Skill-biased labor market reforms and international competitiveness

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Introduction
The establishment of a common currency union fueled a lively debate about labor market reforms and its effects on competitiveness and trade imbalances within the Euro area. Detractors argue that a common currency shuts down one important channel of adjustment, the nominal exchange rate. Countries within a common currency union are unable to restore a loss in international competitiveness -for instance due to labor market reforms in its partner countries -through changes in their monetary policy.
This paper contributes to this discussion by analyzing the effects of labor market reforms on international competitiveness in a model that features a continuum of industries and heterogeneous workers. The latter facilitates to distinguish between labor market reforms that have similar effects on high-and low-skilled workers and labor market reforms that are skill-biased in that they have different effects on different skill-groups. The aim of this second exercise is to evaluate the spillover effects on income and unemployment in groups that are affected indirectly. Our thought-experiment will focus on the effects of a reform that reduce the lowskill workers' outside option through lower unemployment benefits. 1 Wages in the low-income group are directly affected by this reform, which leads to a reduction in unemployment. Competitiveness is affected through production costs. Lower unit labor costs at home are associated with increasing competitiveness and an expansion of the production to industries formerly associated with the foreign country. The direct effect on high-skilled is negligible simply because unemployment benefits are less relevant for the skilled workers. However, labor demand is increasing due to the expansion of production to formerly inactive industries. A surge in demand for both types of workers can only be met by lower unemployment and higher wages. For the low-skilled the effect is ambiguous. The unemployment rate decreases through the direct effect which might be already enough to restore the labor market clearing condition. Yet, high-skill workers benefit from the labor market reform due to higher demand for high-skilled labor associated with a surge in wages.
There exists a wide range of stylized facts that motivate this study. Krugman (2012) for instance argues that capital flows from Europe's core to Europe's South (for instance in form of foreign direct investments) led to wage increases in the South. 2 This soar in capital flows to the South can be explained by an anticipated lower risk for investments into the South after its entry into the European community. Krugman also points out that -at the same time -wages in Germany grew at a much lower rate, associated with a relative shift in competitiveness from the South to Germany.
Back in the early 2000s, Germany initiated a huge labor market reform program that affected a broad array of labor market institutions and slowed down wage growth in non-manufacturing sectors. It is unlikely that those reforms had a great impact on high-skill unemployment rates, mainly due to the fact that high-skill unemployment was already low before the government intervention. Furthermore, reemployment in case of job separation is more likely for high-than for low-skilled. Still, those labor market reforms can explain why wages in Germany grew at a much lower rate of 9 percent compared to the 35 percent growth rates found for Southern Europe. This was mainly through its effect on low-skilled workers.
But is there any evidence which type of worker was affected mostly? The stylized facts for Germany presented in Dustmann et al. (2009) suggest that wage growth at the bottom of the distribution was stagnant or even negative, whereas wages at the top of the distribution were rising shortly after 2000. A reduced outside option for workers due to a labor market reform is a potential explanation for stagnating or even decreasing wages if workers have to search for employers and if unemployment is high. The less likely reemployment in case of job separation, the more important the outside option gets for a worker. Rising wages at the top of the distribution suggest little impact of those institutional reforms in the high income group. The model in this paper distinguishes between low-and high-skill workers but unemployment benefits for instance are modeled as flow values. Thus, 2 "... there were massive flows of capital from Europe's core to its booming periphery. These inflows of capital fed booms that in turn led to rising wages: in the decade after the euros creation, unit labor costs (wages adjusted for productivity) rose about 35 percent in southern Europe, compared with a rise of only 9 percent in Germany. Manufacturing in Europe's south became uncompetitive, which in turn meant that the countries that were attracting huge money inflows began running correspondingly huge trade deficits." (Krugman, 2012, chapter 10) an equal change in unemployment benefits equally affects both skill groups, which is highly unrealistic. We address this issue by assuming that unemployment benefits of the high-skilled remain unaffected by the labor market reform. Workers at the top of the income distribution may have more assets that are generated outside the firm which should be accounted for in the flow value of being unemployed. This is a shortcoming of the standard search and matching framework with more than two skill-groups.
The stylized facts also fit the evolution of skill-specific unemployment. We can observe a massive decrease in low-skill specific unemployment, whereas high-skill specific rates were erratic at a constant low level. This pattern is consistent with labor market reforms that mainly affected low-skilled workers.
The analysis of those effects builds on a multi-industry North-South trade model that goes back to Hanson (1996, 1997), FH model henceforth. All monetary variables, such as wages or prices, are expressed in a common currency and the lack of a financial market rules out any kind of exchange rate policy. Thus, changes in wages directly affect production costs and the country's competitiveness, which is close to a common currency union. The original model features trade in goods and capital (FDI) but labor market institutions are beyond the scope of their study. The extension in this paper enables an analysis of the effects of labor market institutions on capital flows, unemployment, and wage inequality due to search frictions à la Mortensen and Pissarides (1994). The government can affect wages and unemployment through the outside option of workers. More stringent labor market institutions are lower unemployment benefits or less employment protection for instance. Less stringent labor market regulations in the extended FH framework increase competitiveness and thus trade and foreign direct investment at home. The aim of this paper is to assess different channels through which labor market institutions affect foreign direct investment, trade, and wage inequality at home and foreign. Therefore, the paper sorts into a large and emerging literature on spillover effects of labor market institutional changes regarding trade and unemployment between the integrated countries. In his seminal paper, Davis (1998) was among the first researchers who stressed that institutions are crucial for the explanation of different labor market patterns in countries that are internationally interdependent. Egger, Greenaway, and Seidel (2011) distinguish between the long-and short-run effects of capital mobility in their theoretical and empirical analysis of labor market rigidities and its effects on the share of intra-industry trade measured by a bilateral Grubel-Loyd index. Felbermayr, Larch, and Lechthaler (2009) show that institutional changes in one country equally affect their trading partners' labor market outcomes. The model presented herein contributs to the literature by developing a model that allows to assess how unilateral changes in labor market institutions affect labor markets not only in the respective but also the integrated countries. The outcome of the model differs in so far that it can explain skill-specific effects due to the assumption of heterogeneous workers along the lines proposed by Hanson (1996, 1997) and Moore and Ranjan (2005). Moreover, an expansion of production to industries formerly associated with foreign leads to a reduction in unemployment at home but increases unemployment at foreign. This contrasts with Felbermayr, Larch, and Lechthaler (2009), where all economies are equally affected. This stems from the fact that adjustments in the non-reforming country are mainly due to the effects at the extensive margin in our multi-industry framework.
