Pierpaolo Parrotta
email: p.parrotta@maastrichtuniversity.nl.

Dario Pozzoli

Mariola Pytlikova

Labor Diversity and Firm Productivity

Keywords: JEL Classication: J24, J61, J82, L20 Labor diversity, substitutability, complementarity, communication barriers, total factor productivity

Using a matched employer-employee data-set, we analyze how workforce diversity associates with the productivity of rms in Denmark, following two main econometric routes. In the rst one, we estimate a standard Cobb-Douglas function, calculate the implied total factor productivity and relate the latter to diversity statistics in a second stage. This reduced-form approach allows us to identify which types of labor heterogeneity appear to descriptively matter. In the second approach, we move toward a richer production function specication, which takes dierent types of labor as inputs and that allows for exible substitution patterns, and possible quality dierences between types. Both methods show that workforce diversity in ethnicity is negatively associated with rm productivity. The evidence regarding diversity in education is mixed.

Introduction

Diversity in the labor force is an increasing reality in many developed countries. This diversity results from, among other things, the following major factors: policy measures that counteract population aging and antidiscrimination measures, the growth in immigration from diverse countries experienced in recent decades and the educational and skill upgrading of workforces.

1 All of these factors lead to increasing diversity within the labor force in terms of age, gender, ethnicity and skills.

We observe increasing diversity across many workplaces and often hear about the importance of further internationalization and demographic diversication for rms. In many countries, rms' hiring decisions are aected by governmental armative action policies. Additionally, rms are under social pressure to increase diversity. At the same time, rms are challenged by the constantly changing demand for goods and services, as well as by new customers and markets, in today's globalized world. A diverse workforce may be a key factor in helping rms to understand and meet these new needs.

The popular press usually emphasizes workforce diversity as benecial for rms, but is this really true? Do rms benet from labor diversity and does it generate competitive advantage? What is the relationship between workplace labor diversity and rm performance? Although the issue is very important, there is considerable ambiguity surrounding this topic.

Economic theory suggests that workforce diversity may aect rm performance dierently and through various channels. Diversity in skills and education may generate knowledge spillover among the employees within a rm (as long as workers' knowledge sets do not overlap and are relevant to one another), which positively aects rm performance [START_REF] Lazear | Globalisation and the Market for Team-Mates[END_REF]. However there are certain activities for which having workers with similar skills and education is preferable, as in the case of [START_REF] Kremer | The O-Ring Theory of Economic Development[END_REF] O-ring production function, where prot-maximizing rms should match workers of similar skills/education together. Similarly, diversity in age can be benecial to rms because the human capital of younger and older workers can complement each other. Younger employees have knowledge of new technologies and IT, and older employees have a better understanding of (and more experience with) intra-rm structures and the operating process 1 Demographic projections by the United Nations suggest that during the next four decades, populations in Europe might ceteris paribus decline by 12 % (United Nations, 2000). The main factor responsible for population aging is a large decline in the total fertility rate over the last half century. As a consequence of this trend, governments have adopted a number of measures to counteract the problem of population aging, including policies that encourage people to work longer, to increase female labor participation and to attract skilled immigrants. In many countries, governments have increased the regular and early retirement age, restricted access to early retirement by changing economic incentives and promoted anti-discrimination measures related to age. Female labor participation has grown in most of the world during the last century (OECD, 2005). This growth is partly due to policies encouraging women to work, e.g., better childcare and parental leave provisions and gender anti-discrimination measures. Furthermore, we can observe an increase in immigration, including to developed countries, and a broader diversity of immigrants with respect to their countries of origin [START_REF] Adsera | The Role of Language in Shaping International Migration: Evidence from OECD Countries 1985-2006[END_REF][START_REF] Pedersen | Selection and Network Eects -Migration Flows into OECD Countries 1990-2000[END_REF]). As a result of this change, the diversity of the workforce with respect to gender, age and ethnicity has increased. Finally, as a consequence of the worldwide globalization process and skill-biased technological changes, governments in many countries have taken steps to increase the skill level of the workforce (e.g., by increasing the supply of university-educated people and enhancing the availability of lifelong learning). [START_REF] Lazear | Personnel Economics for Managers[END_REF]. However, [START_REF] Becker | The Economics of Discrimination[END_REF] model of co-worker discrimination suggests that demographic heterogeneity among workers may create communication friction if workers are prejudiced and may thus result in some productivity costs.

The expected contribution of ethnic and cultural diversity to rm performance is also unclear. Ethniccultural diversity may aect rm performance negatively because it may (i) hinder potential knowledge transfer among workers due to linguistic and cultural barriers, (ii) reduce peer pressure by weakening social ties and trust, and (iii) create non-pecuniary disutility associated with joining or remaining in a ethnically diverse rm [START_REF] Lazear | Globalisation and the Market for Team-Mates[END_REF]. A similar point regarding trust is made by [START_REF] Glaeser | Measuring Trust[END_REF] and [START_REF] Alesina | Who Trusts Others?[END_REF], who show that people often distrust members of other ethnic groups and tend to prefer interacting in culturally homogeneous communities. Conversely, ethnic diversity can be benecial to rm performance, improving decision making and problem solving (Hong and[START_REF] Hong | Problem Solving by Heterogeneous Agents[END_REF]2004), stimulating the creation of new ideas and favoring knowledge transfers [START_REF] Berliant | Knowledge Creation as a Square Dance on the Hilbert Cube[END_REF]. Further, workforce diversity may provide useful information to a rm about a product market, which can enhance the rm's ability to compete in global markets [START_REF] Osborne | The Deceptively Simple Economics of Workplace Diversity[END_REF][START_REF] Rauch | Overcoming Informational Barriers to International Resource Allocation: Prices and Ties[END_REF].

