What drives the substitutability between native and foreign workers? Evidence about the role of language

Transcription

1 What drives the substitutability between native and foreign workers? Evidence about the role of language Elena Gentili Fabrizio Mazzonna January, 2017 Draft version Abstract In this paper we investigate the role of language in determining the degree of substitutability between foreign and native workers. To this end, we focus on Switzerland, an immigration-receiving country with four official languages, three of which are also spoken in bordering countries. In Switzerland there are both native workers with a different linguistic background with respect to the linguistic area of residence and immigrant workers sharing the same linguistic background as native population. We modify the model proposed by Ottaviano and Peri (2012) to account for the linguistic background of native and immigrant workers. We find that language plays a central role in determining the elasticity of substitution between foreign and native workers and accounts for much of the imperfect substitutability between the two. These findings are robust to a number of robustness checks, such as different specifications of the model structure and the inclusion of cross-border workers. Then, we also compute the total wage change for native and foreign workers caused by an inflow of new immigrants. We find small positive wage effects for natives (around 1%) and negative wage effects for foreigners (between -2% and -5%). Keywords: International migration, Immigrant-native substitutability, Language JEL codes: J31, J61 Corresponding author: Fabrizio Mazzonna, Institute of Economics, via Buffi 13, 6904 Lugano, Switzerland (fabrizio.mazzonna@usi.ch). Institute of Economics (IdEP), Università della Svizzera Italiana (USI), Switzerland. Institute of Economics (IdEP), Università della Svizzera Italiana (USI), Switzerland; Munich Center for the Economics of Aging (MEA).

2 1 Introduction In the economic literature there is a long-standing debate about the impact of migrant workers on native wages and employment opportunities. A key element of this discussion is the degree of substitutability between foreign and native workers, especially among the low skilled. If foreign workers are perfect substitutes of native workers, migration inflows should only increase the stock of the labour force in the destination country, with negative consequences on native wages (Borjas, 2003; Borjas and Katz, 2007). On the contrary, if foreign workers are imperfect substitutes of native workers, they might specialize in different occupations and improve the efficiency of the labour market, with little effects on native wages. To account for this possibility, Ottaviano and Peri (2012) and Manacorda et al. (2012) extend the classic labor demand model developed in Borjas (2003) allowing native and immigrant workers within the same education-experience group to be imperfect substitutes in production. This might happen if immigrant and native workers with similar observable characteristics (i.e., education and experience) are still characterized by a different skill-mix that creates different comparative advantages on the labor market (Peri and Sparber, 2009). One potential determinant of the complementarity between foreign and native workers can be the proficiency in the language spoken in the destination country. Indeed, low levels of language proficiency are associated to worse wage trajectories for migrants (see Chiswick and Miller, 2014 for a review). In addition, Peri and Sparber (2009) show that in the US natives tend to specialize in more communication intensive tasks, while immigrants tend to specialize in more manual intensive tasks, probably because of the different comparative advantages related to language proficiency. However, there might be several other unobservable characteristics (e.g., preferences and motivations) that could make immigrants and natives somewhat complementary in the production function, but so far the literature has not been able to distinguish among them. In this paper we shed some light on the role of language in driving the complementarity between native and foreign workers by focusing on the Swiss labor market. Switzerland is a multi-cultural country with four official languages spoken, three of which are in common with bordering countries (German, French and Italian). Moreover, starting from the 50s Switzerland experienced several immigration waves from different sending countries and its immigration rate is one of the highest among OECD countries (about 27%). As a result, we observe both immigrants sharing the same linguistic background as the native population, and immigrants with a different linguistic background. To the same extent, Swiss nationals that moved to other linguistic areas in Switzerland share the same nationality as natives but not the same language. This provides the necessary 1

3 variation for our identification strategy. Our empirical analysis extend the nested-cell labor demand model developed by Ottaviano and Peri (2012, OP henceforth) to account for the role played by language. In particular, we first replicate the OP model (Model A) to estimate the elasticities of substitution between foreign and native workers. In replicating their model we find evidence of imperfect substitutability between native and foreign workers (with an elasticity of substitution of about 11). Then, we compare this elasticity with two alternative models encompassing workers main language. In Model B, we assume ex-ante perfect substitutability between natives and foreigners with the same linguistic background and we group them together as opposed to foreign workers with different linguistic background. As expected, we find a much stronger complementarity between these two groups than in the original OP model (with an elasticity of substitution of about 6). Finally, in Model C, we add the linguistic background as an additional worker characteristic to education and experience. After accounting for the linguistic background the substitutability between nationality groups increases substantially, and the perfect substitutability between foreign and native workers cannot be rejected. Overall, the linguistic background seems to play a fundamental role in determining the elasticity of substitution between different nationality groups. These results are quite robust to several robustness checks, such as the inclusion of cross-border workers and different specifications of the cell structure. In the last part of the paper, we also compare the total wage effects of an inflow of foreign workers focusing on models A and C. We find small positive effects on native wages for all the models considered (around +1%), and negative effects on foreign wages (between 2% and 5%). However, results are seldom significant and the hypothesis of 0 impact on wages cannot be rejected. Considering the linguistic background as an additional worker characteristic (model C) decreases the negative impact on wages for foreign workers, showing that accounting for linguistic diversity may better capture the complementarities between different groups of workers, especially among foreign workers. The rest of this paper is organized as follows. The next subsection describes the Swiss context. Then, Section 2 presents the details of the theoretical framework adopted. Section 3 discusses the data. Section 4 presents the estimates of the elasticities of substitution, while Section 5 shows the simulated total wage effects of an inflow of foreign workers. Finally, Section 6 concludes. Background With one of the highest immigration rates among the OECD countries (about 27% of the working age population according to Liebig et al., 2012) and 4 official European languages spoken in 2