The model employed in this paper is based on Schmerer (2012), where search frictions are also introduced into a Hanson (1996, 1997) trade model but without distinguishing between skill-specific unemployment rates. The model proposed in this paper is tied closer to the original Hanson (1996, 1997) approach due to the distinction between low-and high-skill workers, which facilitates an analysis of skill-specific institutional spillover effects. A government can increase its country's competitiveness by influencing wages and unemployment of the low-skilled through less stringent labor market institutions concerning lowskilled workers only. It will be shown that such a policy improves the position of high-skilled workers, while low-skilled loose in terms of wages but benefit in terms of employment through its feedback effects at the extensive margin, where shifts in competitiveness between countries lead to shifts of production from one country to another. Therefore, increasing labor demand at the extensive margin translate into job creation in industries that were formerly inactive within the respective country.
Two closely related papers also investigate the link between trade, capital flows and labor market institutions. Beissinger (2001) studies spillover effects of unilateral labor market reforms on capital flows between two countries in a monopolistic competition framework. Beissinger (2001) focuses on reforms that reduce unemployment benefits or the bargaining power of unions. Whether labor market reforms induce spillover effects on foreign labor market outcomes depends on the assumptions about the degree of capital mobility and the households' income situation. Mitra and Ranjan (2010) and Davidson, Matusz, and Shevchenko (2008) study the effects of outsourcing on labor market outcomes in trade models with search frictions. Mitra and Ranjan (2010) have a two sector model with labor being the only input factor. In their model, outsourcing decreases equilibrium unemployment. Conversely, Davidson et al. (2008) propose a model where outsourcing forces some of the high-skill workers in the North to search for jobs in the low-skill intermediate sector. This stirs up job competition in that sector and thus triggers a rise in unemployment. Kohler and Wrona (2010) stress the non-monotonic relationship between offshoring and labor demand/unemployment within industries by showing that the sign of the effect in their model may depend on the level of offshoring. 3 Although the theoretical literature on global sourcing and unemployment is sparse, the number of studies focusing on the effects of trade liberalization on unemployment is numerous. Brecher (1974) introduced minimum wages in a classical Heckscher Ohlin environment and analyzed how equilibrium unemployment changes when moving from autarky to free trade. Matusz (1988, 1999) were among the first to extend canonical trade models by implementing search frictions. Building on their work, Moore and Ranjan (2005) propose a model that permits studying how globalization affects skill specific unemployment in a Heckscher Ohlin world.
More recently, researchers started to focus on labor market effects in the popular Melitz (2003) international trade model with heterogeneous firms. Egger and Kreickemeier (2009) Felbermayr andPrat (2011) andFelbermayr, Prat andSchmerer (2011) introduce search frictions in the Melitz model. Exit of less productive firms boosts firms' recruiting efforts and hence reduces unemployment in the long run in the latter approach. Helpman, Itshkoki and Redding (2010 a,b) address worker heterogeneity. Larch and Lechthaler (2011) distinguish between high-and low-skill workers and analyze the effects of trade liberalization on skill-specific unemployment in a model with heterogeneous firms and search frictions.
To summarize the stylized facts discussed in the motivation, standard labor market models predict that a higher capital to labor ratio rises labor productivity and thus wages in the South but decreases wages in capital outflow country. This affects prices and therefore competitiveness of the countries iff there are no other channels of price adjustments. Joint labor market interventions within Europe would ease the problem but it remains questionable to what extent such a wage coordination policy can be implemented in the future. Moreover, one-sided labor market policy interventions also affect a country's competitiveness and the pattern of trade between the integrated countries.
Section 2 lays out the benchmark model and discusses the existence of an unique equilibrium. Different scenarios of labor market reforms and their impact on wages, unemployment and competitiveness are discussed in Section 3. Section 4 concludes.

The benchmark model
The model is general equilibrium and features two countries that are integrated into a common currency union. Thus, all nominal variables are expressed in terms of a common currency and the total GDP generated within the union is normalized to unity. Effects arising through trade with non-members are not studied in the underlying paper.
Both countries can produce the same continuum of goods but we will show that countries can also specialize on a certain range of goods and trade them internationally. Final good assemblers or downstream producers use high-and low-skill specific intermediates and capital as input for the final good production. High-skill specific intermediates are produced by input of high-skill labor, whereas low-skill specific intermediates are produced by firms that employ low-skill labor only. Intermediate good producers are henceforth called upstream producers.
Workers and upstream producers take expected prices charged by downstream producers into consideration and bargain about wages. The existence of search frictions drives a wedge between labor costs and prices charged by skill-specific upstream producers. The production and consumption side is interacted over all stages since labor and capital costs pin down national income, union income, and (international) goods' prices together.
