546300 research-article2014
ILRXXX10.1177/0019793914546300Industrial & Labor Relations ReviewNative–Immigrant Wage Gap In Germany
Understanding the Native–Immigrant Wage Gap Using Matched Employer-Employee Data: Evidence from Germany Cristian Bartolucci*
In this article, the author proposes a new method for measuring wage discrimination that builds on the methodology first developed by Hellerstein and Neumark (1999). The author’s method has three main advantages: It is robust to labor market segregation, it does not impose linearity on the wage-setting equation, and it is not only a test for discrimination but also produces a measure of discrimination. Using matched employer-employee data from Germany, the author finds that immigrants are being discriminated against. They receive wages that are 13% lower than native workers in the same firm.
I
n Altonji and Blank (1999), labor market discrimination is defined as a situation in which individuals who provide labor market services and who are equally productive in a physical or material sense are treated unequally in a way that is related to an observable characteristic such as race, ethnicity, or gender. The most widely used approach to test for labor market discrimination takes the unexplained gap in Mincer-type wage regressions as evidence of discrimination. This method, also known as the residual method, estimates the Mincer equations for two groups and then decomposes the difference in mean-wages into explained and unexplained components. The fraction of the gap that cannot be explained by differences in observable *Cristian Bartolucci is affiliated with Collegio Carlo Alberto. I thank Manuel Arellano, Stéphane Bonhomme, Raquel Carrasco, Jose María Labeaga, Pedro Mira, Enrique Moral-Benito, Diego Puga, JeanMarc Robin, the editor, two anonymous referees, and members of the audiences at the Spanish Economic Association (SEA) Meetings (Madrid 2010), Collegio Carlo Alberto, the Institut zur Zukunft der Arbeit–Centre for Economic Policy Research (IZA-CEPR), the European Summer Symposium in Labour Economics (ESSLE) (Munich 2009), the European Economic Association (EEA) Meetings (Barcelona 2009), Workshop on Wages and Firms: New Research Using Linked Employer-Employee Datasets (Budapest 2009), and Centro de Estudios Monetarios y Financieros (CEMFI) for very helpful comments and suggestions. Special thanks is due to Emily Moschini for excellent research assistance and to Nils Drews, Daniela Hochfellner, and Dana Muller from the Institute for Employment Research for invaluable support with the data. The data used in this paper can be made available to other researchers from the Institute for Employment Research (IAB), Federal Employment Agency (BA), Postfach, Nuremberg 90327, Germany, subject to federal data protection regulations and the approval of the German Federal Employment Office. The computer code for replication of the results presented in this paper can be obtained from the author at
[email protected]. Keywords: labor market discrimination, immigration, matched employer-employee data ILR Review, 67(4), October 2014, pp. 1166-1202 DOI: 10.1177/0019793914546300. © Cornell University 2014 Journal website: ilr.sagepub.com Reprints and permissions: sagepub.com/journalsPermissions.nav
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characteristics is considered to be discrimination. In spirit of Altonji and Blank’s definition, the residual approach may be understood as a comparison of wages and productivity where the latter is approximated using a function of observable characteristics. However, if unobservable characteristics are different across groups and are correlated with productivity,1 this discrimination measure may be biased. The availability of matched employer-employee data allows a response to this potential weakness of the residual approach. In the absence of good enough worker-level data to control for differences in productivity, one option is to directly estimate the productivity gap using output measures at the firm level. If wages are equal to productivity, any difference in wages that is not driven by a difference in productivity may be considered discrimination. Hellerstein, Neumark, and Troske, in a number of influential papers, proposed a method that builds on that intuition. This method uses firmlevel data to estimate the relative marginal products of various types of workers, which are then compared with their relative wages. The productivity of each type of worker is estimated in terms of the proportion of workers of each group in the firm. Given that its implementation and the interpretation of its results are extremely simple, this approach has been notably popular in the last years. A large number of papers have applied this method to data from different countries: Hellerstein and Neumark (1999) using Israeli data; Hellerstein, Neumark, and Troske (1999) using U.S. data; Verner (1999) using data from Ghana; Crepon, Deniau, and Pérez-Duarte (2003) using French data; Lopez-Acevedo, Tinajero, and Rubio (2005) using data from Mexico; Dong and Zhang (2009); Rickne (2012) using Chinese data; Van Biesebroeck (2009) using data from three sub-Saharan countries; and Campos-Vazquez (2008) using German data. Here I propose a method to test for labor market discrimination that builds on the Hellerstein and Neumark (1999) idea of directly using productivity data to measure discrimination. I take advantage of matched employer-employee panel data to estimate a reduced-form wage-setting equation at the firm level that tests, while controlling for productivity and firms’ fixed characteristics, whether wages differ between natives and immigrants. This approach exploits the within-firm variation of the native–immigrant composition across time to identify different wage policies toward those groups. This approach adds to the existing test of wage discrimination in three main ways. First, it provides quantitative measures of wage discrimination, whereas comparing relative wages and relative productivity is informative only about the existence of wage discrimination. Second, it does not assume perfect competition in the labor market. Comparing relative wages and relative productivity is informative with regard to discrimination only when the function that links wages and productivity is linear. The strategy I propose is 1In the specific case of immigrants, we typically think of environmental variables, tastes, quality of education, and language skills.
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more flexible, allowing the wage–productivity elasticity to be different from 1. Finally, and more important, it produces measures of discrimination that are robust to labor market segregation. Controlling for unobserved differences in productivity is especially relevant in the case of wage discrimination against immigrants. A significant portion of the empirical literature on discrimination focuses on gender and racial discrimination. Wage differentials between natives and immigrants have generally been understood as an assimilation process that involves differences in productivity based on language skills (e.g., Chiswick and Miller 1995; Borjas 1999; Carnevale, Fry, and Lowell 2001; Dustmann and van Soest 2002), differences in quality of education (Sweetman 2004), or differential returns to foreign schooling and labor market experience (e.g., Friedberg 2000; Bratsberg and Ragan 2002). Because 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 from discrimination, few studies address labor market discrimination against immigrants. Some exceptions, also using matched employer-employee data, are Aydemir and Skuterud (2008) and Aeberhardt and Pouget (2010), which explore the sources of immigrants’ wage differentials within and across establishments. Also, Campos-Vazquez (2008) uses the same linked employeremployee data (LIAB) from the Institute for Employment Research (IAB) as I do and replicates the Hellerstein and Neumark (1999) (HellensteinNeumark) analysis to test for discrimination against German immigrants. As a spin-off of the main results, the method proposed here also allows us to estimate firm-specific discrimination parameters following the strategy presented by Arellano and Bonhomme (2012). Although these estimates are noisy (I have a small-T panel), the unbiased correlation with other firm variables, such as profit or tenure of immigrants, may be estimated and used to obtain indirect evidence of different discrimination theories by testing for some of their implications. I use the LIAB, a 1996 to 2005 panel of matched employer-employee data provided by the IAB.2 This data set is especially useful for the current study for two reasons: 1)it contains essential data about the workers’ nationalities, and 2) it tracks firms as opposed to individuals, which is necessary for obtaining estimates in the wage-setting equation that are robust to a correlated firm fixed effect. Germany is a very interesting country for the study of immigration. After the Second World War, the strong economic development in West Germany and the resulting demand for labor led to a large inflow of immigrants, mainly from eastern and southern European countries and Turkey. The percentage of immigrants in Germany increased from less than 1% in 1955 to more than 8% in 1995 but has been a stable fraction of the population over 2This data set is subject to strict confidentiality restrictions. It is available only after the IAB has approved the research project. The Research Data Center (FDZ) can provide on-site use or remote access to external researchers.
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the last 15 years. In the sample used in this article, the fraction of foreignborn workers is slightly higher and ranges from 9.4 to 10.9% between 1996 and 2004. The results show that immigrants suffer from wage discrimination. Depending on the measure of productivity and the specification used, the immigrant wage premium ranges between −7% and −17% and is always significantly negative. Although the reduced-form wage-setting equation is very simple, it fits the wage-bill data properly and the main results are remarkably robust to many specification tests. I find neither significant evidence of immigrants moving to less discriminatory firms nor significant evidence in favor of a statistical discrimination model; nevertheless, I do find evidence against a taste-based discrimination model. These findings are different from the conclusions drawn by both the residual approach and the Hellerstein-Neumark approach. When estimating a Mincer-type equation, I found that immigrants receive higher wages than natives with similar observable characteristics. Moreover, as did Campos-Vazquez (2008), using the Hellerstein-Neumark approach with the LIAB data I did not find significant evidence of discrimination against immigrants. These differences in results suggest that segregation and the linearity assumption in the Hellerstein-Neumark approach are relevant sources of bias in the measurement of wage discrimination against immigrants in Germany. The elasticity of wages to productivity is found to be significantly less than 1. Furthermore, I find significant evidence of the positive segregation of immigrants into good firms. In this article, I first present the test and formally compare it to the Hellerstein-Neumark approach. I then describe the data set in more detail and present the results and robustness check. Finally, I show how this method can be used to distinguish among discrimination theories. A Test of Wage Discrimination According to the Altonji and Blank (1999) definition of labor market discrimination, individual productivity should be a sufficient statistic to explain wages. Therefore, discrimination could be detected by estimating the following generic wage-setting equation: (1)
Wijt = F ( Pijt , I i )
where Wijt is the wage of individual i in firm j at time t, Pijt is the individual productivity, and I i is an indicator function that takes the value 1 if the individual is foreign-born. We could check for evidence that firms discriminate against immigrants by testing F ( Pijt , I i = 1) ≠ F ( Pijt , I i = 0) . Without making structural assumptions about the labor market model generating the data, however, the functional form of F(.,.) is unknown. As a baseline, let us consider a log-linear approximation to F(.,.):
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(2)
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wijt = α j + β pijt + γ I i + ε ijt
where wijt is the log-wage of individual i in firm j at time t, pijt is the individual log-productivity, and I i is the immigrant indicator. In this context, I interpret ε ijt as an econometric mean-zero residual term due to the imposed log-linearity in the wage-setting equation. Firms can differ in terms of observed characteristics such as region, sector, and unionization of the workforce, but they can also differ in terms unobserved characteristics such as human resources practices, technology, and managerial quality. It is likely that some of these differences imply differences in a firm’s wage-setting equation. Therefore, in the simpler specification, I include a firm-idiosyncratic component in the wage equation, a j . 3 Here, discrimination is defined as the situation in which workers who provide labor market services and who are equally productive in a physical or material sense are treated unequally in a way that is related with their immigrant status. According to this definition, a direct test for discrimination is to test γ ≠ 0 (in Equation (2), wage discrimination is captured only by a difference between natives and immigrants in the constant term; later in the article, I also allow for a difference in β according to the immigrant status). The log-linearity assumption is a convenient specification for the following four reasons:4 1. It is the natural specification to connect wages and productivity, which, using firm-level data, have been found to be approximately log-normally distributed (see Figure 1). 2. It provides a direct connection to the residual approach, where the logwage equation is a linear combination of workers and firm characteristics, proxying the match productivity. 3. The interpretation of the parameters is straightforward in terms of constant elasticities. 4. The log-linear wage equation at the firm level has a reasonably good performance in fitting the data; allowing more flexibility in F(.,.) does not significantly improve the fit of the model. Directly estimating Equation (2) is not feasible because individual productivity is generally unobserved. In some jobs, individual productivity can be measured more easily, such as academic positions (Ferber and Green 1982) and jobs under piece-rate contracts (Petersen, Snartland, and Milgrom 2007). Although studies of these occupations have measures of individual productivity, they are likely to be weaker in terms of external validity.
