Wage Discrimination Against Immigrants: Measurement with Firm-Level Productivity Data

This paper is one of the first to use employer-employee data on wages and labor productivity to measure discrimination against immigrants. We build on an identification strategy proposed by Bartolucci (2014) and address firm fixed effects and endogeneity issues through a diff GMM-IV estimator. Our models also test for gender-based discrimination. Empirical results for Belgium suggest significant wage discrimination against women and (to a lesser extent) against immigrants. We find no evidence for double discrimination against female immigrants. Institutional factors such as firm-level collective bargaining and smaller firm sizes are found to attenuate wage discrimination against foreigners, but not against women.


Introduction
Immigration flows into OECD countries are marked by both sharp fluctuations and considerable diversity between countries. Taken all countries together, however, net immigration has been consistently positive since the 1960s. The first decade of the new century witnessed a new surge of inflows: between early 2000 and late 2010, the stock of foreign-born residents in the OECD rose by around 35% from 75 million to 100 million (OECD 2014: 1). In 2011, foreign-born individuals represented less than 10% in most Eastern European countries, Greece and Portugal; between 10% and 20% in the rest of the European Union and the US (14.9% in Belgium); and more than 20% in Australia, Canada, Luxembourg and Switzerland (OECD 2014).
In this paper we are concerned with the relationship between the employment of immigrants and wages, a field of intense empirical and theoretical research in labor economics since the 1950s (Becker 1957, Chiswick 1978, Arrow 1998, Altonji et Blank 1999, Arai and Thoursie 2009, Baert and Cockx 2013Baert and De Pauw, 2014. The empirical research in this area is marked by the observation that on average foreign workers with comparable productivity-related characteristics than natives receive lower wages (Bevelander and Veenman 2008, Chiswick et al. 2008, Meurs and Pailhe 2010, Barrett et al. 2012 Byrne 2014, Arai et al. 2015). The relevance of this relationship partly stems from its connection to a series of distributional issues, and especially concerns about discrimination and retributive justice. It is also related to other policy debates on immigration, for instance whether countries with wage penalties fail to attract skilled foreign labor or whether the labor supply increase due to immigration exerts downward pressure on native wages.
3 Wages of immigrants have been studied at different levels: individual Mincertypes regressions, but also cities, regions and countries have been the most popular levels of analysis (Borjas and Katz 2007;Arai and Nekby 2007, Arai and Thoursie 2009, Meurs and Pailhe 2010, Dustmann et al. 2013Mitaritonna et al. 2014, Simon et al 2014, Arai et al. 2015. While studying wage discrimination at these levels is often justified on empirical and theoretical grounds (Ottaviano and Peri 2012), they are unable to capture appropriately the most important explanans in economic wage theory: labor productivity. Arguing that the latter depends to a large extent on the immediate context in which the employee operates -how much capital is at her disposition? how qualified are her co-workers? what type of technology does the firm use? etc -a small strand of the literature started to explore wage discrimination against immigrants with firm-level data Aydemir and Skuterud 2008).
Our paper adds to the literature that consists of the few existing studies that measure wage discrimination against immigrants while accounting directly for productivity effects at the firm level. First, we apply a very recent approach to estimating firm-level wage discrimination against immigrants developed by Bartolucci (2014); we are the first to estimate these effects with a large matched employeremployee dataset covering the Belgian labor market, a country that is generally considered as having comparatively strong anti-discrimination legislation. Second, we address various econometric issues neglected in previous studies such as the potential endogeneity of foreign workers and unobserved time-invariant firm characteristics (we present both FE and GMM-IV estimators). Third, we improve on firm-level studies that focus only on male migrants (Aeberhardt and Pouget 2010) and study the respective wage effects of the employment of male natives, female natives, male immigrants and female immigrants. Fourth, we test additional hypotheses on whether 4 wage discrimination against foreigners is affected by the level of collective bargaining and firm size.
The paper is structured as follows. Section 2 summarizes the literature on wage discrimination against immigrants and discusses three potential sources of productivity differences between natives and immigrants. Section 3 presents our methodological approach for measuring the relationship between foreign employment, on the one hand, and average wages at the firm level on the other hand. Section 4 presents our dataset and descriptive statistics, whereas Section 5 includes the results of our regression analysis that are discussed in the concluding Section 6.

