industries spill over on the rest of the economy. From an empirical point of view, the probably most notable change in labor market institutions is the significant decline in union relevance. This deunionization process induces an increase in the competitive as well as the union wage. In a setting with MPFs the associated cost increase renders production of those varieties that have the largest distance to a firm’s core competence unattractive, so that firms reduce the scope of their product range and thus shrink at the extensive margin. Both the cost increase and the shortening of the product range induce a decline in total firm scale. Furthermore, by focusing on the production of high-competence, i.e. low-cost, varieties, all firms (except for the newly deunionized ones) can produce a higher level of output with a given level of labor input and thus are more productive on average. Finally, it is shown that deunionization by lowering the union wage premium makes firms more similar in both size dimensions, scale and scope. In a second part of this chapter, I investigate how firm scale and scope are affected if a country opens up for free trade with a symmetric partner country. Access to international trade stimulates labor demand and raises the competitive as well as the union wage, thereby lowering firm scope in all industries. Since the labor market distortion becomes less severe, unionized and non-unionized firms become more similar in the size of their product range. While scope effects are unambiguous, adjustments in firm scale turn out to be less clearcut and inter alia depend on the degree of product differentiation. Studying the role of firms for matching workers with tasks and discussing how access to trade affects the matching outcome is the main purpose of Chapter 3.5Starting point of the analysis is a Melitz (2003) model, in which firms are heterogeneous due to differences in their productivity levels. As in Acemoglu and Autor (2011), it is assumed that production consists of a continuum of tasks that differ in their skill requirements. For performing these tasks, firms hire heterogeneous workers. Heterogeneity is horizontal in the sense that workers differ in their ability to perform specific tasks because their human capital is occupation-specific, while they are equally productive over the whole range of activities. This implies that all workers have the same value to firms and, lacking information about abilities of individual workers, firms randomly draw their employees from the labor supply pool. This lack of information generates a source of mismatch between task-specific skill requirements and worker-specific abilities within the boundaries of a production unit. To reduce this mismatch, firms can invest into a screening technology for gathering some (imperfect) information about the abilities of their workforce. A higher investment provides better knowledge about the abilities of workers and therefore leads to a better match of these workers with the different tasks in the production process. The incentives to screen are more pronounced in larger firms, and hence there is an additional source of heterogeneity in this model, which is endogenous and reinforces heterogeneity of firms due to exogenous differences in firm productivity. This model is used to shed new light on the consequences of trade for labor market outcome, thereby focussing on adjustments in the firm-internal labor market. To be more specific, it is analyzed how trade affects underemployment arising from a mismatch be5This chapter is based on Egger, Koch (2013). When working on this chapter, I have benefited from comments by Carsten Eckel, James Harrigan, Frode Meland, Marc Muendler, Frank St¨ahler and participants at the European Trade Study Group Meeting in Leuven, the GEP Postgraduate Conference in Nottingham, the G¨ottingen Workshop on International Economics, the Midwest International Economics Meeting at the Indiana University, the Brown Bag Seminar of the Department of Economics at the University Bayreuth, the Research Workshop of the Bavarian Graduate Program in Economics (BGPE) and the Economics Research Seminars at the University of Bergen and the University of Tuebingen. 3 tween worker-specific abilities and task-specific skill requirements. To keep the analysis simple, the focus is on trade between symmetric countries while considering the empirically relevant case, in which only the most productive firms export in the open economy. Having access to the export market, high-productivity firms can expand their market share in the open economy, which provides an incentive for these firms to screen their workforce more intensively, as this further improves the matching quality and thus lowers production costs. Low-productivity non-exporters, on the other hand, lose market share and thus lower their investment into the screening technology, which raises their production costs. By changing the cost structure, this asymmetric response to trade liberalization exerts a feedback effect on the entry/exit decision of firms in both the domestic and the export market, which is not present in other trade models with heterogeneous firms. Furthermore, it alters the productivity distribution of active firms by driving a wedge between matching efficiency of exporters and non-exporters. Finally, adjustments in the firm-internal labor allocation process lower the aggregate mismatch between worker-specific abilities and task-specific skill requirements, thereby generating a productivity stimulus that reinforces the gains from trade in an otherwise identical Melitz (2003) model. Chapter 4 builds upon the framework studied in Chapter 3 and sets up a heterogeneous firms model in which a firm’s output is manufactured using a continuum of tasks.6Firms hire low-skilled and high-skilled workers for the performance of tasks. Tasks differ in their complexity and workers differ in their ability to perform these tasks, with high-skilled workers having a comparative advantage in performing more complex tasks. How firms organize the firm-internal production process by assigning skills to tasks depends on the respective factor costs and productivity advantage of high-skilled workers in performing more complex tasks. This framework is used to analyze how imperfections in the labor market affect the firm-internal assignment of skills to tasks in the closed economy. After characterizing the autarky equilibrium outcome with fully flexible wages for both skill types, a (real) minimum wage is introduced, that is set by the government for low-skilled workers and causes involuntary unemployment of that skill type. As relative factor prices are changed and low-skilled task production becomes more costly, firms assign high-skilled workers to a broader range of tasks. This firm-internal skill upgrading improves a firm’s labor productivity. However, as more high-skilled workers are employed for the performance of tasks, less of them are left to manage firms and the mass of firms therefore declines. Firm exit triggers a decline in aggregate output, income and welfare. After discussing migration of low-skilled and high-skilled workers under the two different labor market regimes, the model is used to discuss how trade between two countries affects the firm-internal production process. Only when low-skilled wages are set by a binding minimum wage, trade exerts an impact on the firm-internal assignment process. The opening up to trade raises demand for each firm due to a standard division of labor effect. When the factor price for low-skilled workers is fixed, the skill premium increases implying that high-skilled task production becomes relatively unattractive. Firms respond in broadening the range of tasks produced with lowskilled workers, which reduces labor productivity of each firm. Beside this negative productivity effect, trade increases the mass of producers in each country and reduces the unemployment rate of low-skilled workers. This causes an increase in the relative income of both workers with the respective increase being more pronounced for high-skilled workers. Furthermore, aggregate output, income and welfare goes up. Moreover, high-skilled workers gain in relative terms as their skill premium and relative per-capita income increases. After discussing the movement from autarky to trade, it is shown how changes in local endowments and labor market institutions 6When working on this chapter, I have benefited from comments by Carsten Eckel, Hartmut Egger and participants at the European Trade Study Group Meeting in Birmingham, the IO and Trade Seminar at the Department of Economics at the University of Munich and the Brown Bag seminar at the University of Bayreuth. 4CHAPTER 1. INTRODUCTION spill over to the partner country. Thereby, it is shown that an increase in the minimum wage abroad reduces the range of tasks performed by low-skilled workers at home, while it increases the productivity of active producers there. Both skill types end up with a lower per-capita income, and thus welfare is reduced at home. Finally, Chapter 5 concludes with a brief summary of the most important results. Chapter 2 Labor Unions and Multi-Product Firms in Closed and Open Economies 2.1 Introduction In this chapter, we analyze how labor market imperfection affects scale and scope of multiproduct firms (MPFs). To address this issue, we set up a general oligopolistic equilibrium (GOLE) model with MPFs along the lines of Eckel and Neary (2010) and enrich this framework by assuming union wage setting in a subset of industries. The asymmetry of sectors with respect to their labor market institutions is a key aspect of our analysis. It allows us to study the consequences of union wage setting on firm scale and scope in unionized industries and it provides novel insights on how labor market imperfections in certain industries spill over on firm organization in the rest of the economy. Within this framework, we undertake two comparativestatic experiments. First, we investigate the consequences of deunionization on firm scale and scope in industries that are directly exposed to this institutional change as well as in industries whose labor market institutions do not change. Second, we study the differential impact of trade liberalization on firm scale and scope in unionized and non-unionized industries. Relying on the Eckel and Neary (2010) framework, we assume a continuum of industries and a small (exogenous) number of firms competing in quantities within each of these industries. Firms employ labor to produce a range of differentiated product varieties. They have a core competence in one of these varieties which they produce at the lowest marginal cost. By expanding the scope of their product range, firms start manufacturing varieties with a larger distance to their core competence and thus higher marginal production costs.1Setting a markup on the competitive 1Abstracting from any additional costs of introducing a new variety the model captures the idea of flexible manufacturing, which is a widely used concept of representing MPFs (see Milgrom and Roberts, 1990; Eaton and Schmitt, 1994; Norman and Thisse, 1999; Eckel, 2009). While there are many alternative ways of modeling MPFs (see, for instance, Feenstra and Ma, 2008; Nocke and Yeaple, 2008; Arkolakis and Muendler, 2010; Mayer, Melitz, and Ottaviano, 2010; Bernard, Redding, and Schott, 2011), there are good reasons for relying on the Eckel and Neary (2010) approach when accounting for union wage setting. With oligopolistic competition between a small number of competitors and linear demand in each industry, our model is related to a large and well-established literature on unionized oligopoly. Thus, we can directly compare our results with findings from this literature to highlight whether and how previous insights on the interplay between labor market and product market imperfections have to be modified if one accounts for multiinstead of single-product firms. 5 6CHAPTER 2. LABOR UNIONS AND MULTI-PRODUCT FIRMS wage, labor unions enforce a reduction in the output and employment level of unionized firms. While this effect does also exist in other models of unionized oligopoly, there is an additional adjustment margin in a setting with MPFs. By raising marginal production costs, unions reduce the incentive of firms to operate a wide product range and thus lower firm scope. Furthermore, union wage setting lowers aggregate employment ceteris paribus and thus induces a fall in the market-clearing competitive wage. The decline of the competitive wage raises firm scale and scope in non-unionized industries. This points to a new facet of spillovers associated with union wage setting. Unions do not only influence wage payments in other sectors (due to labor market clearing) but also affect the product range of non-unionized producers – and thus labor productivity in our setting. In the comparative-static experiments, we focus on two specific research questions that have sparked considerable interest in academic circles and, at the same time, are relevant for policy makers who aim at introducing measures of deregulation in product and/or labor markets. The first question we are interested in is how firms absorb changes in labor market institutions, and how institutional changes in certain industries spill over on the rest of the economy. From an empirical point of view, the probably most notable change in labor market institutions is the significant decline in union relevance. This deunionization process is a worldwide phenomenon which has been observed in all industrialized economies over the last four decades (see OECD, 2004). From Bastos and Kreickemeier (2009) we know that in an otherwise similar framework with single product firms (SPFs), deunionization – captured by a decline in the share of unionized industries – raises the competitive as well as the union wage and thus lowers scale of both unionized and non-unionized firms. Since the union wage increases less than proportionally, deunionization lowers the scale differential between the two types of producers. In this chapter, we show that firm-level adjustments become more sophisticated when firms produce more than just a single variety and that the endogeneity of the product range leads to further interesting results upon how firms respond to changes in labor market institutions. To be more specific, deunionization induces an increase in the competitive as well as the union wage, similar to the model with SPFs. However, in a setting with MPFs the associated cost increase renders production of those varieties that have the largest distance to a firm’s core competence unattractive, so that firms reduce the scope of their product range and thus shrink at the extensive margin. Both the cost increase and the shortening of the product range induce a decline in total firm scale. Furthermore, by focusing on the production of high-competence, i.e. low-cost, varieties, all firms (except for the newly deunionized ones) can produce a higher level of output with a given level of labor input and thus are more productive on average. Finally, we show that deunionization by lowering the union wage premium makes firms more similar in both size dimensions, scale and scope, in our setting. In a second application of our model, we investigate how firm scale and scope are affected if a country opens up for free trade with a symmetric partner country. As pointed out by Brander (1981), a movement from autarky to trade raises competition in an oligopolistic market and thus provides a stimulus for the production of all firms ceteris paribus. In a general equilibrium environment with factor market clearing, this induces an increase in the competitive wage, which counteracts the partial equilibrium production stimulus. As outlined by Neary (2009), in a model with SPFs, symmetric industries, and no labor market distortions, the two effects cancel and thus firm scale remains unaffected by the trade shock. In an otherwise identical model with MPFs, firms lower their scope in response to a higher competitive wage, thereby leaving more labor for employment in activities that are closer to the firms’ core competences. To put it in the words of Eckel and Neary (2010) firms are leaner and meaner in the open economy and they experience a productivity surge as their total output increases for a given level of labor 2.2. MPFS AND IMPERFECT LABOR MARKETS: THE CLOSED ECONOMY 7 input. This points to a new channel through which gains from trade can materialize, one that is specific to models of MPFs. By extending the Eckel and Neary (2010) framework to one with labor market imperfections, we further enrich the picture of possible firm-level adjustments to globalization. As in textbook models of unionized oligopoly with SPFs, trade exerts a union-disciplining effect and thus lowers union wage claims ceteris paribus (Huizinga, 1993; Sørensen, 1993). Hence, both scale and scope effects of trade are more pronounced in unionized industries, so that economic activity shifts towards these sectors. All other things equal, this lowers production in non-unionized industries and the shift effect may actually be strong enough to dominate the output stimulus from being more focused on the production of high-competence varieties. Hence, labor market imperfections render firm-level adjustments to international trade more sophisticated and less clearcut than one might have expected from the analysis in Eckel and Neary (2010). Aside from looking at pure level effects, we are particularly interested in the differential impact that trade exerts on unionized and non-unionized firms. In this respect, we show that trade weakens the labor market distortion and thus lowers the union wage premium. This effect is instrumental for a reduction in the scope differential between the two types of producers. Similarly, the decline in the union wage premium also reduces the domestic output differential of local producers. However, this effect is counteracted by a widening of the output gap at the extensive margin as, after a country’s opening up for trade, firms start exporting and the respective exports are larger for non-unionized than for unionized firms. Which of these two effects dominates is not clearcut in general and depends on the degree of product differentiation. Smaller degrees of product differentiation reinforce the pro-competitive effect of trade and thus amplify the union-disciplining effect of foreign competition. This strengthens the negative impact of trade on the domestic production gap between unionized and non-unionized producers, so that the scale differential decreases for small degrees of product differentiation. On the contrary, for high degrees of product differentiation it is the output expansion effect in the export market that dominates so that the firm scale differential increases in response to trade. The remainder of the chapter is organized as follows. In Chapter 2.2 we introduce the main assumptions, describe the basic model structure, and characterize the autarky equilibrium. After a brief discussion on how union wage setting affects firm scale and scope, we study how MPFs respond to deunionization. In Chapter 2.3, we characterize the equilibrium in an open economy with free trade between two symmetric countries and compare the outcome in the open economy with the one in the closed economy to shed light on how trade affects union wage setting as well as firm scale and scope in the presence of labor market imperfection. Chapter 2.4 concludes with a brief summary of the most important results. 2.2 MPFs and imperfect labor markets: The closed economy The country under consideration hosts a continuum of industries, with an oligopolistic market structure and a small (exogenous) number nof firms in each of these industries. The industries are identical in all respects except for the prevailing labor market institutions. While firms in a subset of industries are exposed to union wage-setting, firms in the rest of the economy pay the competitive wage, which is determined by a standard labor market clearing condition – provided that labor is homogeneous and fully mobile across sectors. With respect to union wage-setting, we apply a monopoly union framework, in which unions unilaterally set wages prior to the firms’ choice of employment, which in our setting involves the simultaneous decision upon firm scale 8CHAPTER 2. LABOR UNIONS AND MULTI-PRODUCT FIRMS and scope. 2.2.1 Preferences and consumer demand There exists a representative consumer, whose preferences are represented by a two-tier quasihomothetic utility function. The upper tier is an additive function of a continuum of sub-utilities, each of them corresponding to one industry z∈[0,1]: U[u{z}] = Z1 0 u{z}dz. (2.1) Each sub-utility is a quadratic function of consumption levels q(i, z), i∈[1, N(z)], where N(z) is the measure (or, in the interest of a more accessible interpretation, the number, henceforth) of differentiated varieties produced in industry z. To be more specific, we assume u{z}=aZN(z) 0 q(i, z)di −1 2b (1 −ρ)ZN(z) 0 q(i, z)2di +ρ ZN(z) 0 q(i, z)di!2 ,(2.2) where a,bdenote non-negative preference parameters with the usual interpretation and ρis an inverse measure of product differentiation, which is assumed to lie between 0 and 1.2 Aggregate demand in this setting is determined by maximizing utility of the representative consumer subject to her budget constraint Z1 0ZN(z) 0 p(i, z)q(i, z)didz ≤I, (2.3) where p(i, z) denotes prices for variety iin industry zand Iis aggregate income of the economy. This gives p(i, z) = 1 λ a−b[(1 −ρ)q(i, z) + ρZN(z) 0 q(i, z)di]!,(2.4) where λis the representative consumer’s marginal utility of income. As it has become standard in the literature, we choose utility as the num´eraire and set λequal to one. Thus, all nominal variables are measured relative to the representative consumer’s marginal utility of income (see Neary, 2009, for further discussion). From Eq. (2.4) we can infer insights upon the role of preference parameter ρin our setting. As mentioned above, ρis a measure of product differentiation and lies in interval [0,1]. If ρ= 1 products are homogeneous (perfect substitutes), so that the price is linear in total industry consumption: p(i, z) = a−bRN(z) 0q(i, z)di. In the other limiting case with ρ= 0, goods are perfectly differentiated in the perception of consumers, so that the price for each variety only depends on consumption of this variety but is independent of the consumption of all other varieties in this industry. In the latter case, indirect demand is given by p(i, z) = a−bq(i, z). 