3In the section Testing Implications of Discrimination Models, I also explore the case where γ is firmspecific. 4The assumption is relaxed in Appendix A.
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Figure 1. Log-Productivity and Log-Wages. n = 24,444 observations. The top 1% and bottom 1% of the distribution of output per worker have been excluded.
The Hellerstein-Neumark Approach The Hellerstein-Neumark approach has been found to be a very convincing method for detecting wage discrimination. Hellerstein and Neumark (1999) and Hellerstein et al. (1999) used matched employer-employee data from Israel and the United States to estimate the relative marginal products of various types of workers. Then they compared the productivity differentials, ρ=
E ( Pijt | I i = 1) E ( Pijt | I i = 0)
,
with the wage differentials, λ=
E (Wijt | I i = 1) E (Wijt | I i = 0)
.
Most of the popularity of the Hellerstein-Neumark approach arose because it is very intuitive. Because observable worker characteristics are not a convincing enough proxy of worker productivity, we cannot trust the residual approach. Therefore, it is convenient to directly estimate productivity. Assuming that wages are a linear function of productivity, the test is straightforward.
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The wage differential λ is estimated by exploiting data on firms’ wage bills and differences in the composition of the workforce across firms. The method requires the estimation by nonlinear least squares (NLLS) of the following equation: ln( w jt ) = ϑ + ln(1 + (λ − 1)
LI jt L jt
),
where w jt is the mean-wage paid by firm j, L jt is the total number of workers I in the plant j, L jt is the number of foreign-born workers in firm j, and ϑ is a constant term. The productivity differential ρ is estimated using production functions, assuming Cobb-Douglas or translogarithmic functional forms with qualityadjusted labor input. Adapting the method to the case of discrimination against immigrants, we have to estimate marginal products of immigrants and natives by NLLS in the equation: Ln(Y jt ) = aLn( K jt ) + bLn( M jt ) + cLn( LQ jt ) + g ( K jt , M jt , LQ jt ) Q
where K jt is the capital; M jt is the material; g ( K jt , M jt , L jt ) is the secondQ order term in the production function; and L jt is quality of labor aggregate, defined as: LI LQ jt = L jt 1 + ( ρ − 1) jt L jt I
where L jt is the total number of workers in the plant, and L jt is the number of immigrants in the plant.5 The Hellerstein-Neumark strategy can be interpreted within the framework presented in this article. When estimating Equation (2) is not feasible because individual productivity is not observed, we can aggregate Equation (2) at the group level and then recover γ. Taking averages of Equation (2) across groups (immigrants and natives), we have:
∑ ( w | I = 0) β ∑ ( p = ∑1( I = 0) ijt
(3)
i
i
ijt
i
i
i
| I i = 0) + ∑ (α j | I i = 0) + γ ∑1( I i = 0) + ∑ (ε ijt | I i = 0) i
∑1( I
i
i
= 0)
i
,
i
and
5The Hellerstein-Neumark model is slightly more complicated because it allows for several population groups. See Hellerstein and Neumark (1999) for details.
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Native–Immigrant Wage Gap In Germany
∑ (w | I = 1) β ∑ ( p = ∑1( I = 1) ijt
i
ijt
i
(4)
i
| I i = 1) + ∑ (α j | I i = 1) + ∑ (ε ijt | I i = 1) i
i
∑1( Ii = 1)
i
1173
i
i
Subtracting Equation (4) from Equation (3) and noting that ∑(εijt | Ii = 1) = 0 and ∑(εijt | Ii = 0) = 0,6 we have:
∑ (α | I = 1) ∑ (α | I = 0) λ − ρ = γ + (1 − β )(1 − ρ )+ − ∑1( I = 1) ∑1( I = 0) j
i
j
i
(5)
Linearity Bias
i
i
i
i
i
i Segregation Bias
where λ is the ratio between the mean-wage of immigrant workers and the mean-wage of native workers, and ρ is the immigrant–native relative productivity. Then λ − ρ is informative about wage discrimination when β = 1 and cov(α j , I i ) = 0 . Hellerstein and Neumark (1999) draw an inference about discrimination (i.e., γ) simply by comparing λ and ρ estimated at the firm level. Although they are very cautious in their interpretation of this difference, arguing that λ − ρ gives evidence of discrimination, if β ≠ 1 or, cov(α j , I i ) ≠ 0 an a priori direction of the bias does not exist and, hence, how informative this statistic is cannot be determined. To clarify this explanation, I decompose the bias into two components: linearity bias and segregation bias. Linearity Bias The linearity bias addresses the fact that, whenever a change in productivity is not fully transferred to wages, two groups with different productivity may have larger or smaller relative differences in wages that do not imply discrimination. As we will see later, β is found to be significantly different from 1. Depending on the specification and the measure of productivity used, its point estimate ranges between 0.25 and 0.45. To show numerically how important this bias can be, let us consider a very simple example in which there are two groups, A and B, and A is 20% more productive than B. If no discrimination is present against either group and if we assume that β = 0.4, 6This is easily shown, noting that: → E ( wijt | I i =1) − E ( wijt | I i = 0 ) ≈ λ −1
→ E ( pijt | I i =1) − E ( pijt | I i = 0 ) ≈ρ −1
∑ ( wijt | I i = 1) ∑ ( wijt | I i = 0) ∑ ( pijt | I i = 1) ∑ ( pijt | I i = 0) i − β i − i − i ∑1( I = 1) 1 ( I = 0 ) 1 ( I = 1 ) I = 1 ( 0 ) ∑i i ∑i i i i i ∑ i ∑i (α j | Ii = 1) ∑i (α j | Ii = 0) =γ+ − ∑1( Ii = 1) ∑1( Ii = 0) i
i
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the wages paid to the workers in group A will be only be 8% higher than the wages paid to the workers in group B. But the Hellerstein-Neumark approach would wrongly find that the workers in group A are being discriminated against because the productivity gap is larger than the wage gap. Wages are equal to productivity if perfect competition exists in the labor market. But labor market frictions are important in Germany and significantly larger than in countries such as the United Kingdom or the United States (Ridder and van den Berg 2003). In terms of employment protection, Germany is clearly above the average found in Organisation for Ecomonic Co-operation and Development (OECD) countries (OECD 2008).7 Unless we make structural assumptions about the labor market model generating the data, the function that links productivity and wages is unknown; therefore, allowing for a specification that is as flexible as possible is prudent. My baseline specification for the wage equation is log-linear in productivity; however, I also present robustness checks allowing the wage equation to be a polynomial of different orders in productivity. Segregation Bias The second part of the bias is relevant if labor market segregation is present. Segregation bias, the last term in Equation (5), is connected to Altonji and Blank’s (1999) remarks on Hellerstein and Neumark (1999). They argued that the variation in worker composition is likely to be correlated with heterogeneity in the production technology and may be endogenous to the model. In this context, the firm’s technology is captured by the firm’s fixed effect, a j . Many attempts have been made to obtain measures of discrimination robust to segregation. Hellerstein and Neumark (2007) proposed that segregation be taken into account by dealing with omitted plant-specific productivity parameters, as in Olley and Pakes (1996). Although this method proposes a potential solution to the estimation of some parameters of the production function, its implications in this context are not totally clear. For example, as Griliches and Mairesse (1998) pointed out, the Olley and Pakes method may not be the best alternative if the firm-specific productivity term consists of mostly fixed components.8 Also, the Olley and Pakes model implies a correlation of the firm’s labor input with the plant-specific productivity parameter but does not generate endogeneity in worker composition.9 7Source: OECD (2008). OECD measures of employment protection includes information on protection of permanent workers against individual dismissal, specific requirements for collective dismissal, and regulations on temporary forms of employment. 8This is because the firm’s capital has already adjusted to the firm-specific productivity term and, hence, the investment at time t would not depend on the firm’s capital. 9This is because the Hellerstein-Neumark approach includes worker heterogeneity in a Cobb-Douglas production function with quality-adjusted labor input. This production function imposes perfect substitution between workers’ groups; therefore, in the context of Olley and Pakes (1996), the rent-maximizing firm takes into account only the total labor input in efficiency units, and the composition of this input should be exogenous.
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Finally, it is not clear how the wage gap should be estimated once we have estimated the productivity gap using this strategy. An alternative strategy is to control for endogenous composition by following a more standard fixed effects panel data approach (Hellerstein and Neumark 1998). If we exploit within-firm variation, both the wage gap and the productivity gap are well defined, but achieving precise estimates of the relative productivity parameter is problematic. The lack of precision in the quality parameter estimates is a pervasive problem in Cobb-Douglas production functions with quality-adjusted labor input if the econometrician is exploiting only within-firm variation. The approach presented in this article also exploits within-firm variation, but it avoids the estimation of production functions and, therefore, produces precise measures of wage discrimination. Detecting Discrimination at the Firm Level Because we do not have measures of individual productivity and have shown that aggregating at the group level might also be problematic in some cases, a second-best option is to aggregate the Equation (2) within the firm: w jt = α j + β p jt + γ I jt + ε jt
(6)
where w jt is the mean of the log-wages in firm j, p jt is the mean of the individual log-productivities of firm j, and I jt is the proportion of immigrants in firm j at time t.10 Aggregating Equation (2) within the firm makes the estimation of β and γ feasible. Although individual productivity is unobserved, productivity measures at the firm level are available. The conceptually relevant measure of productivity should be the marginal productivity of workers in firm j. We assume the standard Cobb-Douglas function with quality-adjusted labor input production: Y jt = Aj ( K jt )φK ( LQ jt )φL ,
where Aj is the firm fixed effect; Y jt is the output of firm j at time t; K jt is its Q capital; and L jt is its quality-adjusted labor input, defined in efficiency units, as in the Hellerstein-Neumark approach. The marginal productivity Q φ φ −1 Q of native workers is given by φL Aj ( K jt ) ( L jt ) , which equals φ Y jt / L jt . The φ φ −1 marginal productivity of immigrant workers is given by ρφL Aj ( K jt ) ( LQ jt ) , Q which equals γφ Y jt / L jt . Therefore, the mean marginal productivity ( Fl ) is: K
L
L
K
L
L
φK
Fl = ρφL Aj ( K jt ) ( L jt ) Q
( φL −1)
LI jt L jt
LI jt φK ( φL −1) Q + φL Aj ( K jt ) ( L jt ) 1 − L jt
10The migration status indicator, I , is worker-specific, but the proportion of immigrant workers is i firm- and time-specific.