Wage discrimination
The conventional definition of wage discrimination in labor economics is inseparably linked to the notion of productivity. According to the definition of Heckman (1998), wage discrimination corresponds to a situation in which an employer pays a different wage to two otherwise identical individuals but who differ with respect to a characteristic such as gender or race -with the crucial qualification that these characteristics have no direct effect on productivity.
A mismatch between wage gaps and productivity gaps may arise for different reasons, the classical explanations provided by Phelps (1972) and Arrow (1973) being 'statistical discrimination' and 'preference-based discrimination'. The first theory refers to the effect of negative stereotypes or a general lack of information of employers on the productivity of immigrants, a situation that can turn into a "self-5 fulfilling prophecy" if it decreases the expected returns on human capital investments made by immigrants (Aeberhardt and Pouget 2010: 119). In other words, due to employer beliefs or the limited transferability of credentials, immigrants may be penalized for difficulties in signaling their productivity. The second theory refers to a situation in which the tastes of employers (or their employees or customers) translate into lower demand and lower wages for foreign workers. A third theory on wage discrimination relates to differences in career dynamics, for instance if self-selection and self-censorship leads to immigrants behaving differently from native colleagues with identical productivity (Duguet et al. 2010: 7). These different mechanisms can be associated to the attributes of both being female and being foreign, so that female immigrants might cumulate wage penalties ("double discrimination").
Starting from these premises, it is obvious that empirical research needs data on wages but also on productivity to be able to assert the presence of discrimination against (female) immigrants. Recent advances in empirical research have provided at least three types of plausible explanations for why immigrants affect productivity differently than natives. These explanations can be divided into intrinsic productivity differences and segregation into groups with different productivity.

Intrinsic productivity differences
Intrinsic productivity differences refer to the value of the human capital or ability of immigrants. They have been documented in studies on the language abilities of immigrants van Soest 2002, Hellerstein andNeumark 2003), literacy 6 skills (Ferrer et al. 2006) or the quality and transferability of foreign education and training (Bratsberg and Ragan, 2002).
According to Friedberg (2000: 221), education and labor market experience acquired abroad are less valued than domestically acquired human capital. According to his study on the Israeli labor market, this difference can fully account for the wage penalty of immigrants compared to natives with similar characteristics. Bratsberg and Ragan (2002: 63) document a link between wage penalties and foreign education for the US. Their study suggests that this effect is either due to the inadequacy of foreign education or signaling problems and show that any additional schooling in the US "upgrades or certifies" the education previously acquired in the sending country. More recently, Aeberhardt and Pouget (2010: 130) found that education remains the most important explanations for wage differentials between native and foreign workers in the French wage distribution. Results in Dustmann and van Soest (2002) based on panel data from Germany show that language proficiency is considerably more important than what is conventionally assumed in the literature. A key result of this line of research is that a substantial portion of observed wage differentials is linked to intrinsic productivity differences, but also that wage penalties could diminish over time if intrinsic differences taper out in the assimilation process. A serious limitation of research in this area is that only few studies use direct information on productivity and investigate gender biases in intrinsic productivity differentials between immigrants and natives (Hellerstein and Neumark 2006;Bartolucci 2014

Segregation into categories with different productivity
A second source of productivity differences between natives and immigrants can be subsumed under the concept of segregation, i.e. the non-random sorting into categories with different productivity. The most common categories associated with segregation include job types, tasks, occupational nomenclatures, firms with different technologies or capital endowments and sectors of activity. Whereas intrinsic productivity effects refer to differences between natives and immigrants within the same category (e.g. unequal productivity within the same occupation), segregation points to differences in the distribution of natives and immigrants across categories that each capture a certain level of productivity (e.g. overrepresentation of immigrants in occupations with lower productivity). Bayard et al. (1999) argue that large parts of the wage gap between whites and non-whites in the US can be attributed to different types of labor market segregation. Elliott and Lindley (2008) conclude that occupational segregation contributes to immigrant-native wage gaps in the UK. Similarly, Aeberhardt and Pouget (2010: 118) find no wage discrimination but modest occupational segregation in their matched employer-employee data from France. Aydemir and Skuterud (2008) use Canadian matched employer-employee data to document non-random sorting of immigrants into firms that pay lower wages, an effect that appears to be stronger for immigrant men than for women. Peri and Sparber (2009: 135) use US Census data from 1960-2000 show that foreign-born workers appear to specialize in manual and physically demanding occupations while natives sort into jobs requiring intensive communication and language skills, which can be interpreted as sorting into jobs with different productivity. Findings by Aslund and Nordstöm Skans (2010) suggest that path 8 dependency can explain part of heterogeneous sorting in Sweden as immigrants are more likely to work in firms which already employ immigrants.
Although segregation does not fall under 'wage discrimination' in the sense of Heckman's definition quoted above, recent research suggests that labor economists have overlooked that segregation not necessarily "explains" observed wage differentials. Firstly, studies using firm-level panel data on productivity conclude that it is not clear to what extent categories such as occupations are actually accurate proxies for productivity (Gottschalk 1978, Kampelmann andRycx 2012). Indeed, none of the studies cited above use direct measures of productivity and therefore have to rely on more or less accurate proxies. Secondly, non-random sorting is hardly a satisfying explanation but rather points to structural differences in terms of origin or gender that call themselves for explanations. For instance, segregation raises equity issues if immigrants are systematically "downgraded" into low-wage categories that lie below their observed skills, as suggested in recent work by Dustmann et al. (2013) and McGuinness and Byrne (2014). As mentioned above, most available studies on gender or ethnic biases in segregation suffer from the absence of direct productivity measures (Hellerstein and Neumark 2006;Bartolucci 2014).
Female immigrants are potentially exposed to both intrinsic productivity differences and segregation into categories with lower productivity, again suggesting lower pay or, in the case of wages below marginal products, a risk of "double discrimination" for this group. 9