2By formulating the respective preferences of the representative consumer, we have presumed that the following two conditions are fulfilled for any individual consumer: participation in the market for any good iand nonsatiation in the consumption of these goods. Clearly, both of these conditions depend on endogenous variables. However, under the additional assumption of identical consumer preferences, we know from previous work that these conditions are fulfilled if a lump-sum tax-transfer system redistributes a sufficient level of income from rich to poor agents. Being not interested in income distribution or individual welfare levels per se, we can thus safely assume that the two conditions are fulfilled throughout our analysis. 2.2. MPFS AND IMPERFECT LABOR MARKETS: THE CLOSED ECONOMY 9 2.2.2 Technology, production, and profit maximization We associate MPFs with the idea of flexible manufacturing, and thus assume that firms can expand their product range “with only a minimum of adaptation” (Eckel and Neary, 2010, p.192). The costs of adaptation are modeled by higher labor requirements for producing a unit of output of a firm’s non-core competence product, and the respective adaptation costs are assumed to be monotonically increasing in the distance between a specific product to the firm’s core competence variety. However, adding a new variety to the product range does not alter the costs of producing other varieties nor does it involve any fixed costs. To put it formally, we denote marginal production costs of firm j= 1, ..., n in industry zfor producing variety iby cj(i, z) = γj(i)wj(z), with γj(i) being the constant labor input coefficient for producing variety i and wj(z) being the wage rate in industry z. We associate firm j’s core competence with variety i= 0 and capture flexible manufacturing by assuming ∂cj(i, z)/∂i =∂γj(i)/∂i ×wj(z)> 0. While the main mechanisms of our analysis do not hinge on a specific functional form of γj(i), we impose the additional assumption γj(i) = eiin the interest of analytical tractability. Furthermore, we assume that product ranges are firm-specific, implying that each firm has its own core competence and produces its own set of varieties.3Finally, as pointed out above, we allow for sectoral differences in labor market institutions and thus end up with industry-specific wage rates. Hence, in contrast to Eckel and Neary (2010) marginal production costs in our model comprise both a product-specific component, γj(i), and a sector-specific one, wj(z). Considering the technology assumptions above and denoting by δj(z) the scope of the product range, profits of firm jin industry zare given by Πj(z) = Zδj(z) 0pj(i, z)−cj(i, z)xj(i, z)di, (2.5) where xj(i, z) denotes output of variety i. Firms simultaneously choose the output level of all of their products as well as the scope of the product range. Wages (and thus marginal production costs cj(i, z)) are exogenous from the perspective of individual producers. While the competitive wage is an economy-wide variable and thus not affected by a single firm’s decision upon its scale and scope, the unionized wage is determined before the firm sets xj(i, z) and δj(z) and thus also treated as exogenous in the output game. Taking account of the market clearing condition xj(i, z) = qj(i, z) and maximizing j’s profits in (2.5) with respect to xj(i, z) gives the first-order condition ∂Πj(z) ∂xj(i, z)=pj(i, z)−cj(i, z)−b[(1 −ρ)xj(i, z) + ρXj(z)] = 0, with Xj(z)≡Rδj(z) 0xj(i, z)di denoting firm scale. Substituting (2.4) and denoting industry-wide output of all nproducers by Y(z) = RN(z) 0x(i, z)di we can solve for xj(i, z) = a−cj(i, z)−bρ(Xj(z) + Y(z)) 2b(1 −ρ).(2.6) The negative impact of industry output Y(z) on firm j’s profit-maximizing output of variety icaptures the fact that under Cournot competition (and linear demand) output levels are 3Adaptation costs do not depend on the degree of product differentiation in consumer demand. This renders the analysis simple and allows us to study preference and technology changes as two independent phenomena. However, the respective results from our analysis may be restrictive if adaptation costs vary systematically with the degree of product differentiation, which could be the case in industries in which products are tailored to specific needs of individual consumers. 10 CHAPTER 2. LABOR UNIONS AND MULTI-PRODUCT FIRMS strategic substitutes. Furthermore, the additional negative impact of this firm’s own total output Xj(z) reflects the cannibalization effect, i.e. under Cournot competition MPFs internalize that increasing output of a certain variety lowers prices for this as well as all other varieties in the firm’s product range. Both of these effects do exist if and only if ρ > 0, i.e. if products are not perfectly differentiated (see above). Furthermore, maximizing profits (2.5) with respect to δj(z) gives the first-order condition ∂Πj(z) ∂δj(z)= [pj(δj(z)) −cj(δj(z))] xj(δj(z)) = 0, which can be solved for firm j’s optimal product range δj(z) = ln a−bρ(Xj(z) + Y(z)) wj(z).(2.7) Comparing Eqs. (2.6) and (2.7), we see that firms add new varieties to their product portfolio until the marginal costs of the last variety δj(z) equals the marginal revenue of this variety at zero output. Using the latter insight in Eq. (2.6), we can derive a second expression for optimal output of variety i, by expressing the respective output level of this variety in terms of the difference between its own marginal cost and that of the marginal variety: xj(i, z) = wj(z)[eδj(z)−ei] 2b(1 −ρ).(2.6′) Integrating output xj(i, z) over all varieties i, finally gives total output, i.e. the scale, of firm j: Xj(z) = wj(z) 2b(1 −ρ)heδj(z)δj(z)−1+ 1i,(2.8) which, all other things equal, increases in the firm’s product range δj(z) and, for a given scope, increases in wage rate wj(z). The latter effect has to be interpreted with care, as it does not imply that higher factor costs increase firm size. Rather, higher wages lead to output adjustments at the internal and the external margin. The former is associated with a firm’s relocation of production from goods with a large distance towards goods with a small distance to its core competence, holding the product range and output of the marginal variety constant. The latter is associated with a change in the product range. The positive impact of an increase in wj(z) on Xj(z) for a given δj(z) only captures the firm’s output adjustment at the intensive margin and accordingly should be interpreted as a partial effect. As outlined below, this adjustment at the internal margin is counteracted and dominated by a firm’s output adjustment at the external margin, so that total firm size decreases in response to higher labor costs, as can be expected. 2.2.3 Union wage setting and the labor market Regarding factor endowments, we assume that the country under consideration is populated by Lworkers, each of them supplying one unit of labor. Workers are mobile across sectors, with sectors differing in the prevailing labor market institutions. To be more specific, we apply the labor market model of Bastos and Kreickemeier (2009) and assume that a subset of industries is unionized, while in the rest of the economy, the labor market is perfectly competitive. Without loss of generality, we order industries such that unions are active in all sectors with z≤˜z. Provided that unions are only active in a subset of industries, i.e. ˜z < 1, involuntary unemployment 2.2. MPFS AND IMPERFECT LABOR MARKETS: THE CLOSED ECONOMY 11 does not materialize in this setting, as workers who do not find a job in unionized industries will move to non-unionized industries, and the competitive wage will fall until all workers can find employment there. With respect to wage setting in industries z∈[0,˜z], we consider sector-level unions which unilaterally set wages that are binding for all workers of the respective industry, while, at the same time, leaving the right-to-manage employment to firms. Since all firms of an industry pay identical wages they are symmetric, and hence we can combine (2.8) and (2.7) to obtain4 eδ(z)=a/w(z)−φ 1 + φδ(z)−φ,(2.9) where φ≡ρ(n+ 1)/[2(1 −ρ)] is a measure of product market competition, which positively depends on the number of competitors, n, and negatively depends on the degree of product differentiation, as captured by the inverse of ρ. Eq. (2.9) establishes a negative relationship between wage rate w(z) and firm scope δ(z). Furthermore, Eqs. (2.8) and (2.9) determine firm scale X(z) as an implicit function of w(z), and it is shown in the Appendix that dX(z)/dw(z)< 0, as argued above. The response of firm scale and scope to changes in the wage rate is taken into account by unions. As in other models of union wage setting, unions face a trade-off between higher wages and higher employment when deciding upon their wage claims. How unions evaluate this tradeoff depends on their objective function. We impose the common assumption that unions are utilitarian and have an objective function of the form Ω(z) = [w(z)−wc]nl(z), where wcis the economy-wide competitive wage. Substituting l(z) = Rδ(z) 0eix(i, z)di,x(i, z) from (2.6′), and eδ(z)from (2.9) into union objective Ω, we obtain5 Ω = n 4b(1 −ρ)(wu−wc)wua/wu−φ 1 + φδu−φ−12 .(2.10) Totally differentiating the latter with respect to wuand setting the resulting expression equal to zero gives the first-order condition dΩ dwu=n 4b(1 −ρ)a/wu−φ 1 + φδu−φ−1(2wu−wc)a/wu−φ 1 + φδu−φ−1 −2 (wu−wc)eδu(1 + φδu−φ) + φ 1 + φδu= 0. Rearranging terms and accounting for (2.9) allows us to derive the union wage claim as an implicit function of the competitive wage wc: wu=1 2wc+a [1 + φδu][eδu−1] 1−wc wu.(2.11) Unions set wages wu> wcand thus end up with lower scale and scope. Furthermore, our model reproduces the common result that a higher competitive wage (and thus a higher alternative income) provides a stimulus for the union wage, i.e. dwu/dwc>0.6 4We suppress firm indices from now on to simplify notation. 5Since sectors only differ in their labor market institutions, we introduce superscripts uand cto refer to unionized and non-unionized industries, respectively, and suppress sector index zfrom now on. 6The proof of this result is deferred to the Appendix. 18 CHAPTER 2. LABOR UNIONS AND MULTI-PRODUCT FIRMS cation. In a further extension, we have accounted for firm-level instead of sector-level unions.17 While in the borderline case of perfect product differentiation, this modification has no impact on our analysis, it renders the formal analysis much more complicated if one accounts for partial product differentiation. However, it is still possible to characterize the autarky as well as the trade equilibrium, and results from numerical simulation exercises indicate that the main insights from our analysis on adjustments in firm scale and scope are robust to this modification. A further restrictive assumption of our model is the exogenous and equal number of competitors within each industry. This assumption closes one important adjustment margin and restricts our analysis to a short-run perspective. In the long run, it is plausible that firm owners de-invest their capital stock and search for the best investment opportunities in the whole economy. If there are no extra costs of moving capital across sectors, firm owners will adjust their investment strategy in the long run until the return to their investment is the same in all industries. In comparison to our short-run model with an exogenous and equal number of competitors in all industries, this induces a movement of producers towards non-unionized industries. Since non-unionized firms are larger than unionized ones, this gives a labor demand stimulus, thereby raising the competitive as well as the union wage. Hence, compared to our short-run model firm scale and scope shrink in both unionized and non-unionized industries if capital is mobile across industries (at least as long as products are sufficiently differentiated). Another extension of our model which is worthwhile to consider is one that allows for analyzing the consequences of marginal trade liberalization. Since the introduction of trade impediments would significantly complicate our analysis, such a modification is beyond the scope of this chapter. However, we can follow Eckel and Neary (2010) and associate marginal steps of trade liberalization with an increase in the number of trading partners. In the case of perfect product differentiation, opening up for trade with an additional (symmetric) partner country reinforces the respective effects identified in the previous chapter. While this result can be extended to sufficiently high degrees of (partial) product differentiation, determining the respective effects for arbitrary levels of ρis not a trivial task and, hence, we leave a more detailed discussion of this issue open for future research. 17Derivation details are deferred to the Appendix. 2.5. APPENDIX 19 2.5 Appendix The link between wages and firm scale and scope Applying the implicit function theorem to (2.9) gives dδ(z) dw(z)=−1 w(z) eδ(z)1 + φδ(z)−φ+φ eδ(z)(1 + φδ(z)) <0.(2.13) Furthermore, substituting (2.9) into (2.8) and differentiating the resulting expression with respect to w(z) gives dX(z) dw(z)=−eδ(z)−1 2b(1 −ρ)[1 + φδ(z)] <0.(2.14) This proves the respective statements in the main text. QED. The link between the competitive wage and the union wage To show that a higher competitive wage provides a stimulus for the union wage, i.e. dwu/dwc> 0, we can define the implicit function Γ(wc, wu)≡wu−1 2wc−a (1 + φδu)(eδu−1) 1−wc wu= 0,(2.15) according to (2.11). Partially differentiating Γ(·) with respect to wcand accounting for a/wu= eδu(1 + φδu−φ) + φ, according to (2.9), we obtain ∂Γ(·) ∂wc=(eδu+ 1)(1 + φδu)−2φ(eδu−1) 2(1 + φδu)(eδu−1) ,(2.16) which is positive.18 Partially differentiating Γ(·) with respect to wugives ∂Γ(·) ∂wu= 1 −wc wu a/wu (1 + φδu)(eδu−1) +1−wc wuaeδu(1 + φδu) + φeδu−1 (1 + φδu)2(eδu−1)2 dδu dwu.(2.17) Using (2.13) and substituting a/wu=eδu(1 + φδu−φ) + φ, we can further calculate ∂Γ(·) ∂wu=−(α2β−1) −wc wu(α2β−α),(2.18) with α≡eδu(1 + φδu)−φeδu−1 (eδu−1)(1 + φδu), β ≡eδu(1 + φδu) + φeδu−1 eδu(1 + φδu)>1.(2.19) Hence, α > 1, which is equivalent to 1 −φ(eδu−δu−1) >0, is sufficient for ∂Γ(·)/∂wu<0. Using (2.9) together with (2.11), we can conclude that 1 −φ(eδu−δu−1) >0 is equivalent to ω > 1, so that ∂Γ(·)/∂wu<0 and, by applying the implicit function theorem to (2.15), also dwu/dwc>0 are immediate. 18It is immediate that the denominator of this expression is positive, while the numerator is strictly increasing in δuand equals 2 at δu= 0. 20 CHAPTER 2. LABOR UNIONS AND MULTI-PRODUCT FIRMS Proof of Proposition 1 Let us first differentiate f(z)≡w(z)[eδ(z)−1]2with respect to w(z). Accounting for (2.13), this gives19 df(z) dw(z)=−eδ(z)−1 1 + φδ(z)h(eδ(z)+ 1)(1 + φδ(z)) −2φ(eδ(z)−1)i<0.(2.20) This implies wu(eδu−1)2< wc(eδc−1)2, so that the right-hand side of (2.12) unambiguously falls in ˜z, when holding wages constant. Furthermore, combining df(z)/dw(z)<0 with dwu/dwc>0, we can conclude that the right-hand side of (2.12) determines a negative relationship between economy-wide labor demand and the competitive wage wc. Applying the implicit function theorem to Eq. (2.12), we therefore get dwc/d˜z < 0, dwu/d˜z < 0, which, in view of dδ(z)/dw(z)<0 and dX(z)/dw(z)<0 (see Eqs. (2.13) and (2.14)), establishes a positive relationship between ˜zand the scale and scope of MPFs. Finally, substituting x(i, z) from (2.6′) into l(z) = Rδ(z) 0eix(i, z)di, gives l(z) = w(z)eδ(z)−12/[4b(1 −ρ)]. Using the latter together with Eq. (2.8) X(z)/l(z) gives labor productivity, ξ, as a function of firm scope: ξ(z) = 2eδ(z)(δ(z)−1) + 1 eδ(z)−12(2.21) It is straightforward to show that dξ(z)/dδ(z)<0, so that dξ(z)/d˜z < 0 is immediate. This completes the proof of Proposition 1. QED. Deunionization and the number of product varieties when ρ= 0 The total number of product varieties is given by N≡˜zNu+ (1 −˜z)Nc= ˜znδu+ (1 −˜z)nδc. Differentiating the latter with respect to ˜z, we obtain dN d˜z=nln 1 ω−dwc d˜z˜z1 wu a+wu 4wu−wc+ (1 −˜z)1 wc,(2.22) according to (2.7).20 Totally differentiating (2.12) and accounting for a/wu= 2ω−1, a/wc= ω(2ω−1) from (2.11)21, we can calculate dwc d˜z=wc4ω(ω−1)2−[ω(2ω−1) −1]2 8˜zω3(4ω−1)−1(ω−1) + (1 −˜z)[(ω(2ω−1))2−1].(2.23) Substituting the latter into (2.22), we get dN d˜z=n(ln 1 ω−4ω(ω−1)2−[ω(2ω−1) −1]22˜zω(4ω−1)−1+ (1 −˜z) 8˜zω3(4ω−1)−1(ω−1) + (1 −˜z)[(ω(2ω−1))2−1] ).(2.24) Evaluating dN/d˜zat ˜z= 0 gives dN d˜z˜z=0 =nln 1 ω−4ω(ω−1)2−[ω(2ω−1) −1]2 [(ω(2ω−1))2−1] ,(2.25) 19For a negative sign of (2.20) the bracket term on the right-hand side of this equation must be positive. To show that this is the case, we can differentiate the bracket term and obtain eδ(z)(1 + φδ(z)−φ)+φ=a/wu>0. Furthermore, evaluating the bracket term at δ(z) = 0 gives 2. Hence, we can safely conclude that the bracket term is positive for any δ(z)>0. 20Note that with ρ= 0 total firm scope reads δ(z) = ln[a/w(z)]. 21With ρ= 0 we have wu= 1/2 [wc+a/ω]. 2.5. APPENDIX 21 which is negative for any ω > 1. Evaluating dN/d˜zat ˜z= 1 gives dN d˜z˜z=1 =nln 1 ω−ω−1 ω+[ω(2ω−1) −1]2 4ω2(ω−1) ,(2.26) which is positive for any ω > 1. This proves the respective statement in the main text. QED. Welfare effects of deunionization when ρ= 0 Setting ρ= 0 and accounting for λ= 1, we can rewrite (2.4) in the following way: q(i, z) = 1 b[a−λp(i, z)]. Substituting the latter into (2.2), gives u{z}= [n/(2b)] ha2δ(z)−Rδ(z) 0p(i, z)2i and, accounting for p(i, z) = (1/2)[a+w(z)ei], we can calculate u{z}=n 16b6a2ln[ a w(z)]−4a2+ 4aw(z)−a2+w(z)2.(2.27) And adding over all industries, we thus get U=n 16b˜zh6a2ln[ a wu]−4a2+ 4awu−a2+ (wu)2i +n 16b(1 −˜z)h6a2ln[ a wc]−4a2+ 4awc−a2+ (wc)2i(2.28) Differentiating the latter with respect to ˜z dU d˜z=n 16b6(wc)2a wc2ln 1 ω+ (wc)24a wcω+ω2−4a wc−1+ +dwc d˜z˜zdwu dwcwu4a wu+ 2 −6a wu2+ (1 −˜z)wc4a wc+ 2 −6a wc2 (2.29) Using a/wu= 2ω−1 and a/wc=ω(2ω−1) and dwu/dwc= (a+wu)/4wu−wc) = 2ω2/(4ω−1), further implies dU d˜z=n 16b(wc)224ω4−24ω3+ 6ω2ln 1 ω+ (wc)28ω3−11ω2+ 4ω−1 +dwc d˜zwc˜z2ω3 4ω−1−24ω2+ 32ω−8+ (1 −˜z)−24ω4+ 24ω3+ 2ω2−4ω+ 2 And substituting dwc d˜z=wc4ω(ω−1)2−[ω(2ω−1) −1]2 8˜zω3(ω−1)(4ω−1)−1+ (1 −˜z)[(ω(2ω−1))2−1] (2.30) we finally arrive at dU d˜z=n 16b(wc)2(24ω4−24ω3+ 6ω2ln 1 ω+ 8ω3−11ω2+ 4ω−1 +˜z2ω3 4ω−1−24ω2+ 32ω−8+ (1 −˜z)−24ω4+ 24ω3+ 2ω2−4ω+ 2ρ(ω)),(2.31) 22 CHAPTER 2. LABOR UNIONS AND MULTI-PRODUCT FIRMS with ρ(ω)≡dwc/d˜z×(wc)−1. Evaluating the latter at ˜z= 0, gives dU d˜z˜z=0 =n 16b(wc)2(24ω4−24ω3+ 6ω2ln 1 ω+ 8ω3−11ω2+ 4ω−1 +24ω4−24ω3−2ω2+ 4ω−2(4ω2+ 1)(ω−1) 4ω3+ω+ 1 ),(2.32) which is negative for any ω > 1. Furthermore, evaluating dU/d˜zat ˜z= 1, gives dU d˜z˜z=1 =n 16b(wc)2(24ω4−24ω3+ 6ω2ln 1 ω+ 8ω3−11ω2+ 4ω−1 +6ω2−8ω+ 2(4ω2+ 1)(ω−1)),(2.33) which can shown to be positive for any ω > 1. This completes the proof. QED. Proof of Proposition 2 Let us first consider the benchmark case of ρ= 0, which implies φ= 0. Rearranging terms in (2.11) and accounting for φ= 0, we can calculate wc= (a/ω) (2ω−1)−1, with ω=wu/wcand dω/dwc<0. Noting dwc/d˜z < 0 from Proposition 1, this implies dω/d˜z > 0. Furthermore, substituting δ(z) from (2.9) into ∆ = δc−δuand evaluating the resulting expression at ρ= 0, gives ∆ = ln(ω), with d∆/dω > 0 and, in view of dω/d˜z > 0, also d∆/d˜z > 0. Finally, substituting (2.8) into Ξ = Xc−Xuand evaluating the resulting expression at ρ= 0, we can calculate Ξ = a 2bln(ω)−ω−1 ω(2ω−1)(2.34) Differentiating the latter with respect to ωand evaluating the resulting expression at ω > 1, gives dΞ/dω > 0.We can thus safely conclude that dΞ/d˜z > 0. Unfortunately, we are not able to show that the insights from the benchmark scenario with perfect product differentiation (ρ= 0) extend to the more general case of partial product differentiation, when allowing for arbitrary levels of ρ. However, with all variables of interest being continuously differentiable in ρ, we can at least conclude that the respective insights from the benchmark scenario are robust to small changes in ρ. This completes the proof of Proposition 2. QED. Proof of Proposition 3 Let us first consider the benchmark case of ρ= 0. With firms being a monopolist in all submarkets of their production, opening up to trade leaves Eqs. (2.6′), (2.7) and (2.11) unaffected. Furthermore, with firms serving two instead of just a single market total firm output is given by X(z) = 2D(z) in the open economy, where D(z) equals local output in (2.8), when setting ρ= 0. As a consequence, labor demand, as determined on the right-hand side of (2.12), doubles for any wage configuration. This implies that wcand wumust increase to restore labor market clearing (see the formal discussion in the closed economy). With wcand wuincreasing, 2.5. APPENDIX 23 firm scope and domestic output must fall, according to (2.13) and (2.14). Furthermore, labor productivity increases, according to (2.21). To determine the impact of trade on total firm scale X(z), we can make use of the following fact: The impact of trade on X(z) is qualitatively the same as the impact of trade on Y(z)≡ ˆnX(z), where ˆn=nunder autarky and ˆn= 2nunder free trade. Differentiating Y(z) with respect to ˆn, accounting for (2.8) and setting ρ= 0, we can calculate dY (z) dˆn=1 2baln a w(z)−1+w(z)−w(z)a w(z)−1ˆn w(z) dw(z) dˆn.