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Table 1. Firms’ Descriptive Statistics Measurement
Mean
Number of workers Outputa (millions of euros) Depreciated capitala(millions of euros) Value-added a(millions of euros) Total wage bill a(millions of euros) Unionized (%) Single establishment (%) Migrant’s proportion (%) Migrant’s proportion within-firm SD (%) Number of observations
211.86 54.3 1.38 23.0 8.24 63.4 70.2 7.7 2.6 24,943
Notes: The proportion of immigrants is estimated using the panel of workers. All the remaining statistics are obtained from the panel of firms. SD, standard deviation. aAmount per annum.
Rearranging, we have:
Fl = φL
(7)
LI jt Y LI jt 1 − + = φL jt ρ I Lit L jt L jt L Lit 1 + ( ρ − 1) it Lit Y jt
Therefore, using the log of the output per worker or using the log of the mean marginal productivity would modify only the constant term a j in Equation (6) by adding β log(φL ) to it. Equation (7) holds if workers of different types are perfect substitutes in the production function. Perfect substitutability is a common assumption in this literature (e.g., Hellerstein and Neumark 1999; Hellerstein et al. 1999). Although the large within-firm variation of the proportion of immigrants reported in Table 1 supports to this assumption, new evidence suggests that the elasticity of substitution between natives and immigrants depends heavily on their occupation and experience. (See the Results section for an estimate of γ and β in a slightly modified version of Equation (6) that includes a more detailed characterization of the workforce in terms of age and occupation.) This specification has the advantage of controlling for differences in productivity between-groups without estimating the relative productivity, as in the Hellerstein-Neumark approach. The use of group-specific productivity measures usually involves the estimation of a production function with qualityadjusted labor input. To have estimates that are robust to any correlation of inputs, including labor input composition, with the firm fixed effect, the production function should be estimated exploiting only the within-firm variation of the data. A within-firm ordinary least squares (OLS) estimation of this kind of specification is problematic and usually produces imprecise estimates. (See Appendix C for NLLS estimates of the production function
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in levels to compare the results of my approach with those obtained using the Hellerstein-Neumark approach.11) Data The data I use in the present study are from the LIAB, covering 1996 to 2005, for West German workers.12 LIAB was created by matching the data from the IAB Establishment Panel to the process-produced data from the Federal Employment Services (social security records). The IAB Establishment Panel is an annual survey of German establishments that started in western Germany in 1993 and was extended to eastern Germany in 1996. The sample of establishments was selected randomly and stratified by industries, establishment size, and regions. The sample unit is the establishment. The establishments in the survey were selected from the parent sample of all German establishments that employ at least one employee who is covered by social security. The participation of the establishments in the survey was voluntary, but the response rates were high (they exceeded 70%).13 The firms’ data give details of total sales, value-added, investment, total wage bill, depreciation, number of workers, and sector. I considered only firms with strictly positive output. To ensure a consistent comparison of results across specifications, I excluded from the data used for each specification observations with missing values for any of the independent variables used in the regressions. Firms in the financial and public sectors were excluded from my subsample. Table 1 presents some descriptive statistics. The distinctive feature of these data is the combination of information about individuals and details concerning the firms in which these people work. The workers’ source contains valuable data on age, gender, immigrant status,14 daily wage (censored at the upper-earnings limit for social security contributions), schooling/training, occupation (based on a three-digit code), and the establishment number. In Table 2, I present descriptive statistics for both immigrants and natives, estimated from the sample of workers. The proportion of women is significantly higher in the native population. Immigrants are younger, and they have less tenure and experience. Important differences are present in terms of occupations and sectors. Immigrants are more concentrated in the manufacturing sector and in low-qualification occupations than are natives.15 11The last set of results is equivalent to results presented in Campos-Vazquez (2008), which uses the Hellerstein-Neumark approach and the same data set used here to test whether wage discrimination exists against immigrants in Germany. 12All employees and trainees subject to social security are included; the self-employed, family workers, a subgroup of civil servants (Beamte), students enrolled in higher education, and those in marginal employment are excluded. 13For a more precise description of this data set, see Alda, Bender, and Gartner (2005). 14I consider immigrants to be workers who do not have German citizenship. In 1999, a reform of the Citizenship and Nationality Law came into effect, modifying the criteria for naturalization. The main results presented in this article are valid independent of the change in this law (see Appendix A). 15Following the FDZ’s criteria, I considered the following to be low-qualification occupations jobs: agrarian occupations, manual occupations, services, and simple commercial or administrative occupations. I considered the following to be high-qualification occupations: engineering, professional or semi-professional occupations, qualified commercial or administrative occupations, and managerial occupations.
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Table 2. Demographic Differences Variable
Immigrants
Natives
Female (%) Age (years) Tenure (years) Experience (years) Low-qualification occupation (%) Part-time jobs (%) Agriculture (%) Manufacturing (%) Construction (%) Trade (%) Services (%) Daily wages (€) Number of observations
25.6 39.6 10.5 15.1 80.9 9.2 2.5 70.3 3.0 3.5 20.6 94.7 1,185,362
31.2 40.4 11.1 16.7 52.4 12.8 3.9 59.1 3.3 6.9 26.7 109.0 11,832,370
Notes: Descriptive statistics estimated from the panel of workers. Because wages are censored at the upper earnings limit for social security contributions, the mean-wages were obtained using maximumlikelihood, assuming log-normality.
Results In this section, I present results of the estimation of the baseline specification in Equation (6), and I examine the robustness of these benchmark estimates. To estimate Equation (6), I replace wij with the log of the mean-wage in firm j at time t and pij with the log of the output per worker in firm j at time t. Equation (7) presents an equivalence between the log of the output per worker and the log of the mean marginal productivity. This equivalence is calculated without taking materials into account in the production function. Therefore, the conceptually most convenient measure of productivity would be value-added per worker, which already partials out the cost of materials. Unfortunately the measure of value-added provided in the LIAB may have reliability problems.16 Assuming that a constant fraction of the output is spent on materials, both measures would be equivalent for my purposes, but, as a proof of robustness, I report results using both measures. In Table 3, I present the results. Columns (1) and (2) list the estimates without including any measure of productivity. The OLS estimate of γ in column (1) is understood to be the unconditional wage gap, controlling only for time effects. This wage gap is obtained from firm-level data, and it is not statistically different from the unconditional wage gap obtained using worker-level data.17 On the other hand, γ estimated by within-groups, without further controls, refers to the average unconditional wage gap within firms. The difference between the overall wage differential and the withinfirm wage gap is informative about sorting of immigrants into firms. 16See 17The
Addison, Schank, Schnabel, and Wagner (2006) for a thorough discussion of this issue. unconditional wage gap obtained from worker-level data is −13.1% (see Table B.1).
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Table 3. Wage-Setting Equation wij
(1)
(2)
(3)
(4)
(5)
(6)
βOutput
—
—
—
—
—
0.486 (0.006) —
—
βValue-added
0.426 (0.013) —
−0.181 (0.044) No 29,943 1.2 — —
−0.258 (0.043) Yes 29,943 — 1.4 0.2
0.070 (0.040) No 29,943 37 — —
−0.126 (0.041) Yes 29,943 — 28 38
0.392 (0.013) 0.032 (0.039) No 29,943 33 — —
0.233 (0.005) −0.168 (0.049) Yes 29,943 — 13 35
γ Firm fixed effects Number of observations R 2 (%) R 2 -within (%) R 2 -between (%)
Notes: Each column represents a single linear regression using the panel of firms. Time dummies are included in every specification. Values in parentheses are standard errors. In the OLS regressions (columns (1), (3), and (5)), standard errors were calculated using clustering by firm.
In Table 3, columns (3) and (4) list estimates using output per worker as a measure of productivity. In this specification, the estimated premium for being an immigrant is 7%, which is positive and marginally significant (p = 0.082). But estimating the same specification including firm fixed effects yields a noteworthy discrimination parameter of −12.6%, also significant but now negative, which implies that immigrants are being discriminated against.18 This finding is surprising if we take into account that, using the same data, both the traditional approach and the Hellerstein-Neumark approach conclude that immigrants are not receiving significantly lower wages than natives (see Appendices B and C). When I estimate Equation (6) including value-added per worker as a measure of productivity, β is lower in both estimations, regardless of the inclusion of firm fixed effects. I find the same pattern in terms of γ as shown in Table 3, columns (3) and (4). The lower punctual estimate of βValue-added and the lower R 2 may be understood as evidence of measurement error in the value-added, as pointed out by Addison et al. (2006). It is important to note that the value of β, the elasticity of wages to productivity, is found to be significantly different from 1 in every specification. These results suggest that the linearity bias described for the HellersteinNeumark approach is relevant in this data set. Also, note that when no measure of productivity is included the fit of the wage data is obviously very poor. In contrast, when productivity is included in these regressions, the R 2 becomes acceptable and similar to the R 2 obtained using standard individuallevel wage regressions.
18To examine the robustness of this results, I present estimates of the model in Appendix A, controlling for gender, job qualification, and original country.
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Table 4. Segregation wij βOutput Γ Region Sector Firm characteristics Firm fixed effects Number of observations R2 βValue-added Γ Sector Region Firm characteristics Firm fixed effects Number of observations R2
(1)
(2)
(3)
(4)
(5)
0.426 (0.014) 0.070 (0.040) No No No No 24.943 0.372
0.419 (0.014) 0.026 (0.042) Yes No No No 20,886 0.372
0.446 (0.015) 0.039 (0.038) No Yes No No 23,720 0.433
0.427 (0.016) −0.066 (0.040) Yes Yes Yes No 19,663 0.445
0.486 (0.006) −0.126 (0.042) — — — Yes 24,943 0.369
0.392 (0.014) 0.033 (0.040) No No No No 24,943 0.335
0.385 (0.014) 0.014 (0.041) Yes No No No 20,886 0.334
0.372 (0.014) 0.010 (0.038) No Yes No No 23,720 0.369
0.355 (0.014) −0.081 (0.040) Yes Yes Yes No 19,663 0.387
0.233 (0.005) −0.168 (0.046) — — — Yes 24,943 0.328
Notes: Each column represents a single linear regression using the panel of firms. Time dummies are included in every specification. Values in parentheses are standard errors. In OLS regressions (columns (1)–(4)), standard errors are calculated clustering by firm. R 2 in column (5) does not take into account the variation in firm fixed-effects.