4 different linguistic areas, Switzerland represents the ideal setting to study the impact of immigrant language skills on labour market outcomes. The four languages spoken are German, which is spoken in the Central and Eastern part of the country, French, which is spoken in the West, Italian which is spoken in the South, and Romansh, which is spoken in some specific valleys in the South-East (Figure 1). Except for Romansh, which is spoken by only 0.8% of the population, the languages spoken in Switzerland are in common with other bordering countries. Thus, many Swiss immigrants share the same linguistic background as Swiss natives. However, starting from the post-wwii period, Switzerland experienced several waves of immigration from different sending countries, also with different linguistic background. The first immigration wave in the post-war period mainly involved Italians. Then, during the 60s, new sending countries emerged: Germany, France, Austria and Spain. In the 80s a new inflow of workers arrived from Spain, Portugal, Turkey and former Yugoslavia. The inflow of ex-yugoslavians became particularly pronounced during the 90s, because of the Balkan wars. Finally, with the enactment of the bilateral agreements with the EU on the free movement of persons in 2002, Switzerland experienced a new wave of immigration from European countries, especially from Germany (Liebig et al., 2012). Figure 2 shows the share of immigrants respectively with same linguistic background (upper part of Figure 2) and different linguistic background (bottom part of Figure 2) out of total employment in Map units are spatial mobility regions, i.e. regions with homogeneous labour market characteristics. The share of foreign workers with the same linguistic background is stronger in the Italian and in the Eastern part of Switzerland. On the contrary, foreign workers with a different linguistic background are more concentrated in the Western and in the Northern part of Switzerland. 1 2 Theoretical framework As in OP, our baseline specification originate from a nested-ces production function in which labour aggregates are defined according to workers education, experience and nationality. Then, we investigate the role of language in driving the substitutability between native and foreign workers modifying the structure of the nested-ces and re-estimating the elasticities of substitution for these different models. Overall, this section provides a simple sketch of the model. The interested reader should refer to OP and Borjas (2003) for further details. Subsection 2.1 provides an overview of the theoretical model, Subsection 2.2 presents the nesting 1 However, the map about foreign workers with same linguistic background underestimates the incidence of these workers, since it only accounts for resident workers. Indeed, the phenomenon of cross-border workers, i.e. workers residing in a bordering country but daily commuting to Switzerland to work, is quite relevant in Switzerland. Further details are provided in Sections 3 and 4. 3

5 structure of the three specifications we are estimating and Subsection 2.3 describes the empirical strategy adopted to estimate the relevant elasticities of substitution. Finally, Subsection 2.4 presents the intuition behind the estimation of the total wage effect of immigration. 2.1 Theoretical model The idea behind the model proposed by OP, Borjas (2003) and Manacorda et al. (2012) is that immigrant workers should be direct competitors of native workers endowed with their same skillmix, while they should be imperfect substitutes for native workers with different skill-mix. The nested-ces structure of the model provides the necessary flexibility to estimate the elasticities of substitution between different groups of workers while imposing some structure to the problem. This section contains a simple sketch of their procedure. Assume that the economy shows a Cobb-Douglas production function: Y t = A t K α t L 1 α t (1) where output Y t is produced combining the capital aggregate K t and the labour aggregate L t. A t is total factor productivity, while α is the share of income going to capital. The subscript t indicates the time at which each of these aggregates is measured. Within a Solow model framework (Solow, 1956), the Cobb-Douglas production function predicts constant capital-output ratio and detrended capital-labour ratio in the long run, because capital readjusts to short term shocks in labour supply. Thus, in the long run the aggregate wage does not depend on the amount of labour supply and the impact of immigration on wages is 0. Now, to capture the different skill-mix of native and immigrant workers, we need a partition of the labour aggregate L t which accounts for workers heterogeneity. For instance, OP define workers skill-mix according to education, experience and nationality. Then, workers characteristics are ranked according to an increasing degree of workers substitutability. In this way, workers within the same labour aggregate are more and more homogeneous as we partition the labour aggregate in an increasing number of characteristics. Turning to the model, we number each characteristic with i = 1,..., I. Then, the M i groups within each characteristic are numbered with g(1) = 1,..., M 1 for the first characteristic, g(2) = 1,..., M 2 for the second characteristic, etc. As a result, each labour aggregate can be written as: L g(i 1)t = g(i) g(i 1) θ g(i) L σ i 1 σ i g(i)t σ i 1 σ i (2) 4