Institutional factors
Wage discrimination against groups such as women or foreigners can be either exacerbated or attenuated by institutional factors. In this context, different authors have hypothesised that collective bargaining could diminish wage discrimination against minority groups (Freeman 1980;Plasman et al 2007). In many countries, including Belgium, trade unions have presented themselves as advocates of "fair pay" for vulnerable groups (Dell'Aringa and Lucifora 1994; ETUC 2014). One way to assess the role of collective bargaining on wage discrimination is to use firm-level data for examining whether productivity-adjusted wage effects related to foreigners are smaller in companies with firm-level collective bargaining compared to those without firmlevel agreements. In our dataset from Belgium, this hypothesis can be tested by splitting the sample into a) firms that are only covered by national-and sectoral-level bargaining and b) firms that have an additional round of bargaining at the firm level.
According to the standard hypothesis on multi-level bargaining, we expect that wage discrimination is more likely to occur in firms without firm-level bargaining (Dell'Aringa et al 2004;Plasman et al. 2007).
A second hypothesis associated with institutional factors relates to the role of firm size. According to Lallemand and Rycx (2006), the wage bargaining process could be more likely to allow for wage discrimination if firms are relatively small. The main argument for this prediction is that larger firms tend to have more efficient and transparent human resource management, including clearly defined pay scales and job evaluation criteria. This being said, the effect of firm size could also magnify discrimination due to a general tendency that larger firms have been shown to be more unequal in terms of pay (Ferrer and Lluis 2008). Moreover, larger firms generally have a larger range of occupational and job categories that could make it easier to associate a specific group with a specific category and pay scale. For example, the clustering of foreign workers in specially created low-pay job categories in large companies has been documented for the case of Turkish immigrants in German car factories during the 1970s (Kampelmann 2011). Smaller firms typically have less detailed job nomenclatures so that minority groups are less likely to be clustered in discriminated categories. In order to examine which of these mechanisms predominates, we have estimated the effect of firm size by splitting the sample into firms below and above the median firm size (which equals 57 workers in our dataset).
As for the preceding issues of intrinsic productivity differences and segregation, we have tested the hypotheses regarding institutional factors with firm-level data from Belgium that controls for productivity and a wide range of observable and nonobservable characteristics.

Wage-setting equations at the firm level
Over several decades the contributions by Oaxaca (1973) andBlinder (1973) have provided the most commonly used tools for studying potential wage discrimination against immigrants. As a tool for disentangling productivity and wage discrimination, the standard version of the Oaxaca-Blinder decomposition has attracted increasingly sharp criticism (Hellerstein and Neumark 2006). First, by definition the residual gap confounds any unobserved intrinsic productivity differences or unobserved sorting with discrimination. Second, the method controls for differences in occupational or 11 sectoral composition between natives and immigrants rather than explaining the process of sorting into groups with different productivity; it is therefore prone to a "potential selectivity bias" (Aeberhardt and Pouget 2010: 119). Third, the individuallevel equations of the Oaxaca-Blinder framework ignore productivity spillover effects that occur at the level of the firm. The conclusion that Bartolucci (2014: 3) draws from this is harsh: "As discrimination has normally been detected through the unexplained gap in wage equations and this approach is not the best option for disentangling differences in productivity and discrimination, there are few papers that address labor market discrimination against immigrants." The increasing availability of firm-level matched employer-employee data facilitated the emergence of an alternative approach to measuring discrimination. The new method has been developed by Hellerstein et al. (1999) and refined by Vandenberghe (2011a,b) and van Ours and Stoeldraijer (2011)  The Hellerstein-Neumark method captures compositional and sorting effects that are ignored by the Oaxaca-Blinder framework; crucially, the productivity differences associated with observable characteristics are directly measured instead of being assumed. However, these advantages often deliver potential rather than actual mileage: while the firm-level wage setting equations in the Hellerstein-Neumark framework are generally robust to different specifications and provide precise estimates, the identification of the production function is often far more problematic due to high standard errors and noise in the productivity measures (Göbel andZwick 2012, Vandenberghe 2013). Bartolucci (2014: 9) argues that it is difficult to obtain precise estimates of the relative productivity parameter. Indeed, the search for the appropriate form of the production function is a long-standing theme in the micro-econometric literature (Olley and Pakes 1996;Petrin et al 2004;Ackerberg et al. 2006). While empirical studies focusing only on the firm-level productivity function are more flexible in the choice of both the functional form and the statistical estimator, the Hellerstein-Neumark method imposes a symmetry between both wage-setting and productivity equations in order to ensure the comparability of the respective parameters, which is why most studies use the simple CES or Cobb-Douglas form and FE or GMM-IV estimators for both equations. The underlying problem is that the compelling theoretical reasons to use Olley-Pakes or Levinson-Petrin estimators for the production functions often lack a theoretical rationale in the case of wage equations.
The fact that some firm-level studies on immigration estimate only productivity functions (Nicodemo 2013, Paserman 2013) and others only wage equations (Böheim et al. 2012) is a way to circumvent this issue but comes at the price of renouncing from measuring wage discrimination.
In this paper, we build on a new solution developed by Bartolucci (2014) that a) avoids the specification of the functional form of the productivity equation but nevertheless directly uses firm-level productivity data to measure discrimination against immigrants; b) neither assumes perfect competition in the labor market nor a 13 linear relationship between wages and productivity (it allows for non-unitary wageproductivity elasticities); and c) produces a measure of wage discrimination against immigrants that is robust to labor market segregation. i The wage-setting equation proposed by Bartolucci is similar to the wage equation in the Hellerstein-Neumark framework but directly estimates a parameter for the logarithm of average firm-level productivity. The integration of measured productivity yields the following wage equation: is the logarithm of the average hourly wage in firm j in year t; the variable ( ) t j p , log the logarithm of average hourly productivity; I jt is the proportion of immigrants and γ the parameter that captures wage discrimination; X jt is a vector containing a set of observable characteristics of firm j and its labour force in year t. In addition to Equation 1, we estimate a second equation that distinguishes between the proportions of male immigrants, female immigrants and female natives (respectively denoted as IM jt , IW jt and NW jt -male natives are the reference category):