Segregation The positive difference γ OLS − γ FE , where the subscript FE indicates the inclusion of fixed effects in the model, may be understood to be evidence in favor of the positive segregation of immigrants into firms with higher fixed effects. This positive segregation implies an underestimation of discrimination when the within-firm variation is not isolated. Comparing the wage premium of immigrants, as estimated using different sets of controls, I provide indirect evidence of the relative importance of various dimensions of immigrant segregation in generating differences in wages. The results are reported in Table 4. To facilitate a comparison with the previous results, the first and last columns of the table replicate the results reported in Table 3. In column (2), I report the results when only controls for region are included. When I control for region, I observe that the estimated γ is not significantly different from 0 and smaller than the value reported in column (1). This finding connects with Borjas (1999), who argued that immigrants are not randomly assigned to regions; presumably, they choose areas that provide them with better opportunities. The presence of a lower value of γ when we control for region is consistent with this assessment because it indicates that part of the positive premium that immigrants obtain is due to their choice of region. Positive segregation in term of region has also been found in Canada by Aydemir and Skuterud (2008). Downloaded from ilr.sagepub.com at Univ Studi Torino on November 18, 2014
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Table 4, column (3) lists the results when only controls for industry are included. These controls may be important if we take into account the fact that sectoral composition is significantly different across immigrant status (see Table 2). When I control for industry, again the estimated γ is not significantly different from 0 and is smaller than the value reported in column (1). This difference in γ suggests the positive segregation of immigrants into better industries. Although several studies measure the proportion of the gender and racial wage gaps due to interindustry differences in worker composition, for immigrants this literature is smaller. One example is Aydemir and Skuterud (2008), which used Canadian matched employer-employee data and found that immigrants are employed in industries with slightly lower wage effects. In Table 4, column (4) shows the results when region effects, sector effects, and other firm characteristics are included. I consider firm size, an indicator of unionization,19 and an indicator that takes the value 1 if the firm is a single establishment. The value of γ is not significantly different from 0, but it is significantly lower than the coefficient reported in column (1). This finding suggests that part of the positive wage premium that immigrants receive according to the estimates presented in column (1) is a consequence of their choices of sector, region, and the firm’s observable characteristics. It is surprising that a large part of the wage differential is not accounted for by observable segregation. When we compare the values of γ in Table 4, columns (4) and (5), it is noteworthy that, once we control for the observable and unobservable firm fixed characteristics, the wage premium for immigrants is still significantly lower than that reported in column (4). These findings show that immigrants are hired in better firms than natives within each region, sector, and firm-characteristics cell. Nevertheless, within each firm they receive wages that are between 13% and 17% lower than natives. This result suggests that clustering the analysis in terms of observable characteristics will not be sufficient to robustly test for the existence of wage discrimination. Although the differences in γ for different set of controls are not precise, the main patterns are stable across specifications. After partialling out all the firm fixed characteristics, we always find a significantly lower estimate of γ, which suggests that immigrants are systematically sorted into high-wage firms (see Appendix A). Perfect Substitution between Immigrants and Natives Equation (7) holds if workers of different types are perfect substitutes in the production function. Perfect substitutability is a common assumption in the literature (e.g., Hellerstein and Neumark 1999; Hellerstein et al. 1999). Although the large within-firm variation in the proportion of immigrants reported in Table 1 supports this assumption, new evidence suggests that the elasticity of substitution between natives and immigrants heavily depends on 19In
the IAB Establishment survey, an explicit question asks whether the establishment is bound by industry-wide wage agreements, is bound by a company agreement concluded between the establishment and trade unions, or not bound by collective agreements.
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their age and level of education. In particular, Ottaviano and Peri (2012) found that, within education and age cells, immigrants and natives are almost perfect substitutes. Here I estimate γ and β using a slightly modified version of Equation (6) that includes a more detailed characterization of the workforce in terms of age and occupation. I compare two types of occupation, high-qualification and low-qualification occupations (as previously defined), and two age groups, workers younger than 35 and workers older than 35. I first estimate the following model: w jt = α j + β p jy + γ IHO
(8) +γ NHY
L jt NHY L jt
+ γ IHY
L jt IHO L jt
L jt IHY L jt
+ γ NHO
+ γ ILY
L jt NLO
L jt ILY L jt
L jt
+ γ ILO
+ γ NLY
L jt ILO L jt
L jt NLY L jt
+ ε jt
IHO
where L jt is the number of immigrants older than 35 years of age working NLO is the number of in firm j at time t in high-qualification occupations, L jt natives older than 35 working in firm j at time t in low-qualification occupaILO tions, L jt is the number of immigrants older than 35 working in firm j at NLY is the number of natives time t in low-qualification occupations, L jt younger than 35 working in firm j at time t in low-qualification occupations, L jt NHY is the number of natives younger than 35 working in firm j at time t in IHY high-qualification occupations, L jt is the number of immigrants younger than 35 working in firm j at time t in high-qualification occupations and L jt NHY is the number of immigrants younger than 35 working in firm j at time t in low-qualification occupations. Native workers older than 35 in highqualification occupations are the reference group. The OLS estimates of Equation (8) using data on output per worker and value-added per worker as indicators of productivity are presented in Table 5, columns (1) and (5). These estimates are consistent if a j , the firmidiosyncratic component in the wage equation, is not correlated with the regressors. In light of the evidence presented in Table 4, I also present in Table 5 estimates robust to segregation. Columns (2) and (6) list the withinfirm OLS estimates of Equation (8). Results indicate that, after I partial out the firm fixed effect, immigrants older than 35 in white-collar (highqualification) occupations are the only ones that do not suffer discrimination. Furthermore, when we control for productivity differences using output per worker, immigrants belonging to this group receive higher wages than natives. Younger immigrants receive lower wages than their native counterparts, but these differences are not always statistically significant.20 In contrast, immigrants older than 35 in low-qualification occupations receive significantly lower wages than their native counterparts. The point estimates are economically significant, but the standard errors are large. 20The values of γ measure the difference in wages with respect to the reference group. If we want to compare similar groups, we have to calculate the difference in differences. For example, in the case of younger workers in low-qualification occupations, we have to calculate the difference between γ ILY and γ NLY.
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Table 5. Wage-Setting Equation (1) wij
(2)
(3)
Equation (8)
βOutput
(4)
(5)
Equation (9)
0.403 (0.014) —
0.478 (0.006) —
0.462 (0.001) —
0.486 (0.026) —
γ IH
—
—
γ NL
—
—
γ NL
—
—
γ Young
—
—
γ IHO
0.012 (0.360) −0.282 (0.040) 0.059 (0.069) −0.465 (0.258) −0.468 (0.258) −0.195 (0.063) −0.392 (0.068) No 24,943
0.609 (0.178) −0.263 (0.038) −0.464 (0.068) −0.294 (0.040) −0.350 (0.132) −0.024 (0.042) −0.313 (0.065) Yes 24,943
0.192 (0.160) 0.068 (0.014) 0.220 (0.045) 0.007 (0.016) —
0.241 (0.209) −0.052 (0.028) −0.118 (0.038) 0.149 (0.048) —
—
—
—
—
—
—
—
—
—
—
—
—
No 24,943
Yes 24,943
βValue-added
γ NLO γ NLO γ NLY γ IHY γ NHY γ ILY Firm fixed effects Number of observations
(6)
(7)
(8)
Equation (8)
Equation (9)
—
—
—
—
0.368 (0.014) —
0.227 (0.005) —
—
—
—
—
—
—
0.156 (0.385) −0.286 (0.042) −0.013 (0.071) −0.486 (0.042) −0.514 (0.274) −0.225 (0.067) 0.433 (0.067) No 24,943
0.279 (0.193) −0.487 (0.042) −0.720 (0.073) −0.487 (0.044) −0.375 (0.143) −0.097 (0.046) −0.489 (0.071) Yes 24,943
0.685 (0.001) 0.419 (0.174) 0.142 (0.016) 0.240 (0.044) −0.093 (0.016) —
0.232 (0.014) 0.049 (0.130) −0.096 (0.032) −0.173 (0.049) 0.232 (0.061) —
—
—
—
—
—
—
—
—
—
—
—
—
No 24,943
Yes 24,943
Notes: Each column represents a single regression using the panel of firms. Time dummies are included in every specification. Values in parentheses are standard errors. In OLS and NLLS regressions (columns (1), (3), (5), and (7)), standard errors were calculated using clustering by firm.