Consumer preferences. Following Hanson (1996, 1997) preferences for x(z) are modeled by where x(z) denotes the amount of goods demanded from industry z and ϕ(z) is industry z's Cobb Douglas consumption share. 4 The aggregate consumption good is produced without costs and sold for an aggregate price level P. Prices and wages are jointly determined by upstream producers, workers, and downstream producers. Aggregate demand for the final output good equals total expenditure Y P = E. The aggregate demand function (1) implies that a constant fraction ϕ(z) of world expenditure is spent on the consumption of good z. Thus, consumer demand for output generated in industry z reads as The share of expenditure spent for that particular industry z is equal to the revenue generated in the respective industry. Perfect competition implies that total revenue in industry z is equal to the quantity produced, x(z), times unit costs, κ(z). One can solve the standard utility maximization problem of the representative consumer who maximizes utility (1) subject to the budget constraint, which depends upon prices, consumption, and income available for consumption. The first order condition of the utility maximization problem implies equation (2).

Final consumption goods producers
We borrow the heterogeneous worker concept from Hanson (1996, 1997) by assuming that goods are produced in a continuum of industries using the input factors capital, high-, and low-skill workers. However, the model setup is different in so far that workers are not directly used by the final output good producers. Instead those final goods are produced using intermediates obtained from small firms hiring either low-or high-skill workers. The input coefficients which determine input of intermediates in the production in z are given exogenously. 5 Goods in the continuum are ranked according to their skill intensities a h (z) and a l (z), both described by linear functions increasing in z.
The assumption that the input coefficient curves that pin down low-and high-skill labor requirement are both steeper in the home country than in the foreign country give rise to gains from trade and determine the free trade pattern that stems from cross-country differences in production costs. Countries produce goods where they have a comparative advantage by means of lower unit costs compared to the unit costs in the competing country. However, it is sensible to link the input requirement curves to relative factor endowments so that, on average, low-skill abundant countries have a relatively higher low-skill labor demand in all industries. In the following, all countries are assumed to be low-skill abundant and therefore all industries have higher low-skill requirement on average. 6 The functional form of both input coefficient curves is where i is the country identifier, l denotes low-, and h denotes high-skill. In the following we will use k as an index for skill, which can take the values l or h.
For the input coefficients we assume that α is a country-specific constant and 5 Demand for intermediate goods produced maps into labor requirement due to the small firm assumption and perfect competition. Each upstream producer hires exactly one worker to produce one intermediate good. 6 Whether a country is high-or low-skill abundant highly depends on how both categories are classified. On average the world is medium-skill abundant. Using WDI data in order to decompose the total labor force into low-, medium and high-skill components we find that on average 33 percent of the labor force has a low-skill education and only 16 percent of the work force hold a high-skill qualification.
γ denotes the industry specific component of labor requirement depending on z. Moreover, industries are ranked according to unit costs, which implies that γ i > 0. Parameter ψ > 0 is a shift parameter that relates low-and high-skill demand. Similar to Hanson (1996, 1997) the final intermediate good is assembled according to the nested Leontief production function Input over high-and low-skill intermediates is assumed to be Leontief, which implies that the relation between high-and low-skill intermediates is fixed. The aggregated intermediate-good is nested into a Cobb Douglas production function that combines intermediates with capital to produce the final consumption good. Iranzo et al. (2008) use matched employer-employee data in order to estimate the between-and within-group elasticity of substitution among heterogeneous workers. Their results suggest complementarity between different skill groups but substitutability within a certain skill group, which supports the choice of a Leontief production technology. Let p(z) denote the price of each final intermediate input good, l l (z) is lowskill labor demand in industry z, and l h (z) is high-skill labor demand in industry z. Under autarky the whole continuum of goods is produced domestically. Under free trade however, both countries specialize and the range of active industries within each country is determined by the cutoff condition Downstream producer prices equal production costs depending on the firm's input coefficients, wages earned by workers producing intermediates for the upstream producers, and search cost paid by upstream producers in order to recruit workers. Goods are ordered according to their relative skill intensity. We know that intermediate good prices are equalized over the whole continuum. This implies that the ranking of industries according to production costs solely depends on the input coefficients, which are exogenously given and increasing in z. Wages in both countries are equalized across sectors z but not across skill groups. Each firm has to pay q h for high-skill intermediate goods and q L for low-skill intermediates.
Intermediate goods' prices are taken as given in the final production stage and set in the stage below where firms use high-and low-skill labor to produce the intermediates. Downstream producers adjust their labor demand with respect to prices charged by upstream producers. Perfect competition implies that the industry price level equals the respective industry unit costs where and κ(z) denotes minimum unit costs in sector z obtained by solving the standard cost minimization problem for firms producing according to the production function (5).

Search and matching between workers and intermediate producers
Firms in this stage use labor to produce intermediate input goods. There are two different types of firms, one producing high-skill specific intermediates by input of high-skill labor, and one producing low-skill specific intermediates by input of low-skill labor. This assumption is consistent with the notion of firms producing different parts with different skill requirements in separated plants. The number of potential firms is given by low-skill labor endowment, L i , and high-skill labor endowments, H i . Each intermediate good producer employs one worker, and since demand for high-and low-skill intermediates is dictated by the Leontief production function (5) in the downstream production process, the maximum number of intermediate goods that can be produced in the economy equals endowments. However, search frictions reduce the number of firms since some of the workers are unemployed. 7 Labor markets are not perfect. Employers and employees have to be matched to each other and firms have to post vacancies before hiring workers. Bargaining between firms and workers is separated according to the workers' skills without intra firm bargaining across skills. Though, there is an interaction between high-and low-skill workers since upstream producers take downstream retail prices into consideration when negotiating wages. Equation (5) implies that there is no substitution between high-and low-skill workers as both inputs are used in a certain relation. Thus, firms' revenue is zero if bargaining with one or the other type of worker fails. Even if the relation in the production process is different, their importance for the revenue generated is equal because the real amount of both input factors is equal in production. Factors with higher input coefficients are more productive and therefore less units are used. Given that the price for the intermediate good depends on wages paid by upstream producers, labor market clearing hinges on a certain pair of equilibrium market tightness to secure that revenue generated by the downstream producers is exactly equal to κ i (z)x i (z).