Estimation methods
Equations 1 and 2 can be estimated using different methods. Basic pooled OLS estimators of productivity models have been criticized for their potential 14 "heterogeneity bias" (Vandenberghe 2013) due to the fact that firm productivity and mean wages depend to a large extent on firm-specific, time-invariant characteristics that are not measured in micro-level surveys. As a consequence, these estimators might be biased since unobserved firm characteristics may simultaneously affect the firm's added value (or wage) and the composition of its workforce.
Empirical in which firm j operates. ii The rationale for this instrument is that sector shares can be shown to be correlated with the proportion of immigrants in firm j while being unrelated to the productivity of firm j and the error term (Garnero 2014 Two filters have been applied to the original data set. Firstly, we deleted firms that are publicly controlled and/or operating in predominantly public sectors from our sample. The rationale of this filter derives from standard productivity theory and the requirement that prices have to be economically meaningful. All regressions are therefore applied to privately controlled firms only. iv Secondly, in order to ascertain that firm averages are based on a sufficient number of observations we filtered out firms that provided information on less than 10 employees. v Our final sample consists of an unbalanced panel of 9,430 firms and 555,963 individuals, yielding 23,712 firm-year-observations during the 12 year period (1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010). It is representative of all medium-sized and large firms employing at least 10 employees within sections C to K of the NACE Rev. 1 nomenclature, with the exception of large parts of the financial sector (NACE J) and almost the entire electricity, gas, and water supply industry (NACE E).