(2.35) Distinguishing between non-unionized and unionized industries, accounting for a/wc=ω(2ω−1) and a/wu= 2ω−1, according to (2.11), and using dwc/dˆn= (wc/ˆn)β(ω), with β(ω)≡4˜zω(ω−1)2+ (1 −˜z) [ω(2ω−1) −1]2 8˜zω(ω−1)2ω2/[4ω2−5ω+ 1] + (1 −˜z) [ω(2ω−1) −1] [ω(2ω−1) + 1],(2.36) according to (2.12), the latter can be rewritten as dY c dˆn=wc 2bnω(2ω−1) hln ω(2ω−1)−1i+ 1 −hω(2ω−1) −1iβ(ω)o,(2.37) dY u dˆn=wc 2bω(2ω−1) hln 2ω−1−1i+ω−4(ω−1)ω2 4ω−1β(ω),(2.38) respectively. It is tedious but straightforward to show that the right-hand sides of (2.37) and (2.38) are positive, implying that dY c/dˆn > 0, dY u/dˆn > 0. Noting from the analysis of the closed economy that ∆ = ln(ω) if ρ= 0 and recollecting from above that ωshrinks if wcincreases, it is immediate that the scope differential declines in response to a country’s movement form autarky to free trade with a symmetric partner economy. In a further step, we now look at the impact of trade on firm size differential Ξ. Noting that, with a constant number of competitors in either country, changes in Ξ are qualitatively the same as changes in Ψ ≡Yc−Yu, we can conclude from Eqs. (2.37) and (2.38) that dΞ/dˆn >, =, < 0 is equivalent to [4ω−1] ω(2ω−1) ln(ω)−(ω−1)−(ω−1) 4ω2+ 2ω−1β(ω)>, =, < 0. Furthermore, taking into account β(ω) is increasing in ˜zand that β(ω)|˜z=1 =4ω2−5ω+ 1/(2ω2), we can further conclude that ζ(ω)≡2ω2ω(2ω−1) ln(ω)−(ω−1)−(ω−1)24ω2+ 2ω−1>0 is sufficient for dΞ/dˆn > 0.22 Noting finally that the variables of interest are continuously differentiable in ρ, we can conclude that the insights from above are robust to small changes in ρ. This completes the proof of Proposition 3. QED. Characterization of the open economy equilibrium: the case of ρ > 0 In the open economy, a firm’s domestic output, D(z), is given by Eq. (2.8). Due to symmetry of trading partners, a similar expression is obtained for the foreign economy: D∗(z), where the asterisk is introduced to indicate foreign variables. Total sector output in the open economy is 22Differentiating ζ(ω) three times gives ζ′′′(ω) = 96ωln(ω)−12 ln(ω) + 8ω+ 2 >0. Together with ζ′′(1) = 0, this proves that the second derivative of ζ(·) is strictly positive for any ω > 1. Noting further that ζ′(1) = 0, we can also conclude that the first derivative of ζ(·) is strictly positive for any ω > 1. Noting finally that ζ(1) = 0, therefore proves that ζ(·) has a positive sign for any ω > 1. 24 CHAPTER 2. LABOR UNIONS AND MULTI-PRODUCT FIRMS then given by Y(z) = nD(z) + nD∗(z). Substituting the latter together with (2.8) – separately for the home and the foreign country – into (2.7) and noting that in the open economy D(z) assumes the role that X(z) had in the closed economy, we can calculate eδ(z)=1 w(z) a−w(z)φ−w∗(z)φ[n/(n+ 1)][eδ∗(z)(δ∗(z)−1) + 1] 1 + φδ(z)−φ,(2.39) eδ∗(z)=1 w∗(z) a−w∗(z)φ−w(z)φ[n/(n+ 1)][eδ(z)(δ(z)−1) + 1] 1 + φδ∗(z)−φ(2.40) for domestic and foreign firms’ scope, respectively. Thereby, φ=ρ(n+ 1)/[2(1 −ρ)] is the same as in the closed economy. In the case of symmetry, with δu=δu∗and wu=wu∗, Eq. (2.39) can be simplified to δ(z) = ln a/w(z)−φ(2n+ 1)/(n+ 1) 1 + φ(δ(z)−1)(2n+ 1)/(n+ 1).(2.41) Equipped with these insights we can now solve the wage-setting problem of labor unions. Following the steps from the analysis in the closed economy and using eδufrom (2.39) instead of (2.9), we can calculate the first-order condition for the Ω-maximization problem as follows dΩ dwu=n(eδu−1 2b(1 −ρ)(2wu−wc)eδu−1+ 2wu(wu−wc)eδudδu dwu= 0.(2.42) Applying the implicit function theorem to system (2.39), (2.40) and evaluating the resulting expression at δu=δu∗(symmetry), we get dδu dwu=−1 wueδu(1 + φδu−φ) + φ(1 + φδu)−φ2[n/(n+ 1)]2eδu(δu−1) + 1δu eδuh(1 + φδu)2−(φδu)2[n/(n+ 1)]2i.(2.43) Substituting (2.43) into (2.42), we obtain after tedious but straightforward calculations: wu=wc1 2 (eδu−1) 1−eδu+H(δu)+ 1,(2.44) where H(δu)≡(1 + φδu)eδu(1 + φδu−φ) + φ−φ2δu[n/(n+ 1)]2eδu(δu−1) + 1 (1 + φδu)2−φδu[n/(n+ 1)]2.(2.45) Finally, we can write the full employment condition as follows L=n 2b(1 −ρ)˜zwueδu−12+ (1 −˜z)wceδc−12.(2.46) Putting all elements together, the open economy equilibrium is characterized by (2.8), (2.41) – separately for uand c–, (2.44), and (2.46). This completes the characterization of the open economy. 2.5. APPENDIX 25 2.5.1 Extension – Linear cost function In the main text, we represent adaptation costs by an exponential unit cost-density function. In this extension, we check the robustness of our results when changing our assumption, regarding the functional form of adaptation costs. To be more specific, we consider the linear specification γj(i) = 1 + i, and investigate whether the main insights from our analysis remain the same in this modified framework. To keep the analysis tractable, we focus on a benchmark scenario with ρ= 0 throughout the subsequent discussion. With a linear cost specification, product-specific output and the product range are given by xj(i, z) = a−(1 + i)w(z) 2bδj(i, z) = a w(z)−1 (2.47) instead of (2.6) and (2.7), while product-specific output relative to the marginal good is given by xj(i, z) = w(z)[δ(z)−i] 2b(2.48) instead of (2.6′). Integrating xj(i, z) over all varieties gives, after straightforward calculations, total firm output Xj(z) = w(z)δ(z)2/(4b). To calculate firm-level labor demand lj(z) we use (2.48) in lj(z) = Rδ(z) 0xj(i, z)γ(i)di and obtain lj(z) = ah(a/w(z))2−3 + 2w(z)/ai/(12b). With these insights at hand, we are now well equipped to calculate the union wage. For this purpose, we substitute lj(z) into the union objective function Ω = [w(z)−wc]nl(z) (and suppress firm indices in the interest of better readability). Differentiating Ω with respect to wu and setting the resulting expression equal to zero, we can calculate23 wu= 2wc(δu)2+ 3δu+ 3 (δu)2+ 3δu+ 6.(2.49) Furthermore, accounting for δu=a/wu−1, we can rewrite (2.49) as follows wu= 2wca2+awu+ (wu)2 a2+awu+ 4(wu)2.(2.50) Applying the implicit function theorem, we can furthermore calculate dwu dwc= 2 a2+awu+ (wu)2 a2+ 2a(wu−wc) + 4wu(3wu−wc).(2.51) Hence, (2.50) establishes a positive relationship between wcand wu. Before turning to the general equilibrium outcome, it is worth inspecting the firm scale and scope differential between non-unionized and unionized firms. The scope differential is given by ∆ = δc−δu=a/wc−a/wu, which, in view of (2.47), can be rewritten as ∆ = [1 + δc]1−1 ω,(2.52) which is unambiguously positive, as wu> wcand thus ω > 1. The scale differential is given by Ξ = Xc−Xu=wc(δc)2−wu(δu)2/(4b) and, accounting for (2.47), we can calculate Ξ = wc 4bha wc(δc−δu) + 1 −ωi,(2.53) 23Noting that [(δu)2+ 3δu+ 3]/[(δu)2+ 3δu+ 6] ≥1/2, we can easily confirm that wu≥wc. 26 CHAPTER 2. LABOR UNIONS AND MULTI-PRODUCT FIRMS which is positive as a > wu> wc.24 The general equilibrium outcome is characterized by the labor market clearing condition L=R1 0Rδ(z) 0nx(i, z)γ(i)didz =nR1 0l(z)dz. Rearranging terms, we get25 L=an 12b˜za wu2−3 + 2wu a+ (1 −˜z)a wc2−3 + 2wc a (2.54) We are now prepared to study the implications of deunionization in the closed economy. In analogy to the model variant in the main text, a decrease in ˜zraises economy-wide labor demand and hence wcmust increase in order to restore a labor market equilibrium. Formally, this can be shown by applying the implicit function theorem to (2.54). Furthermore, a higher competitive wage provides a stimulus for the union wage, according to (2.51), so that wualso increases in response to a decline in ˜z. Due to these wage effects, it is immediate that unionized as well as non-unionized firms lower the scope in response to deunionization, i.e. δcand δu decrease, according to (2.47). Accounting for X(z) = w(z) 4bδ(z)2=1 4ba2 w(z)−2a+w(z)(2.55) it is straightforward to show that both Xcand Xudecline in response to deunionization, i.e. all firms, except of the newly deunionized ones, shrink if ˜zfalls. Aside from these firm-level effects, we can also analyze the differential impact of deunionization on unionized and non-unionized firms. For this purpose, we can first analyze the impact of a decline in ˜zon ω. From (2.49) ω= 2(δu)2+ 3δu+ 3 (δu)2+ 3δu+ 6.(2.56) Since the right-hand side of the latter increases in δu, it follows from our insights above that a decline in ˜zinduces a fall in ω. However, since wcincreases while ωfalls in response to deunionization, it follows from (2.52) that the scope differential between non-unionized and unionized producers shrinks if ˜zdeclines. With firms concentrating more on their core competence products, labor productivity is stimulated by deunionization in our model. Regarding the impact of deunionization on the firm scale differential, it is worth noting that (2.55) implies Ξ = 1 4ba2 wc1−1 ω+wc(1 −ω)(2.57) Differentiating Ξ with respect to ˜z, then implies dΞ d˜z=1 4b−a wc21−1 ω+ 1 −ωdwc d˜z+wca wu2−1dω d˜z.(2.58) 24To see this, note that (1 + δc)(δc−δu) = (1 + δc)2(1 −1/ω), according to (2.52). Hence, Ξ >0 is equivalent to (1 + δc)2> ω and, in view of (2.47), equivalent to (a/wc)2> wu/wc. This implies that a > wu> wcis sufficient for Ξ >0. 25Defining f(z)≡a3/w(z)2−3a+ 2w(z) and accounting for ∂f(z)/∂w(z) = 2[1 −(a/w(z))3]<0, it is easily confirmed that the right-hand side (RHS, in short) of (2.54) is strictly decreasing in wc. Furthermore, noting that limwc→0RHS =∞, while limwc→aRHS = 0, we can safely conclude that there exists a unique equilibrium with factor market clearing in our model. 2.5. APPENDIX 27 And noting dwc/d˜z < 0, dω/d˜z > 0 from above, we can conclude that the firm size differential shrinks if ˜zdeclines. This completes our discussion upon firm-level adjustments in response to deunionization. And we can now turn to analyzing the open economy.26 Similar to the scenario with an exponential cost-distance function, trade raises economy-wide labor demand, so that wcincreases. This provides a stimulus for wu, while δuand δcshrink. As firms produce less varieties their productivity increases. Furthermore, similar to the model variant in the main text, we find that any firm’s total domestic sales, D(z), shrink, that ωfalls and that the scope differential, ∆, decreases. To analyze the impact on total firm output we follow the analysis in the main text and note that the impact of trade on total firm output can be inferred from dY/dˆn, where Y(z) = ˆnX(z) = ˆn 4bw(z)a w(z)−12 (2.59) is industry-wide output. Straightforward calculations give dY (z) dˆn=1 4bw(z)a w(z)−12 +ˆn 4b dw(z) dˆn"1−a w(z)2#.(2.60) And, following the derivation in the main text step by step, we arrive at dY c dˆn=1 4bwcha wc−1i2+1 4b g(wc) g′(wc)a wc2−1,(2.61) where g(wc)≡˜za a wu2−3 + 2wu a+ (1 −˜z)aa wc2−3 + 2wc a>0 (2.62) and g′(wc) = 2˜zdwu dwc1−a wu3+ 2(1 −˜z)1−a wc3<0.(2.63) We can thus conclude that dY c/dˆn >, =, < 0 is equivalent to 0>, =, < wcha wc−1i2g′(wc) + g(wc)a wc2−1(2.64) Accounting for g(wc) and g′(wc) from above and substituting κ≡a/wu, we can further note that dY c/dˆn >, =, < 0 is equivalent to 0>, =, <˜zωκ3−3κ+ 2(κω + 1) −2κ3−1(κω −1) dwu dwc + (1 −˜z)κ3ω3−3κω + 2(κω + 1) −2κ3ω3−1(κω −1) ,(2.65) 26We have also analyzed the impact of deunionization on the total number of available product varieties N. While we do not present details of this analysis here, it is worth noting that similar to the main text, deunionization does not exert a monotonic impact on N. To be more specific, our results indicate that N increases in response to deunionization if ˜zhas been small initially, while the opposite is true if ˜zhas been large prior to the deunionization shock. 34 CHAPTER 2. LABOR UNIONS AND MULTI-PRODUCT FIRMS Print["Scale unionized autarky: ", Du=(wu1(Exp[δu1](δu1-1)+1))/(2b(1-ρ))];18 Print["Scale non-unionized autarky: ", Dc=(wc1(Exp[δc1](δc1-1)+1))/(2b(1-ρ))];19 In a next step we use Equations (2.44), (2.41) and (2.46) from the open economy to define Hδut=20 21 ((φ+(1+φ*δut-φ)Exp[δut])(1+φ*δut)-((ρ*n)ˆ2*δut(Exp[δut](δut-1)+1))/(4(1-ρ)ˆ2))/22 ((1+φδut)ˆ2-((ρ*n)ˆ2*δutˆ2)/(4(1-ρ)ˆ2));23 g10=wct(1+(0.5(Exp[δut]-1))/(1-Exp[δut]+Hδut));24 g20=Log[(a/wut-φ((2n+1)/(n+1)))/(1+((2n+1)/(n+1))(φ*δut-φ))];25 g30=Log[(a/wct-φ((2n+1)/(n+1)))/(1+((2n+1)/(n+1))(φ*δct-φ))];26 g40=(2*b(1-ρ)L/n-z*wut(Exp[δut]-1)ˆ2)/((1-z)(Exp[δct]-1)ˆ2);27 where the letter tadded to wu, wc, δu and δc refers to trade. To solve the open economy situation, we use the FindRoot command and print the variables of interest: B=FindRoot[{wut==g10,δut==g20,δct==g30,wct==g40},{wct, 75},{wut, 89},{δct,28 0.15},{δut, 0.1}];29 Print["Union wage trade: ", wut1=g10/.B];30 Print["Scope unionized trade: ", δut1=g20/.B];31 Print["Scope non-unionized trade: ", δct1=g30/.B];32 Print["Competitive wage rate trade: ", wct1=g40/.B];33 Print["Scale home unionized trade: ",34 Dut=(wut1(Exp[δut1](δut1-1)+1))/(2*b(1-ρ))];35 Print["Scale home non-unionized trade: ",36 Dct=(wct1(Exp[δct1](δct1-1)+1))/(2*b(1-ρ))];37 Print["Scale unionized trade: ", Xut=(wut1(Exp[δut1](δut1-1)+1))/(b(1-ρ))];38 Print["Scale non-unionized trade: ",39 Xct=(wct1(Exp[δct1](δct1-1)+1))/(b(1-ρ))];40 Finally, we compare the free trade with the closed economy variables, to derive the values as reported in Table 2.1. Print["Impact on union wage: ", Round[wut1-wu1,0.01]];41 Print["Impact on competitive wage: ", Round[wct1-wc1,0.01]];42 Print["Impact on scope unionized: ", Round[δut1-δu1,0.01]];43 Print["Impact on scope non-unionized: ", Round[δct1-δc1,0.01]];44 Print["Impact on scale home unionized: ", Round[Dut-Du,0.01]];45 Print["Impact on scale home non-unionized: ", Round[Dct-Dc1,0.01]];46 Print["Impact on scale unionized: ", Round[Xut-Du,0.01]];47 Print["Impact on scale non-unionized: ", Round[Xct-Dc,0.01]];48 Program code for Table 2.2 In the following we offer the source code to derive the reported values from Table 2.2. At first, we set the parameter values: a= 100, b= 1, ρ= 0.8, n= 5, L= 20, which determines φ=ρ(n+ 1)/[2(1 −ρ)] and set the share of unionized industry equal to ˜z= 0.1, ˜z= 0.3 or ˜z= 0.5. Clear["Global‘*"];1 2.5. APPENDIX 35 a=100;2 b=1;3 ρ=0.8;4 n=5;5 L=20;6 φ=(ρ(n+1))/(2(1-ρ));7 z=0.1; (* z=0.3 ; z=0.5 *)8 In a next step we use Equations (2.9), (2.85) and (2.12) to define Gδu=9 (((ρ(n+1))(Exp[δu]δu+1)-(3*ρ*n-2*ρ*n)Exp[δu])(4(ρ-1)-ρ(n+1)δu)+10 4(1-ρ)ˆ2(n-1)Exp[δu])/ ((2*n(ρ-1)-ρ(n+1)δu)(4(ρ-1)-(ρ(n+1)δu))-4(1-ρ)ˆ2(n-1));11 g1=wc(1-0.5(Exp[δu]-1)/(Exp[δu]-1+Gδu));12 g2=Log[(a/wu-φ)/(1+φδu-φ)];13 g3=Log[(a/wc-φ)/(1+φδc-φ)];14 g4=(4*b(1-ρ)L/n-z*wu(Exp[δu]-1)ˆ2)/((1-z)(Exp[δc]-1)ˆ2);15 To solve the autarky situation, we use the FindRoot command and print the variables of interest, that are listed in Table 2.2: B=FindRoot[{wu==g1,δu==g2,δc==g3,wc==g4},{wc, 40},{wu, 50},{δc, 0.15},{δu,16 0.1}];17 Print["Competitive wage: ", wc1=g4/.B];18 Print["Union wage: ", wu1=g1/.B];19 Print["Scope non-unionized: ", δc1=g3/.B];20 Print["Scope unionized: ", δu1=g2/.B];21 Print["Scale non-unionized: ", Xc=(wc1(Exp[δc1](δc1-1)+1))/(2*b(1-ρ))];22 Print["Scale unionized: ", Xu=(wu1(Exp[δu1](δu1-1)+1))/(2*b(1-ρ))];23 Print["Union wage premium: ", ω=wu1/wc1];24 Print["Scope Differential: ", Δ=δc1-δu1];25 Print["Scale Differential: ", Ξ=Xc-Xu];26 Print["Number of varieties: ", Nt=z*n*δu1+(1-z)n*δc1];27 Program code for Table 2.3 In the following we offer the source code to derive the reported values from Table 2.3. At first, we set the parameter values: a= 100, b= 1, ρ= 0.8, n= 5, L= 20, which determines φ=ρ(n+ 1)/[2(1 −ρ)] and set the share of unionized industry equal to ˜z= 0.1, ˜z= 0.3 or ˜z= 0.5. Clear["Global‘*"];1 a=100;2 b=1;3 ρ=0.8;4 n=5;5 L=20;6 φ=(ρ(n+1))/(2(1-ρ));7 z=0.1; (* z=0.3 ; z=0.5 *)8 In a next step we use Equations (2.9), (2.85) and (2.12) to define 36 CHAPTER 2. LABOR UNIONS AND MULTI-PRODUCT FIRMS Gδu=9 (((ρ(n+1))(Exp[δu]δu+1)-(3*ρ*n-2*ρ*n)Exp[δu])(4(ρ-1)-ρ(n+1)δu)+10 4(1-ρ)ˆ2(n-1)Exp[δu])/ ((2*n(ρ-1)-ρ(n+1)δu)(4(ρ-1)-(ρ(n+1)δu))-4(1-ρ)ˆ2(n-1));11 g1=wc(1-0.5(Exp[δu]-1)/(Exp[δu]-1+Gδu));12 g2=Log[(a/wu-φ)/(1+φδu-φ)];13 g3=Log[(a/wc-φ)/(1+φδc-φ)];14 g4=(4*b(1-ρ)L/n-z*wu(Exp[δu]-1)ˆ2)/((1-z)(Exp[δc]-1)ˆ2);15 To solve the autarky situation, we use the FindRoot command and print the variables of interest: B=FindRoot[{wu==g1,δu==g2,δc==g3,wc==g4},{wc, 40},{wu, 50},{δc, 0.15},{δu,16 0.1}];17 Print["Union wage autarky: ", wu1=g1/.B];18 Print["Scope unionized: ", δu1=g2/.B];19 Print["Scope non-unionized: ", δc1=g3/.B];20 Print["Competitive wage autarky: ", wc1=g4/.B];21 Print["Scale unionized autarky: ", Du=(wu1(Exp[δu1](δu1-1)+1))/(2*b(1-ρ))];22 Print["Scale non-unionized autarky: ",23 Dc=(wc1(Exp[δc1](δc1-1)+1))/(2*b(1-ρ))];24 In a next step we use Equations (2.41), (2.46) and (2.85) to define Gδut=25 (((ρ(2n+1))(Exp[δut]δut+1)-(6*ρ*n-4*ρ*n)Exp[δut])(4(ρ-1)-ρ(2*n+1)δut)26 +4(1-ρ)ˆ2(2*n-1)Exp[δut])/27 ((4*n(ρ-1)-ρ(2*n+1)δut)(4(ρ-1)-(ρ(2*n+1)δut))-4(1-ρ)ˆ2(2*n-1));28 g10=wct(1-0.5(Exp[δut]-1))/(Exp[δut]-1+Gδut);29 g20=Log[(a/wut-φ((2*n+1)/(n+1)))/(1+((2n+1)/(n+1))φδut-φ)];30 g30=Log[(a/wct-φ((2*n+1)/(n+1)))/(1+((2n+1)/(n+1))φδct-φ)];31 g40=(2*b(1-ρ)L/n-z*wut(Exp[δut]-1)ˆ2)/((1-z)(Exp[δct]-1)ˆ2);32 To solve the open economy situation, we use the FindRoot command and print the variables of interest: B=FindRoot[{wut==g10,δut==g20,δct==g30,wct==g40},{wct, 40},{wut, 50},{δct,33 0.15},{δut, 0.1}];34 Print["Union wage trade: ", wut1=g10/.B];35 Print["Scope unionized trade: ", δut1=g20/.B];36 Print["Scope non-unionized trade: ", δct1=g30/.B];37 Print["Competitive wage rate trade: ", wct1=g40/.B];38 Print["Scale home unionized trade: ",39 Dut=(wut1(Exp[δut1](δut1-1)+1))/(2*b(1-ρ))];40 Print["Scale home non-unionized trade: ",41 Dct=(wct1(Exp[δct1](δct1-1)+1))/(2*b(1-ρ))];42 Print["Scale unionized trade: ", Xut=(wut1(Exp[δut1](δut1-1)+1))/(b(1-ρ))];43 Print["Scale non-unionized trade: ",44 Xct=(wct1(Exp[δct1](δct1-1)+1))/(b(1-ρ))];45 Finally, we compare the free trade with the closed economy variables, to derive the values as reported in Table 2.1. 2.5. APPENDIX 37 Print["Impact on union wage: ", Round[wut1-wu1,0.01]];46 Print["Impact on competitive wage: ", Round[wct1-wc1,0.01]];47 Print["Impact on scope unionized: ", Round[δut1-δu1,0.01]];48 Print["Impact on scope non-unionized: ", Round[δct1-δc1,0.01]];49 Print["Impact on scale home unionized: ", Round[Dut-Du,0.01]];50 Print["Impact on scale home non-unionized: ", Round[Dct-Dc1,0.01]];51 Print["Impact on scale unionized: ", Round[Xut-Du,0.01]];52 Print["Impact on scale non-unionized: ", Round[Xct-Dc,0.01]];53 38 CHAPTER 2. LABOR UNIONS AND MULTI-PRODUCT FIRMS Chapter 3 Trade and the Firm-Internal Allocation of Workers to Tasks 3.1 Introduction In any industrialized economy, labor markets have to solve the complex problem of matching task-specific skill requirements and worker-specific abilities. The outcome of this matching process is typically not efficient. This is not only because some workers do not find a job at all. Rather, a significant share of workers cannot exploit full productivity because they are not matched with the best occupation (see Legros and Newman, 2002; Eeckhout and Kircher, 2011). In recent years, this source of inefficiency has also sparked considerable attention in the trade literature. With an increasing general interest in the consequences of trade for underemployment, several authors have highlighted improvements in matching quality as a key aspect of gains from trade in terms of both welfare and employment (Amiti and Pissarides, 2005; Davidson, Matusz, and Shevchenko, 2008; Larch and Lechthaler, 2011). Thereby, the typical approach is to associate the quality of the matching process with its ability to match heterogeneous workers with heterogeneous firms in an efficient way, assuming implicitly that the production process covers just a single task with a certain skill requirement. However, this ignores the sophisticated structure of modern production processes and thus misses an important role of firms in reducing the requirement-ability mismatch by improving the assignment of workers to specific tasks within the boundaries of a single production entity.1 Studying the role of firms for matching workers with tasks and discussing how access to trade affects the matching outcome is the main purpose of this chapter. Starting point of our analysis is a Melitz (2003) model, in which firms are heterogeneous due to differences in their productivity levels. As in Acemoglu and Autor (2011), we assume that production consists of a continuum of tasks that differ in their skill requirements. For performing these tasks, firms hire heterogeneous workers. Heterogeneity is horizontal in the sense that workers differ in their ability to perform specific tasks because their human capital is occupation-specific (see 1The idea that the quality of worker-task matches are important for firm performance at least dates back to work by Barron and Loewenstein (1985) and Barron, Black, and Loewenstein (1989). Meyer (1994) points to the relevance of optimal task assignment in the context of team production. Burgess, Propper, Ratto, von Hinke Kessler Scholder, and Tominey (2010) show that productivity losses from a mismatch of workers and tasks in teams can indeed be significant and that one important channel through which incentive payments to managers can improve the outcome of production units is the better assignment of workers to tasks. 39 40 CHAPTER 3. TRADE AND THE ALLOCATION OF WORKERS TO TASKS Kambourov and Manovskii, 2009; Sullivan, 2010, for empirical evidence), while they are equally productive over the whole range of activities. This implies that all workers have the same value to firms and, lacking information about abilities of individual workers, firms randomly draw their employees from the labor supply pool. This lack of information generates a source of mismatch between task-specific skill requirements and worker-specific abilities within the boundaries of a production unit. To reduce this mismatch, firms can invest into a screening technology for gathering some (imperfect) information about the abilities of their workforce. We model the screening investment in a rudimentary way, allowing for two possible interpretations that are common in the literature. On the one hand, screening may be part of the recruitment process as in Helpman, Itskhoki, and Redding (2010) and can help narrowing the pool of suitable applicants. On the other hand, screening may take place after the recruitment of workers, for instance, in the form of job rotation (see Li and Tian, 2013).2In both interpretations, a higher investment provides better knowledge about the abilities of workers and therefore leads to a better match of these workers with the different tasks in the production process (cf. Pellizzari, 2011). The incentives to screen are more pronounced in larger firms, and hence there is an additional source of heterogeneity in our model, which is endogenous and reinforces heterogeneity of firms due to exogenous differences in firm productivity. We use this model to shed new light on the consequences of trade for labor market outcome, thereby focussing on adjustments in the firm-internal labor market.3To be more specific, we are interested in how trade affects underemployment arising from a mismatch between workerspecific abilities and task-specific skill requirements. To keep the analysis simple, we focus on trade between symmetric countries and consider the empirically relevant case, in which only the most productive firms export in the open economy (see, for instance, Bernard and Jensen, 1995, 1999). Having access to the export market, high-productivity firms can expand their market share in the open economy, which provides an incentive for these firms to screen their workforce more intensively, as this further improves the matching quality and thus lowers production costs. Low-productivity non-exporters, on the other hand, lose market share and thus lower their investment into the screening technology, which raises their production costs. By changing the cost structure, this asymmetric response to trade liberalization exerts a feedback effect on the entry/exit decision of firms in both the domestic and the export market, which is not present in other trade models with heterogeneous firms. Furthermore, it alters the productivity distribution of active firms by driving a wedge between matching efficiency of exporters and nonexporters. This provides an alternative to the ‘learning-by-exporting’ hypothesis for explaining the empirical finding that firms become more productive when entering the export market (see Fryges and Wagner, 2008).4Finally, adjustments in the firm-internal labor allocation process lower the aggregate mismatch between worker-specific abilities and task-specific skill requirements, thereby generating a productivity stimulus that reinforces the gains from trade in an otherwise identical Melitz (2003) model. The firm-level adjustments to trade liberalization 2The literature distinguishes three motives for job rotation: employee learning (job rotation as a training device); employee motivation (job rotation makes work more interesting) and employer learning (job rotation as a way to discover in which jobs different employees are best at). Our model is in line with the ‘employer learning’ view, which was first discussed by Ortega (2001). Empirical support for this motive is provided by Eriksson and Ortega (2006). 