To gain precision, I reduce the number of parameters by estimating a less flexible specification using the model: w jt = α j + β p jy + γ IH
(9)
+γ young
L jt
L jt IHO L jt
+ γ NL
L jt NLO L jt
NHY
L jt
+ 1 − (1 + γ young )(1 + γ IH )
+ γ IL L jt
L jt ILO L jt
+ 1 − (1 + γ young )(1 + γ NL )
IHY
L jt
+ 1 − (1 + γ young )(1 + γ IL )
L jt
L jt NLY L jt
ILY
L jt
+ ε jt
In Equation (9), I constrain the wage differential between workers older and younger than 35 years so that it is the same for natives and immigrants in both kind of occupations. I impose the following constraints:
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γ NLY = 1 − (1 + γ young )(1 + γ NL ) , γ NHY = γY ,
γ IHY = 1 − (1 + γ young )(1 + γ IH ) , and
γ ILY = 1 − (1 + γ young )(1 + γ IL ) ,
where γ young is the wage differential between workers older and younger than 35 years, irrespective of their immigrant/native status and occupation; γ NL is the wage differential between natives in low-qualification occupations and the reference group, irrespective of age; γ IL is the wage differential between immigrants in low-qualification occupations and the reference group; and γ IH is the wage differential between immigrants in high-qualification occupations and the reference group. The NLLS estimates of Equation (9) using data on output per worker and value-added per worker as indicators of productivity are presented in Table 5, columns (3) and (7). Columns (4) and (8) list the within-firm NLLS estimates of Equation (9). Even though Equation (9) is not linear in parameters, because the firm fixed effect is additive it can be estimated using within-firm NLLS. The results indicate that immigrants receive salaries higher than natives when they work in high-qualification occupations, but this difference is not significant. On the contrary, immigrants working in low-qualification occupations receive wages significantly lower than their native counterparts. As in the case of the simpler model, the estimates are significantly different depending on the estimation strategy. Wage differentials between natives and immigrants estimated using NLLS exploiting only within-firm variation are significantly lower than the differentials estimated using standard NLLS, suggesting again that immigrants are systematically sorted into high-wage firms. In this exercise, I have compared immigrants with natives in the same occupation/age cell. Immigrants and natives have been shown to be highly substitutable within education/age cells, but I do not have high-quality data on education level. This exercise sets up better comparison groups than the baseline specification; however, it still requires perfect substitution between occupation/age categories. Wage-Setting Equation with Group-Specific Elasticity to Productivity In the baseline specification, I assume that the wage elasticity to productivity is constant across groups. In this section, I test whether relaxing this assumption modifies my main results. Let us consider the following wage-setting equation: (10)
w jt = α + I jt β I pI , jt + β N (1 − I jt ) pN , jt + γ I jt + ε jt
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where pI , jt is the log-productivity of immigrants in firm j at time t, pN , jt is the log-productivity of natives in firm j at time t, βI is the elasticity of wages with respect to the immigrants’ productivity and β N is the elasticity of wages with respect to natives’ productivity. Assuming again a Cobb-Douglas production function with quality-adjusted labor input, we know from the section titled A Test of Wage Discrimination that the log of the natives’ marginal productivity can be written as Y jt , pN , jt = log φL L jt (1 + ( ρ − 1) I jt )
and the immigrants’ marginal productivity can be written as: Y jt pI , jt = log ρφL + ( ρ − ) L 1 1 I ( ) jt jt
Hence,
(11)
Y jt Y jt + β N (1 − I jt ) log φL + γ I jt + ε jt wit = α + β I I jt log ρφL L jt (1 + ( ρ − 1) I jt ) L jt (1 + ( ρ − 1) I jt )
After rearranging and noting that as ϑ should be near 1, log (1+ (ϑ–1)Ijt) ≅ (ϑ–1)Ijt, and log(ϑ) ≅(ϑ − 1), we have:21 Y wit = α + β N log(φL ) + β Ν log jt L jt Y +( β I − β N ) I jt log jt L jt
+ [ ( β I − β N ) log( ρφL ) + γ ] I jt
2 + ( β I − β N )(1 − ρ ) I jt + ε jt
Therefore, we can estimate:
wit = A + Bp jt + CI jt + Dp jt I jt + EI jt2 + ε jt where,
as
before,
Y jt p jt = log L jt
,
and
A = α + β N log(φL ) ,
B = βN ,
E = (1 − ρ )( β I − β N ) . Therefore, we can recover estimates of the difference β I − β N to evaluate the assumption C = ( β I − β N ) log( ρφL ) + γ , D = β I − β N , and
made in the baseline specification. Note that, without further information (e.g., an external estimation of φL ), γ cannot be recovered in this exercise.
21Paserman
(2011) uses this approximation in a similar context.
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Table 6. Wage-Setting Equation with Group-Specific β wij
(βN − βI ) log(ρϕ) + γ
( β N − βI )
(βN − βI ) (ϕ − 1) Sector, region, and firm characteristics Firm fixed effects Number of observations R 2 (%)
(1)
(2)
(3)
0.345 (0.626) 0.034 (0.055) −1.04 (0.114) No No 24,943 37.56
0.135 (0.604) −0.017 (0.052) 0.025 (0.012) Yes No 20,886 49.92
−0.504 (0.379) 0.009 (0.031) −0.461 (0.101) — Yes 24.943 39.18
Notes: Each column represents a single linear regression using the panel of firms. A quartic on productivity and time dummies are included in every specification. Values in parentheses are standard errors. In OLS regressions (columns (1) and (2)), standard errors were calculated using clustering by firm.
The parameter C, which corresponds to the proportion of immigrants in the firm, can identify γ only when β I = β N . The results are presented in Table 6. The wage elasticity with respect to productivity is not found to be different between natives and immigrants. The value of β I − β N is not statistically different from 0, and the estimated standard deviation of this difference remains within reasonable bounds and ranges between 0.03 and 0.05. This last result gives additional support to the baseline specification, where β has been assumed to be homogeneous across groups. Testing the Implications of Discrimination Models The approach presented in this article allows us to estimate Equation (6) with firm-specific γ. Hence, it provides a firm-specific measure of wage discrimination against immigrants, which is useful when we test some of the implications of the different discrimination models. Two main branches have emerged in the theoretical discrimination literature: taste-based discrimination and statistical discrimination. These models emphasize two broad types of discrimination. The first focuses on prejudice, which Becker (1971) formalizes as a taste held by at least some members of the majority group against interacting with members of the minority group. The second model focuses on statistical discrimination by employers in the presence of imperfect information about the skills or behavior of members of the minority group. Even though it is difficult to empirically distinguish between the two theoretical models, some lessons can be drawn. One of the implications of the model presented in Becker (1971) is that discriminating employers earn lower profits than nondiscriminators22 22This
is pointed out in several papers; see, for example, Black (1995); Bowlus and Eckstein (2002). Both papers analyze employer taste discrimination in a search model that predicts profits will decrease in the discrimination coefficient.
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because the nondiscriminators pay less for their labor by hiring workers who are discriminated against. This implication can be directly tested in the present framework; if taste-based discrimination is the true model, we should observe a positive correlation between and firm profits. Statistical discrimination was first discussed by Phelps (1972) and Arrow (1973). The basic premise of this literature is that firms have limited information about the skills and turnover propensity of applicants; hence, they have an incentive to use easily observable characteristics such as race or gender to statistically discriminate among workers if these characteristics are correlated with performance.23 Two main branches exist in the statistical discrimination literature. The first investigates whether biased racial and gender stereotypes might be self-confirming when the payoff for hard-toobserve worker investments depends on employer beliefs. Therefore, an a priori, unfounded belief about a group’s performance may be confirmed a posteriori. This issue, mainly addressed by Arrow (1973) and Coate and Loury (1993), is not analyzed here because it should be captured by controlling for productivity. The second branch concerns the consequences of group differences in the precision of the information that employers have about individual productivity. It was developed mainly by Aigner and Cain (1977), with subsequent work by Lundberg and Startz (1983) and Lundberg (1991). If this is the case in the present study, as firms continuously acquire more information about their workers’ productivity, pay will become more dependent on actual productivity and less dependent on easily observed characteristics such as immigrant status. Therefore, we should observe a positive correlation between tenure and gj. Having firm-specific discrimination parameters also allows us to have a better understanding of immigrant self-selection into firms with less discriminatory employers. If immigrants self-select into these firms, the expected value of obtained here should be different from the γj obtained in the previous section. To estimate the firm-specific discrimination parameters, I follow Arellano and Bonhomme (2012). I estimate Equation (6) in two simple steps. First, I obtain the common parameters. To do this, I regress the residual of firmspecific regressions of the total wage bill and the variables with constant coefficients on the proportion of immigrants and a constant term: Qw jt = Qz jtδ + Qε jt −1
where Q j = ( IT − X j ( X j ’X j ) X j ) , X j is a 2×T j matrix with a column of 1’s that identifies the firm fixed effect and a column with the firm proportion of immigrants, T j is the individual length of the panel (because the data set is an unbalanced panel, T is firm-specific), and Z j is a matrix that contains those j
23Although it is illegal to make hiring, pay, or promotion decisions based on predictions about worker performance because of gender or immigrant status, such behavior would be hard to detect in many circumstances.
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variables with constant coefficients. These are also time dummies and output per worker (or value-added per worker, depending on the specification). Second once I have estimated δ gj is easily recovered:24 α˘ j −1 −1 ˘ = X j ( X j ’X j ) ( w jt − Z jt ’δ ) = X j ( X j ’X j ) ε jt γ j
Note that the estimated firm-specific fixed effect and the firm-specific dis0.5 crimination parameter are equal to the true parameters plus a term O(1 / T j ) . For fixed T, aˆ j and γˆ j are inconsistent, but consistent correlations with exogenous variables can be easily recovered (see Arellano and Bonhomme 2012 for more details). The sample used in this exercise is the panel of firms. Given that I estimate two firm-specific coefficients, I consider only firms with more than two observations. Firm-specific gj are identified only in firms where the proportion of immigrants varies; therefore, firms with no variation or marginal variation in the proportion of immigrants have been excluded.25 The results are presented in Table 7. Given the short time dimension, most of the variation in the firm-specific coefficients is only noise; hence, the second step is usually imprecise. Firm fixed effects are found to be negatively correlated with the firm profits.26 Because these fixed effects represent wages, given the productivity this finding is not surprising. Firms with higher average tenure are found to be better payers. Although the covariance is marginally significant when we use output as a measure of productivity, single establishments are in general worse payers. The proportion of immigrants is not found to be significantly correlated with the firm-specific discrimination parameter. This is important for the robustness of the main results of the article, in which γ is assumed to be homogeneous. To test some of the implications of the taste-based discrimination and statistical discrimination theories, I regressed the firm-specific discrimination parameter in each firm’s mean profits and the firm’s mean tenure of immigrants. I find that the mean tenure of immigrants in a firm is negatively, but not significantly, associated with the discrimination parameter. In contrast, profits have a significantly negative correlation with the discrimination parameter; this means that firms with higher profits discriminate more, which contradicts what is predicted by the taste-based discrimination literature. Therefore, this may be interpreted as indirect evidence against the taste-based discrimination model. 24The MATA code used to estimate a linear model with random coefficients is available from the author upon request. 25In particular, to exclude firms with low variation in I jt from the whole sample of firms with positive variation in I jt , I excluded every firm for which the standard deviation of the proportion of immigrants is below the 10th percentile of the firm’s distribution of the standard deviations of I jt . 26The covariance between firm fixed effects and profits is significant only when using value-added.