6 where θ g(i) are group fixed effects and σ i is the elasticity of substitution between labour aggregates L g(i)t. Fixed effects are normalized such that g(i) g(i 1) θ g(i) = 1. The nesting order of characteristics implies that σ i+1 > σ i. Differentiating the production function with respect to each labour aggregate and equating it to its marginal productivity we find the optimality condition for each group g within characteristic i. As an example, the optimality condition for group g and characteristic I is: ln(ω g(i)t ) = ln[(1 α)aκ α t ] + 1 σ 1 ln(l t )+ I I 1 ( 1 ln(θ g(i) ) 1 ) ln(l σ i σ g(i)t ) 1 ln(l i+1 σ g(i)t ) I i=1 i=1 (3) where ω g(i)t is the wage paid to workers in group g(i) at time t. κ t is the capital-labour ratio, while σ 1 is the elasticity of substitution between groups of the first characteristic. θ g(i) are fixed effects for groups g, σ i are elasticities of substitution for characteristic i and L g(i)t are the labour aggregates corresponding to groups g(i) at time t. 2.2 Nesting structure Even though the definition of groups will be carefully explained in Section 3, here it is useful to provide a sketch about the nesting structure of the models we are estimating. Figure 3 shows these nesting structures. As previously mentioned, model A replicates the OP model, where workers are subdivided according to three characteristics: education, experience and nationality. However, to better tailor the model to the Swiss labour market, we adopt different groupings of workers within each characteristic. Specifically, we partition labour aggregates according to three education groups (low, medium and high), two experience groups (young and old), and two nationality groups (Swiss nationals and foreigners). 2 Then, to investigate the role of language in driving the substitutability between native and foreign workers, in models B and C we modify this structure. If language plays a role, foreigners with different linguistic background should be less substitutable with respect to native workers than foreigners with the same linguistic background. Thus, in model B we assume ex-ante perfect substitutability between foreigners with the same linguistic background and natives and we group them together in the definition of nationality groups, as opposed to foreigners with a different linguistic background. Then, we attempt to control directly for the linguistic background of natives and foreign workers considering the linguistic background as an additional characteristic of the worker skill-mix. As a result, in model C we further partition the labour aggregates according to the linguistic background, assuming that workers within the same linguistic background but 2 Further details on group construction are provided in Section 3. 5

7 different nationalities are more substitutable than workers with same nationality but different linguistic background. Even though this assumption may be reasonable, we also test for the other possibility, i.e. that workers with same nationality but different linguistic background are more substitutable than workers with different nationality and same linguistic background. Moreover, in Appendix B we provide an additional robustness check inverting the order between the experience and the linguistic background characteristics in model C and presenting the estimated elasticities of substitution. 2.3 Empirical strategy We start estimating the elasticities of substitution between nationality groups. The empirical specification to be estimated can be obtained taking the ratio between the optimality conditions in Equation (3) with respect to nationality groups, i.e. foreigners and natives. Particularly, we regress the ratio of average wages against the ratio of total hours supplied by Swiss and foreign workers. To grasp the idea, indicating with r the generic labour aggregate partitioning up to nationality, the first equation to be estimated is: ln ( ωrf t ω rnt ) = ψ r + λ t + β nat ln ( LrF t L rnt ) + ε rt (4) where the coefficient β nat is the inverse of the elasticity of substitution between nationality groups (i.e., β nat = 1/σ nat ). This implies that the smaller the beta coefficient, the larger the elasticity of substitution, i.e. the substitutability between workers. ψ r are group fixed effects and correspond to the ratio between nationality fixed effects (i.e., ψ r = ln(θ rf /θ rn )). Group fixed effects should capture the differences in productivities between different education-experience-linguistic background combinations. λ t accounts for time fixed effects and ε rt is a stochastic component independent of ln (L rf t /L rnt ). Indeed, if fixed effects are correctly specified, the error term is independent of the labour aggregates, since all the endogeneity should be absorbed by group and time specific fixed effects. 3 If this assumption holds, immigration can be regarded as an exogenous shock allowing for the identification of the beta parameter (and thus, of the elasticity of substitution between nationality groups). Since fixed effects sum up to 1, they can be retrieved from the definition of ψ r through the formulas θ rf = exp(ψr) 1+exp(ψ and θ 1 r) rn = 1+exp(ψ. r) Now, we can retrieve the labour aggregate L rt from Equation (2). In this way, in constructing the labour aggregates of less substitutable characteristics we account for the imperfect substitutability 3 Notice that taking the ratio between the optimality conditions in Equation (3) it would be sufficient to control for group fixed effects ψ r, since all the other terms are washed out. However, in our baseline econometric specification we prefer to include time fixed effects as well, to account for possible year-specific differential trends in wages between nationality groups. 6