3According to Doeringer and Piore (1971) an internal labor market is “an administrative unit, such as a manufacturing plant, within which the pricing and allocation of labor is governed by a set of administrative rules and procedures. [... This market] is to be distinguished from the external labor market of conventional economic theory where pricing, allocating and training decisions are controlled directly by economic variables” (pp. 1f). 4Greenaway and Kneller (2007) and Wagner (2007) summarize existing empirical evidence regarding the feedback effects of exporting on firm productivity. Our reading of the literature is that there is some support for such a positive feedback effect, but not all existing studies can identify a significant impact. 3.1. INTRODUCTION 41 are not so different, in principle, from the adjustments in Helpman, Itskhoki, and Redding (2010). In their model, firms can invest into a screening technology in order to receive a more precise signal about the quality of applicants. More specifically, screening allows the firm to detect (and reject) applicants below a certain ability threshold. The higher the investment, the more effective is screening and the higher is the average ability of workers employed by the firm. The screening investment is endogenous and responds to trade in a similar way as the screening investment does in our model. It increases in exporting firms and shrinks in non-exporting ones. Aside from these similarities, there is a crucial difference between the focus of Helpman, Itskhoki, and Redding (2010) and the focus of this chapter. Whereas Helpman, Itskhoki, and Redding (2010) study imperfections in the external labor market, we are interested in the firm-internal allocation of workers. To be more explicit, in our setting all workers are equally valuable to firms and only differ in their ability to perform specific tasks, whereas workers in Helpman, Itskhoki, and Redding (2010) differ in the productivity they can elicit in a firm of a specific type. Hence, there is an efficiency loss in the Helpman, Itskhoki, and Redding (2010) model, because firms are not matched with the ideal worker, while there is an efficiency loss in our setting, because workers do not perfectly fit the skill requirements of tasks they are performing within the boundaries of a firm. By opening up the black box of production and modeling explicitly the firm-internal labor allocation process, our model not only identifies a new channel through which positive trade effects can materialize, but also contributes to a growing literature on the role of globalization for firm organization. A first line of research in this literature has pointed to the role of openness for the boundaries of firms (see Grossman and Helpman, 2002; Antr´as, 2003; Antr´as and Helpman, 2004; Conconi, Legros, and Newman, 2012). In contrast to these studies, we focus on the question how trade changes the organization of labor within these boundaries. This renders our analysis akin to Marin and Verdier (2008a, 2012) who investigate the impact of trade on the hierarchy structure in firms and the incentives to empower human capital. The hierarchy structure of firms is also addressed by Caliendo and Rossi-Hansberg (2012) who analyze how access to exporting changes the number of layers of management.5In contrast to all of these studies, we do not look on changes in the hierarchy structure but on matching quality, so that our findings are complementary to the results in this literature. Finally, the key mechanism discussed in this chapter differs from a pure division of labor effect, which arises if there is a change in the number of tasks performed by a single worker (Becker and Murphy, 1992) or a team of workers (Chaney and Ossa, 2013). In our setting, it is not the number of tasks performed by a single worker but rather the matching of workers with these tasks that matters. The remainder of the chapter is organized as follows. In Chapter 3.2, we set up a baseline model with a perfect labor market and characterize the equilibrium in the closed economy. In Chapter 3.3, we consider trade between two symmetric countries, characterize the open economy equilibrium, and investigate how a movement from autarky to trade affects the allocation of labor ‘inside’ the firm as well as per capita income. We also shed light on the consequences of marginal trade liberalization. In Chapter 3.4, we extend the baseline model to one with search frictions in the hiring process and analyze how imperfections in the outside labor market alter our insights regarding the impact of trade on the firm-internal organization of workers. Chapter 3.5 provides a calibration exercise that allows us to quantify the impact of trade on welfare and underemployment. Chapter 3.6 concludes with a brief summary of the most important results. 5In a recent study, Sly (2012) investigates the composition of management teams and shows that trade can alter this composition significantly. 42 CHAPTER 3. TRADE AND THE ALLOCATION OF WORKERS TO TASKS 3.2 The closed economy 3.2.1 Model structure We consider an economy that is populated by an exogenous mass of workers L, who supply one unit of labor in a perfectly competitive labor market. There are two sectors of production: a perfectly competitive final goods industry that produces a homogeneous output good by assembling differentiated intermediate goods; and a monopolistically competitive intermediate goods industry that hires labor for its production of differentiated goods. Similar to Egger and Kreickemeier (2009, 2012), we represent the final goods technology by a constant-elasticity-ofsubstitution (CES) production function without external scale economies. To be more specific, we assume that the technology for producing final output Yis given by Y=M−1 σZω∈Ω x(ω)σ−1 σdωσ σ−1 ,(3.1) where x(ω) denotes the quantity of intermediate good ωused in the final goods production, Mis the Lebesgue measure of set Ω and represents the mass of available intermediate goods, and σ > 1 denotes the (constant) elasticity of substitution between different product varieties. Yserves as num´eraire in our analysis, implying that the price index corresponding to the production function in Eq. (3.1) is equal to one, by assumption. Denoting by p(ω) the price of intermediate good ω, we can write total costs of producing output Yas follows: Rω∈Ωp(ω)x(ω)dω. Maximizing final goods profits with respect to x(ω), then gives intermediate goods demand x(ω) = Y Mp(ω)−σ.(3.2) At the intermediate goods level, there is a continuum of firms, each of them supplying a unique variety under monopolistic competition. Following Acemoglu and Autor (2011), we assume that intermediate goods production is a composite of different tasks. To be more specific, there is a continuum of tasks that is represented by the unit interval. The production technology is of the Cobb-Douglas type and given by x(ω) = φ(ω) exp Z1 0 ln x(ω, i)di,(3.3) where x(ω, i) is the production level of task iin firm ωand φ(ω) is this firm’s baseline productivity. Task x(ω, i) is performed (produced) by workers who are employed in a linear-homogenous production technology, which is the same for all tasks. To keep things simple, we assume that task-level output is equal to the effective labor input: the mass of workers performing the task multiplied by these workers’ average productivity. The productivity of workers in performing a specific task differs, because workers differ in their abilities, whereas tasks differ in their skill requirements. To capture this in a tractable way, we assume that both workers and tasks are uniformly distributed along the unit interval, and the gap between ability and skill requirement is measured by the distance of a worker to the task in the unit interval. In the hiring process firms have to solve the problem of matching specific workers with specific tasks, and this is essential because firms face an efficiency loss from mismatch if workers do not end up in those occupations, in which they have the highest competence. The degree of mismatch depends on the average distance between workers and tasks in a firm’s production process. To determine this average distance, we can first note that the expected distance when 3.2. THE CLOSED ECONOMY 43 randomly assigning workers from interval [0, b] to a task located at t∈[0, b] is given by dist(t) = 1 b"Zt 0 (t−j)dj +Zb t (j−t)dj#=1 bt2−tb +b2 2,(3.4) where jgives the location of workers in the considered interval. Accordingly, the expected distance when drawing trandomly from interval [0, b] amounts to d dist =1 b2Zb 0t2−tb +b2 2dt =b 3.(3.5) From (3.5) it follows that the extent of mismatch crucially depends on the length of the interval, b. We interpret bas the amount of information firms have about the location of workers in the unit interval. Without screening, firms are uninformed about the specific abilities of their applicants. Hence, they hire workers by randomly selecting them from the labor supply pool at the common market-clearing wage rate w.6This gives b= 1 and d dist = 1/3. However, firms do not have to accept this outcome. They can reduce the efficiency loss from mismatch by screening their applicants. Similar to Helpman, Itskhoki, and Redding (2010), we associate the implementation of a screening technology with a fixed cost expenditure fµ= [1+µ(ω)]γand assume that screening provides an imprecise signal about worker ability, with the quality of the signal increasing in screening effort µ(ω). To be more specific, by screening with effort µ(ω), a firm can divide the ability interval into 1+µ(ω) segments of equal length. Firms can then hire workers at the market-clearing wage rate, w, for a specific task by randomly selecting them from the respective ability segment, so that the average distance between worker-specific abilities and task-specific skill requirements reduces to d dist(ω) = (1/3) [1 + µ(ω)]−1.7 At the firm level, efficiency of workers in the performance of tasks is inversely related to d dist(ω) and denoted by κ(ω). In the interest of analytical tractability, we choose a specific functional form and capture the relationship between κ(ω) and d dist(ω) by κ(ω)≡(1/3)d dist(ω)−1. This gives κ(ω) = 1 + µ(ω). Effective labor input at the task level is therefore given by [1 + µ(ω)]l(ω) and, since tasks enter production function (3.3) symmetrically, total output of firm ωcan be written in the following way: x(ω) = φ(ω) [1 + µ(ω)] l(ω).(3.6) According to (3.6), firm productivity consists of two parts: an exogenous baseline productivity φ(ω), which captures the efficiency of coordinating the bundle of different tasks within the boundaries of the firm, and an endogenous productivity term κ(ω) = 1 + µ(ω), which captures how effectively the heterogeneous abilities of workers are used for performing the different tasks in the production process. Crucially, firms can increase their productivity by investing into a screening technology which improves the matching quality in the firm-internal labor allocation process and thus raises κ(ω).8 The baseline productivity is drawn by firms in a lottery from the common Pareto distribution, G(φ) = 1−φ−ν. To participate in this lottery, firms have to pay a fee fein units of final output Y. This investment allows just a single draw and is immediately sunk. After productivity levels 6Due to symmetry, all workers receive the same wage in equilibrium, irrespective of their location in the ability interval. 7We ignore integer problems and, due to symmetry, suppress task indices. 8This mechanism is not too different, in principle, from an R&Dinvestment that lowers variable production costs (see, for instance, Eckel, 2009). 50 CHAPTER 3. TRADE AND THE ALLOCATION OF WORKERS TO TASKS Proof. Analysis in the text. Due to asymmetric firm-level consequences, it is clear that access to trade exerts counteracting effects on the general equilibrium variables of interest: wage rate (welfare) wand underemployment u. Similar to the autarky scenario, the wage rate in the open economy, can be derived by combining r(φ∗) = p(φ∗)x(φ∗) with the adding up condition Y=M(1 + χfx/f)r(φ∗)ν/(ν−ξ). Substituting (3.2) and (3.10) – with M(1 + χ) presuming the role of Min the open economy – and accounting for (3.14), (3.16), and (3.24), we can calculate w=1 + χfx/f 1 + χ1 σ−11 + χfx f1 ν wa.(3.27) Hence, gains from trade are guaranteed if fx/f ≥1, while losses from trade cannot be ruled out if fx/f < 1.13 Trade can be welfare-deteriorating in our setting, because under production technology (3.1) the outcome of decentralized firm entry is not socially optimal. To the extent that trade aggravates the distortion of firm entry, the resulting welfare loss may outweigh the welfare stimulus from market integration (cf. Shy, 1988). In our setting, the existence of net gains from trade depends on the relative strength of two selection effects. On the one hand, there is selection of the best producers into exporting, which raises labor demand ceteris paribus. On the other hand, there is selection of the least productive firms out of the market, which lowers labor demand. The two selection effects are interdependent and their relative strength depends on fixed cost ratio fx/f. If this fixed costs ratio is sufficiently high, it is the selection into exporting that dominates rendering the overall effect of trade on labor demand and thus welfare positive. As outlined in Proposition 4, there are asymmetric firm-level effects of trade on the mismatch between abilities and skill requirements. Exporting firms increase their screening expenditures, and hence their matching outcome is improved. The opposite is true for non-exporting firms. However, there is an additional positive effect on economy-wide underemployment because labor is relocated towards exporting firms in the open economy and, due to this change in labor composition, the overall impact of trade on the average quality of worker-task matches is positive. To see this, we can explicitly solve for our measure of underemployment in the open economy. As formally shown in the appendix, we get: u=1 + a(τ)χ1+ξ/(νγ)fx/f 1 + χfx/f ua,with a(τ)≡1 + τ1−σ(γ−1)ξ γ(σ−1) −1 (1 + τ1−σ)ξ σ−1−1 .(3.28) Noting that a(τ)<1, it is immediate that u < ua, which proves that trade reduces the average mismatch between task-specific skill requirements and worker-specific abilities, thereby lowering underemployment. We can summarize the main insights from our analysis as follows. Proposition 5 Opening up to trade improves the average quality of worker-task matches, thereby reducing economy-wide underemployment due to a misallocation of workers to tasks. The impact of trade on welfare is not clear-cut in general. Only if fixed costs of exporting relative to production fixed costs, fx/f, are sufficiently high, there are gains from trade in our setting. 13For instance, with a parametrization of ν= 8, σ= 3, τ= 1.5, and γ= 10, there are losses from trade if fx/f ≤0.77 – with fx/f ≥0.58 establishing selection of only the most productive firms into export status, i.e. χ∈(0,1). 3.4. A MODEL VARIANT WITH INVOLUNTARY UNEMPLOYMENT 51 Proof. Analysis in the text. We complete the analysis in this chapter by shedding light on the consequences of a marginal reduction in transport cost parameter τ. Such a decline increases expected income from exporting, and thus raises χ, according to (3.23), as well as average profit income ¯π, according to (3.24). On the other hand, there is a stimulus on labor demand, which enforces additional market exit at the lower bound of the productivity distribution and therefore leads to an upward shift in cutoff productivity φ∗. Furthermore, a marginal decline in the iceberg transport cost parameter augments the heterogeneity in screening effort between non-exporting and exporting producers, according to (3.20). With respect to adjustments in the wage rate, we can infer from (3.27) that dw/dτ < 0 if fx/f > 1. In this case, a gradual reduction in the iceberg transport cost parameter exerts a positive monotonic impact on welfare. In contrast, if fx/f < 1, changes in τneed not exert a monotonic impact on w. Finally, from the analysis above we know that a country’s movement from autarky to trade with an arbitrary transport cost level unambiguously improves the average quality of worker-task matches. We can therefore safely conclude that a marginal decline in τmust lower uif transport costs have been large initially. In the appendix we show that this effect extends to the case where τhas already been low prior to the fall in the iceberg transport cost parameter, so that a gradual decline in τreduces underemployment umonotonically. 3.4 A model variant with involuntary unemployment In this chapter, we introduce search frictions as an additional source of inefficiency in the allocation of labor to show how mismatch between the abilities of workers and the skill requirements of tasks interact with traditional forms of underemployment. For this purpose, we consider a competitive search model along the lines of Rogerson, Shimer, and Wright (2005), in which firms post wages and workers direct their search to the most attractive employer to queue for a job, there.14 The mass of matches between workers and jobs, m, depends positively on the number of applicants, s, and the number of open vacancies, v. In the interest of analytical tractability, we choose a Cobb-Douglas specification and write m(s, v) = As1−ζvζ, where ζ, A ∈(0,1) are the same for all producers.15 Measuring by q≡s/v the queue length of workers applying for jobs, the probability of the firm to fill a specific vacancy is given by αe(q)≡m(s, v)/v =Aq1−ζ. In our static model, this equals the share of vacancies filled in the respective firm. The probability of a worker to be hired, when queuing for a job, is given by αw(q)≡m(s, v)/s =Aq−ζ. In the subsequent analysis we focus on interior solutions with αe(q), αw(q)∈(0,1). For which parameter domain such an interior solution is realized will be discussed below. Setting unemployment compensation equal to zero and denoting by Vthe highest income a worker can expect when applying for a job at a different firm, queuing for vacancies in a firm with productivity φis only attractive for the worker if V≤αw[q(φ)]w(φ). Since firms set the same wage for all workers in our setting (see above), additional workers apply for jobs in this 14Rogerson, Shimer, and Wright (2005) provide an excellent overview of different search-theoretic approaches, their main advantages and disadvantages. In the context of heterogeneous firms, a competitive search model has also been considered by Ritter (2011) and Felbermayr, Impulliti, and Prat (2012). 15In a competitive search model it is not necessary to choose an ad hoc specification of the matching function. Instead, one can as well take the coordination problem of directed search seriously and provide a clean microfoundation of this problem by choosing an urn-ball matching function (see Peters, 1991, for an early contribution and King and St¨ahler, 2010, for an application in the context of trade). A disadvantage of this more advanced approach is its lower analytical tractability, and we therefore prefer treating the matching function as a black box as it is still common in the literature. 52 CHAPTER 3. TRADE AND THE ALLOCATION OF WORKERS TO TASKS firm as long as the inequality is strict. This lowers the probability of being hired by the firm, αw[q(φ)], and the adjustment process continues until the expected return of workers is the same in all active firms. Hence, V=Aq(φ)−ζw(φ) must hold in equilibrium, and the directed search mechanism therefore establishes a positive link between queue length q(φ) and the posted wage w(φ): w(φ) = q(φ)ζV A.(3.29) The mass of vacancies set up by a firm with productivity φ,v(φ), is linked to this firm’s employment level, l(φ), according to v(φ) = l(φ)/[Aq(φ)1−ζ]. The costs of installing and advertising a vacancy are measured in units of final output and are given by k > 0. With these insights at hand, we can write firm-level profits in the closed economy as follows: π(φ) = p(φ)x(φ)−q(φ)ζV Al(φ)−[1 + µ(φ)]γ−f−kl(φ) Aq(φ)1−ζ.(3.30) The firm sets l(φ), q(φ), and µ(φ) simultaneously to maximize profits (3.30) subject to (3.2), (3.6), and a set of non-negativity constraints. The (interior) solution to this maximization problem is characterized by the following three first-order conditions: πl(φ) = σ−1 σp(φ)φ[1 + µ(φ)] −w(φ)−k Aq(φ)1−ζ= 0,(3.31) πq(φ) = −l(φ)ζq(φ)ζ−1V A+ (1 −ζ)l(φ)k Aq(φ)2−ζ= 0,(3.32) πµ(φ) = σ−1 σp(φ)l(φ)φ−γ[1 + µ(φ)]γ−1= 0.