Definition of main variables
Our earnings measure corresponds to total gross wages, including premia for overtime, weekend or night work, performance bonuses, commissions, and other premia. Work hours represent total effective remunerated hours in the reference period (including paid overtime hours). The firm's added value per hour is measured at factor costs and based on the total number of hours effectively worked by the firm's employees. All variables in the SES-SBS are provided by the firm's management and therefore more precise compared to self-reported employee or household surveys.
The OECD statistics on immigration we cited in the introduction define immigrants as individuals who reside in a different country than the one in which they were born. For at least three reasons this is an imperfect indicator for the presence of immigrants on the labor market. First, some of the "otherness" of foreign-born workers is erased through the process of assimilation: an individual who was born abroad but who spent her entire adult life in the host country is often so assimilated that she ceases to be an "immigrant" in the eyes of her employer, co-workers and even herself.
Second, the children of foreign-born immigrants are by this definition not counted as "immigrants" even though they are often perceived as such in their host society. Third, while all immigrants differ to some extent from natives -even if only by the country of birth in their passport -some immigrants differ more from natives than others: a German in Austria or a Frenchman in Belgium arguably stands less out than a Turkish or a Moroccan.
In the literature on wage discrimination against immigrants, most studies operationalize the distinction between immigrants and natives by using information on the country of birth and/or the nationality of the individual. For instance, Böheim et al.
(2012: 15) distinguish between Austrian-born workers and those born in any other country. The authors use country of birth rather than nationality on the grounds that "ethnic background may be more relevant for productivity spillovers than citizenship".
As argued above, the simple native-immigrant dichotomy is problematic because it does not account for the unequal otherness of immigrants: for instance, it does not distinguish between the different socio-economic status of German and Turkish immigrants in Austria. Another problem with this definition is that "being an immigrant" can be associated with both the country of birth and the nationality of an individual.
For the case of Belgium, existing evidence suggests that we can address the problem of heterogeneity among immigrants by distinguishing between individuals from the European Union and those from outside of the EU. Martens et al. (2005) show that workers born in Morocco and by France (1.7%), Italy (1.5%), Germany (0.8%) and the Netherlands (0.7%). The second group -"non-EU workers" -consists of individuals who were either born outside of the EU or with a non-EU nationality, which is the case for 8.2% of observations. The most frequent country of birth in this group is Morocco (21.3%), Belgium (20.9% of non-EU workers were born in Belgium but with a non-EU nationality), Turkey (12.6%), Congo (7.7%) and Serbia (4.1%).
Male and female non-EU workers represent respectively 6.4% and 1.8% of the sample (35,690 and 9,999 observations). This equals a gender ratio of 22% among non-EU workers and 27% among EU workers. It should be noted that the relatively small share of women in the sample is not a bias but merely reflects the fact that women are underrepresented in the Belgian private-sector economy on which we focus in this paper. However, these averages mask the distribution of wages within each group. The density plots in Figure 1 show that the distribution of non-EU men and women (black curves) is more compressed compared to EU workers (grey curves). Moreover, the density curves of both EU and non-EU women (solid lines) peak at lower hourly wages compared to the curves of both male groups (dashed lines), but the curve for EU women (in grey) lies above the curve for non-EU men (in black) for wages above 16 euros.
[Insert Figure 1 about here] Table 1 underlines why it is important to take differences in human capital and sorting into jobs, firms, sectors and regions into account. Indeed, the four groups under analysis have distinct statistical profiles. Women in our sample are on average better educated than men, although the difference between non-EU women and EU men is only small. Non-EU men are by far the group with the lowest human capital from schooling. Another indicator for human capital is labour market experience, which in 21 our data can be (imperfectly) proxied through the employee's tenure with her current employer. More than half of EU men and women have more than five years of experience with their current employers, whereas this holds only for 38% of non-EU men and less than 30% of non-EU women. Foreigners and natives also differ with respect to the type of contracts on which they are employed: the proportion of fixedterm contracts is very small among men from the EU (2.5%) and 5.7 percentage points lower compared to non-EU women.
The group of immigrants is on average younger compared to natives, with EU men being the oldest and non-EU women the youngest group in the sample. The Whereas foreign men work on average for relatively small firms (measured in terms of the size of the workforce), foreign women work in larger firms. Firm-level collective bargaining is more prevalent in firms with a more masculine workforce: only 14% of non-EU women are employed in firms that renegotiate wages through firm-level bargaining, a proportion that is 6.8 percentage points lower compared to EU men. 22 Finally, Table 1 shows the relative concentration of immigrants in the Brussels region and their marked underrepresentation in Flanders.
[Insert Table 1 about here] A simple way to explore these descriptives is to apply the conventional method for disentangling the productivity effects and wage discrimination by regressing human capital and compositional characteristics on the logarithm of individual hourly wages.

In our sample, an OLS Mincer equation vi yields a coefficient of determination of 54%
and a negative and significant coefficient for the non-EU dummy equal to -0.04, thus suggesting that a non-EU worker whose observed characteristics are identical to a EU worker suffers from a wage penalty of 4%. This is in line with results from an Oaxaca-Blinder decomposition which indicates that around 77% of the gross wage gap in our sample can be attributed to observable differences. The highest contribution to the explained part in the Oaxaca-Blinder decomposition comes from individual and job characteristics (60.1% of the explained wage gap), while firm characteristics also matter (31%). Introducing interaction variables between immigrant status and gender improves the fit of the OLS Mincer equation: the coefficient of determination rises by 3 percentage points and all three interaction variable are highly significant. Compared to the reference group of EU men, the ceteris paribus wage penalty of non-EU men remains at around 4%. Women appear to suffer from relatively higher discrimination because the respective coefficients for non-EU and EU women are -0.15 and -0.14 (all three interaction coefficients are significantly different from each other). As explained above, however, these results suffer from severe methodological issues and need to be complemented with more sophisticated identification techniques.

Firm-level statistics
Our identification strategy uses information on individual worker and job characteristics with matched data on their employers, including average hourly productivity in the firm.
While the composition of firms in terms of observable individual and job characteristics does not differ substantially from the individual-level descriptive statistics (see last column in Table 1), firm-level data allow to assess the distribution of EU and non-EU workers across firms (Aydemir and Skuterud 2008). According to Mitaritonna et al. (2014), insufficient attention has been paid to the large share of firms that do not hire any immigrants. The highly unequal distribution that Mitaritonna et al. For our identification strategy based on Equations 1 and 2, the concentration of immigrants is potentially problematic if firms with no immigrants differ from the other firms in terms of some unobserved characteristic that is correlated with differences in labor productivity. In order to evaluate the relevance of this issue in our sample, we have estimated a logistic regression in which a dummy variable that equals 1 if there are any immigrants in the firm is regressed on firm composition and firm characteristics. The corresponding pseudo-coefficient of determination equals 8.5% and the log pseudolikelihood -15003.8. Importantly, neither the coefficient for the average hourly productivity nor the share of women in the firm is significantly correlated with the presence of immigrants in the firm. A significantly positive relationship is found for the regional dummies for Brussels and Wallonia (in line with the higher presence of immigrants in these regions compared to the reference region Flanders); the share of young workers; and the size of the firm. The sectoral and occupational composition of the firm is not always significant in the logistic regression. As a consequence, immigrants do not appear to be sorted according to differences in hourly productivity between firms, but rather according to region, age and size, i.e. variables consistent with sorting according to networks (Dustmann et al. 2011).
[Insert Figure 2 about here] Figure 2 shows the distribution of firms with respect to their respective shares of male and female immigrants (the plot is restricted to the firm-year observations employing any non-EU workers). We observe that both distributions are highly skewed and illustrate that the vast majority of firms have less than 20% of immigrants 25 on their payroll; only very few firms are composed of more than 40% and virtually none of more than 80% of immigrants.