8 between workers of different nationalities. The average wages, instead, can be computed averaging the wages of different nationality groups by the share of labour provided by that group, i.e.: ( ) ( ) LrF t LrNt ω rt = ω rf t + ω rnt L rt L rt Then, we can proceed to the 2SLS estimation of the other characteristics elasticities of substitution from the optimality condition in Equation (3) instrumenting the labour aggregate L rt with the share of immigrants L rf t. Again, the estimated beta coefficients are the inverse of the elasticities of substitution (i.e. β i = 1/σ i ). This procedure is iterated up to the estimation of the elasticity of substitution across education labour aggregates Total wage effect Thus, within this conceptual framework, the labour aggregate is subdivided into different groups according to several characteristics. The main advantage of such a nested CES framework consists in the possibility to combine the estimated elasticities of substitution with the wage shares of different groups of workers to derive the total wage effect of immigration. The reduced form approach usually focuses only on a partial wage effect, i.e. the impact of foreign workers on the wage of native workers within the same education and experience group. However, an inflow of foreign workers does not only affect native workers in the same group, but also native workers in different groups, because of the imperfect substitutability between different groups of workers. These additional wage effects can be tackled by the nested CES structure, which is able to take into account these imperfect substitutabilities in estimating the total wage effect, overcoming the major flaw of a reduced form approach. For the details about the estimation of total wage effects, the interested reader can refer to OP. In our context, we focus on the percentage variation in wages and foreign labour between the first and the last available years, that is 1999 and Once the elasticities of substitution for each characteristic have been estimated, we define our set of preferred estimates and we perform a simulation using the estimated parameters as key elements to determine the overall total wage impact. Particularly, for each parameter we execute random draws from a joint normal distribution and we average them according to the nested structure adopted to obtain the wage 4 Notice that controlling for the correct specification of fixed effects is extremely important for the estimation of upper level beta coefficients, since all the terms in Equation (3) that washed out taking the ratio between nationality groups do not vanish anymore. Thus, including time fixed effects becomes now very important to account for the group-invariant terms of Equation (3) (i.e. ln[(1 α)aκ α t ] + 1 σ edu ln(l t)). In addition, group fixed effects account for the time-invariant terms (i.e. I ( i=1 ln(θ g(i))). The fixed effects, controlling for the other terms in Equation (3) (i.e. I 1 i=1 1 σ i 1 σ i+1 ) ln(l g(i)t )), depend on the structure of the model chosen and are further discussed in Section 4. 7

9 effects and the simulated standard errors for each experience-education (or experience-educationlinguistic background) group. Then, wage effects and standard errors are aggregated at higher levels using the appropriate wage shares. In this way, it is possible to obtain the total wage impact of an inflow of foreign workers on both natives and foreigners. 3 Data In this section we discuss the major data issues, while the details are left to Appendix A. Data are drawn from the Swiss Labour Force Survey (SLFS) for the period We restrict the dataset to people aged 18 or above with active working status and remunerated work in the previous week. Our sample size prior to collapsing by cell consists of 358,065 observations. However, given the large number of cells (192 year-education-experience-nationality cells in model A and B and 384 year-education-experience-linguistic background-nationality cells in model C) we prefer to report the main estimates without further partitioning by gender. Separate results for men and women are available in Appendix B. A serious limitation of the SLFS is the lack of cross-border workers, who represent a nonnegligible share of foreign workers. Particularly, in the Swiss labour market there are around 300,000 cross-border workers, representing roughly 6% of total employment and 25% of foreign workers. In Appendix B we perform a robustness check complementing the SLFS data with data coming from the Swiss Earning Structure Survey (SESS), a biannual survey administered to approximately 35,000 firms about the earnings of employees in the secondary and tertiary sectors, including crossborder workers. The results are in line with our main findings and are further discussed in Section 4. The following two subsections describe the construction of cells, wage and labour aggregates using data from the SLFS. Then, Subsection 3.3 presents some descriptive statistics. 3.1 Cell construction Given the Swiss education system structure, we subdivide workers according to three education groups. In the first group we include workers that only completed compulsory education or basic vocational training. In the second group we include workers with full vocational training, high school diploma, or tertiary vocational training. Finally, in the third group we include workers with college education. Then, we subdivide individuals according to their potential experience on the labour market. Particularly, we group them into two groups, young and old. Potential experience is computed as the difference between the individual current age and the age at which he should have completed 8