(3.33) Equations (3.29) and (3.32) jointly determine q(φ) = (1 −ζ)k ζV ≡q, w(φ) = (1 −ζ)k ζAq1−ζ≡w, (3.34) implying that all firms pay the same wage, irrespective of the prevailing productivity differences. This outcome is in line with models of random matching between workers and heterogenous firms, in which wages are determined by individual Nash bargaining. For instance, Felbermayr and Prat (2011, p. 286) point out that in their setting all firms pay the same wage, because “multiple-worker firms exploit their monopsony power until employees are paid their outside option [that] is constant across firms because it depends solely on aggregate outcomes.” This gives a prominent role to over-hiring in models with individual wage bargaining, which, however, is not present under wage posting. Instead, in our model the finding of a uniform wage level is a consequence of three model ingredients: linear hiring costs, the same outside option of workers with differing abilities, and the isoelastic demand structure.16 16There are different possibilities to modify the model such that it gives rise to the empirically well-documented pattern that larger, more productive firms pay higher wages. For instance, one could consider convex instead of linear recruitment costs, as suggested by Helpman and Itskhoki (2010). Alternatively, one could modify the wage setting process and assume that firms post fair wages, as in Egger and Kreickemeier (2009, 2012) and Amiti and Davis (2012). Finally, one could also give up the symmetry of firm-worker matches and instead assume that ability is firm-specific and employers can learn about this ability during the recruitment process by installing a screening technology, as suggested by Helpman, Itskhoki, and Redding (2010). While all of these modifications would allow for firm-specific wage payments, the costs of these extensions in terms of analytical tractability would be enormous, and we therefore decided to stick to the more parsimonious model variant without wage differentiation. 3.4. A MODEL VARIANT WITH INVOLUNTARY UNEMPLOYMENT 53 Combining (3.31) and (3.34) gives the modified price-markup rule p(φ) = σ (σ−1)φ[1 + µ(φ)] k ζAq1−ζ,(3.35) where marginal labor costs are augmented by recruitment expenditures. Contrasting (3.9) and (3.33), we see that the existence of search frictions does not change the profit-maximizing choice of screening. Since search frictions do also not affect firm entry decisions, cutoff productivity φ∗and revenues of the marginal firm r(φ∗) remain to be given by (3.14). Similarly, the zerocutoff profit condition and the free entry condition remain to be given by (3.15) and (3.16), respectively, and hence neither ¯πnor φ∗depend on the prevailing search frictions or the costs of establishing and posting vacancies, k. With the firm-level variables at hand, we can now solve for the general equilibrium outcome in the closed economy. For this purpose, we first look at queue length q. Substituting (3.2) into r(φ∗) = p(φ∗)x(φ∗) and accounting for Y=Mr(φ∗)ν/(ν−ξ) gives p(φ∗)σ−1=ν/(ν−ξ). Using (3.35) and noting that φ∗[1 + µ(φ∗)] = [(fξ)/γ]1/γ {(fξ)/[fe(ν−ξ)]}1/ν follows from (3.14)-(3.16), we can derive q=(kσ Aζ(σ−1) ν−ξ ν1 σ−1fe f ν−ξ ξ1 νγ fξ 1 γ)1 1−ζ .(3.36) To solve for economy-wide unemployment ˆu, we can substitute V= (1 −ˆu)winto (3.29). Rearranging terms, yields 1 −ˆu=Aq−ζ, which establishes the intuitive result that a larger queue length at individual firms leads to higher economy-wide unemployment. Accounting for qfrom (3.36), we can compute 1−ˆu=(ζ(σ−1) kσ ν ν−ξ1 σ−1f fe ξ ν−ξ1 νfξ γ1 γ)ζ 1−ζ A1 1−ζ.(3.37) Eq. (3.37) characterizes involuntary unemployment as one important aspect of underemployment and measures the efficiency loss due to search frictions. However, it does not capture the efficiency loss, arising from a mismatch between workers and tasks in the firm-internal allocation of labor. This form of underemployment can be measured by the average distance between task-specific skill requirements and worker-specific abilities and is represented by u. Crucially, the existence of search frictions does not impact firm-level screening (see above), and hence it does not alter firm-internal labor allocation. Due to this, uremains to be given by (3.18) in the closed economy.17 Finally, welfare in the closed economy is given by (1 −ˆu)w, which, in view of (3.34), (3.36), and (3.37), can be expressed as (1 −ˆu)w=1−ζ ζ k q= (1 −ζ)A1 1−ζζ kζ 1−ζ ˜w1 1−ζ= (1 −ζ)(1 −ˆu) ˜w, (3.38) 17Eqs. (3.36) and (3.37) can be used for characterizing the parameter domain that establishes an interior solution with αe(q), αw(q)∈(0,1). More specifically, we can conclude that αe(q) = Aq1−ζ<1 and αw(q) = Aq−ζ<1 simultaneously hold if A1 ζ<kσ ζ(σ−1) ν−ξ ν1 σ−1fe f ν−ξ ξ1 νγ fξ 1 γ<1, while the two probabilities are positive if ζ, k, A > 0 (and ν > ξ as previously assumed). 54 CHAPTER 3. TRADE AND THE ALLOCATION OF WORKERS TO TASKS where ˜wequals the wage rate in the benchmark model with a perfect labor market, given by (3.17). From (3.38) it is obvious that the existence of search frictions reduces per capita labor income and thus welfare in our setting. This completes the discussion of the closed economy. We now turn to the open economy and shed light on the effects of trade for the two sources of underemployment. Thereby, we impose the same assumptions as in the baseline model and consider two symmetric countries, iceberg transport costs for shipping intermediate goods across borders and fixed exporting costs to generate selection of only the best firms into export status. With these assumptions at hand, we can now repeat the analysis of the closed economy step by step in order to derive the main variables of interest for the open economy. However, since the respective calculations are straightforward, we leave them to the interested reader and only summarize the main results from this analysis, here. From the closed economy, we know that the existence of labor market imperfection does not affect the allocation of workers to tasks, and hence our insights regarding the consequences of trade for the firm-internal mismatch remains unaffected by adding a search friction. This implies that the open economy level of uremains to be given by (3.28). Furthermore, it is easily confirmed that the existence of a search friction does not alter Eqs. (3.19)-(3.21), therefore leaving the exporting decision unaffected. As a consequence, the share of exporting firms remains to be given by (3.23). Noting from (3.38) that per capita labor income in the more sophisticated model variant with search frictions is a convex function of the wage rate in the benchmark model with a perfect labor market, we can infer the welfare effects of trade by considering Eq. (3.27). To more specific, we can write (1 −ˆu)w (1 −ˆua)wa=˜w ˜wa1 1−ζ ="1 + χfx/f 1 + χ1 σ−11 + χfx f1 ν#1 1−ζ .(3.39) Hence, the existence of search frictions does not change the welfare effects of trade in a qualitative way, but it magnifies the (positive or negative) welfare implications identified in Chapter 3.3. To understand, where the additional welfare effect comes from, it is worth noting that we can write w wa=q qaζ−1 =1 + χfx/f 1 + χ1 σ−11 + χfx f1 ν ,(3.40) according to (3.34) and (3.39). From (3.27) and (3.40) it follows that in the presence of search frictions the wage adjustments triggered by trade are of equal magnitude as in the benchmark model with a perfectly competitive labor market. Therefore, any additional welfare effect must come from adjustments in the employment rate. Looking at 1−ˆu 1−ˆua=q qa−ζ =(1 −ˆu)w (1 −ˆua)waζ ="1 + χfx/f 1 + χ1 σ−11 + χfx f1 ν#ζ 1−ζ (3.41) provides support for this conclusion. Eqs. (3.39)-(3.41) show that there is a direct link between employment, wage, and welfare effects of trade in our setting. From Chapter 3.3 we know that lacking an external scale effect in the production of final goods, selection of exporters must be sufficiently strong in order for trade to provide a stimulus on aggregate labor demand and equilibrium wages. In this case, the price of the final good falls relative to the wage rate. This lowers the costs of installing and advertising vacancies relative to the costs of compensating workers, and thus alleviates the search friction with positive consequences for aggregate employment. 3.4. A MODEL VARIANT WITH INVOLUNTARY UNEMPLOYMENT 55 Both of these effects contribute to a welfare gain if search frictions exist. Things are different if selection effects are weak. In this case, it is possible that labor demand is dampened in the open economy, so that wages decline. However, if wages decline relative to the price of the final good, the establishment of new vacancies becomes less attractive, rendering the search friction more severe than under autarky, with adverse effects on economy-wide employment. The following proposition summarizes the main insights from the analysis in this chapter. Proposition 6 The existence of search frictions does not alter our insights from the benchmark model regarding the impact of trade on the mismatch between workers and task in the firminternal labor market. Furthermore, with search frictions, trade triggers wage and employment effects that go into the same direction. As a consequence, the welfare implications of trade, while not altered qualitatively, are reinforced in the model variant with search frictions. Proof. Analysis in the text. We complete the discussion in this chapter by having a closer look on the specific role played by adjustments in the firm-internal allocation of workers for the impact of trade on welfare and economy-wide unemployment. In particular, we want to shed light on whether one over-estimates or under-estimates the effects of trade, when disregarding the firms’ ability to endogenously adjust the quality of worker-task matches. For this purpose, it is worth noting that our model degenerates to one without screening if γ→ ∞. We can therefore infer insights upon the role played by the firm-internal labor allocation from differentiating (3.39)-(3.41) with respect to γ. More specifically, we can determine how changes in γalter the employment and welfare effects of trade, by studying the sign of d(w/wa) dγ =d(w/wa) dχ dχ dγ .(3.42) Differentiating (3.23) with respect to γgives dχ dγ =−νχ γ   1 γ−σ+ 1 1 + τ1−σξ σ−1 (1 + τ1−σ)ξ σ−1−1 ln 1 + τ1−σ−1 γln χξ ν  <0.(3.43) A higher γimplies that fixed costs are more responsive to changes in the screening effort. Accordingly, firms will adjust their screening effort less strongly when facing the opportunity of exporting, so that the fixed cost increase due to exporting is less pronounced (see Eq. (3.20)), and hence the share of exporters increases ceteris paribus if γgoes up. On the other hand, the now lower wedge of screening effort eats up part of the productivity advantage of exporters relative to non-exporters, thereby lowering the incentives of firms to sell abroad. In our model, it is the second effect that dominates, so that a higher γreinforces self-selection into exporting, and therefore implies a smaller share of exporting firms χ. Furthermore, differentiating (3.40) with respect to χyields d(w/wa) dχ =w/wa ν(1 + χfx/f) (1 + χ)ν σ−1fx f−1+ (1 + χ)fx f.(3.44) It is easily confirmed that the bracket term on the right-hand side of (3.44) is increasing in fx/f, and hence wages increase monotonically in the share of exporting firms if fx/f (and thus the selection effect) is sufficiently large. In line with our insights from Chapter 3.3, fx/f ≥1 is sufficient (not necessary) for a monotonically positive impact of an increase in χon w/wa. 56 CHAPTER 3. TRADE AND THE ALLOCATION OF WORKERS TO TASKS If such a monotonic effect exists, an increase in γunambiguously lowers the positive wage, employment, and welfare effects of trade, and hence positive economy-wide effects would be underestimated if one ignores endogenous adjustments in the firm-internal allocation of workers to tasks. However, if the impact of a higher χon w/wais non-monotonic, things are even more worrying, because in this case ignoring endogenous adjustments in the way workers are assigned to tasks may give wrong predictions regarding the existence of positive wage, employment, and welfare effects of trade. The following proposition summarizes these results. Proposition 7 The ability of firms to adjust the quality of worker-task matches leads to weaker selection of firms into exporting, and thus a larger share of exporting firms. Provided that an increase in the share of exporting firms exhibits a positive monotonic impact on wages, adjustments in the firm-internal allocation of workers to tasks therefore strengthen the employment and welfare stimulus relative to a model where such adjustments do not exist. If the relationship between the share of exporting firms and wages is non-monotonic, adjustments in the firm-internal allocation of labor may reverse the employment and welfare effects of trade. Proof. Analysis in the text. 3.5 A calibration exercise In this chapter, we aim at quantifying the effects of trade in our setting. For this purpose, we calibrate our model, using parameter estimates from the literature. A first set of useful parameter estimates is provided by Egger, Egger, and Kreickemeier (2011). Egger, Egger, and Kreickemeier (2011) structurally estimate the main parameters of a trade model with heterogeneous firms and labor market imperfections due to a fair-wage effort mechanism, using firm-level data from five European countries – Bosnia and Herzegovina, Croatia, France, Serbia, and Slovenia – for the period 2000 to 2008. For our calibration exercise, we consider the parameter estimates for France, which hosts the majority of firms in the respective data-set. A first parameter available from the empirical application in Egger, Egger, and Kreickemeier (2011) is the elasticity of substitution, for which they report a value of σ= 6.7. This estimate is similar to other findings in the literature (see, for instance, Broda and Weinstein, 2006). Furthermore, using the structural relationship between revenues of exporting firms, Egger, Egger, and Kreickemeier (2011) estimate an analogon to ξ/ν, for which they report a value of 0.87, when relying on information for French firms. This is fairly close to the estimate of 0.83 reported by Arkolakis and Muendler (2010) for Brazilian firms. Unfortunately, there are no direct estimates available for γ, and we are therefore not able to calculate the parameter values for γand νseparately. However, from the formal discussion in Chapter 3.2 we can infer that existence of an interior solution requires a sufficiently high level of ν. With ξ/ν = 0.87, νmust be larger than 6.5 in our calibration exercise. Since we cannot further confine the possible parameter values, we consider three parameter values that are in line with this constraint and choose ν= 7, ν= 9 and ν= 11 for our calibration exercise.18 Taking account of σ= 6.7 and ξ/ν = 0.87, we can then calculate the corresponding γ-levels: γ= 89.01 for ν= 7, γ= 20.95 for ν= 9 and γ= 14.10 for ν= 11. An additional variable of interest is the share of exporters, χ. Eaton, Kortum, and Kramarz (2011) report from official administrative statistics that 15 percent of French manufacturing firms were exporters in 1986. Egger, Egger, and Kreickemeier (2011) find a significantly larger 18These ν-values are well in line with shape parameters of the productivity distribution applied in other numerical applications of the Melitz (2003) model. For instance, Arkolakis and Muendler (2010) consider 5 and 8 as low and high values for the shape parameter, whereas Felbermayr and Prat (2011) consider a value of 9.23. 3.5. A CALIBRATION EXERCISE 57 share of exporters, using the Amadeus data-set. According to their data-base, 45 percent of French firms did export in the average year between 2000 and 2008. Since it is well known that the Amadeus data is biased towards large, incorporated firms, we consider the evidence provided by Eaton, Kortum, and Kramarz (2011) to be more reliable and accordingly set χ= 0.15 in our calibration exercise. Recent empirical research aims at estimating compulsory measures of the iceberg trade cost parameter τby employing information on observed international trade flows into a structural gravity equation. Existing results from this literature suggest setting τ= 1.5 (see, for instance, McGowan and Milner, 2013; Novy, 2013). With the iceberg trade cost parameter and the share of exporters at hand, we can then compute a theory-consistent value of fixed cost ratio fx/f. Using the parameter values from above, we obtain fx/f = 0.93 if ν= 7, fx/f = 0.96 if ν= 9, and fx/f = 0.98 if ν= 11. Finally, we follow common practice in the search literature and set ζ= 0.5 (see Petrongolo and Pissarides, 2001, for supportive empirical evidence). Table 3.1: Quantifying the impact of trade on welfare and underemployment Parameter values Changes in percent ν γ fx/f ∆(1 −ˆu)w∆(1 −ˆu) ∆u 7 89.01 0.93 3.45 1.71 −0.37 9 20.95 0.96 2.81 1.39 −1.54 11 14.10 0.98 2.45 1.22 −2.29 Notes: An exporter share of χ= 0.15, an iceberg trade cost parameter of τ= 1.5, a σ-value of 6.7, a ζ-value of 0.5, and a parameter ratio ξ/ν = 0.87 have been considered for computing the figures in this table. Table 3.1 summarizes the main insights from our calibration exercise and reports employment and welfare effects associated with a movement of France from autarky to its observed degree of openness: χ= 0.15. From Column 4 we see that gains from trade seem to be rather small in our setting, which at least partly may be explained by the absence of external scale economies in the production of final goods. However, the welfare gains documented in Table 3.1 are in the range of welfare effects reported by Eaton and Kortum (2002), who set up a multi-country Ricardian model for 19 OECD economies and investigate how much countries in their data-set would lose if trade were entirely abolished. They compute losses ranging from 0.2 percent for Japan and 10.3 percent for Belgium, and for France they report a welfare loss of 2.5 percent. This is fairly close to the welfare loss from abolishing trade entirely when setting ν= 11 in our model, which amounts to 2.4 percent. The effects of trade on economy-wide employment are reported in Column 5. At a first glance, the employment effects may seem not sizable. However, it is noteworthy that evaluated at a current unemployment rate of about 10 percent, an employment effect of ∆(1 −ˆu) = 1.22 (for ν= 11) implies that the observed degree of openness has lowered the French unemployment rate by 1.1 percentage points relative to autarky. Column 6 reports our calibration results for the impact of trade on the average mismatch in the firm-internal allocation of workers to tasks. In line with our theoretical result, this mismatch is reduced in the open economy and the more so, the larger is ν. This is intuitive, as we see from Column 2 that higher levels of νare associated with smaller levels of γand thus a smaller elasticity of screening costs in screening effort. As a consequence, for higher values of νfirms will adjust their screening effort more strongly to new 58 CHAPTER 3. TRADE AND THE ALLOCATION OF WORKERS TO TASKS exporting opportunities, leading to a more pronounced reduction in the economy-wide mismatch of workers and tasks in response to trade. For providing insights on the extent to which adjustments in the firm-internal allocation of workers govern the employment and welfare implications of trade in our setting, we can contrast the findings in Table 3.1 with those from an otherwise identical model variant in which such adjustments are not feasible. For this purpose, we look at the limiting case of γ→ ∞, which, as outlined in the previous chapter, implies that producers do not screen their applicants, so that µ(φ) = 0 for all φ. Considering ν= 11 as the preferred value for the shape parameter of the Pareto productivity distribution and thus setting fx/f = 0.98 according to Table 3.1, we can compute a theory-consistent share of exporters that corresponds to the parameter values at hand. We compute χ= 0.02, which confirms our insight from the formal analysis that higher levels of γlower the share of exporters monotonically (see Eq. (3.43)). From the analysis in Chapter 3.4, we are warned that changes in the share of exporting firms need not exhibit a monotonic effect on employment and welfare if fx/f < 1, which is the case in our exercise. It is therefore a priori not clear whether the movement of France from autarky to the observed degree of openness would have been beneficial in the absence of screening. In the numerical application, we can evaluate the welfare and employment effects of trade for the limiting case of γ→ ∞. For the preferred parametrization, this gives ∆(1 −ˆu)w= 0.28 and ∆(1 −ˆu) = 0.14, respectively. Therefore, eliminating the ability of firms to screen their workforce and endogenously adjust the quality of worker-task matches would not alter the welfare and employment effects of trade qualitatively, but it would lead to a significant decline of its beneficial consequences. Finally, recollecting from Chapter 3.4 that gains from trade in our model are a composite of positive employment and positive wage effects, we can ask which of these two partial effects is the more important source of welfare stimulus. The answer to this question is simple. Setting ζ= 0.5, we obtain ∆(1 −ˆu) = ∆w, according to (3.40) and (3.41). Since ∆wcorresponds to the welfare effect of trade in the absence of search frictions, we can therefore conclude that disregarding labor market imperfections leads to a significant downward bias in the calibrated welfare effects of trade. 