Intermediate input prices. Since the product market equilibrium depends on the labor market equilibrium more clarification is needed to shed light on the implications from vacancy posting costs for intermediate input prices. Firms can pay vacancy posting costs in terms of income, in terms of the good produced by the respective firm, aggregate price or in terms of the wage rate. The Pissarides (2000) assumption that vacancy posting costs are paid in terms of goods' prices is used in the following sections in order to solve for a unique equilibrium.
Proposition 1. a) The intermediate input prices are governed by b) An increase in the equilibrium market tightness θ k directly affects wages and thus intermediate good prices. The effect is positive since the partial derivative This proposition holds irrespective of whether vacancy posting costs are paid in terms of numéraire or in terms of intermediate input prices.
Proof. Part a) can be solved as in Pissarides (2000) or Dutt et al. (2009). The small firm assumption implies that each high-skill (low-skill) specific intermediate good is produced by a firm that employs exactly one high-skilled (low-skilled) worker. Firms have to post vacancies in order to recruit new workers, which incurs vacancy posting costs c. We follow Pissarides (2000) in so far that we assume that vacancy posting costs are paid in terms of intermediate good prices. As an alternative, firms' recruitment costs could be paid in terms of the numéraire good. The conclusions drawn from the comparative static exercise in section 3 would not change. Apparently, to let firms pay recruitment costs as share of revenue generated within the firm instead of world income, which is the numéraire in our setup, is a more reasonable assumption. The matching process itself is modeled according to a standard Cobb-Douglas matching function m(θ k ), which is concave and has constant returns to scale properties. The labor market tightness θ k is skill-specific. The higher the number of posted job vacancies v relative to the number of job seekers u within a certain skill-group, the more potential matches will be created but the lower the success rate of a match. The equilibrium market tightness governs wages and unemployment through the Beveridge-curve, the Wage-curve, and the Job-creation condition. The Wage-and the Job Creation-curves are derived as in Pissarides (2000).
Job creation. J k in (10) denotes the present discounted value of expected profits from an occupied job in skill group k, V k in (11) denotes the value of a vacant job in skill group k, and η denotes the exogenously given discount rate. 8 The value of a vacant job negatively depends on unit recruitment costs but increases in the difference between the value of the filled job and the opportunity costs given by the value of the vacant job. The matching function itself pins down the probability of a successful match due to the assumption of constant returns to scale. The flow value of the filled job is revenue generated by the worker minus the wage rate paid to the worker. 9 Job separation due to an exogenous shock hits the firm with poisson arrival rate λ and destroys the value associated with that firm, which reads as At this stage we do not know whether per-worker revenue, ρ(z), is equal across industries. In equilibrium the value of unoccupied jobs is zero since firms continue to post vacancies until all profits are exploited It is sufficient to compute the optimal wage/equilibrium market tightness for the cutoff firm. However, unit costs/prices differ across firms in different industries. The Job Creation curve reads Wage curve. The worker evaluates a job based on the offered wage and the opportunity cost of accepting the wage offer. The value of the job becomes zero if the job is destroyed. The worker receives the value of her outside option worth ηU k in case of job separation, depending on the flow value of being unemployed b k = τ k + ι k B. Following Pissarides (2000) we assume that unemployment benefits, B, enter the flow value of being unemployed additively. Moreover, we assume that high-skilled workers do not take unemployment benefits into their consideration. Hence, changes in unemployment benefits do not affect their outside option. The parameter ι k is an indicator variable that can take the value zero if a workers assets are higher than a certain threshold so that unemployment benefits are irrelevant for them. For skill-biased labor market reforms we assume that high-skilled workers are above that ceiling so that they do not receive any additional income from the government in case of getting unemployed. The intuition behind that is the assumption that unemployment benefits are low relative to their permanent income and thus relatively unimportant. In addition, we assume that all other values of being unemployed, τ k , are skill-specific as well and such that τ h > τ l . Workers find new jobs with a certain probability that depends on the market tightness, which translates into We follow Dutt et al. (2009) and introduce W e k in order to take into account that workers are randomly matched to firms and therefore have to build expectations about W . This also implies that all firms pay the same wage rate and hence only differ with respect to production. Wages itself are bargained and satisfy the bargaining condition Thus, the distribution of total gains depends on the workers' bargaining power, β , so that the equilibrium bargaining outcome must satisfy It can be shown that the existence of recruitment costs increases wages through the outside option. An unsuccessful match incurs additional recruitment costs which is anticipated by the workers We obtain a wage condition by combining the equilibrium conditions (18) and (17) as shown in the appendix to solve for which is equivalent to the labor supply curve in the standard Hanson (1996, 1997) model.
Equilibrium in the high-skill intermediate sector.
In equilibrium, the wage and the equilibrium market tightness θ k are determined by interacting the wage curve and the job creation curve so that Simplifying then yields Therefore, equation (21) implies that all downstream producers pay the same price for intermediate goods denoted Intermediate good prices only depend on exogenous parameters and the equilibrium market tightness, which is common to all firms in all industries. Moreover, we suppose that the discount rate η and the capital rental r are tied to the capital rental and we assume that the discount rate is predetermined by the capital rental.
Equilibrium in the low-skill intermediate good sector. Following the same line of reasoning we can derive the equilibrium condition for low-skill intermediate input prices as We denote the price paid by downstream producers for the purchase of low-skill intermediate inputs q l (z) = ρ l (z), which is possible due to the small firm assumption. Each firm employs one worker and produces exactly one unit of the intermediate good. The firm's revenue is thus equal the intermediate good price paid by the final output good producers. Moreover, the assumption that search costs are paid in terms of intermediate goods prices gives rise to the solution presented in Proposition 1. Part b) of Proposition 1 is easily proved by deriving the first derivative of the labor market equilibrium condition with respect to θ k , which is increasing since the vacancy filling rate is decreasing in the equilibrium market tightness ∂ m(θ k ) ∂ θ k < 0. Thus the first derivative of (8) and (9) with respect to θ k is positive.