10 education. 5 Then, we drop from the sample people with 0 or more than 40 years of experience, and we define as young workers up to 15 years of experience and as old workers with more than 15 years of potential experience on the labour market. While OP adopt a specification with 8 experience groups, in the present context partitioning workers into such a large number of experience cells leads to implausible high estimates of the elasticity of substitution between experience groups with respect to the existing literature, suggesting almost no role for experience. On the contrary, grouping workers into two experience cells results in estimates of the elasticity of substitution between experience groups which are in line with the previous literature. Further discussion on this issue and some sensitivity analysis are provided in Section 4.1. Nationality cells are defined according to citizenship. People with Swiss citizenship are defined as Swiss, while people with non-swiss citizenship are defined as non-swiss. 6 Finally, linguistic background cells are defined according to the main language spoken by the individual. The main language spoken by Swiss citizens is inferred by the language in which the questionnaire has been completed. are German, French and Italian. The languages available to complete the questionnaire For simplicity, we drop from the sample individuals living in Romansh-speaking areas (less than 930 individuals out of around 360,000). Swiss citizens that decide to complete the questionnaire in a different language from the main language spoken in the area of residence are counted as different linguistic background. They are counted as same linguistic background otherwise. To the same extent, the main language spoken by foreigners is inferred from the official languages of their country of citizenship and foreigners are assigned to linguistic background cells accordingly. The specific nationalities included in each linguistic group are listed in Appendix A Wage and labour aggregates We focus on the number of hours actually provided the week before (as opposed to the number of hours defined by contract) and we drop from the sample individuals with missing values or 0 hours worked. Then, we multiply the hours worked by each individual by his personal weight and we sum up the number of weighted hours by cell. To compute the average weekly wage by cell we divide annual net income by 52 and we drop 5 We assume that people with compulsory education entered in the labour market at 14, people with basic vocational training entered at 16, people with apprenticeship or full time vocational training at 18, people with high school diploma at 19, people with tertiary vocational training at 22 and people with college education at Indeed, OP define nationality according to the country of birth. However, given that in the SLFS the information about country of birth is available only from 2004 on, we decide to adopt the definition of nationality according to citizenship in order to increase the number of observations available. More details are provided in the Appendix A.3. 9

11 observations with income equal to 0. 7 Also, we trim 1% of the observations at the top and at the bottom of the income distribution. Then, we obtain real wages adjusting nominal wages according to the price consumer index. Finally, we average wages by cell weighting each observation by the number of hours worked times the personal weight Descriptive statistics Figure 4 shows the yearly share of immigrants labour supply by education attainment and linguistic background. For all the three education groups, the share of immigrants with a different linguistic background seems to outweigh the share of immigrants with a similar linguistic background. This gap is largest among the low educated. Again, this may be due to the omission of cross-border workers. Figure 5 shows the evolution of average wages over time for Swiss and foreigners distinguished by linguistic background. For low educated workers wages of immigrants with different linguistic background are quite in line with wages of Swiss nationals. However, the low incidence of immigrants with the same linguistic background makes the average wages for this group much more volatile than the others and the omission of cross-border workers may be of particular relevance for this education category. Therefore, we cautiously refer to the robustness check in Section 4 before drawing any conclusion from this graph. For middle educated workers, instead, immigrants with a different linguistic background seem to lag behind the other two categories, suggesting a role of language in the substitutability between immigrant and Swiss workers. For the highly educated wages seem to be quite aligned for all the three categories with some convergence over time across the three groups. Finally, it is worth noting that the three education groups do not show large differences in their long term trends. At most, the trend in wages for low educated workers seems less steep than the trends for the middle and high educated workers. Finally, Table 1 shows the percentage variation in native wages and incidence of foreign labour supply between 1999 and 2014 by nationality and linguistic group. Notice that the incidence of foreign workers decreased among the low educated and dramatically increased among the highly educated. Moreover, workers with different linguistic background experienced the largest percentage changes in labour supply. This suggests a change over time in the skill-mix of foreign workers. On the other hand, native real wages increased for all groups, with almost no exception. However, the increase in wages is less pronounced among those groups that experienced the largest inflow of foreign workers, i.e. the highly educated. 7 In the SLFS there is no information about the number of weeks worked in a year. 8 Since in Switzerland part-time jobs are widespread, differently from OP we do not restrict the sample to full-time workers. Indeed, restricting the sample to people working 30 hours per week or more reduces our sample size by 25%. 10