3.6 Concluding remarks This chapter sets up a model of heterogeneous firms along the lines of Melitz (2003) and enriches this workhorse of modern trade theory by associating production with a continuum of tasks that differ in their skill requirements. Furthermore, we assume that workers differ in their abilities to perform these tasks, and firms therefore face the complex problem of matching heterogeneous workers with heterogeneous tasks. To solve this allocation problem in a satisfactory way, firms require information about worker ability and they can get this information by screening their applicants. Screening involves fixed costs and provides an imprecise signal about the ability of workers. The higher the investment into the screening technology, the better is the signal and the better is therefore the match between abilities of workers and skill requirements of tasks. Intuitively, firms that have a higher ex ante productivity install a better screening technology, so that heterogeneity of firms is reinforced by the endogenous investment into screening. We use this framework to study the consequences of trade for welfare and underemployment, arising from the mismatch between workers and tasks. If only the best (most productive) firms self-select into exporting, trade exerts an asymmetric effect on the screening incentives of highand low-productivity firms. High-productivity firms expand production due to exporting, and therefore find it attractive to install a better (more expensive) screening technology than in the closed economy. In contrast, low-productivity firms do not export and lose market share at 3.6. CONCLUDING REMARKS 59 home. In response, they lower their screening expenditures. Despite this asymmetry in firmlevel adjustments to trade, we show that the average mismatch between worker-specific abilities and task-specific skill requirements unambiguously shrinks in the open economy. This points to a so far unexplored channel through which trade can improve the labor market outcome and stimulate welfare. In an extension to our baseline model, we consider imperfections in the external labor market due to search frictions. Relying on a competitive search model with wage posting, we show that this modification does not alter our insights regarding the consequences of trade for the firm-internal allocation of workers to tasks. However, due to adjustments in involuntary unemployment, there is now a second channel through which trade affects economy-wide underemployment. Whether more or less workers find a job in the open economy is in general not clear and depends on the strength of selection of firms into exporting. If fixed costs of exporting are high relative to domestic fixed costs, selection into exporting is strong and in this case trade increases welfare and lowers underemployment due to a higher matching efficiency inside and outside the firm. In a calibration exercise, we rely on parameter estimates for French firms to quantify the relative importance of adjustments in the firm-internal and the firm-external labor market. We find that both adjustments are important channels for gains from trade to materialize. For instance, eliminating the ability of firms to screen their applicants and to adjust the quality of worker-task matches endogenously would lower gains from trade by almost 90 percent, whereas disregarding improvements in the outside labor market would lower gains from trade by 50 percent when relying on the preferred parametrization of our model. To put it in broader perspective, one can interpret our analysis as an attempt to widen the picture of underemployment and to show that positive labor market consequences of trade need not only materialize due to a reduction in involuntary unemployment. Rather efficiency gains may be triggered by adjustments in the firm-internal organization of labor and according to our results these gains may indeed be sizable. Of course, more research is needed before one can draw a definite conclusion about how trade affects the way labor is used in modern production. We hope that the insights from our analysis encourage such research. 66 CHAPTER 3. TRADE AND THE ALLOCATION OF WORKERS TO TASKS Chapter 4 Trade and the Firm-internal Assignment of Skills to Tasks 4.1 Introduction The organization of production within firms is a key determinant of firm performance. The ability to allocate scarce resources within the boundaries of firms efficiently, is essential for firms to compete in modern economic life.1When it comes to the organization of labor within firms, this topic is discussed in the literature on personnel economics. However, in the trade literature, firms were treated as a black box over centuries. This perspective has changed over the last few years, where recent contributions have provided new insights, how trade shapes the internal organization of national and multinational firms. Thereby, the focus has been on corporate hierarchies. For instance, Caliendo and Rossi-Hansberg (2012) highlight that a firm’s productivity depends on how production is organized, and this organization changes in the process of globalization.2This chapter takes a different approach and introduces the idea of a task-based production process into a framework of international trade. Of course, with the production process consisting of different tasks, firms face new problems that are ignored in the existing literature. If the set of tasks in a firm differ in complexity and workers differ in their abilities to perform these tasks, the organization of workers to specific tasks inside the firm becomes relevant.3Modeling the assignment of workers to tasks and a discussion on how this assignment changes in an open economy is in the center of this chapter’s interest. For this purpose, I introduce a task based production process along the lines of Acemoglu and Autor (2011) into a standard trade model with monopolistic competition among heterogeneous firms, as in Melitz (2003). In this framework, firm output is assembled from a continuum of tasks that differ in complexity. For the performance of tasks, firms can hire low-skilled or highskilled workers, while a higher skill level causes a comparative advantage in the performance of more complex tasks. How firms assign skills to tasks depends on the comparative advantage of high-skilled workers and their skill premium. By altering the range of tasks performed by 1In a recent paper by Giroud and Mueller (2012), it is shown that firm-level productivity increase, due to the efficient resource reallocation within firms. 2See also Marin and Verdier (2008b, 2012). 3Clearly, there exists a large theoretical literature, that discusses how heterogeneous workers sort to different industries, how they match with other workers, firms, and with other factors of production and how trade affects this matching and the wage distribution (see Grossman, 2013, for a recent survey of this literature). 67 68 CHAPTER 4. TRADE AND THE ASSIGNMENT OF SKILLS TO TASKS high-skilled workers, firms do not only affect their labor costs but also their productivity. To determine the optimal skill range and to manage the firm and organize the complex production process, firms need a fixed input of high-skilled workers. In a benchmark model, I assume that labor markets are perfectly competitive. After solving for the general equilibrium in a closed economy, I analyze changes in factor endowments, which can be interpreted as migration problem. The main insights from this analysis are that an increase in the supply of low-skilled workers raises the range of tasks performed by this skill type, which triggers a decline in the productivity of firms. While low-skilled workers lose due to a reduction in their real wage, highskilled workers gain in absolute and relative terms, as they see their real wage and skill premium rising. Even though the mass of firms increases, overall welfare effects are ambiguous due to the decline in productivity. In the case of high-skilled migration, firm productivity increases as firms use this skill type for the performance of a broader range of tasks. While low-skilled workers experience an increase in their income, the impact on high-skilled wages are less clear-cut and depend on model parameters. As firm number and productivity increases, overall welfare effects are positive. In a second step, I consider a minimum wage for the group of low-skilled workers, to account for the empirical fact that unemployment is persistent especially among this group of workers. This reduces welfare relative to a benchmark with fully flexible wages and generates unemployment of low-skilled workers. Moreover, the introduction of a minimum wage lowers per-capita income of high-skilled and low-skilled workers and increase the relative income of high-skilled workers. Similar to Brecher (1974), in such an economy migration of low-skilled workers is fully absorbed by a pari passu increase in unemployment and a reduction in welfare but leaves all other variables unaffected. In contrast to a situation with fully flexible wages, migration of high-skilled workers reduces the range of tasks performed by this group of workers, and thus firm-level productivity, due to a magnification effect at the entrance of firms. Moreover, highskilled workers gain in absolute and relative terms, and the unemployment rate for low-skilled workers goes down, implying that welfare must increase. To shed light on the assignment of skills to tasks and a firm’s production process if the country under consideration opens up to trade, I discuss trade between two fully symmetric countries. Similar to Krugman (1979), in a situation with fully flexible wages, trade only increases the real wage for each skill type and aggregate welfare, while leaving all other variables unaffected. However, when low-skilled wages are fixed by the government, trade also affects a firm’s production process. Due to a standard division of labor effect, demand for firms in each country is higher in the open economy. This stimulates aggregate labor demand, and, as low-skilled wages are fixed, the skill premium in each country. Firms respond to this change in relative factor prices and assign low-skilled workers to a broader range of tasks. This skill downgrading reduces productivity of firms and accounts for a so far unexplored channel, through which trade affects local production practices. However, as trade reduces high-skilled task production, more firms can enter the market, implying that welfare effects are positive. After shedding light on how trade between two countries affects the task based production process, I use the framework to discuss how changes in a countries labor market institutions spill over to the partner country. Starting from an equilibrium with trade between two minimum wage economies, an increase in one country’s minimum wage also affects the assignment of skills to tasks in the partner country. Due to a reduction in aggregate labor demand which reduces the skill premium, firms produce a broader share of tasks with high-skilled workers and therefore become more productive. However, beside these positive productivity spillovers, firm number and per-capita income for high-skilled workers are reduced, while low-skilled workers face a higher unemployment rate, which, in sum, are instrumental for a decline in welfare. 4.1. INTRODUCTION 69 Accounting for differences in factor endowments has no impact on the insights from an open economy scenario with fully flexible wages. However, if both countries set a minimum wage for the group of low-skilled workers, high-skilled migration in one country increases the mass of firms and the range of tasks performed by low-skilled workers in the partner country, and reduces firm-level productivity, there. Low-skilled workers face a lower unemployment rate, while highskilled workers face an increase in the real wage, but see their relative income shrinking, and welfare in the partner country rises. By shedding light how trade affects the firm-internal labor market, this chapter is related to a growing literature that analyzes how globalization shapes the organization of production. In this chapter, changes in the assignment of workers with different skills to tasks with differing complexity affects a firm’s productivity level. This is a novel mechanism that differentiates this model from other trade models with a task-based production function. For instance, recent contributions to the literature on offshoring builds upon Grossman and Rossi-Hansberg (2008).4 In the Grossman and Rossi-Hansberg (2008) framework, production also consists of a continuum of low-skilled and high-skilled tasks. However, their model provides a perfect mapping between skills and tasks, as the set of tasks for each skill type is exogenous: low-skilled workers are restricted to work in low-skill tasks and high-skilled workers are only assigned to high-skill tasks. In my framework, things are more sophisticated, because each skill type can in principle perform the whole range of tasks within a firm and the assignment decision depends on the relative performance of low-skilled and high-skilled workers in task production and on the respective factor costs. The endogenous assignment of workers with differing abilities to tasks with differing skill requirements is also discussed in a recent paper by Egger and Koch (2013). While the production side is similar to my framework, they differ with respect to heterogeneity in the workforce. In the Egger and Koch (2013) framework, workers are horizontally differentiated, implying that workers differ in their ability to perform certain tasks because their human capital is occupation-specific. Moreover, firms have to invest into a screening mechanism to get some information about the hidden task-specific abilities of workers. By increasing the screening intensity, firms can improve the matching of workers to tasks and thereby firm productivity. In the present model, firms have perfect information about the abilities of workers and the focus is on how firms assign low-skilled and high-skilled workers to tasks with differing complexity. Thereby, high-skilled workers have an absolute productivity advantage in the performance of all tasks. However, they are also more expensive, and hence firms find it attractive to assign high-skilled workers only to tasks with high complexity, since their comparative advantage is declining with less complexity. The range of tasks performed by high-skilled workers determines firm-productivity, and hence firms with higher skill intensity end up being more productive. An alternative mechanism, that relates firm productivity to the organization of workers in the production process is discussed by Caliendo and Rossi-Hansberg (2012). In their model it is the hierarchy structure within firms, i.e. the number of layers of management and the knowledge and span of control of each agent that is instrumental for firm performance. By allowing for changes in the firm-internal assignment of workers to tasks, the chapter also contributes to a vivid discussion on how trade affects productivity. The seminal paper by Melitz (2003) proposes an increase in aggregate productivity due to a change in the composition of active producers, while leaving firm-level productivity unaffected. Bustos (2011) extends the Melitz-framework by allowing firms to invest into their technology. Since exporters gain market size in the open economy, they find it more attractive to invest into their technology, and hence end up having a higher productivity. In Helpman, Itskhoki, and Redding (2010), exporters extend their screening investments and thus have a better workforce composition and therefore 4See, for instance, Kohler and Wrona (2011), Benz (2012) or Grossman and Rossi-Hansberg (2012). 70 CHAPTER 4. TRADE AND THE ASSIGNMENT OF SKILLS TO TASKS higher productivity than in the closed economy. In Egger and Koch (2013) the expansion of screening leaves the workforce composition unaffected but improves the assignment of workers to tasks with positive productivity effects. Interestingly, empirical evidence at the firm-level is not conclusive.5My model provides a reasoning for this. Because trade expand demand for highskilled workers as a fixed input in the production process, it leaves less high-skilled resources for task production. This worsens the skill composition with correspondent consequences for firm-level productivity.6This effect, however, does only exist if labor markets are not perfectly competitive, with labor market imperfection being modeled by means of a binding minimum wage. By introducing a minimum wage for low-skilled workers, this chapter is related to a sizable literature that accounts for different forms of labor market imperfections in the Melitz (2003)- framework.7One feature in these studies is that the labor market imperfection has no impact on the productivity of a specific firm but affects the average productivity of all active producers due to changes in the composition of firms. For instance, in Egger and Kreickemeier (2009), a more important rent sharing motive in workers’ fair wage preferences reduces labor costs for low productive firms relative to their more productive competitors, because wages in high productive firms increase disproportionately with the rent sharing motive. This implies, somewhat counterintuitive, that profits for the cutoff firm increase. With more unproductive firms being able to survive in the market, the average productivity falls. A different mechanism is studied in Egger, Egger, and Markusen (2012). In their paper, a more severe labor market imperfection increases the common wage and the marginal production costs proportionally. This forces the least productive firms to exit and thus increases average productivity, because the composition of firms improves. In my model, productivity effects arise from different wage setting institutions for low-skilled and high-skilled workers which affect the firm-internal assignment of skills to tasks and thus a firm’s productivity. Hence, the labor market imperfection leads to a reallocation of workers within firms, while in existing studies on heterogeneous firms, labor is reallocated between firms. Allowing for differences in the prevailing labor market institutions between two trading partners, the chapter is also related to a literature that discusses labor market linkages in open economies. Starting with the seminal work by Davis (1998), several authors have discussed how labor market imperfections in one country spill over to foreign markets.8In a recent paper, Egger, Egger, and Markusen (2012) build upon a similar framework as the one considered in this chapter. In particular, they also consider monopolistic competition between heterogeneous firms. However, in contrast to the approach taken here, production in Egger, Egger, and Markusen (2012) only consists of a single task. They furthermore differ in the underlying entry mechanism, by assuming an exogenous mass of potential entrants. This modification turns out to be instrumental for their results. In particular, the exogenous pool of potential entrants establishes a link between the minimum wage and the cutoff productivity of the marginal firm and implies that if two countries with differing minimum wages engage in trade, they end up 5Wagner (2007) provides a survey on the link between exporters and productivity on the evidence from firm level data. After studding 45 microeconometric studies he concludes that ”exporting does not necessarily improve productivity” (p.1). 6This effect is well in line with empirical evidence. For instance, Harrigan and Reshef (2011) argue the ”empirical studies have failed to find large effects of trade liberalization on firm-level or plant-level skill upgrading” (p.3). 7Prominent examples are Davidson, Matusz, and Shevchenko (2008); Davis and Harrigan (2011); Egger and Kreickemeier (2009, 2012); Egger, Egger, and Markusen (2012); Felbermayr, Prat, and Schmerer (2011); Helpman and Itskhoki (2010); Helpman, Itskhoki, and Redding (2010). 8Prominent examples are Oslington (2002), Kreickemeier and Nelson (2006), Meckl (2006) or Felbermayr, Larch, and Lechthaler (2013). 4.2. THE CLOSED ECONOMY 71 with differing compositions of local producers. In the present chapter, firm entry is modeled along the line of Melitz (2003), and this renders the cutoff productivity level independent of the prevailing minimum wage. Nonetheless, despite differences in the level, minimum wages can be binding in both countries, because the endogenous assignment of skills to tasks allows to absorb for differences in local labor market institutions. Taking stock, the model presented in this chapter suggests that differences in labor market institutions lead to different skill intensities and firm productivities, but leave the composition of producers unaffected.9 The remainder of the chapter is organized as follows. In Chapter 4.2, I introduce the model and characterize the equilibrium outcome in the closed economy. I start with a benchmark model, in which wages are fully flexible and then consider a model variant with a binding minimum wage. Furthermore, I conduct two comparative static experiments and analyze how changes in the endowment with low-skilled and high-skilled workers affect the equilibrium outcome in the closed economy under the two labor market regimes. In Chapter 4.3, I provide insights into the impact of trade on the firm-internal assignment of skills to tasks when labor markets are perfectly competitive or low-skilled wages are set by the government. In Chapter 4.4, I discuss how labor markets are linked in open economies and analyze to what extent previous insights from my analysis depend on the assumption of symmetric countries. Chapter 4.5 concludes with a brief summary of the most important results. 4.2 The closed economy 4.2.1 Model structure and firm-level analysis Consider an economy that is populated by an exogenous mass of Llow-skilled and Hhigh-skilled workers and hosts two sectors of production: a final goods industry that assembles intermediates, and an intermediates goods industry, which employs labor for performing different tasks. The final good Yis homogeneous and produced under perfect competition, according to a constantelasticity-of-substitution (CES) production function (see Matusz, 1996): Y=Zω∈Ω x(ω)σ−1 σdωσ σ−1 ,(4.1) where x(ω) denotes the quantity of intermediate variant ωused in the production of Y, set Ω represents the mass of available intermediate goods with Lebesgue measure M, and σ > 1 denotes the (constant) elasticity of substitution between variants of the intermediate. Choosing the final good as num´eraire, profits in the final goods industry are Y−Rω∈Ωp(ω)x(ω)dω, where p(ω) denotes the price of variety ω. Maximizing these profits with respect to x(ω) gives intermediate goods demand10 x(ω) = Y p(ω)−σ.(4.2) Intermediate goods producers compete with rival firms in a monopolistically competitive environment. Each firm produces a unique variety, by combining a continuum of tasks represented by the unit interval. I follow Acemoglu and Autor (2011) and use a simple Cobb-Douglas 9This mechanism would also be effective in a Krugman (1979)-type model with homogeneous producers. However, in line with the recent literature in international economics and to contrast my results with Egger, Egger, and Markusen (2012), I prefer a setting with heterogeneous firms along the lines of Melitz (2003), where firms differ in terms of their (exogenous) productivity. 