Skill-specific unemployment. Solving the product and labor market equilibrium pins down the low-and high-skill equilibrium market tightness and unemployment in both countries via the skill-specific Beveridge curves u(θ ki ) = λ λ + θ k m(θ ki ) .
The Beveridge curve relates the unemployment-to-vacancy ratio such that the flow into unemployment equals the flow out of unemployment and therefore pins down long-run equilibrium unemployment rates in the economy. The Beveridge curve is convex due to the concave matching technology. Thus, the magnitude of the relationship between θ k and u is stronger for relatively low values of unemployment.
Labor market clearing. The labor market clears when labor supply equals labor demand. However, due to search frictions labor supply is the fraction of matched workers outside the pool of unemployed workers. On the other hand, firms adjust their labor demand to the intermediate input prices that now do depend on wages and search costs. Thus, search costs drive a wedge between intermediate input prices and the wage earned by the firms' workers, but perfect competition still implies that prices are equal to production cost. Final good producers are price takers and base their labor demand decision on the (already optimal) high-and low-skill intermediate goods' prices, given that wages are bargained between intermediate goods producers and workers, and given that those wages are optimal. Therefore, wages map into intermediate goods' prices.
Applying Shephard's Lemma the demand for produced intermediates is equal to l k (z) = ∂ κ k (q h , q l , r; z) ∂ q k (z) = Dζ a k (z)(q l a l (z) + q h a h (z)) ζ −1 r 1−ζ .
Domestic labor market equilibrium requires that labor demand at the aggregate level is equal to total labor supply which is satisfied if and hold. The right hand side is aggregate labor demand obtained by aggregating industry level labor demand over all industries. The specialization pattern under free trade is ex-ante unknown and depends on the unit cost schedule over all industries, wherez i denotes the upper and z i the lower bound of the continuum of active industries in the respective country.
If we allow for free trade both countries are better off by specializing on production in sectors where they have a comparative advantage. A free trade equilibrium requires one unique cutoff z * ∈ (0, 1) for which each of the four labor markets is in equilibrium and for which the cutoff condition is fulfilled. However, each cutoff z * ∈ [0, ∞] is associated with one unique combination of θ l and θ h . Thus, a necessary requirement for the free trade equilibrium is a cutoff associated with a combination of equilibrium market tightness parameters for which all labor markets clear and for which domestic equals foreign unit costs. Obviously, there is no upper bound for z which means that -given the exogenous parameters -such a cutoff might be outside the feasible space of industries, which is restricted to lie within the continuum z ∈ [0, 1]. If the cutoff condition is fulfilled for z * > 1 only, we would obtain a corner solution where one country could produce all goods cheaper. In that case there are no incentives for one of the countries to participate in international trade so that both economies remain under autarky and produce the whole continuum domestically. Both cost schedules are increasing in z. Thus, an increase in the capital rental or the intermediate goods shift the unit cost schedules up. This shift in unit costs over the whole continuum will result in a loss of the comparative advantage in some industries located close to the former cutoff, resulting in a shift of z * .
We assume that the input coefficient curves are such that home has a comparative advantage in industries closer to the lower bound of industries, whereas foreign has a comparative advantage in industries closer to the upper bound of industries. This assumption allows us to write the labor market clearing conditions as a function of the cutoff z * .
Prices of high-and low-skill intermediates depend on the endogenous equilibrium market tightness, and some exogenous parameters only. q can be substituted in the labor market clearing condition so that this condition only depends on θ k . Following Hanson (1996, 1997) we exploit equation (2) and (7) in order to link the labor-, and product-market equilibrium at home and foreign via Thus, the number of matches equals the number of available intermediate goods.
The consumption share for each industry z is constant and by assumption equalized over the whole continuum.
Existence of an unique equilibrium. Labor market clearing requires that labor demand equals labor supply in each country and skill group. The labor market clearing conditions therefore determine four θ ik 's, and each θ ik in turn pins down the respective wage and skill-specific unemployment rate. The equilibrium is unique since there exists exactly one pair of equilibrium market tightness in each country that satisfies all 2 × 2 labor market clearing conditions for a given cutoff z * . To see that an unique equilibrium exists we let Γ L denote the left-, and Γ R the right hand side of the labor market clearing condition. We further define The left hand side of both labor market clearing conditions has its origin in zero and converges to an upper bound. The right hand side is also well behaved. Labor demand is decreasing in θ k . An increase in θ k triggers an increase in intermediate input good prices, which in turn reduces demand for intermediates. We compute the partial effects by application of the Leibniz rule to the right hand side of the labor market clearing condition and assuming that the bounds of the integral being constant yields where world income is set as numéraire so that E = 1. 10 The first derivative approaches 0 when q k goes to infinity and ∂ 2 Γ R ∂ q 2 k > 0. Therefore, firms' labor demand is decreasing in θ k and converges to zero. Intermediate good prices converge towards the positive constant b k if θ k approaches zero but go to infinity when θ approachesθ k which is defined as βθ k + η+λ m(θ k ) = (1−β ) c . Labor demand is thus positive for θ k = 0 and converges to zero when θ approachesθ k . Figure 1 illustrates the equilibrium. Notice, that there is an interaction between the low-and high-skill labor market clearing condition. The high-skill labor market tightness shifts low-skill labor demand Γ R through the increase in the wage rate that enters both groups' labor market clearing condition.  Figure 2 depicts the left and right hand side of the labor market clearing condition in both skill groups. The focus lies on the interaction between equilibrium market tightness θ k and labor demand / supply. For the sake of clarity we assume that the labor supply function Γ L are equal in both sectors. 11 A change in one skill group's equilibrium market tightness also affects the respectively other skill-groups Γ R . The equilibrium is unique since Γ L has its origin at zero and converges to the upper bound whereas Γ R converges to zero when θ k goes to infinity.