Baseline regressions
Regression results for the Bartolucci firm-level wage-setting model are presented in Table 2. The first four columns show alternative specifications of a pooled OLS estimator in order to illustrate the impact of different forms of observed heterogeneity.
The wage gap between EU and non-EU employees is captured by the parameter γ. In the first model without control variables, this corresponds to the gross wage differential and is estimated to be -0.24, i.e. a 10 percentage point increase in the share of immigrants is on average associated with a 2.4% decrease (= 0.1*-0.24) of the average hourly wage in Belgian firms. This effect collapses once we include observed individual and job characteristics: the same increase in the immigrant share is now associated with an insignificant decrease in average wages, whereas a 10 percentage point rise in the share of female workers is related to a 1.9% drop in wages.

Segregation of workers across sectors and regions affects the immigrant and female
wage penalties only marginally (column 3). The full-blown specification of Equation 1 includes the average hourly productivity in the firm and other firm-level control variables (firm size, capital stock and level of wage bargaining) on the right-hand side (column 4). The productivity parameter β is positive and significant and the inclusion of observed firm characteristics increases the coefficient of determination by 5 percentage points. However, the coefficient capturing wage discrimination against 26 immigrants remains insignificant, while the female wage penalty is slightly reduced but remains high (the significant coefficient equals -0.17).
[Insert Table 2 about here] The specifications in columns 5 and 6 take into account unobserved time-invariant firm heterogeneity, i.e. some of the differences between firms that could be related to hourly wages (and hourly productivity) and therefore bias the OLS results. The fixedeffect model (column 5) shows a small and significant immigrant wage penalty (a 10 percentage point increase in the share of immigrants is associated with a 0.2% decrease in the average wage), and the wage coefficient of women is reduced by almost 50% to -0.09. Unobserved time-invariant firm heterogeneity appears to be highly correlated with hourly labor productivity since the associated coefficient remains significant but decreases to 0.01. viii The GMM-IV estimator (column 6) not only takes firm-level heterogeneity into account through its specification in first differences, but also addresses the potential endogeneity of the firm's labor force by using the lagged levels and average industry shares as instruments. Applying GMM-IV yields an insignificant wage penalty for immigrants and a somewhat higher (and significant) wage penalty for women (the corresponding coefficient equals -0.13). A series of statistical tests suggests that our instruments are valid and that the model is correctly identified: the model passes the tests for under-, weak-and overidentification. However, the endogeneity test indicates that the potentially endogenous worker shares can actually be treated as exogenous (the p-value equals 54%), which means that the fixed-effect model should be preferred.

27
As argued in Section 3, the coefficients in the Bartolucci  zero. This corroborates the finding of the Bartolucci wage equation that some of the lower pay received by foreigners and (especially) women is due to discrimination and not to measurable differences in labour productivity. Table 3 reproduces Table 2 but the estimated models now allow for the respective effects of non-EU men, non-EU women and EU women to differ. Relative to the reference group of EU men, the significant gross wage differential in the parsimonious OLS estimator (column 1) is the highest for non-EU men (a 10 percentage point increase of this group is associated with a 2.9% drop of the average firm wage), followed by non-EU women (-1.2%) and EU women (-0.8%). This order arguably reflects both the sorting of non-EU men into low-productivity firms and the fact that this group has the lowest level of human capital (see Table 1). The order is indeed inverted once we control for observed individual and job characteristics (column 2).

Interactions between foreigner and gender variables
Segregation into sectors and regions accounts for around 40% of the gross wage 28 penalty for non-EU women (column 3), but is less consequential for non-EU men and EU women.
[Insert Table 3 about here] Adding average hourly productivity and firm-level characteristics to the model slightly reduces the relative wage penalty for EU women (column 4). The GMM-IV estimator (column 6) again passes our identification tests but also rejects the endogeneity of the worker shares so that the fixed-effect estimator (column 5) is our preferred model. It suggests that the ceteris paribus wage penalty is the highest for EU women (a 10 percentage point increase in EU-women is associated with a 1% lower hourly wage), followed by the penalty for non-EU women (-0.6%), but the difference between the two coefficients is not statistically significant. By contrast, the wage coefficient for non-EU men equals -0.03 and is significantly lower compared to the penalty against EU women.