10Due to the choice of the num´eraire, the CES price index corresponding to Y,P= [Rω∈Ωp(ω)1−σdω]1/(1−σ), is equal to one. 72 CHAPTER 4. TRADE AND THE ASSIGNMENT OF SKILLS TO TASKS function to formalize the assembly of tasks in the production of intermediates: x(ω) = φ(ω) exp Z1 0 ln x(ω, i)di,(4.3) where φ(ω) is a firm’s baseline productivity that measures the efficiency to coordinate and bundle tasks and x(ω, i) is the production level of task iin firm ω. Tasks are performed by low-skilled and high-skilled workers, l(ω, i) and h(ω, i) respectively, who are employed in a linear-homogeneous production function of the form11 x(ω, i) = αl(i)l(ω, i) + αh(i)h(ω, i),(4.4) where αl(i) and αh(i) are the labor productivities of the two skill types, when performing task i. The task level production function in (4.4) implies that low-skilled and high-skilled workers are substitutes in the performance of tasks. However, the productivity of workers in performing a specific task differs, because workers differ in their abilities, while tasks differ in their skill requirements. To capture performance (i.e. productivity) differences across tasks between the two skill groups in a simple way, I impose the following assumption on absolute and comparative advantages in the performance of tasks: Assumption 1 Denoting the labor productivity ratio between highand low-skilled workers in tasks i by α(i)≡αh(i)/αl(i), it is assumed that α(i)is a continuously differentiable, strictly increasing and convex function of i, i.e. α′(i)>0,α′′(i)≥0, with α(0) = 1. To implement these properties in a tractable way, I consider αl(i) = 1 and αh(i) = α(i) = exp[i]for all i∈[0,1]. This assumption captures the idea that tasks can be ordered according to their complexity, with a higher index referring to higher complexity. A high-skilled worker that is assigned to the least complex task, is as productive as her low-skilled coworker, since her specific skills are not required for performing the respective task. Things are different in the case of a more complex task, where the higher skill level causes an absolute productivity advantage over low-skilled coworkers. Changes in the assignment of workers of different skill levels to the different tasks affect a firm’s productivity level. This is a novel mechanism that plays a crucial role in the subsequent analysis and differentiates this model from other trade models with a task-based production function. Intermediate goods producers maximize their profits according to a two-stage optimization problem. In a first step, firms assign skills to tasks and thereby determine the range of tasks performed by low-skilled and high-skilled workers, respectively. In a second step, they choose task-level output, which is equivalent to determining the task-level employment for a given skill assignment. In the subsequent analysis, I solve this two-stage problem through backward induction. For a given assignment of workers to tasks, intermediate goods producers set task-level output x(ω, i), to maximize their profits π(ω) = p(ω)x(ω)−Z1 0 x(ω, i)ck(ω, i)di −fwh,(4.5) subject to (4.2) and (4.3), where ck(ω, i) denotes the unit costs of a firm ωperforming task i with the preassigned skill type k=l, h and fmeasures the fixed input of high-skilled labor 11Acemoglu and Autor (2011) additionally account for medium-skilled workers in their model, since their main motivation is to analyze the observed increase of employment in high-skilled and low-skilled occupations relative to middle skilled occupations, which they call ”job polarization”. To keep the model tractable, I abstract from this third skill type, here. 4.2. THE CLOSED ECONOMY 73 that is required to manage the firm and organize the production process.12 With a CobbDouglas production function, this gives the standard result of a constant cost share for each task. Furthermore, in the special case of each task entering the production function symmetrically, cost shares for all tasks are the same. To be more specific, substitution of (4.2) into the first-order condition ∂π(ω)/∂x(ω, i) = 0 gives σ−1 σp(ω)x(ω) = x(ω, i)ck(ω, i).(4.6) Integrating over the unit interval, shows that prices are set as a constant markup σ/(σ−1) over variable unit costs C(ω)/x(ω): p(ω) = [σC(ω)]/[(σ−1)x(ω)], where C(ω)≡R1 0x(ω, i)ck(ω, i)di are a firm’s total variable labor costs. With these insights at hand, I am now equipped to determine the optimal range of tasks performed by a specific skill type. For this purpose, I focus on the case of interior solutions and assume that both skill groups are used for the production of intermediates.13 Since tasks are ordered according to their complexity, I can then define a unique threshold task z(ω)∈(0,1), for which the firm is indifferent between hiring low-skilled or high-skilled workers, at prevailing relative wages s≡wh/wl. To put it formally, the unit costs ck(ω, z(ω)) of a firm ωperforming task z(ω) are the same irrespective of the assigned skill type k=l, h. This implies cl(ω, z(ω)) = ch(ω, z(ω)) or, equivalently wl=wh αh(z(ω)) (4.7) and establishes s≡wh/wl=α(z). Due to the absolute advantage of high-skilled workers in the performance of all tasks, the existence of an interior solution, z(ω)∈(0,1), requires a skill premium, i.e. s > 1. Furthermore, due to relative advantage of high-skilled workers in performing more complex tasks, it follows that low-skilled workers will be assigned to all tasks i < z(ω), while high-skilled workers will be assigned to all tasks i≥z(ω).14 Notably, since all firms are price takers in the labor market and pay the same wh,wl, the threshold task z(ω) is the same for all intermediate goods producers, and hence I can write z(ω)≡zfor all ω. With the threshold task at hand, I can combine Eqs. (4.3) and (4.4) to rewrite firm output as x(ω) = φ(ω)ϕ(z) exp Zz 0 ln l(ω, i)di +Z1 z ln h(ω, i)di(4.8) where ϕ(z)≡exp hRz 0ln αl(i)di +R1 zln αh(i)dii= exp[(1 −z2)/2]. According to (4.8), firm productivity consists of two parts: an exogenous baseline productivity φ(ω) and the endogenous productivity term ϕ(z), which varies with the assignment of skills to tasks, and thus is a function of threshold task z. From ϕ′(z) = −ϕ(z) ln α(z) = −zϕ(z) it follows that firms can raise their productivity when performing a larger share of tasks with high-skilled workers. However, if s > 1, this comes at the cost of higher wages and is therefore not necessarily beneficial. A direct implication of the identical cost share (see above) is that the amount of workers of a specific skill type employed for performing tasks is the same for all tasks performed by 12The assumption that high-skilled workers are needed to manage the firm and organize the production process is in line with the literature focusing on the internal organization of firms in economies with heterogeneous workers (see, for instance, Marin and Verdier, 2008b, 2012). 13Below, I will discuss a parameter constraint that needs to be fulfilled in order for such an interior solution to materialize. 14For convenience, it is assumed that firms hire high-skilled workers for performing task z(ω). 74 CHAPTER 4. TRADE AND THE ASSIGNMENT OF SKILLS TO TASKS workers of this skill type. This can be seen from substitution of (4.4) and ck(ω, i) = wk/αk(i), with k=lif i < z and k=hif i≥z, into (4.6), which gives wll(ω, i) = wll(ω) for all i < z and whh(ω, i) = whh(ω) for all i≥z. Similarly, it follows from (4.4), (4.6) and (4.7) that wll(ω) = whh(ω). This implies s=l(ω) h(ω)=1−z z L(ω) H(ω),(4.9) where L(ω) = Rz 0l(ω, i)di =zl(ω) and H(ω) = R1 zh(ω, i)di = (1 −z)h(ω) are firm ω’s total lowskilled and high-skilled variable labor input, respectively. Accordingly, a firm’s skill intensity is given by H(ω)/L(ω) = (1 −z)/[zα(z)] and thus decreasing in z. Putting together, I can thus write a firm’s total variable labor costs as C(ω) = [wL(ω)/H(ω) + wh]H(ω), while this firm’s output is given by x(ω) = φ(ω)ϕ(z){[(1 −z)/z]L(ω)/H(ω)}zh(ω). Substitution of (4.9), then gives me for the variable unit cost of this firm: C(ω)/x(ω) = wz lw1−z h/[φ(ω)ϕ(z)], which is equal to the marginal cost of the respective producer. Constant markup pricing therefore implies p(ω) = σ σ−1 wz lw1−z h φ(ω)ϕ(z).(4.10) Noting that revenues of firm ωare given by r(ω) = p(ω)x(ω) and taking into account that wl, whand ϕ(z) are the same for all producers, it follows from (4.2) and (4.10) that the revenue ratio of two firms 1 and 2 with productivity levels φ(ω1), φ(ω2) is given by r(ω1)/r(ω2) = [φ(ω1)/φ(ω2)]σ−1. Hence, relative firm performance is fully characterized by the baseline productivity ratio. I can thus skip firm index ωfrom now on, and instead refer to firms by their productivity levels. Regarding firm entry, I follow the literature on heterogeneous firms along the lines of Melitz (2003) – with the mere difference that I consider a static model variant along the lines of Helpman and Itskhoki (2010) and Helpman, Itskhoki, and Redding (2010) – and assume that the baseline productivity is drawn by firms in a lottery from the common Pareto distribution, G(φ) = 1 −φ−k.15 The participation fee for the lottery is fewhand this fee gives a firm a single productivity draw. Having revealed their productivity, producers decide upon setting up a plant and starting production by making the additional investment of funits of high-skilled labor (see above). With revenues (and thus profits) increasing in baseline productivity, I can identify a cutoff productivity level, φ∗, which separates active firms with φ≥φ∗from inactive ones with φ < φ∗. The profits from production of a firm with cutoff productivity φ∗are equal to zero by definition and I can thus characterize the marginal firm with cutoff productivity level φ∗by means of a zero profit condition π(φ∗) = 0. This zero profit condition is usually referred to by the term zero-cutoff profit condition. In view of a Pareto distribution of baseline productivity levels, there is a proportional link between revenues of the marginal producer and average revenues of all active producers. As outlined in the appendix, this link can be used to establish the modified zero-cutoff-profit condition ¯π=fwh(σ−1) k−σ+ 1 ,(4.11) where k > σ −1 is required for a positive, finite value of ¯π. In equilibrium the costs of entering the productivity lottery, fewh, must be equal to the expected profit of doing so, ¯π(1 −G(φ∗)). 15Corcos, Del Gatto, Mion, and Ottaviano (2012) provide evidence for the Pareto distribution, using firm level data for European countries. 4.2. THE CLOSED ECONOMY 75 This establishes the free entry condition ¯π=fewh(φ∗)k.(4.12) Combining (4.11) and (4.12), I can explicitly solve for cutoff productivity level φ∗: φ∗=f fe σ−1 k−σ+ 11/k .(4.13) Eqs. (4.11) and (4.13) are the key firm-level variables, which are also informative for economywide variables. In particular, with φ∗at hand, I can calculate the productivity average ˜ φ≡ [k/(k−σ+ 1)]1/(σ−1)φ∗,16 which is useful because key aggregate variables in this model of heterogeneous firms are the same as they would be in an otherwise identical model of homogeneous firms with productivity ˜ φ:R=Mr(˜ φ), Π = Mπ(˜ φ), and, Y=Mσ/(σ−1)x(˜ φ) and P=M1/(1−σ)p(˜ φ). With these insights at hand, I can now turn to study the general equilibrium outcome in my model. 4.2.2 General equilibrium with perfect labor markets To solve for the general equilibrium outcome in the closed economy, I have to specify how wages are determined. I start with a benchmark scenario, in which wages of low-skilled and high-skilled workers are flexible and determined in perfectly competitive markets. Using the adding up condition, which simply says that adding up employment of a given skill type over all producers must give total employment of the respective skill group, market clearing for low-skilled workers establishes17: L=MZ∞ φ∗ L(φ)dG(φ) 1−G(φ∗)=zMsfk(σ−1) k−σ+ 1 ,(4.14) whereas for high-skilled workers, I obtain H=MZ∞ φ∗ H(φ)dG(φ) 1−G(φ∗)+Mf +Mefe=Mfk k−σ+ 1[(1 −z)(σ−1) + 1].(4.15) Furthermore, there exists a third condition, which I have to consider for characterizing the general equilibrium outcome in the closed economy: I have to make sure that profit-maximizing price-setting is in accordance with firm entry. Following Egger, Egger, and Markusen (2012) I call the respective condition profit maximization condition and combine the solution for the CES price index, P=M1/(1−σ)p(˜ φ), with the choice of num´eraire, P= 1, and the price markup condition in (4.10), applied for the firm with productivity ˜ φ. Using (4.13) and the definition of ˜ φ, I can solve for M=wz lw1−z hζ ϕ(z)σ−1 ,(4.16) 16As discussed in Melitz (2003), the average productivity ˜ φequals the weighted harmonic mean of the φ’s of active producers, with relative output levels x(φ)/x(˜ φ) serving as weights. 17In view of constant markup pricing, labor costs are a constant share (σ−1)/σ of a firm’s revenues: wlL(φ)+ whH(φ) = r(φ)(σ−1)/σ. Using L(φ) = zl(φ), H(φ) = (1 −z)h(φ) and accounting for wll(φ) = whh(φ), further implies L(φ) = z[(σ−1)/σ]r(φ)/wland H(φ) = (1 −z)[(σ−1)/σ]r(φ)/wh, respectively. Finally, combining wh=α(z)wland MR∞ φ∗r(φ)dG(φ)/[1 −G(φ∗)] = Mσkfwh/(k−σ+ 1) from the appendix and Me=M(φ∗)k, allows me to compute (4.14) and (4.15). 82 CHAPTER 4. TRADE AND THE ASSIGNMENT OF SKILLS TO TASKS this issue, I can substitute r(˜ φ) = σkfwh/(k−σ+ 1) together with (4.7) and the two labor market clearing conditions (4.14) and (4.15) into W= (Lwl+Hwh)/(L+H) = Mr(˜ φ)/(L+H) to calculate W=σwh z(σ−1)(exp[z]−1) + σ.(4.28) From inspection of (4.28), the increase in whtriggered by the higher supply of low-skilled workers stimulates per-capita income, while the implied increase in zreduces welfare due to the negative productivity effect, as all producers perform less tasks with high-skilled workers. Accounting for (4.26) I can furthermore calculate W= exp 1 2(1 + z2)[(1 −z)(σ−1) + 1]−1 σ−1 zexp[z](σ−1) + (1 −z)(σ−1) + 1 ˆ ζ, (4.29) where ˆ ζ≡[H(k−σ+ 1)/fk]1/(σ−1)σζ−1and dW dz =W(exp[z]−1)(z2−z−1)(σ−1) + z z(σ−1)(exp[z]−1) + σ+1 (1 −z)(σ−1) + 1.(4.30) Eq. (4.29) establishes a non-trivial relationship between zand W, with the sign of (4.30) depending on σand the initial value of z. Clearly, if zis close to zero, dW/dz > 0 holds for all σ, while things are different for z > 0. In particular for large σ-values it cannot be ruled out that dW/dz < 0 for sufficient large z. To see this, one can evaluate (4.30) for instance at σ= 2 and σ= 8, with corresponding ˆz-values of ˆz|σ=2 = 0.382 and ˆz|σ=8 = 0.69, respectively. This gives dW/dz|σ=2 z=0 = 0.5, dW/dz|σ=2 z=0.3= 0.53, dW/dz|σ=2 z=ˆz= 0.53 and dW/dz|σ=8 z=0 = 0.125, dW/dz|σ=8 z=0.3=−0.14 and dW/dz|σ=8 z=ˆz=−0.29. Let us now turn to the minimum wage economy, for which the effect of changes in Lare depicted by Figure 4.4. Since in this case a higher Ldoes neither affect the position of locus (4.15) nor the position of locus (4.16′), it leaves the mass of producers Mas well as the threshold task zunaffected. Furthermore, since a change in Ldoes not affect the position of locus (4.7) in the lower right panel of Figure 4.4 either, the skill premium also remains unaffected by an expansion of low-skilled labor supply. Of course, an increase in Lshifts locus (4.17) outwards in the lower right panel of Figure 4.4 and thus triggers a clockwise rotation of locus (4.25) in the lower left panel of the figure. This implies an increase in unemployment rate u. Similar to Brecher (1974), labor supply of unskilled workers in the minimum wage economy is not a binding constraint, and hence an increase in the respective supply is fully absorbed by a pari passu increase in unemployment. As a consequence, an increase in labor supply Lleaves high-skilled workers unaffected and lowers per-capita income of low-skilled workers, which is instrumental for a decline in welfare. Proposition 9 With competitive labor markets, an increase in Lraises the range of tasks performed by low-skilled workers. This triggers a decline in the productivity of intermediate goods producers and leads to additional firm entry. The higher supply of Lreduces per-capita income of low-skilled workers and increases welfare of high-skilled workers while overall welfare effects are ambiguous. With a binding minimum wage, an increase in the supply of low-skilled workers is fully absorbed by a pari passu increase in unemployment. This lowers welfare and leaves all other variables unaffected. Proof. Analysis in the text The implications of an increase in the supply of high-skilled workers when wages are fully flexible 4.2. THE CLOSED ECONOMY 83 z M s (4.16′) (4.15) (4.7) (4.17) zc Mc sc L↑ L↑ sc L↑ Mc L↑ zc L↑ H↑ H↑ H↑ sc H↑ Mc H↑ zc H↑ Figure 4.3: Equilibrium with fully flexible wages in the closed economy are indicated by the dashed lines in Figure 4.3. A higher Hshifts locus (4.17) inwards and therefore lowers the threshold task (and the skill premium). As a consequence, firms become more productive, because high-skilled workers are now used for a broader range of tasks. However, in an economy with competitive labor markets the additional supply of high-skilled workers is only partly absorbed by this firm-internal adjustment. Since low-skilled workers are replaced by high-skilled ones, additional firms must enter to restore market clearing for low-skilled workers, according to (4.14). This is captured by an upward shift of locus (4.15) in the upper panel of Figure 4.3. And the upward shift of (4.15) paired with the decline in zcimplies that (4.16′) must shift leftwards, which requires an increase in the low-skilled wage wc l. In contrast, the impact of an increase in Hon the real wage of high-skilled workers is less clearcut. On the one hand, an increase in the supply of a skill type renders this factor less scare and thus lowers its return ceteris paribus. On the other hand, the increase in the skilled labor supply leads to additional firm entry and thus stimulates demand for high-skilled workers as variable production input as well as demand for high-skilled workers as a fixed input to manage the firm and organize the production process. To shed further light on this issue, I can combine (4.14) and (4.16′) and 84 CHAPTER 4. TRADE AND THE ASSIGNMENT OF SKILLS TO TASKS account for wh=wlα(z) from (4.7) to compute wh=L(k−σ+ 1) fk(σ−1) 1 σ−1 ζ−1exp 1 + z2 2 1 zexp[z]1 σ−1 .(4.31) Differentiating (4.31) with respect to zgives dwh dz =whz−1 + z z 1 σ−1(4.32) which is negative as long as z < (1 + √4σ−3)/2(σ−1) ≡˜z. Noting from the definition of ˆzin (4.22), that ˜z > ˆzas long as σ≤3 + √5, I can furthermore conclude that dwh/dz < 0 and thus dwh/dH > 0 holds in the relevant parameter domain if the elasticity of substitution is low. However, if σ > 3 + √5, I cannot rule out that dwh/dH < 0 for large initial values for z. Finally, as a larger supply of high-skilled workers raises the mass of active firms, total labor income increases. To discuss the impact on a country’s welfare level, I can infer from (4.28), that given the increase in whand the reduction in z, which leads to a positive productivity effect, a country’s per-capita income is increasing in its endowment with high-skilled workers.24 Again, an increase in the supply of high-skilled workers exerts a different impact on the general equilibrium variables of interest, when the wage rate for low-skilled workers is fixed by a binding minimum wage. In a minimum wage economy, an increase in Hshifts locus (4.15) upwards, as indicated by the dotted curve in Figure 4.4. Hence, similar to the benchmark scenario with competitive labor markets, the additional supply of high-skilled workers allows for additional firm entry, so that Mincreases. However, with low-skilled labor supply being not a binding constraint in the minimum wage economy, the additional demand for low-skilled labor at the extensive margin – triggered by the additional firm entry – does not increase the factor return of low-skilled workers implying that intermediate goods producers have no incentive to reduce the range of tasks performed by low-skilled workers. Moreover, since the new intersection point between locus (4.15) and locus (4.16′) moves north-east in Figure 4.4, there is a magnification effect in the sense of dM/dH > 0, so that the range of tasks performed by low-skilled workers increases. Hence, with a binding real minimum wage an increase in Hreduces the range of tasks performed by high-skilled workers and, as can be seen in the lower right panel of Figure 4.4, it raises the skill premium. Moreover, the increase in zimplies a fall in productivity for intermediate goods producers. The implications for the wage rate of high-skilled workers can be seen when rewriting Eq. (4.7) as wh=wexp[z]. Since zrises in H, a higher supply of highskilled workers increases wh. Hence, high-skilled workers gain in relative25 and absolute terms, which is in contrast to the benchmark situation with competitive wages. However, also lowskilled workers gain from the additional supply of H, due to additional employment of this skill type. This can be seen from Figure 4.4, when noting that a higher supply of high-skilled workers shifts locus (4.17) inwards, and therefore rotates locus (4.25) counter-clockwise in the lower left panel of that figure. As a consequence, a higher skill premium must therefore be associated with lower unemployment of low-skilled workers, implying a higher per-capita income (1−u)wof this skill group. This is intuitive as the demand for low-skilled workers is stimulated by a increase in zand M. Finally, the increase in the mass of intermediate producers also leads to higher total labor income and, since both skill groups benefit, to higher per-capita income and thus welfare. 24As shown in the appendix, the positive impact is also present if σis large and dwh/dH < 0 materializes. 25This can bee seen from (4.27). Accounting for dz/dH > 0 and dM/dH > 0, the relative per-capita income of high-skilled workers wh/[(1 −u)w] clearly increases. 4.2. THE CLOSED ECONOMY 85 z M s u (4.16′) (4.15) (4.7) (4.17) (4.25) z M=ML↑ s=sL↑ u L↑ L↑ uL↑ H↑ H↑ H↑ uH↑ sH↑ MH↑ zH↑ Figure 4.4: Endowment changes with a binding minimum wage Proposition 10 With fully flexible wages, an increase in the supply of high-skilled workers reduces the range tasks performed by low-skilled workers, thereby increasing the productivity of active producers and the mass of active firms. Low-skilled workers receive a higher income and the skill premium for high-skilled workers is reduced. The impact on high-skilled wages are ambiguous and depend on the elasticity of substitution between variants of the intermediate. Only if σ≤3+ √5wages will increase, while for σ > 3 + √5the impact on wages is ambiguous. Irrespective of the change in wh, welfare is positively affected by the expansion of H. With a binding minimum wage, an increase in Hraises the mass of firms and the threshold task, thereby reducing the productivity of active producers. High-skilled workers gain in absolute and relative terms, and the unemployment rate for low-skilled workers goes down, implying that welfare must increase. Proof. Analysis in the text. This completes the discussion of the closed economy. 