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Table 7. Wage-Setting Equation with Random Coefficients A. First-stage regressions wij βOutput βValue-added Mean( γ j ) Mean(a j )
(1)
(2)
0.452 (0.009) — −0.489 (0.334) 2.45 (0.030)
— 0.174 (0.006) −0.921 (0.374) 5.84 (0.032)
B. Second-stage regressions
Profits Tenure of immigrants Proportion of immigrants Unionized workforce Single establishment Constant Number of observations
aj
γj
aj
γj
−7.0e (3.2e)−9 3.5e−5 (1.9e)−5 0.025 (0.23) −0.133 (0.081) −0.145 (0.081) 2.61 (0.108)
−9.7e−8
−6.9e−9
(3.6e)−8
(3.5e)−9
−1.5e−4 (2.1e)−4 1.68 (2.60) 0.749 (0.909) 0.887 (0.902) −1.50 (1.20)
4.5e−5 (2.0e)−5 −0.166 (0.249) −0.053 (0.087) −0.284 (0.086) 5.79 (0.115)
−1.4e−7 (4.0e)−8 −1.1e−4 (2.3e)−4 3.39 (2.91) 0.267 (1.02) 0.415 (1.01) –1.03 (1.34)
1,877
1,877
Notes: Each column in panel A represents a single linear regression with fixed -effects and firm-specific γ using the panel of firms. Time dummies are included in both specification. Each column in panel B represents a single linear regression of the estimated aj and gj in panel A on selected firm-specific variables. Sector dummies are included. In both panels, values in parentheses are standard errors. - and Standard deviation of a gj are corrected following Arellano and Bonhomme (2012). j
Conclusion The Hellerstein-Neumark strategy is a very direct and popular method to detect wage discrimination using matched employer-employee data. In this article, I develop a test for wage discrimination that builds on the HellersteinNeumark approach. The proposed method estimates a wage-setting equation at the firm level that exploits changes in productivity and changes in the native–immigrant composition within a firm over time to identify different wage policies toward these two groups. This test is an improvement over the existing one in three ways: it is robust to labor market segregation, it does not impose linearity in the wage-setting equation, and it both tests for discrimination and produces a measure of discrimination. Using matching employer-employee data from Germany, I have found that immigrants are subject to wage discrimination. Depending on which measure of productivity is used, the discrimination ranges between 12.8% and 16.8%. This finding is surprising because, using the same data, both the
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traditional approach and the Hellerstein-Neumark approach conclude that immigrants do not receive significantly lower wages in Germany. The elasticity of wages with respect to productivity is significantly different from 1; hence, assuming that wages are equal to (or a constant fraction of) productivity may be dangerous. Although the reduced-form wage-setting equation is very simple, it has an acceptable fit of the wage data and without controlling for firm fixed characteristics and I obtain similar results to those that would be obtained using employee-level data. When estimating using OLS, I have found discrimination to be significantly lower, which provides evidence for the positive segregation of immigrants into high-wage firms. To understand the nature of this segregation, I then included various sets of controls, and I found that most of the segregation can be accounted for by differences in region, sector, and firm size. I also found that immigrants working in low-qualification occupations receive lower salaries than their native counterparts but that immigrants working in high-qualification occupations receive higher wages than their native counterparts. Estimating a similar specification, but considering wages and output instead of log-wages and log-output or allowing for a more flexible functional form for the effect of productivity, I have found the same results. Although β has been assumed to be the same between natives and immigrants, I do not find evidence of a significant difference in the wage elasticity to productivity between the two groups. I also do not find significant evidence of immigrants moving to less discriminatory firms or significant evidence in favor of the statistical discrimination model. I do, however, find evidence against a taste-based discrimination model. The results presented here rely on simplifying assumptions that would benefit from further scrutiny. The most challenging extension will be to relax the assumption of perfect substitution between natives and immigrants. Using wage data, Ottaviano and Peri (2012), among others, found evidence suggesting that immigrants and natives are perfect substitutes only after controlling for education and age. To the best of my knowledge, no studies obtaining measures of productivity differentials and wage discrimination allow for imperfect substitution in production. This extension is not trivial because it implies the estimation of constant elasticity of substitution (CES) production functions with firm fixed effects and it will represent an important contribution to the literature.
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Appendix A Robustness and Specification Tests Immigrant Status and Gender The empirical strategy proposed in this paper uses firm-level data. Hence, I cannot include a broad set of variables to characterize workers. This may present a problem because previous results may capture different wage policies toward other groups that correlate with the immigrant status. To illustrate this point, let us assume that immigrants are not discriminated against but that women are. Because the gender composition is significantly different between natives and immigrants (see Table 2), I would find that immigrants receive higher salaries than natives. To examine the robustness of my benchmark estimates, I estimate the model while controlling for gender. I estimate Equation (6) but decompose the workforce into four groups in terms of immigrant status and gender: w jt = α j + β p jt + γ IM
(12)
L jt IM L jt
+ γ NW
L jt NW L jt
+ γ IW
L jt IW L jt
IM
ε jt NW
where L jt is the number of immigrant men working in firm j at time t, L jt IW is the number of native women, and L jt is the number of immigrant women. The results are presented in Table A.1. As we can see, immigrant men receive wages that are between 9% and 13% lower than native men. Immigrant women receive wages that are between 20% and 23% lower than native women. Overall, women receive lower wages than men. This difference ranges between 4% and 8% for natives, but it is not always significant. These findings are consistent with the results presented in Bartolucci (2013), which found, estimating a structural model to study gender wage gaps with the same data set, that women do not have significantly lower bargaining power in every sector and that the estimated wage gap caused by discrimination is 9%. Wage-Setting Equation That Is Nonlinear in Log-Productivity The wage-setting equation is assumed to be linear in log-productivity. In this section, I test whether relaxing this assumption modifies the main results of this article. Consider the following wage-setting equation: w jt = α + G ( p jt ) + γ I jt + ε jt
where, as before, productivity is measured as the log-output per worker, and G(.) is a fourth-order polynomial. The results are presented in Table A.2. Although the nonlinear component of the effect of productivity is significant,27 the estimated 27The joint test of the three coefficients being equal to 0 are F(3,9331) = 163.81 (p = 0.00) in column (1), F(3,9331) = 79.93 (p = 0.00) in column (2), F(3,8950) = 113.58 (p = 0.00) in column (3), and F(3,15598) = 434.04 (p = 0.00) in column (4).
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Table A.1. Immigrant Status and Gender W jt
Output
Value-added
γ IM γ NW γ IW Firm fixed effects Number of observations R2
0.486 (0.006) −0.087 (0.053) −0.078 (0.032) −0.283 (0.071) Yes 24,943 0.3829
0,233 (0.005) −0.133 (0.058) −0.039 (0,035) −0.271 (0.077) Yes 24,943 0.3452
Notes: Each column represents a single within-group linear regression using the panel of firms. Native men are the reference group. Time dummies are included in every specification. Values in parentheses are standard errors. R 2 values do not take into account the variation in firm fixed effects.
Table A.2. Wage-Setting Equation Nonlinear on Log-Productivity W jt Output Output2 Output3 Output4 g Firm size Single Union Sector dummies Region dummies Firm fixed effects Number of observations R 2(%)
(1)
(2)
(3)
(4)
0.265 (0.035) 0.290 (0.025) −0.030 (0.003) 0.001 (8 × 10)−5 0.083 (0.039) —
0.311 (0.044) 0.289 (0.027) −0.031 (0.003) 0.001 (9 × 10)−5 −0.027 (0.038) 0.069 (0.033) 0.003 (0.003) 0.018 (0.011) No No No 23,720 45.74
0.266 (0.044) 0.282 (0.030) −0.029 (0.003) 0.001 (1 × 10)−4 −0.063 (0.039) 0.052 (0.004) 0.007 (0.003) 0.016 (0.011) Yes Yes No 19,663 49.71
0.017 (0.037) 0.046 (0.011) −0.004 (0.0001) 0.0001 (2 × 10)−5 −0.069 (0.040) — — — — — Yes 24,943 39.67
— — No No No 24,943 42.80
Notes: Each column represents a single linear regression using the panel of firms. Time dummies are included in every specification. Values in parentheses are standard errors. In OLS regressions (columns (1), (2), and (3)), standard errors were calculated using clustering by firm.
discrimination parameter, γ, is not found to be statistically different from the one estimated using the linear version of the wage-setting equation. Moreover, I find exactly the same pattern in the term of segregation. Estimating the specification by OLS (column (1)), γ is significantly positive.
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OLS estimates of γ become insignificant when controlling for firm-observable characteristics and negative28 when it is estimated controlling for firm fixed effects (column (4)). Wage-Setting Equation That Is Linear in Levels As discussed in the section titled A Test of Wage Discrimination, considering the wage-setting equation in logarithms has important advantages. But, for the sake of robustness, in this section I recalculate the wage-setting equation parameters taking a linear approximation to F(.,.) in Equation (1). I estimate: (13)
W jt = α + G ( Pjt ) + γ I jt + ε jt
where W jt is the wage bill per worker of firm j, and Pjt is the output per worker of firm j. The results are presented in Table A.3. Although these results are less precise than the baseline specification, they are qualitatively and quantitatively compatible with results previously presented. Taking into account that the mean-wage29 is 2,300.10 €, the OLS estimate of γ in column (1) implies that immigrants are receiving wages 5.7% higher than natives. As before, when including a wider set of controls, γ becomes insignificant (see column (2)) and becomes significantly negative when we control for observable and unobservable firm fixed characteristics (see column (3)). The firm fixed effect specification in column (3) suggests that immigrants receive wages that are 15.0% lower than natives. When we allow a more flexible specification for the output, the results do not change significantly (see columns (4) and (5)). The results presented in Table A.3 are for a sample in which observations of firms with outputs below the 5th percentile and above the 95th percentile of the output distribution have been excluded. When we consider the entire sample, the estimated discrimination parameter ranges between −12,957 and 6,071 €. When we take into account that the gross mean monthly wage in the sample is approximately 2,300 €, these results have no economic meaning. The sample trimming does modify the results obtained using the baseline specification (see Table A.4). When we consider a sample that excludes the observations of firms with outputs below the 5th percentile and above the 95th percentile of the output distribution, the estimates of γ in every specification are equivalent to those estimated with the full sample. The 1999 German Reform of the Citizenship and Nationality Law In May 1999, the German Parliament amended the Citizenship and Nationality Law of 1913. The reform had three main elements: changes in the the FE estimation, γ is significant at the 10% level, p value of 8.8%. consider mean-wage to be the average of the total wage bill per worker over the distribution of firms in the sample used in columns (1), (3), and (5). 28In 29I
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Table A.3. Wage-Setting Equation in Levels W jt
(1)
(2)
(3)
Output2
0.055 (0.001) —
0.060 (0.001) —
0.063 (0.002) —
Output3
—
—
—
Output4
—
—
—
132.54 (78.21) No No 24,943 8.79
32.98 (87.85) Yes No 19,663 12.92
−344.64 (124.54) — Yes 24,943 8.58
Output
γ Region, sector, and firm characteristics Firm fixed effects Number of observations R 2 (%)
(4)
(5)
0.301 0.124 (0.023) (0.023) −1.43e−05 −5.06e−07 (2.07)e−06 (1.95)e−06 2.99e−10 −8.68e−11 (6.92)e−11 (6.29)e−11 −2.01e−15 1.58e−15 −16 (7.58)e (6.25)e−16 23.91 −383.08 (87.04) (124.24) Yes — No Yes 19,663 24,943 14.56 9.78
Notes: Each column represents a single linear regression using the panel of firms. Time dummies are included in every specification. Values in parentheses are standard errors. In OLS regressions (columns (1), (2), and (4)), standard errors were calculated using clustering by firm.