Lemma 1. The right hand side of the labor market clearing condition is increasing in z * in the country where z * determines the upper bound of active industries. Conversely, countries where z * pins down the lower bound of industries suffer from a decrease in labor demand if z * increases.
Proof. The proof of Lemma 1 follows directly from the first derivative of the right hand side of the labor market clearing condition with respect of z * , which is positive or negative depending on whether z * is the upper or lower bound of the integral. Notice, that for each country we ex-ante know whether z * is the upper or lower bound from the assumptions about the country's technology parameters which are exogenous. In the two country scenario, both countries have one constant bound (either 0 or 1) and one variable bound z * . We assume that home has a comparative advantage in the production of goods closer to 0 and foreign has a comparative advantage in the production of goods closer to 1. Therefore, for the home country z * is the upper bound of active industries. Changing the bounds and deriving the first derivative with respect to z * therefore yields for home and for foreign, respectively. An increase in the cutoff industry thus reduces labor demand at the extensive margin due to a reduction in active industries. 11 That would be the case if matching functions and labor endowments are equal for both high-and low-skilled. Differences in endowments would shift Γ L without affecting the shape of the curves. Our institutional variables as unemployment benefits, search costs, or the bargaining power of the workers do not affect the labor supply curves directly.

General equilibrium
To close the model we still have to determine world income and capital returns. Income is normalized to unity and equals world factor payments in country d (domestic) and f (foreign) The capital rental is determined exploiting the Cobb Douglas shares and Shephard's Lemma again Thus, the fraction ζ is spent for intermediates which gives us Both equilibrium conditions can be solved for E in order to derive Hence, the equilibrium depends on 8 endogenous variables: 4 equilibrium market tightness, capital return in the foreign and home country, one cutoff, as well as world income. We follow Hanson (1996, 1997) setting world income as numéraire so that we can drop one equilibrium condition as suggested by Walras' law.

Comparative statics
This section analyzes the effects of unilateral changes in labor market institutions on trade, foreign direct investment, and inequality. Labor market institutional changes in the extended FH framework affect a country's competitiveness through production costs. This change in competitiveness not only affects the reforming country's labor market, it also affects foreign labor markets at the extensive margin.
Interest rates are treated as exogenous. A reduction in unemployment benefits for instance shifts the unit cost schedule down, followed by adjustments at the extensive margin through an expansion of production at home. Institutional reforms always affect skill-specific unemployment in both the low-and the high-skill group directly through the wage setting mechanism and/or indirectly through the adjustments at the extensive margin.
Moreover, we distinguish between institutional changes that have equal effects on both skill-groups and institutional changes that are skill-biased. Governments for instance may finance special vocational retraining programs that help workers to switch occupations. Skill-biased effects of changes in the replacement rate are less obvious. Here we assume that high-skilled workers do not take unemployment benefits into consideration due to their higher wealth and higher reemployment opportunities in case of separation.

Non skill-biased effects of institutional reforms
As shown in the appendix, all policies that intend to reduce the workers' labor standards partially increase wages and unemployment in the search and matching framework. This is associated with an downward shift of the unit cost schedule for downstream producers. The direct effect comes along with indirect adjustments in wages through the change of the equilibrium market tightness. It will be shown that the indirect effect will not overcompensate the direct effect although both effects go into opposite directions so that the unit cost schedule shifts down following the direct effect of institutions on wages. Although we assume that changes in labor market institutions are unilateral, spillover effects influence labor markets in countries integrated via trade and FDI. We will focus on the effects of lower unemployment benefits.
Proposition 2. a) An unilateral decrease in unemployment benefits B i directly reduces both skill groups' wages through the workers' outside option. Unemployment in country i decreases accompanied by a rise in wages due to the increasing equilibrium market tightness, which mitigates the direct effect. Lower production costs lead to increased competitiveness at home through a higher z * . b) Country j = i's capital outflows and loss in competitiveness will increase its unemployment but reduce employees' wages in both skill groups.
Proof. a) Wages and unemployment are affected through three different channels. The direct effect works through the reduction of the outside option, which directly reduces wages and thus intermediate input good prices as derived in the appendix. To derive the direct effect of the policy intervention, we made the assumption that the equilibrium market tightness and the cutoff remain unchanged. Two indirect effects that also affect wages and intermediate good prices in the second round mitigate this direct effect. Suppose that the cutoff remains unchanged and remember that world income is not affected by assumption. 12 The equilibrium market tightness must increase in order to restore equilibrium through a lower rate of unemployment, which mitigates the direct effect derived in the appendix. However, the indirect effect cannot overcompensate the direct effect as discussed separately in the next paragraph. A third effect arises through the adjustments in the cutoff z * . Lower unemployment benefits reduce wages and thus production costs, which boosts the country's competitiveness and increases the cutoff z * . This third effect arises only if the direct effect of the institutional change decreases intermediate good prices, which is the case. Moreover, both effects go into the same direction, which implies that labor demand is increasing at the intensive (direct minus indirect effect) and extensive margin. The effect is thus unambiguous.
The direct and the indirect effects. We have seen that a decline in unemployment benefits reduces wages and hence intermediate good prices, which stimulates labor demand through higher demand for intermediates.