86 CHAPTER 4. TRADE AND THE ASSIGNMENT OF SKILLS TO TASKS 4.3 The open economy 4.3.1 Basic structure It is the purpose of this chapter to shed light on the assignment of skills to tasks and a firm’s production process if the country under consideration opens up to trade. I thereby discuss the differential consequences of trade between two countries indexed by j= 1,2, whose economies are characterized as in the previous chapter, when labor markets are perfectly competitive or when there is a binding minimum wage for low-skilled workers. To keep the analysis tractable, I thereby abstract from any trade impediments and assume that all firms export. This simplification seems to be justified, because in my model the revenue ratio of any two firms and thus the export decision is fully characterized by baseline productivity levels, and hence my model is not equipped to shed new light on the exporting decision of firms (see, for instance, Melitz, 2003; Bernard, Redding, and Schott, 2007; Melitz and Ottaviano, 2008). Therefore, I prefer the more parsimonious structure without self-selection of firms into exporting in order to focus on those aspects of the model that are new in the literature. When the country opens up for trade, intermediate goods producers can raise their profits by selling their variety to the foreign market. Abstracting from any trade impediments, Yand P are identical to all firms irrespective of their home country. Furthermore, without selection into exporting, trade does not alter the firm entry mechanism, so that (4.11)-(4.13) still hold after a country’s movement from autarky to trade. As discussed in the previous chapter, the cutoff productivity is independent of the labor market regime, hence φ∗ 1=φ∗ 2≡φ∗and ˜ φ1=˜ φ2≡˜ φ∗ hold in the benchmark scenario of competitive labor markets as well as the minimum wage economy. Constant markup pricing in both economies implies πj(φ∗) = rj(φ∗)/σ −fwhj = 0, and therefore r1(φ∗)/σ =fwh1and r2(φ∗)/σ =fwh2. Accounting for (4.2), (4.7) which is the same as in the closed economy, (4.10) and the definition of β(z) I can compute wl1 wl2 =α(z2) α(z1)1 σβ(z1) β(z2)σ−1 σ = exp z2−z1 22−σ−1 σ(z1+z2),(4.33) which determines z1relative to z2in the open economy and implies z1< z2if wl1> wl2. To compare prices of the marginal firms in the two countries, first substitute (4.7) into (4.10), which entails pj(φ∗) = σwlj/[(σ−1)φ∗β(zj)]. As the cutoff productivity is the same in both economies, I get p1(φ∗)/p2(φ∗) = wl1β(z2)/[wl2β(z1)]. Accounting for (4.33) and the definition of β(z) then gives p1(φ∗) p2(φ∗)=α(z2)β(z2) α(z1)β(z1)1 σ = exp z2 2−z2 1 2σ.(4.34) To analyze the impact of intermediates trade on the general equilibrium variables of interest, note first that both adding up conditions for low-skilled and high-skilled workers are the same as in the closed economy. However, as the final good is now assembled with intermediate varieties from both countries, the corresponding price index and therefore (4.16′) need to be adjusted. In the open economy the mass of available intermediate varieties has changed to Mt=M1+M2, implying that the price index in the open economy is given by P= [M1p1(˜ φ)1−σ+ M2p2(˜ φ)1−σ]1/(1−σ). Accounting for (4.7) and (4.10) together with P= 1 this can be written as (see the appendix) Mj=wljζ β(zj)σ−1"1 + M−j Mjpj(φ∗) p−j(φ∗)σ−1#−1 .(4.35) 4.3. THE OPEN ECONOMY 87 This equation still establishes a positive relationship between the mass of producers and the threshold task in the home country j, for given values of zand Min the foreign country −j. With these insights, I am now equipped to study the impact of trade on the variables of interest. I thereby start with a situation, in which both countries are fully symmetric and postpone a discussion of country asymmetries to the extensions in Chapter 4.4. In Chapter 4.3.2, I thereby analyze the implications of trade when labor markets are perfectly competitive, whereas in Chapter 4.3.3, I shed light on the consequences of trade in a minimum wage economy. 4.3.2 Trade with perfect labor markets With fully flexible wages, the eight endogenous variables in the open economy, wlj,whj,zj and Mj, for j= 1,2 are determined by condition (4.7) and the labor market clearing conditions (4.14) and (4.15) – applied to the two economies – Eq. (4.33) and finally the profit maximization condition in the open economy, Eq. (4.35), applied for country j.26 To illustrate the equilibrium in the open economy, I can use the same graphical tool, as in the previous chapter. If wages are set in perfectly competitive markets, the equilibrium threshold task and the skill premium are jointly determined by (4.7) and (4.17), which are plotted in the lower panel in Figure 4.5. As both loci remain unaffected by an opening up to trade, the skill premium and the threshold task are the same as in the closed economy, i.e. sc a=sc jand zc a=zc j, where index arefers to autarky variables. Moreover, since the labor market clearing condition for high-skilled workers and thus locus (4.15) remains unaffected as well, also the mass of firms in country jstays constant, i.e. Mc a=Mc j. These findings indicate, that the intersection point between loci (4.15) and (4.35) in the upper panel of Figure 4.5 is the same as in the closed economy equilibrium. According to (4.33) and (4.34), prices for the cutoff firm in each market are identical when both countries are fully symmetric, implying that (4.35) reads Mj= [wljζ/β(zj)]σ−1(1/2). Hence, compared to its closed economy counterpart in (4.16′), the profit maximization condition (4.35) is shifted rightwards for any given wage rate for low-skilled workers wa lj. Opening up to trade raises the mass of available intermediate varieties to Mt=M1+M2. This increases country-specific output Yand stimulates demand for each firm, according to (4.2). Therefore, aggregate labor demand for each skill type is stimulated. With fully flexible wages, wlmust increase, to bring the economy back to zc j=zc aand Mc j=Mc a. According to wh=wlα(z) the wage rate for highskilled workers increases by the same extend, so that the skill premium remains at the autarky level. Similar to Krugman (1979), trade between two fully symmetric countries therefore leads to a positive income and thus welfare effect, while leaving all other variables of interest unaffected. These findings are summarized in the following proposition. Proposition 11 If wages are fully flexible, a country’s opening up to trade with a symmetric partner country has no impact on the skill premium, the firm internal assignment of skills to tasks and the mass of active firms. However, trade increases the real wage for both skill types and thus welfare. Proof. Analysis in the text. The findings from Proposition 11 do not hinge on the assumption that both countries are symmetric in their relative endowments with high-skilled and low-skilled workers. This can be easily inferred from the discussion above. As any change in the supply of Lor Hin Foreign, leaves the position of loci (4.7), (4.15) and (4.17) in Home unaffected, it does not affect zj,sj and Mj. Thus, when wages are fully flexible, trade between two countries that differ in their 26Note that (4.35) can only be applied for one country. Applying it for the other country simply confirms that P1=P2= 1. 88 CHAPTER 4. TRADE AND THE ASSIGNMENT OF SKILLS TO TASKS z M s (4.16′)wa lj =(4.35)wlj (4.15) (4.7) (4.17) zc a=zj Mc a=Mj sc a=sj (4.35)wa lj Figure 4.5: Trade with fully flexible wages relative endowments still exerts only a positive income and welfare effect, but does not change the other variables of interest. Moreover, the strength of these effects depends on the stimulus in labor demand for the two skill types. The higher the mass of intermediate producers in the foreign country, the larger is the positive demand shock by opening up for trade from a domestic country’s perspective. As M−jis increasing in L−jand H−j, welfare effects at Home are therefore increasing in the size of the foreign factor markets. 4.3.3 Trade with a minimum wage for low-skilled workers In this chapter, I again study trade between two fully symmetric countries, with the mere difference, that governments in each country now set a binding minimum wage, w1=w2. To determine the eight endogenous variables sj,zj,Mjand uj, for j= 1,2 I can make use of (4.7), (4.15) and (4.24) – applied to both economies – (4.33) and (4.35). As discussed in the closed economy, the labor market clearing condition for high-skilled workers and the profit maximization condition now jointly determine the mass of firms and the threshold task. With perfect symmetry between the two economies, (4.35) reads Mj= [wjζ/β(zj)]σ−1(1/2) and is shifted rightwards relative to its closed economy counterpart in Figure 4.6, implying that M and zare increased compared to the autarky scenario. Since all other things equal, final goods 4.3. THE OPEN ECONOMY 89 producers have access to more differentiated intermediate goods, final output increases due to a standard division of labor effect. This stimulates demand for intermediate goods, according to (4.2), and therefore aggregate labor demand for each skill type. While the factor price for low-skilled workers is fixed and remains unaffected, the wage rate for high-skilled workers will increase.27 Thus, the relative factor costs have changed in favor of low-skilled workers and firms respond to the cost increase by raising the threshold task to z > za. A lower skill intensity implies that more high-skilled workers are left to entering the lottery and to manage the firm and organize the production process, so that the mass of local intermediate goods producers increases in both countries relative to the closed economy. The higher zfurthermore implies an increase in the skill premium, as can be seen in the lower right panel of Figure 4.6. Finally, the adjustment in zand Mcontribute to an increase in low-skilled labor employment and a decline in unemployment rate uas depicted in the lower left panel of Figure 4.6.28 From inspection of Eq. (4.27) there are counteracting effects on the relative per-capita income of high-skilled workers. However, solving (4.15) for Mand substituting the respective expression into (4.27), I can compute wh (1 −u)w=Lfk[(1 −z)(σ−1) + 1] Hz(k−σ+ 1) (4.36) which, according to z < za, implies that trade unambiguously increases the relative per-capita income of high-skilled workers. Finally, the increase in the wage rate for high-skilled workers and the reduction in the unemployment rate triggers an increase in welfare. These findings are summarized in the following proposition: Proposition 12 With a binding minimum wage for low-skilled workers, a country’s opening up to trade with a symmetric partner country reduces the unemployment rate for low-skilled workers and increases the real wage, the skill premium and the relative per-capita income of high-skilled workers. Welfare is unambiguously higher in the open economy than in the closed economy and all active firms produce a broader range of tasks with low-skilled workers, which reduces observed labor productivity. Proof. Analysis in the text. The results in Proposition 12 demand further discussion. First, there is a crucial difference to the findings in the literature on heterogeneous firms. Usually, the claim in the literature is that trade liberalization has a positive impact on economy-wide labor productivity by relocating productive factors towards high-productive firms, which have excess to export markets and thus benefit disproportionately from trade liberalization (see Melitz, 2003). Thereby, the firm-level productivity stays constant, but selection to more productive firms increases the economy-wide productivity. In my model, this channel is closed, as trade is costless and all firms participate in exporting. This leaves the relative performance of any two firms unaffected, and hence there is no relocation of productive factors towards high-productive firms. Here, productivity effects arise at the firm-level due to adjustments in the assignment or workers to tasks. Thereby, it follows from Proposition 11 and 12 that the existence of labor market imperfections are instrumental for the impact of trade on firm productivity. With differences in the wage setting institutions among low-skilled and high-skilled workers, a higher labor demand in the open economy changes 27To see this, remember from (4.26), that dwh/dz > 0. 28The reduction in the unemployment rate is also present in the Egger, Egger, and Markusen (2012) framework, where production consists of a single task performed by one type of workers. Similar to this chapter, the positive impact is a consequence of external scale economies in the production of the final good. 90 CHAPTER 4. TRADE AND THE ASSIGNMENT OF SKILLS TO TASKS z M s u (4.16′)w1 (4.35) (4.15) (4.7) (4.17) (4.25) sc 1 za 1 Ma 1 sa 1 ua 1z1 M1 s1 u1 Figure 4.6: Trade between two fully symmetric minimum wage economies the relative factor return and therefore leads to adjustments in the assignment of skills to tasks with consequences for a firm’s labor productivity.29 4.4 Extensions So far I have restricted the analysis to the comparison of open and closed economy equilibria. The aim of this Chapter is to shed light on how labor markets are linked in the open economy, i.e. how variations in national labor market institutions and endowments spill over to the partner country. I thereby focus on trade between two minimum wage economies as discussed in the previous chapter. Starting from a scenario with fully symmetric countries, I discuss how (i) an increase in Foreign’s minimum wage for low-skilled workers and (ii) migration of high-skilled workers into the foreign economy, spill over to the domestic country.30 29I do not discuss endowment asymmetries here, as they are in the context of open minimum wage economies at the agenda of Chapter 4.4.2. 30From the discussion in the closed economy, I know that adjustments in zand Mare only present if there is a change in the supply of high-skilled workers, while any change in Lis fully absorbed in the unemployment rate. 4.4. EXTENSIONS 91 4.4.1 Minimum wage variations in the open economy I start with a situation, in which the foreign country j= 2 adjusts its labor market institutions by increasing the minimum wage, such that w1< w2holds.31 While the implications for country j= 2 are similar to these of the closed economy, the increase in w2implies p1(φ∗)< p2(φ∗) according to (4.34) and a lower mass of firms in country j= 2. This reduction in the mass of intermediate goods producers now exerts an impact on the domestic country j= 1 according to (4.35). A smaller mass of producers in country j= 2, shifts locus (4.35) of country j= 1 leftwards in Figure 4.6, whereas it leaves loci (4.7), (4.15) and (4.17) and thus (4.25) unaffected. As a consequence, the range of tasks performed by low-skilled workers in country j= 1 must fall.32 While the minimum wage for low-skilled workers is fixed in country j= 1, the factor return for high-skilled workers falls according to wh=wα(z). Furthermore, since firms broaden the range of tasks performed by high-skilled workers, all active firms become more productive. However, increasing variable labor demand for high-skilled workers in the production process leaves less resources as a fixed input for firm entry. As a consequence, the mass of intermediate goods producers must fall in country j= 1. The adjustments in M1and z1imply a fall in the labor demand for low-skilled workers and the unemployment rate increases. Looking at the skill premium, high-skilled workers lose, but, according to (4.36), the reduction in zincreases relative per-capita income of high-skilled workers, due to an expansion of L-unemployment. The negative impact on the wage for high-skilled workers and the increase in the unemployment rate furthermore imply a reduction in welfare. These findings are summarized in the following proposition. Proposition 13 Starting from an open economy equilibrium with minimum wages, an increase in the minimum wage in one country reduces the mass of firms and the range of tasks performed by low-skilled workers in the partner country, while it increases the productivity of active producers there. Low-skilled workers face a higher unemployment rate while high-skilled workers face a reduction in the real wage. The relative per-capita income of high-skilled workers increases, whereas welfare is reduced in the partner country. Proof. Analysis in the text and the formal proof in the appendix. Interestingly, an implication of (4.33) and (4.34) is that minimum wages remain binding after opening up to trade and unemployment is persistent in both economies. In his seminal article, Davis (1998) concludes, that ”international trade equalizes factor prices” (p.482), implying that only one minimum wage remains binding. This has been criticized by Egger, Egger, and Markusen (2012), using a model of heterogeneous firms where ”productivity differences of marginal firms compensate for the prevailing wage differences” (p.774) such that minimum wages remain binding in both countries. In the Egger, Egger, and Markusen (2012) framework, trade changes the composition of active firms due to adjustments in the cutoff productivity. Moreover, if countries differ in their minimum wage, adjustments in the entry decisions of firms lead to φ∗ 16=φ∗ 2and establish p1(φ∗ 1) = p2(φ∗ 2). In my model, any adjustment in the cutoff productivity is closed since φ∗remains unaffected from changes in the minimum wage. In contrast, the firminternal adjustment in the task-based production process allows firms to respond to changes in labor market institutions and therefore factor prices. The endogenous assignment of skills to tasks gives more flexibility to absorb differences in revenues, operating profits and fixed costs Thus, I restrict the discussion to the interesting case where countries differ with respect to Hand therefore z,s and Min the closed economy. 31Comparing autarky with free trade between two countries that differ with respect to the minimum wage then follows from adding the insights from this chapter to the discussion in the previous one. 32In the appendix, I provide a formal prove of dz1/dw2<0 and dz2/dw2<0. 98 CHAPTER 5. CONCLUSIONS the mismatch between workers and tasks. If only the best (most productive) firms self-select into exporting, trade exerts an asymmetric effect on the screening incentives of highand lowproductivity firms. High-productivity firms expand production due to exporting, and therefore find it attractive to install a better (more expensive) screening technology. In contrast, lowproductivity firms do not export and lose market share at home. In response, they lower their screening expenditures. Despite this asymmetry in firm-level adjustments to trade, the average mismatch between worker-specific abilities and task-specific skill requirements unambiguously shrinks in the open economy. This points to a so far unexplored channel through which trade can improve the labor market outcome and stimulate welfare. Chapter 4 has presented a heterogeneous firms model along the lines of Melitz (2003). However, the model accounts for a more sophisticated production process, in which a firm’s output is manufactured using a continuum of tasks similar to the framework in the previous chapter. Firms hire low-skilled and high-skilled workers for the performance of tasks. Tasks differ in their complexity and workers differ in their ability to perform these tasks, with high-skilled workers having a comparative advantage in performing more complex tasks. How firms organize the firm-internal production process by assigning skills to tasks depends on the respective factor costs and productivity advantage of high-skilled workers in performing more complex tasks. This framework has been used to analyze how imperfections in the labor market affect the firm-internal assignment of skills to tasks in the closed economy. After characterizing the autarky equilibrium outcome with fully flexible wages for both skill types, a (real) minimum wage has been introduced. The minimum wage is set by the government for low-skilled workers and causes involuntary unemployment for that skill type. As relative factor prices are changed and low-skilled task production becomes more costly, firms assign high-skilled workers to a broader range of tasks. This firm-internal skill upgrading improves a firm’s labor productivity. However, as more high-skilled workers are employed for the performance of tasks, less of them are left to manage firms and the mass of firms therefore declines. Firm exit triggers a decline in aggregate output, income and welfare. After discussing migration of low-skilled and high-skilled workers under the two different labor market regimes, the model has been used to discuss how trade between two countries affects the firm-internal production process. Only when low-skilled wages are set by a binding minimum wage, trade exerts an impact on the firm-internal assignment process. The opening up to trade raises demand for each firm due to a standard division of labor effect. When the factor price for low-skilled workers is fixed, the skill premium increases implying that high-skilled task production becomes relatively unattractive. Firms respond in broadening the range of task production with low-skilled workers, which reduces labor productivity of each firm. Aside from this negative productivity effect, trade increases the mass of producers in each country and reduces the unemployment rate of low-skilled workers. This causes an increase in aggregate output, income and welfare and widens the gap of high-skilled and low-skilled labor income. After discussing the movement from autarky to trade it has been shown how changes in local endowments and labor market institutions spill over to the partner country. Thereby, an increase in the minimum wage abroad reduces the range of tasks performed by low-skilled workers at home, while it increases the productivity of active producers there. Both skill types end up with a lower per-capita income, and thus welfare is reduced at home. Of course, the organization of production has many different dimensions and this thesis cannot provide a comprehensive picture of all possible channels through which globalization and labor market imperfections may affect the organization of production. 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