Institutional factors
We now turn to the results pertaining to the discussion of institutional factors in Section 2.2.3. In order to assess the effect of collective bargaining regimes, Table 4 shows the OLS, FE and GMM-IV estimators including all control variables for two sub-samples: 19.803 firm-year observations in which no firm-level collective bargaining has taken place and 3.909 observations with firm-level bargaining. Contrary to the estimation results presented above, the GMM-IV estimator is the preferred specification for the subsample without firm-level bargaining for which we cannot 29 reject the hypothesis of endogenous labour shares (the endogeneity test returns a pvalue of 0.06 against the null hypothesis of exogenous regressors). For the other subsample the FE estimators remains the preferred specification.
[Insert Table 4 about here] The results provide some evidence for wage discrimination against foreigners in firms without establishment-level collective bargaining: a 10 percentage-point increase is correlated with 2% lower average wages in the preferred GMM-IV regression. By contrast, the corresponding coefficient in the subsample with establishment-level collective bargaining is not significantly different from zero. The difference between the two subsamples with respect to the foreigner coefficient is statistically significant.
As for the coefficient related to the share of female employees, both subsamples display negative coefficients of roughly the same magnitude as in the baseline regression. Comparing the preferred estimators, the difference between the two bargaining regimes is not significant. Additional regressions including interaction variables between gender and foreigner status (not shown here but available upon request) also confirm previous results of wage penalties against both foreigners and women as well as the absence of significant double discrimination against foreign women.
[Insert Table 5 about here] The second factor discussed in Section 2.2.3 is firm size. Table 5 shows results for two subsamples distinguishing the 11.927 firm-year observations below the median 30 firm size ("small firms") from the 11.785 observations above the median ("big firms").
In none of the two subsamples we find evidence for endogenous regressors so that the FE estimator is our preferred specification. Whereas the coefficient for the share of foreigners is not statistically different from zero in small firms, the estimation suggests that a 10% increase of foreigners is associated with 0.4% drop of the average wage in big firms. The difference between the two subsamples with respect to the foreigner coefficient is significant. Regarding the coefficients for gender, Table 5 again produces similar results compared to the baseline specification and additional regressions with interaction variables (not shown) provide no evidence for significant double discrimination of female foreigners.

Discussion and conclusion
This paper is one of the first to use firm-level matched employer-employee data and direct information on wages and labor productivity to measure discrimination against immigrants. We build on a recent identification strategy proposed by Bartolucci (2014) and address econometric issues such as firm fixed effects and the potential endogeneity of worker shares through a diff GMM-IV estimator. Our preferred estimator of a Bartolucci-type wage-setting equation (the fixed-effect model shown in column 5 of Table 2) suggests that an increase in the share of non-EU workers in a firm is correlated with a modest but significant decrease of the average wage paid in Belgian firms.
The wage coefficient associated with the share of women is also significantly negative and three times higher compared to the wage discrimination against non-EU workers. However, wage discrimination against immigrants is likely to interact with gender discrimination -an important contribution of the paper is therefore to estimate 31 these interactions. Our preferred model including interactions between gender and immigrant status (column 5 in Table 3) corroborates modest wage discrimination against men of non-EU origin, but also shows that the wage discrimination against both native and foreign women is significantly higher. Results suggest that origin is not associated with a significantly different wage penalty among women: we therefore find evidence for significant wage discrimination against immigrants and women, but female immigrants do not appear to be exposed to "double-discrimination" by employers in Belgium. This result stands up to a series of tests, including measurement issues such as unobserved time-invariant firm heterogeneity, the potential endogeneity of the firm composition, but also to alternative definitions of the immigrant status and the reduction of our sample to firm-year observations with at least one immigrant per firm.
We also test additional hypotheses regarding institutional factors that could influence the extent of wage discrimination against foreigners and/or women. The first hypothesis relates to the role of the collective bargaining regime. We find evidence that firm-level bargaining seems to eliminate the incidence of wage discrimination against foreigners (see Table 4). This lends some support to the often expressed argument that trade unions strive to protect low-wage groups from unfair pay (cf. Dell'Aringa et al 2004), but also that this protection appears to be only effective at lower levels of bargaining. In Belgium, virtually all firms are covered by national and sectoral collective bargaining agreements, yet only those that engage in additional renegotiation of wages within individual companies -which is the case for around 16.5% of the firms in our sample -seem to curb wage discrimination against foreigners. The second hypothesis concerns the effect of firm size. Our results (Table 5) suggest that wage discrimination against foreigners is concentrated in relatively large firms. This speaks against the capacity of more sophisticated human resource management practices, according to Lallemand and Rycx (2006) a characteristic of large firms, to attenuate wage discrimination against foreigners. By contrast, our results are in line with the generally observed high wage inequality in big firms. It is also coherent with the explanation that larger firms harbour special low-pay categories in which foreigners are clustered -a practice that was documented in the German manufacturing sector during the first wave of massive post-war immigration (Swenson 1989;Kampelmann 2011) and that could have survived in large firms until today. On any account, the regressions capturing specific institutional contexts corroborate significant and sizable discrimination against women and the absence of significant double discrimination against foreign women.
Due to the novelty of the approach we can only compare our findings to results for Germany by Bartolucci (2014), who also finds negative productivity-adjusted wage coefficients for male and female immigrants as well as native women. The size of wage discrimination found by Bartolluci is also relatively modest but somewhat higher compared to our results: a 10 percentage point increase in the share of male immigrants is associated with a 1.3% decrease in the average firm wage in Germany, whereas we find a 0.2% decrease for Belgium. Unlike our estimations, however, Bartolucci (2014) finds evidence for double-discrimination against female immigrants in Germany (a 10 percentage point increase in female immigrants is associated with a 2.7% lower average firm wage).
Our results suggest that not all of the observed wage differences between immigrants and natives are due to productivity differences (for instance due to lower language skills) -despite Belgian's strong anti-discrimination legislation we find evidence for wage discrimination against immigrants. The wage gap between women 33 and men can also not be reduced to productivity differences -and compared to the native-immigrant gap there is arguably a lower theoretical case for productivity differences between men and women to begin with. Interestingly, foreign women do not cumulate the two wage penalties associated to gender and origin and receive roughly the same wage penalty as native women. A possible explanation for this phenomenon might by that origin is of lesser importance among women than among men; indeed, the educational profile of women with foreign origin resembles closely the one of native women. Moreover, certain institutional factors such as firm-level collective bargaining and smaller firm sizes appear to attenuate wage discrimination against foreigners, but not against women. Overall, our results suggest that while wage discrimination against immigrants remains an issue on the Belgian labor market, the magnitude of this discrimination is relatively small compared to the discrimination against (native and foreign) women.