Table A.4. Wage-Setting Equation: Sample Trimming W jt βOutput
γ Region, sector, and firm characteristics Firm fixed-effects Number of observations R 2 (%)
(1)
(2)
(3)
0.351 (0.005) 0.070 (0.024) No No 24,943 19.58
0.364 (0.005) 0.022 (0.025) Yes No 19,663 12.92
0.353 (0.009) −0.094 (0.039) — Yes 24,943 19.29
Notes: Each column represents a single linear regression using the panel of firms. Time dummies are included in every specification. Values in parentheses are standard errors. In OLS regressions (columns (1) and (2)), standard errors were calculated using clustering by firm. The sample used in these estimations excludes observations with output below the 5th percentile and above the 95th percentile of the output distribution.
naturalization criteria, denial of dual citizenship, and the introduction of birthright citizenship. Before the new legislation came into force, foreign nationals were granted entitlement to naturalization only after 15 years of residence in Germany. With the new legislation, a foreign national is entitled to naturalization after lawfully residing in Germany for 8 years. The only other requirements are loyalty to the German Constitution, no need for social security or unemployment benefits, no criminal convictions, and an adequate command of the German language. Although anecdotal evidence suggests than dual citizenship was almost never allowed by officials before the reform, the 1999 reform includes an explicit denial
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Table A.5. Effects of the 1999 German Reform 1996–1999
W jt βOutput
γ Firm fixed effects Number of observations R 2 (%) R 2 -within (%) R 2 -between (%)
2000–2005
(1)
(2)
(3)
(4)
0.405 (0.029) 0.135 (0.058) No 5,660 36.3 — —
0.586. (0.016) −0.104 (0.079) Yes 5,660 — 33.2 39.8
0.431 (0.015) 0.045 (0.047) No 19,283 37.0 — —
0.389 (0.008) −0.211 (0.056) Yes 19,283 — 18.7 38.1
Notes: Each column represents a single linear regression using the panel of firms. Time dummies are included in every specification. Values in parentheses are standard errors. In OLS regressions (columns (1) and (3)), standard errors were calculated using clustering by firm.
of dual citizenship. Before 1999, a child born in Germany gained German citizenship only if at least one parent possessed German citizenship at the time of birth. Under the new regime, a child born of foreign parents gains citizenship at birth if at least one parent has been legally resident in Germany for 8 years. In this article, I use data on citizenship to identify immigrants, and the 1999 law should have implications for the population of immigrants in which I am interested. To take this into account, I estimate the baseline specification with two subsamples, before and after 1999. The results are reported in Table A.5. Although the estimates differ between the two subsamples, these differences are not significantly different from 0. Moreover, the main findings of this article are valid for both time periods. Immigrants are found to have lower wages after we control for observed and unobserved firm fixed characteristics. Based on the differences in γ estimated by OLS and FE, evidence suggests the positive segregation of immigrants both before and after the 1999 reform of the Citizenship and Nationality Law. Furthermore, this exercise is also informative about the robustness of the results with respect to differences in labor market regulation. The main recent changes in the labor market regulations in Germany, the Hartz reforms, took place in 2001 and 2002. Table A.5 shows that the results for the first subsample, which embrace a more stable environment in terms of regulation, are not significantly different from the results obtained using the full sample. Immigrants from Developed Countries and from Developing Countries The results presented in this article consider immigrants to be workers without German citizenship. This is a very heterogeneous group, and it is likely
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Table A.6. Differences between Current and Original OECD Countries
W jt βOutput
βValue-added γ Developing γ Developed Firm fixed effects
R2
Number of observations
Current OECD countriesa
Original OECD countriesb
(1)
(2)
(3)
(4)
(5)
(6)
0.485 (0.006) —
—
0.485 (0.006) —
—
0.0486 (0.006) —
—
−0.117 (0.062) −0.132 (0.053) Yes 0.369 24,943
0.233 (0.005) −0.124 (0.067) −0.200 (0.058) Yes 0.327 24,943
−0.032 (0.058) −0.213 (0.056) Yes 0.368 24,943
Original OECD countries excluding Turkey
0.233 (0.005) −0.063 (0.063) −0.267 (0.061) Yes 0.325 24,943
−0.151 (0.050) −0.076 (0.069) Yes 0.370 24,943
0.0233 (0.005) −0.216 (0.055) −0.075 (0.075) Yes 0.328 24,943
Notes: Each column represents a single fixed-effect regression using the panel of firms. Time dummies are included in every specification. Values in parentheses are standard errors. OECD, Organisation for Ecomonic Co-operation and Development. aCurrent OECD countries are the original 20 plus Australia, Chile, Czech Republic, Estonia, Finland, Hungary, Israel, Japan, South Korea, Mexico, New Zealand, Poland, Slovakia, and Slovenia. bOriginal OECD countries are Austria, Belgium, Canada, Denmark, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg, the Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, Turkey, the United Kingdom, and the United States.
that its labor market performance is also heterogeneous. Here I present results that consider different groups of immigrants in terms of their countries of origin. In particular, I analyze whether wage setting differs if the immigrants are from a developed country or a developing one. I estimate the following model: wij = α j + β p jt + γ Developing I jt Developing + γ Developed I jt Developed + ε jt Developing
where I jt is the proportion of workers in firm j at time t who are citiDeveloped is the proportion of workers who zens of a developing country, and I jt are citizens of a developed country. The classification of developed or developing country is not clear-cut. I first consider as developed countries those countries that currently belong to the OECD. This set consists of 34 countries, including countries such as Chile, Mexico, and many Eastern European countries (e.g., Czech Republic, Hungary, and Poland) that are the source countries of a large proportion of immigrants in Germany. I then consider a more restrictive group of countries that includes only the original members of the OECD. One of these original OECD countries is Turkey, which is the largest source country of immigrants in Germany. Third, I consider the group of original members of the OECD excluding Turkey. The results are presented in Table A.6. When I consider the current members of the OECD to be the group of developed countries, I find that immigrants from both developed and developing countries suffer wage
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discrimination but that, surprisingly, immigrants from developing countries are less discriminated against than those from developed countries. This difference is only marginally significant when I control for productivity using value-added (column 2), but it is not significant when I control for productivity using output (column 1). When I consider the original OECD members as the group of developed countries, I do not find significant evidence of discrimination against immigrants from developing countries. Finally, to check whether the unexpected results in Table A.6, columns (1) to (4) are driven by the presence of Turkey in the group of developed countries, I consider as the developed group the original OECD members without Turkey. When Turkey is placed in the group of developing countries, I find no significant evidence of discrimination against immigrants from developed countries; in contrast, I find significant evidence that immigrants from developing countries are discriminated against. Appendix B Detecting Discrimination: Traditional Approach To compare different strategies for detecting wage discrimination, in this section I provide estimates of discrimination using Mincer-type wage equations. As can be seen in Table B.1, immigrants have positive wage differentials. Controlling for observed characteristics, they receive wages that are, on average, 7.2% higher than natives. Oaxaca-Blinder Decomposition Using results presented in Table B.1, I then performed an Oaxaca-Blinder decomposition, which simply decomposes the wage gap between differences in observable and unobservable characteristics. The results of the Oaxaca-Blinder decomposition are presented in Table B.2. The counterfactual immigrant mean-wage has to be interpreted as the mean-wage that immigrants would have if they had the natives’ distribution of observable characteristics. Therefore, the difference between the counterfactual immigrant mean-wage and the observed immigrant mean-wage is the portion of the gap that is due to differences in observable characteristics. The portion of the unconditional wage gap that is not accounted for by observable characteristics has usually been interpreted as wage discrimination. In this case, immigrants would not be discriminated against. They would be receiving wages that are 2% higher than similar natives.
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Table B.1. Mincer Wage Equations: Censored-Normal Regression, MaximumLikelihood Estimates Variable Sex Immigrant Age Primary education College (incomplete) Technical college (completed) College University degree Tenure Experience High-qualification occupation Part-time job Constant Pseudo-R 2 (%) Number of observations
General
Natives
Immigrants
−0.185 (0.0004) 0.072 (0.0004) 0.061 (0.0001) 0.237 (0.0008) −0.246 (0.0009) 0.370 (0.0007) 0.583 (0.0008) 0.709 (0.0007) 0.020 (0.0001) 0.026 (0.0001) 0.407 (0.0010) −0.696 (0.0004) 2.381 (0.0019) 46.5 13,017,732
−0.186 (0.0003) —
−0.150 (0.0009) —
0.065 (0.0001) 0.241 (0.0004) −0.246 (0.0009) 0.376 (0.0007) 0.588 (0.0008) 0.716 (0.0007) 0.020 (0.0001) 0.025 (0.0001) 0.411 (0.0010) −0.703 (0.0004) 2.319 (0.0020) 50.8 11,832,370
0.035 (0.0003) 0.204 (0.0008) −0.202 (0.0025) 0.314 (0.0026) 0.516 (0.0033) 0.648 (0.0023) 0.014 (0.0002) 0.033 (0.0002) 0.357 (0.0055) −0.616 (0.0013) 2.894 (0.0031) 46.3 1,185,362
Notes: Each column represents a single maximum-likelihood linear regression using the panel of workers. Vaues in parentheses are standard errors. the reference group is native men with no formal education in low-qualification occupations. Time and sector dummies are included.
Table B.2. Oaxaca-Blinder Decomposition
Mean daily wage
(a) Observed natives’ mean daily wage
(b) Observed immigrants’ mean daily wage
(c) Counterfactual immigrants’ mean daily wage
109.0 €
94.7 €
111.2 €
Total wage gap [(b − a)/a] Explained wage gap [(b − c)/a] Unexplained wage gap [(c − a)/a]
Wage gap (%) −13.1 −15.1 2.0
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Appendix C Detecting Discrimination: Hellerstein-Neumark Approach To compare my results with results found using the Hellerstein-Neumark approach, I estimate the firm production function and the firm wage equation. The production function is given by: (14)
Ln(Y jt ) = cons + φk Ln( K jt ) + φL ln( LQ jt ),
using firm level data, where Y jt is the value-added by firm j at time t, K jt is Q depreciated capital30 of firm j at time t, and L jt is the quality-adjusted labor input. LQ jt = Lmns jt + γ w Lwns jt + γ i Lmis jt + γ u Lmnu jt + γ iγ w Lwis jt + γ wγ u Lwnu jt + γ u γ i Lmiu jt + γ iγ wγ u Lwiu jt mns
wns
where L jt is the number of men who are natives and skilled workers; L jt mis is the number of women who are natives and skilled workers; L jt is the mnu number of men who are immigrants and skilled workers; L jt is the numwis ber of men who are natives and unskilled workers; L jt is the number of wnu women who are immigrants and skilled workers; L jt is the number of miu women who are natives and unskilled workers; L jt is the number of men wiu who are immigrants and unskilled workers; and L jt is the number of women who are immigrants and unskilled workers in firm j at time t. The wage equation is given by: (15)
Ln(W jt ) = cons + κ Ln( LQ jt ),
where W jt is the total wage bill paid by firm j at time t. Table C.1 reports the results from the estimations of the production function and wage equations using the total wages and salaries reported in the LIAB as having been paid by the establishment between 1996 and 2004. In column (1), I present parameters estimated from Equation (14) using NLLS regressions; in column (2), I report parameters estimated from Equation (15) using NLLS; and in column (3), I report values of p from tests of equality between parameters in column (1) and (2). Looking first at the production function estimates in column (1), I find that the coefficient for immigrants indicates that foreign workers are somewhat equally productive compared to natives, with an estimate of γ i that is 0.99 (not significantly different from 1). I also find that the productivity of women is surprisingly low and that workers in unskilled occupations produce two-thirds less than workers in skilled occupations. When I look at the 30The survey gives information about investment made to replace depreciated capital. Assuming that d d a constant fraction (d) of capital depreciates by unit of time, K jt = d × K jt ⇒ log( K jt ) = log(d ) + log( K jt ) . Therefore, φK log(d ) goes to the constant term.