12 4 Results We start estimating the elasticity of substitution between natives and immigrants (who share the same characteristics) for our three main models A, B, C. In Table 2 we present the estimates of the beta coefficients, β nat = 1/σ nat, across nationality groups for our models as in equation (4). For each model we present two specifications that differ in the fixed effects included. Particularly, in the first specification we only include group and time fixed effects, while in the second we also include time by education fixed effects. 9 wage trends across education groups. These effects capture possible systematic differences in In model A, our benchmark model based on OP, the inclusion of time by education fixed effects substantially improves the precision of the estimates, leading to a negative and statistically significant coefficient of This implies an elasticity of substitution, σ nat, around 11. This is a fairly small value, even smaller than the one estimated by OP for the US, suggesting some imperfect substitutability between foreign and native workers. This result may be driven by some differences in the actual skill-mix of immigrant and native workers which induce them to specialize into different occupations. More specifically, Peri and Sparber (2009) suggest that the poor language knowledge, especially among low-skilled immigrants, leads many immigrants to specialize in more manual occupations. As largely discussed throughout this paper, we explicitly test this hypothesis in model B and C. Model B assumes perfect substitutability between natives and immigrants with the same linguistic background. The estimated coefficients are much larger than those estimated in Model A, and very precisely estimated (standard errors are between 0.01 and 0.03). These coefficients range between and implying an elasticity of substitution between 6 and 7. This suggests a very low substitutability between immigrants with a different linguistic background and the other workers (natives and immigrants with the same linguistic background). On the contrary, the inclusion of the linguistic background as an additional workers characteristic (model C) leads the estimated coefficients very close to 0 (between and 0.01). Thus, once language is taken into account, we cannot reject the perfect substitutability between native and immigrant workers. Indeed, in the more parsimonious specification (Column 5) the elasticity of substitution between nationality groups scores above 60, which is 5 times larger than the elasticity of substitution found in model A. Overall, these results highlight the importance of language as a driving factor of the substitutability between foreign and native workers. 9 Following Borjas et al. (2008) we also include experience by time fixed effects in model A and B and experience by time and linguistic background by time fixed effects in model C. Results are qualitatively the same and are available upon request. 11

13 In the following tables we use the estimated coefficients reported in Table 2 to estimate the higher level elasticities, i.e. the elasticities of substitution between linguistic background, experience and education cells. Table 3 shows the estimates of the beta coefficient between different linguistic backgrounds for model C (the only model containing the linguistic background as a separate characteristic). The beta coefficient in Column (1) corresponds to an elasticity of substitution of 12. This value is fairly similar to the elasticity of substitution between nationality groups in model A, reinforcing the idea that the main driver of the imperfect substitutability between Swiss and foreign workers is the language spoken. However, in this model the inclusion of education by time fixed effects leads to a weak instrument problem. Indeed, the first stage F-statistic on the excluded instrument is far below the standard thresholds for weak instrument, making it impossible to draw any conclusion from this specification. Also, the weak instrument problem persists after the inclusion of experience by time fixed effects. In Table 4 we show the estimated beta coefficients between experience groups. Since the inclusion of education by time fixed effect leads to very large standard errors, consistently with Figure 5 we also include a less demanding specification that allows the different educational groups to differ only for a linear trend (education specific time trends). In any case, the results are fairly similar across the three models. For instance, if we consider the specification adding time by education fixed effects as the benchmark, model A predicts an elasticity of substitution between experience groups of 7 while model B and C predict an elasticity of 8. Finally, Table 5 presents the beta coefficient estimates for the elasticity of substitution between different education groups. Since we are working with 48 observations, we do not have the sufficient degrees of freedom to include education by time fixed effects. 10 Thus, as in the previous table, we only control for education specific time trends. Again, the results across the three models are very similar, implying an elasticity of substitution between education groups around 4. Before turning to the robustness checks, it is also interesting to understand which is the degree of complementarity between linguistic groups holding fixed workers nationality. In other words, we invert the order between linguistic background and nationality in model C. Even though this nesting structure does not allow for the recursive estimation of higher level elasticities, this result can still be informative about the determinants of workers substitutability. 11 Table 6 presents the results. The estimated beta coefficients are always higher than the beta coefficients estimated for models A and C in Table 2, suggesting that workers with same nationality but different linguistic background are rather imperfect substitutes, with an elasticity of substitution between 6 and We are controlling for 16 year fixed effects and 3 education fixed effects. 11 While foreign workers can be considered as an exogenous inflow of workers, natives with different linguistic background cannot. 12