We can use the labor market clearing conditions to prove that the direct effect must dominate the indirect effects so that the unit cost schedule is still shifting down. We begin by substituting the high-skill specific input coefficient by equation (4). The input coefficients drop out so that the labor market clearing conditions collapse to It is straightforward to show that a decrease in unemployment benefits decreases high-and low-skill specific wages and thus intermediate good prices directly. The right hand sides of equations (42) and (43) increase in the first round through this partial effect of the change in institutions on wages as derived in the appendix. The left hand has to adjust accordingly. First of all we assume that the cutoff remains constant in order to show the effects of the change of the denominator at the right hand side, which is decreasing so that [q ld (θ ld ) + ψq hd (θ hd )] < [q ld (θ ld ) + ψq hd (θ hd )]. Prime is the level of the denominator right after the direct effect of the reform. The cutoff will rise iff the denominator is lower after the labor market reform. The effect is the same for both skill groups so that we have to focus on only one skill group. We choose the low-skilled, where we find Unemployment has to decrease in order to restore labor market equilibrium, which will lead to a decrease of the right hand side through the denominator that is increasing again. We therefore get Left hand side prime is the second round level, whereas right hand side doubleprime is the second round level of labor demand before the change of the cutoff. We know that L d (1 − u ld (θ ld )) > L d (1 − u ld (θ ld )) so that [q ld (θ ld ) + ψq hd (θ hd )] < [q ld (θ ld ) + ψq hd (θ hd )] has to be true, otherwise the equality sign in equation (47) does not hold. If that is true we find that the cutoff increases to z * ' due to lower labor costs, which raises labor demand even more so that we get both sides adjust again so that where ] must be true, otherwise the equality sign in equation (49) does not hold. Figure 2 illustrates the effects at work by plotting the left side of the labor market clearing condition, Γ L , that is independent of unemployment benefits, and the right side, Γ R , which depends on the unemployment benefits through its dependence on wages. It is enough to show the effects for one skill-type since we first focus on the non-skill biased effects that affect both type of skills equally. The first effect is the direct effect as derived analytically above. A reduction in b shifts Γ R up in the (Γ R , θ ) space due to higher demand for intermediates. The restriction β θ k + η+λ m(θ k ) < (1−β ) c k must be fulfilled in order to secure that q k (θ ) > 0. Furthermore, it secures that the indirect effect through θ will be less than the direct effect so that the total production costs after the government intervention are lower. The reason is that this restriction for θ rules out any jumps in q and thus in Γ R so that Γ L , and Γ R converge as depicted in Figure 2 until supply equals demand associated with a change of θ from θ 1 to θ 2 . This indirect effect arises only because the labor market is not in equilibrium anymore, which is accompanied by changes in wages. Yet, if q rises above its initial value, as it could be the case when Γ R is asymptotic, unemployment would have to increase as well. This cannot be the case as long as q increases only in order to facilitate a reduction in unemployment. Thus, q l a l (z) + q h a h (z) (the initial labor cost in sector z before the reform) must be higher than q l a l (z) + q h a h (z) (the total labor costs after the reform) since unemployment has to be decreasing in both skill groups. From equation (7) we know that this is associated with a shift of the unit cost schedule down associated with a higher z * .
The range of active industries increases at the extensive margin and as proved in Lemma 1, further boosts labor demand and shifts Γ R in the same direction as the intensive margin effect that led to a rise of the equilibrium market tightness from θ 1 to θ 2 . Unemployment has to adjust a second time in order to restore labor market equilibrium again. The second effect goes in the same direction so that the final equilibrium is reached in θ 3 , associated with a lower rate of unemployment and a lower price of the intermediate goods price. Unemployment decreases due to ∂ u k ∂ θ k < 0, which follows from equation (23). Part b) follows directly from part a) but the effects go into the opposite direction due to the fact that z * is the lower bound of active industries at foreign. There is no direct effect of unemployment benefits on Γ R due to the assumption that the foreign Γ , Γ Γ Γ Δ * > 0 Figure 3: The effects of the reform abroad government does not react to the labor market reforms at home. The increase in the cutoff shifts Γ R down followed by simultaneous increase in unemployment and decrease in wages through the adjustment of the equilibrium market tightness from θ 1 to θ 2 . This scenario is illustrated in Figure 3. Unemployment increases in both skill-groups due to ∂ u k ∂ θ k < 0, which follows from equation (23). To analyze how capital changes in the aftermath of institutional reforms we have to introduce capital market clearing conditions by aggregating individual industry demand for capital as On the aggregate level capital demand is pinned down by which is found by aggregating individual industry capital demand (50) over the whole continuum of active industries. The cutoff is therefore directly linked to capital demand since interest rates and world capital stock is fixed per assumption and ∂ K i ∂z > 0 and ∂ K i ∂ z < 0. This follows from the two country scenario where z * is always one country's upper and the other country's lower bound of active industries.

Skill-biased effects of institutional changes
Suppose that unemployment benefits enter the high-skilled workers outside option with a very low preference parameter ι h . For the sake of simplicity we focus on the scenario where ι h = 0 so that the reduction of the replacement rate has zero effects on high-skilled wages.
Proposition 3. a) With ι h = 0 the decrease in unemployment benefits B i decreases unemployment and wages of the low-skilled in country i directly through the outside option but leaves wages of the high-skilled unchanged. The direct effect is accompanied by an indirect effect on wages and unemployment in both skill groups: the reduction of low-skilled wages will be partly compensated by the rise in θ l due to the lower low-skill unemployment. Lower low-skill wages are associated with lower high-skill specific unemployment so that wages of the highskilled increase. Total production costs are lower associated with an expansion of industries through a higher competitiveness. High-skilled workers benefit from increased competitiveness due to an increase in their wage and an decrease in high-skill specific unemployment. b) Unemployment in country j = i is increasing in both skill groups through the adjustments at the extensive margin.