References
Ackerberg, D., Caves, K. and Frazer, G. (2006).   Individual and job characteristics include share of workers younger than 40 years, share of 8 occupational groups (reference: service occupations); 3 educational levels (reference: ISCED 1-2); share of fixed-term contracts; share of workers with more than 5 years of tenure. c Sector and regional controls include 9 sectors (reference: manufacturing) and 3 regions (reference: Flanders  Individual and job characteristics include share of workers younger than 40 years, share of 8 occupational groups (reference: service occupations); 3 educational levels (reference: ISCED 1-2); share of fixed-term contracts; share of workers with more than 5 years of tenure. c Sector and regional controls include 9 sectors (reference: manufacturing) and 3 regions (reference: Flanders). d Firm controls include the logarithm of firm size, the logarithm of capital and a dummy for firm-level collective bargaining. All regressions include year dummies. e Underidentifcation test reports p-value of Kleibergen-Paap rk LM statistic; f Weak identification test reports Kleibergen-Paap rk Wald F statistic; g Overidentification test reports p-value of Hansen J statistic. h Endogeneity test shows probability that endogenous regressors can actually be treated as exogenous. i ***,**,* significant at 1, 5 and 10% levels, respectively j HAC standard errors in parentheses.   Individual and job characteristics include share of workers younger than 40 years, share of 8 occupational groups (reference: service occupations); 3 educational levels (reference: ISCED 1-2); share of fixed-term contracts; share of workers with more than 5 years of tenure. c Sector and regional controls include 9 sectors (reference: manufacturing) and 3 regions (reference: Flanders). d Firm controls include the logarithm of firm size and the logarithm of capital. All regressions include year dummies. e Underidentifcation test reports p-value of Kleibergen-Paap rk LM statistic; f Weak identification test reports Kleibergen-Paap rk Wald F statistic; g Overidentification test reports p-value of Hansen J statistic. h Endogeneity test shows probability that endogenous regressors can actually be treated as exogenous. i ***,**,* significant at 1, 5 and 10% levels, respectively j HAC standard errors in parentheses.   Individual and job characteristics include share of workers younger than 40 years, share of 8 occupational groups (reference: service occupations); 3 educational levels (reference: ISCED 1-2); share of fixed-term contracts; share of workers with more than 5 years of tenure. c Sector and regional controls include 9 sectors (reference: manufacturing) and 3 regions (reference: Flanders). d Firm controls include the logarithm of firm size, the logarithm of capital and a dummy for firm-level collective bargaining. All regressions include year dummies. e Underidentifcation test reports p-value of Kleibergen-Paap rk LM statistic; f Weak identification test reports Kleibergen-Paap rk Wald F statistic; g Overidentification test reports p-value of Hansen J statistic. h Endogeneity test shows probability that endogenous regressors can actually be treated as exogenous. i ***,**,* significant at 1, 5 and 10% levels, respectively j HAC standard errors in parentheses.