14 This result reinforces the idea that language plays an essential role in determining the imperfect substitutability between workers, even between workers of the same nationality. 4.1 Robustness checks Tables 8, 9, 10 and 11 in Appendix B present the estimated coefficients separately for men and women. For men, the elasticities between nationality groups are slightly smaller than those for the pooled sample, while the estimated elasticities for women are seldom significant. This can be due to the peculiar structure of the Swiss labour market, where female participation rate is rather high (about 80% in 2015 according to OECD estimates), but about 45% of women are part-time workers with less than 30 hours worked per week (OECD, 2016). The elasticities of substitution between groups for higher level characteristics are often positive for women, suggesting that the cell specification adopted for the pooled sample may not be appropriate for women alone. For men, the elasticities of substitution between linguistic background, experience and education groups show negative coefficients. However, in many cases the first stage F-statistic is very low, suggesting a weak instrument problem. Moreover, where the F-statistic is particularly low, the estimated elasticities of substitution are also implausibly low. As a result, pooling together men and women is particularly important to increase the predictive power of the instrument and the precision of our estimates. We also perform a robustness check by including the cross-border workers. Here, all the labour and wage aggregates are inflated for the presence of cross-border workers, as described in Appendix A.7. Table 12 of Appendix B shows the elasticities of substitution between native and foreign workers. The estimated coefficients are slightly smaller but substantially unchanged for models A and B. However, the beta coefficients for model C are slightly larger in magnitude than those reported in the main text. Particularly, these beta coefficients correspond to an elasticity of substitution of 36. Thus, after accounting for cross-border workers, there could be some imperfect substitutability left between foreign and native workers, even though this elasticity of substitution is still three times larger than the elasticity estimated in model A. Notice that these estimates should be handled with care. To account for cross-border workers we used data from the SESS, which is a biannual survey and does not contain the nationality of immigrants. Thus, we imputed the number of cross-border workers in missing years and we assume that all cross-border workers share the same linguistic background of native workers. Clearly, this may affect the consistency of our results. Since in these models workers characteristics are ordered according to an increasing degree of substitutability between workers, we also provide a robustness check inverting the order of experience and linguistic background characteristics in model C. Results are presented in Table 13 13

15 of Appendix B. This alternative model structure is clearly problematic. The first-stage F-statistics are quite low for most of the estimates. Moreover, in the only specification where the estimated coefficients are reasonable and statistically significant, the elasticity of substitution for the linguistic background is larger than the elasticity of substitution for experience. Overall, these results suggest that the original model specification in model C should be preferred. Then, we also provide some sensitivity analysis about the definition of experience groups. The upper part of Table 14 in Appendix B shows the estimated beta coefficients with 8 experience groups for model A. 12 The estimated elasticities of substitution between different experience groups are implausibly high, as there are no similar results in the literature. Moreover, given the large number of cells and the high substitutability between experience groups, the beta coefficients for nationality groups are not significant anymore. Thus, we re-estimate the model defining experience groups according to terciles, i.e. three experience cells with the same number of observations. The first tercile corresponds to people with less than 15 years of experience, the second tercile corresponds to people between 15 and 25 years of experience and the third tercile corresponds to people between 26 and 40 years of experience. The bottom part of Table 14 shows the beta coefficients estimated in this way. Again, the beta coefficients for nationality are not significant and the elasticities of substitution for experience groups are still implausibly high. Thus, in the main analysis we decided to group together the second and the third terciles. We do so because we deem it reasonable to assume that the median worker in the second and the third experience terciles should differ much less in terms of acquired skills with respect to the median worker in the first tercile. Finally, we replicate the analysis constructing labour aggregates using contract hours or employment instead of the actual number of hours worked the week before. Since results are qualitatively similar, they are not reported here but are available upon request. 5 Simulated total wage effects In this section we present the simulated total wage effect of new immigration flows on both native and foreign workers. In doing this, we focus on models A and C, which are the relevant ones to elicit the impact of foreign workers on native wages. As discussed before, we use the estimated elasticities of substitution to account for the imperfect substitutability between different groups. Results are reported in Table 7. Particularly, the upper part of Table 7 reports the elasticities of substitution that we use in the simulation. Then, in panels A and B of Table 7 we present the wage effects of new immigrants, respectively on native and foreign workers. Each panel reports the 12 Results for models B and C are similar and are not reported. 14