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Table C.1. Hellerstein et al. Approach
Immigrants Women Unskilled ϕK ϕL
κ Constant
R2 Number of observations
(1) Output
(2) Wage
(3) p (%) [(1) − (2)]
0.99 (0.09) 0.34 (0.02) 0.33 (0.01) 0.16 (0.01) 0.89 (0.01) —
0.98 (0.03) 0.38 (0.01) 0.47 (0.01) —
54.2
9.29 (0.62) 0.82 12,259
3.7 0.0 —
—
—
1.05 (0.002) 7.47 (0.02) 0.92 17,224
— — — —
Notes: Columns (1) and (2) represent single nonlinear regressions using the panel of firms. The reference group is men who are natives and in skilled occupations. Time dummies are included in every specification. Values in parentheses are standard errors.
wage equation, I find similar patterns for immigrants and women. Workers in unskilled occupations receive salaries that are 53% lower than workers in skilled occupations. Column (3) of Table C.1 reports the p values of the tests of equality of the coefficients from the production function (column (1)) and the wage equation (column (2)). The results for immigrants are not conclusive because the productivity gap and the wage gap are not significantly different from 0. These results are equivalent to results presented in Campos-Vazquez (2008), which uses the Hellerstein-Neumark approach and the same data set used in this article to test for wage discrimination against immigrants in Germany. As did Campos-Vazquez (2008), I find that when I use the Hellerstein-Neumark approach and this data set, immigrants are not discriminated against. But this result is different from the one that I obtain using the new method presented in this article. The two methods produce different results if segregation exists or if β ≠ 1 (see the Data section). Evidence suggests that both sources of bias (segregation and linearity) are empirically relevant in the case of immigrants in Germany. Immigrants are found to be disproportionally allocated in good firms, and β is found to be significantly lower than 1 in every specification. The results for women show that the productivity gap between men and women exceeds the wage gap. The wedge between relative wages and relative productivity is −0.04 (= 0.34 − 0.038), and the p value of the test of the equality of relative wages and relative productivity for women is 3.7%. The Hellerstein-Neumark approach would conclude that men are being discriminated against.
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References Addison, John, Thorsten Schank, Claus Schnabel, and Joachim Wagner. 2006. Works councils in the production process. Journal of Applied Social Science Studies 126(2): 251–83. Aeberhardt, Romain, and Julien Pouget. 2010. National origin differences in wages and hierarchical positions: Evidence on French full-time male workers from a matched employeremployee dataset. Annals of Economics and Statistics 99(100): 117–39. Aigner, Dennis, and Glen Cain. 1977. Statistical theories of discrimination in labor markets. Industrial and Labor Relations Review 30: 175–87. Alda, Holger, Stefan Bender, and Hermann Gartner. 2005. European Data Watch: The linked employer-employee dataset created from the IAB Establishment Panel and the processproduced data of the IAB (LIAB). Journal of Applied Social Science Studies 125(2): 327–36. Altonji, Joseph, and Rebecca Blank. 1999. Race and gender in the labor market. In Orley C. Ashenfelter and David Card (Eds.), Handbook of Labor Economics, Vol. 3C, pp. 3143–259. Amsterdam: Elsevier, North Holland. Arellano, Manuel, and Stéphane Bonhomme. 2012. Identifying distributional characteristics in random coefficient panel data models. Review of Economic Studies 79(3): 987–1020. Arrow, Kenneth. 1973. The theory of discrimination. In Orley Ashenfelter and Albert Rees (Eds.), Discrimination in Labor Markets, pp. 3–33. Princeton, NJ: Princeton University Press. Aydemir, Abdurrahman, and Mikal Skuterud. 2008. The immigrant wage differential within and across establishments. Industrial and Labor Relations Review 61(3): 334–52. Bartolucci, Cristian. 2013. Gender wage gaps reconsidered: A structural approach using matched employer-employee data. Journal of Human Resources 48(4): 998–1034. Becker, Gary. 1971. The Economics of Discrimination. Chicago: University of Chicago Press. Black, Dan A. 1995. Discrimination in an equilibrium search model. Journal of Labor Economics 13: 309–34. Borjas, George J. 1999. The economic analysis of immigration. In Orley C. Ashenfelter and David Card (Eds.), Handbook of Labor Economics, Vol. 3C, pp. 1697–1760. Amsterdam: Elsevier, North Holland. Bowlus, Audra, and Zvi Eckstein. 2002. Discrimination and skill differences in an equilibrium search model. International Economic Review 43(4): 1309–45. Bratsberg, Bernt, and James Ragan. 2002. The impact of host-country schooling on earnings. Journal of Human Resources 37(1): 63–105. Campos-Vazquez, Raymundo. 2008. Relative wages and relative productivity of immigrants in Germany. Unpublished manuscript. Carnevale, Anthony, Richard Fry, and Lindsay Lowell. 2001. Understanding, speaking, reading, writing, and earnings in the immigrant labor market. American Economic Review 91(2): 159–64. Chiswick, Barry, and Paul Miller. 1995. The endogeneity between language and earnings: International analyses. Journal of Labor Economics 13(2): 246–87. Coate, Stephen, and Glenn Loury. 1993. Antidiscrimination enforcement and the problem of patronization. American Economic Review 83(2): 92–98. Crepon, Bruno, Nicolas Deniau, and Sebastien Pérez-Duarte. 2003. Productivité et salaire des travailleurs âgés. Revue française d’économie 18(1): 157–85. Dong, Xiao-yuan, and Liqin Zhang. 2009. Economic transition and gender differentials in wages and productivity: Evidence from Chinese manufacturing enterprises. Journal of Development Economics 88(1): 144–56. Dustmann, Christian, and Arthur van Soest. 2002. Language and the earnings of immigrants. Industrial and Labor Relations Review 55(3): 473–92. Ferber, Marianne, and Carole Green. 1982. Traditional or reverse sex discrimination? A case study of a large public university. Industrial and Labor Relations Review 35(4): 550–64. Friedberg, Rachel. 2000. You can’t take it with you? Immigrant assimilation and the portability of human capital. Journal of Labor Economics 18(2): 221–51. Griliches, Zvi, and Jacques Mairesse. 1998. Production functions: The search for identification. In Zvi Griliches (Ed.), Practicing Econometrics: Essays in Method and Application, pp. 383–411. Cheltenham, UK: Edgar Elgar.
Downloaded from ilr.sagepub.com at Univ Studi Torino on November 18, 2014
1202
ILR Review
Hellerstein, Judith, and David Neumark. 1998. Wage discrimination, segregation, and sex differences in wage and productivity within and between plants. Industrial Relations 37: 232–60. ——. 1999. Sex, wages, and productivity: An empirical analysis of Israeli firm-level data. International Economic Review 40(1): 95–123. ——. 2007. Production function and wage equation estimation with heterogeneous labor. In Ernst E. Berndt and Charles R. Hulten (Eds.), Hard-to-Measure Goods and Services: Essays in Honor of Zvi Griliches, pp. 31–71. Chicago: University of Chicago Press. Hellerstein, Judith, David Neumark, and Kenneth Troske. 1999. Wages, productivity, and worker characteristics: Evidence from plant-level production function and wage equations. Journal of Labor Economics 17(3): 409–46. ——. 2000. Market forces and sex discrimination. Journal of Human Resources 37: 353–80. Lopez-Acevedo, Gladys, Monica Tinajero, and Marcela Rubio. 2005. Mexico: Human capital effects on wages and productivity. World Bank Policy Research Working Paper No. 3791. Washington, DC: World Bank. Lundberg, Shelly. 1991. The enforcement of equal opportunity laws under imperfect information: Affirmative action and alternatives. Quarterly Journal of Economics 106(1): 309–26. Lundberg, Shelly, and Richard Startz. 1983. Private discrimination and social intervention in competitive labor markets. American Economic Review 73: 340–47. [OECD] Organisation for Economic Co-operations and Development. 2008. Employment outlook. Paris: OECD. Olley, Steven, and Ariel Pakes. 1996. The dynamics of productivity in the telecommunications equipment industry. Econometrica 64(6): 1263–97. Ottaviano, Gianmarco, and Giovanni Peri. 2012. Immigration and the national wages: Clarifying the theory and the empirics. Journal of the European Economic Association 10(1): 157–92. Paserman, Daniele. 2013. Do high-skill immigrants raise productivity? Evidence from Israeli manufacturing firms, 1990–1999. IZA Journal of Migration 2(6): 1–31. Petersen, Trond, Vemund Snartland, and Eva Milgrom. 2006. Are female workers less productive than male workers? Research in Social Stratification and Mobility 25(1): 13–37. Phelps, Edmund 1972. The statistical theory of racism and sexism. American Economic Review 62(4): 659–61. Rickne, Johanna. 2012. Gender, wages, and social security in China’s industrial sector. Review of Income and Wealth 58(2): 307–29. Ridder, Geert, and Gerald J. van den Berg. 2003. Measuring labor market frictions: A crosscountry comparison. Journal of the European Economic Association 1: 224–44. Rudolph, Hedwig. 1994. Dynamics of immigration in a nonimmigrant country: Germany. In Heinz Fassmann and Rainer Münz (Eds.), European Migration in the Late Twentieth Century, pp. 113–27. Aldershot, UK: Edward Elgar. Sweetman, Arthur. 2004. Immigrant source country educational quality and Canadian labour market outcomes. Research Paper Series No. 234, Statistics Canada Analytical Studies Branch. Van Biesebroeck, Johannes. 2009. Wage and productivity premiums in sub-Saharan Africa. In Stefan Bender, Julia Lane, Kathryn L. Shaw, Fredrik Andersson, and Till von Wachter (Eds.), The Analysis of Firms and Employees: Quantitative and Qualitative Approaches, pp. 345– 71. Chicago: University of Chicago Press. Verner, Dorte. 1999. Wage and productivity gaps: Evidence from Ghana. World Bank Policy Research Working Paper No. 2168. Washington, DC: World Bank.
Downloaded from ilr.sagepub.com at Univ Studi Torino on November 18, 2014