Proof. a) Remember that the domestic country has a comparative advantage in industries closer to the lower bound of the mass of industries so that z * is the domestic upper variable bound of active industries. Without a change in the equilibrium market tightness θ ld , the decline in B d reduces wages of the lowskilled through b ld but leaves b hd unchanged. The lower wage stimulates labor demand for both type of workers due to the Leontief production function which must be met by a decrease in unemployment of both high-and low-skilled. This leads to positive wage effects in both skill groups. Nevertheless, production costs, κ(z), are lower over the whole continuum as long as the indirect wage effect does not overcompensate the direct effect as discussed below. This reduction in unit costs shifts the unit costs schedule downwards associated with a higher cutoff z * > z * .
Increased demand for high-skilled can be met only by increases in the highskilled wages so that wage inequality is rising due to the skill-biased labor market reforms.
The direct and indirect effects on wages and intermediate good prices. One can apply exactly the same prove as derived for the non-skill biased labor market reforms using Figure 2, at least for low-skilled. For high-skilled we use equation (43). We know that there is no direct effect but the denominator decreases due to the partial effect on q l , which translates into Unemployment must also decrease in order to restore labor market equilibrium, which will lead to a decrease of the right hand side through the denominator that is increasing again. We therefore get Left hand side prime is the second round level of labor supply, whereas right hand double-prime is the second round level of labor demand before the change of the cutoff. We know that H d (1 − u hd (θ hd )) > H d (1 − u hd (θ hd )) so that [q ld (θ ld ) + ψq hd (θ hd )] < [q ld (θ ld ) + ψq hd (θ hd )] must be true, otherwise the equality sign in equation (53) does not hold. If that is true we find that the cutoff increases to z * ' due to lower labor costs, which raises labor demand even more. The effects can be illustrated exactly as for Proposition 2 using Figure 2 and 3. b) An increase in z * reduces foreign competitiveness associated with an increase in unemployment of both type of skills and a reduction of wages and intermediate good prices. This leads to an expansion of industries at home associated with the following adjustment processes. Firstly, labor demand for both type of skills increased due to the higher domestic output. Secondly, there is excess capital demand at home but excess capital supply at foreign. Capital owners reallocate capital from foreign to home through foreign direct investment iff capital rentals remain constant. Thirdly, both countries demand goods from the whole continuum of industries. Thus, home will export more but import less. Foreign consumers benefit from lower export prices but home consumers are worse off because of higher import prices. Unemployment in the foreign country must rise in both skill groups as the economy contracts and less labor is used to produce low-and high-skill specific intermediates.

Cooperative labor market reforms
One-sided labor market reforms by one country's government without interventions in countries that are integrated through trade and foreign direct investment fosters unemployment in the non-reforming country. Reforms that are skill-biased in that mainly the low-skilled are directly affected benefit the high-skilled in the reforming country through the effects at the extensive margin. Those spillover effects can be mitigated by joint labor market reforms implemented by all governments within the community. Suppose that both governments reduce unemployment benefits such that the unit cost schedule in both countries shift such that the cutoff remains unchanged. Wages and unemployment of the low-skilled would be decreasing in both countries but the effects at the extensive margin would be zero without an effect on foreign direct investments or the pattern of trade between both countries.

Conclusion
In a nutshell, this paper's main contribution is to extend the Hanson (1996, 1997) international trade model by Pissarides (2000) search frictions in a way that enables the analysis of different types of labor market institutions on skill-specific wages, unemployment and the pattern of trade and foreign direct investment. This in turn implies that wages and capital flows can be affected by both, trade liberalization and changes in labor market institutions. Moreover, the notion of a continuum of industries not only permits the study of spillover effects across countries, it also gives rise to a new channel through which labor market reforms affect labor demand at the extensive margin through competitiveness. Whole industries are shifted abroad. As a result, it is possible to show that countries benefit from institutional changes in foreign countries through an expansion of their production to industries formerly associated with the reforming country. Put differently, labor market reforms can be associated with a rise in competitiveness if other channels such as exchange rate policies are disregarded like we do in the model studied in this paper. The widening of the production to initially inactive industries, combined with the adjustments at the intensive margin reduce unemployment and increase wages in the new equilibrium. However, the reforming country's workers suffer from the loss in competitiveness in some of its initially active industries located close to the former cutoff.
The effect works through wages. Wages in the original Hanson (1996,1997) model adjust independently from labor market institutions. Though, the novel micro-founded wage setting mechanism in the Feenstra and Hanson model facilitates the analysis of changes in labor market institutions. The fact that workers are heterogeneous facilitates to distinguish between reforms that equally affect all workers and reforms that are skill-biased in that only low-skilled are affected. We are able to show that high-skilled benefit from those skill-based labor market reforms through higher wages but lower unemployment, whereas foreign workers loose in terms of unemployment irrespective their level of skill. It is also possible to show that those institutional changes not only affect workers' wages and unemployment, those reforms also indirectly affect FDI flows across countries. Surging labor costs render FDI more attractive and therefore lead to an increase in FDI outflows accompanied by higher wages and higher rates of unemployment.
One possible policy implication is that high-skilled workers benefit from those skill-biased labor market reforms and that governments should stick to joint labor market intervention in order to avoid negative spill-over effects.
intermediates must be lower after the reform. This shifts the respective unit cost curve down. Again the former equilibrium z * is not optimal anymore and has to adjust.
The unit cost schedules at home and foreign. The following graph, Figure 4, illustrates the shifts in the unit cost schedules at home (red figures) and at foreign (black figures) in a unilateral reduction of unemployment benefits. The unit cost schedule shifts down and becomes flatter at home, illustrated by a shift of the unit cost schedule from κ d (z) to κ d (z). The new unit cost schedule intersects κ f (z) at a higher cutoff. This increase in z * reduces foreign competitiveness so that unemployment is increasing and intermediate good prices are decreasing. The unit cost schedule shifts up and becomes steeper at foreign, illustrated by a shift of the unit cost schedule from κ f (z) to κ f (z). The cutoff increases from z to z due to the labor market reform. The scenario holds for both non skill-biased and skill-biased labor market reforms.