16 overall wage effect and the wage effects by education group. Aggregating the total wage impact on natives and foreigners the total wage effect becomes 0, since the model relies on the assumption that immigration does not have an impact on wages in the long run. The education group which seems to bear the most adverse consequences of migration is the group with the largest inflow of immigrants in the period, i.e. the highly educated, even though the simulated coefficients are seldom significant. This effect is particularly strong among foreign workers, since new immigrants are more readly substitutable for them than for native workers. The overall impact on native wages is fairly stable across the models and around +1%. The wage effects for foreigners are much more pronounced, with a simulated impact between 2% and 5%. The inclusion of the linguistic background as an additional level in model C seems to reduce the total wage impact of immigration, especially among foreigners. This suggests that adding the linguistic background of workers as an additional characteristic allows to better capture the imperfect substitutability between the skill-mix of foreign and native workers. As a robustness check, we also re-estimate the total wage effect including cross-border workers in the labour and wage aggregates. However, results are very similar and are not reported here. 6 Conclusion This paper investigates the role of language in determining the substitutability between foreign and native workers. To this end, we exploit the linguistic diversity of Switzerland and we modify the model proposed by Ottaviano and Peri (2012) to account for the linguistic background of immigrants and natives. The results confirm the importance of language in determining the substitutability between native and foreign workers. Particularly, after accounting for the linguistic background, the elasticity of substitution between foreign and native workers dramatically increases, approaching perfect substitutability. This result suggests that immigrants sharing the same linguistic background of the incumbent population are potentially more able to substitute for native workers than immigrants with a different linguistic background. Then, we exploit the nested CES structure to compute the total impact of immigration on wages. Overall, models A and C give similar results, with slightly positive total wage effects on natives (around 1%) and negative effects on immigrants (between 2% and 5%). However, results are seldom significant and the null hypothesis of 0 impact cannot be rejected. Nevertheless, including the linguistic background as a separate characteristic (model C) reduces the total wage effects for both natives and foreigners. As a result, including the linguistic background can be important to correctly model the complementarities between the different skill-mix of workers. This simulation only considered total wage effects in the long run, assuming perfect readjustment 15

17 of capital. However, it would also be interesting to compute short run total wage effects considering sluggish response of capital and discontinuities in immigration policies that took place in the period considered. Particularly, after the enactment of the bilateral agreements on the free movement of persons in 2002 Switzerland experienced a dramatic increase in foreign workforce from the EU-15 member states. However, it took some time to completely remove the barriers to foreign workers. Thus, it would be interesting to disentangle the total wage effects of immigrants on native workers before 2002, during the transition phase and after the full enactment of the bilateral agreements. Future research will be devoted to analyze the effect of this important policy change. 16

18 References Borjas, G. J., The labor demand curve is downward sloping: Reexamining the impact of immigration on the labor market. Quarterly Journal of Economics 118. Borjas, G. J., Grogger, J., Hanson, G. H., Imperfect substitution between immigrants and natives: a reappraisal. Borjas, G. J., Katz, L. F., The evolution of the Mexican-born workforce in the United States. In: Mexican immigration to the United States. University of Chicago Press, pp Chiswick, B. R., Miller, P. W., International migration and the economics of language. In: Handbook of the Economics of Immigration. pp Liebig, T., Kohls, S., Krause, K., The labour market integration of immigrants and their children in Switzerland. Tech. rep., OECD Publishing. Manacorda, M., Manning, A., Wadsworth, J., The impact of immigration on the structure of wages: theory and evidence from Britain. Journal of the European Economic Association 10 (1), OECD, OECD Family Database. Indicator LMF 1.6: Gender differences in employment outcomes. Available at Ottaviano, G. I., Peri, G., Rethinking the effect of immigration on wages. Journal of the European economic association 10 (1), Peri, G., Sparber, C., Task specialization, immigration, and wages. American Economic Journal: Applied Economics 1 (3), Solow, R. M., A contribution to the theory of economic growth. The quarterly journal of economics,

19 Figure 1: Linguistic areas across Switzerland Notes - Colors correspond to different linguistic areas. Green corresponds to the French speaking area, brown to the German speaking area, purple to the Italian speaking area, and violet to the Romansh speaking area. Linguistic areas: FRE - French; GER - German; ROM - Romansh; ITA - Italian. Sources: c OFS, ThemaKart. 18

20 Figure 2: Incidence of immigrants with same and different linguistic background out of total population by spatial mobility region Share same linguistic background (%) Share different linguistic background (%) Notes - Share of immigrants from the same and from different linguistic background out of total population by spatial mobility region. Shares are computed summing up individual weights by spatial mobility region. Data refers to year Sources: Base maps: c OFS, ThemaKart; Data: SLFS.

21 Figure 3: A comparison of the three models Notes - Education groups are defined as: Low education (L): Compulsory education, elementary vocational training, household work, school for general education; Middle education (M): Apprenticeship, full-time vocational training, high school education, tertiary vocational training; High education (H): College education. Experience groups are defined as: Young (Y): up to 15 years of potential experience on the labour market; Old (O): Between 16 and 40 years of potential experience in the labour market. Linguistic background types are defined as: Different linguistic background (DL); Same linguistic background (SL). Nationality groups are defined as: Foreigners (F); Swiss Nationals (N). In model C the nationality groups are defined as: Foreigners with different linguistic background (Fdl); Swiss nationals (N) and foreigners with same linguistic background (Fsl). 20