To the best of our knowledge, the empirical evidence concerning diversity and economic performance is fairly scarce, and most of the previous work in this area has employed case studies of one rm (e.g., [START_REF] Hamilton | Team Incentives and Worker Heterogeneity: An Empirical Analysis of the Impact of Teams on Productivity and Participation[END_REF][START_REF] Hamilton | Diversity and Productivity in Production Teams[END_REF][START_REF] Kurtulus | What Types of Diversity Benet Workers? Empirical Evidence on the Eects of Co-Worker Dissimilarity on the Performance of Employees[END_REF]; [START_REF] Leonard | Diversity, Discrimination, and Performance[END_REF] or has used aggregate regional data (e.g., Ottaviano and[START_REF] Ottaviano | The Economic Value of Cultural Diversity: Evidence from US Cities[END_REF]2011;[START_REF] Suedekum | Cultural Diversity and Local Labor Markets[END_REF]. The use of more comprehensive data in this eld is fairly rare [START_REF] Barrington | Workforce Diversity and Productivity: An Analysis of Employer-Employee Matched Data[END_REF][START_REF] Iranzo | Skill Dispersion and Firm Productivity: An Analysis with Employer-Employee Matched Data[END_REF][START_REF] Navon | Human Capital Spillovers in the Workplace: labor Diversity and Productivity[END_REF]; Grund and Westergaard-Nielsen, 2008, Garnero and Rycx, 2013). Furthermore, most previous studies have focused on only one dimension of diversity, with the studies by [START_REF] Barrington | Workforce Diversity and Productivity: An Analysis of Employer-Employee Matched Data[END_REF], [START_REF] Kurtulus | What Types of Diversity Benet Workers? Empirical Evidence on the Eects of Co-Worker Dissimilarity on the Performance of Employees[END_REF] and [START_REF] Leonard | Diversity, Discrimination, and Performance[END_REF] being the only exceptions, and none of these studies has determined the eect of diversity on rm performance. Within this largely explorative and descriptive literature, there seems to be some consensus with respect to skill diversity as a positive factor in rm performance [START_REF] Hamilton | Team Incentives and Worker Heterogeneity: An Empirical Analysis of the Impact of Teams on Productivity and Participation[END_REF][START_REF] Hamilton | Diversity and Productivity in Production Teams[END_REF][START_REF] Leonard | Diversity, Discrimination, and Performance[END_REF][START_REF] Iranzo | Skill Dispersion and Firm Productivity: An Analysis with Employer-Employee Matched Data[END_REF][START_REF] Navon | Human Capital Spillovers in the Workplace: labor Diversity and Productivity[END_REF]Kurtulus, 2011, Garnero andRycx, 2013), but the evidence regarding diversity along ethnic and demographic lines is rather mixed. Case studies, for example, nd that diversity with regard to age and race is negatively associated with rm performance [START_REF] Hamilton | Team Incentives and Worker Heterogeneity: An Empirical Analysis of the Impact of Teams on Productivity and Participation[END_REF][START_REF] Hamilton | Diversity and Productivity in Production Teams[END_REF][START_REF] Leonard | Diversity, Discrimination, and Performance[END_REF][START_REF] Kurtulus | What Types of Diversity Benet Workers? Empirical Evidence on the Eects of Co-Worker Dissimilarity on the Performance of Employees[END_REF], whereas studies using aggregated regional data nd a positive correlation between ethnic diversity and performance (e.g., Ottaviano and[START_REF] Ottaviano | The Economic Value of Cultural Diversity: Evidence from US Cities[END_REF]2011;[START_REF] Alesina | Ethnic Diversity and Economic Performance[END_REF][START_REF] Sparber | Racial Diversity and Aggregate Productivity in US Industries: 1980-2000[END_REF][START_REF] Suedekum | Cultural Diversity and Local Labor Markets[END_REF][START_REF] Giovanni | The Eect of Immigration on Productivity: Evidence from U.S. States[END_REF]. As this study, Fox and Smeets (2011) make use of the Danish matched employer-employee data-set and consider dierent skills levels of workers. Their work is primarily focused on quality dispersion within labor rather than on the role that diversity of inputs plays in making rms more or less productive.

In this article, we use a unique register-based linked employer-employee data-set (LEED) from Denmark, which allows us to overcome many of the limitations of previous studies and to contribute to the literature in several ways. We follow two main econometric routes to investigate the association between diversity and rm productivity. First, we estimate a standard Cobb-Douglas function, that includes labor as a single undierentiated input, calculate the implied total factor productivity and in a second stage relate the latter to three relevant dimensions of diversity, i.e., cultural background, education and demographics, and using two alternative specications of diversity, i.e., an aggregate and a disaggregate one. Implementing this reduced-form approach, we also explore the possible mechanisms through which workforce diversity aects rm productivity by attempting to test a set of hypotheses derived from existing theories. Specically, we look at whether the impact of diversity on productivity arises from diversity within distinct occupational groups rather than the establishment's labor force in total, because we expect that diverse problem-solving abilities and creativity will be more strongly related to productivity in white-collar occupations than in blue-collar occupations. Additionally, we investigate the importance of communication costs and the costs of cross-cultural dealing by excluding certain groups of foreigners (i.e., individuals with tertiary education or those who speak a Germanic language) in calculating the ethnic diversity measures. The reduced-form approach allows us to identify which types of labor heterogeneity appear to descriptively matter but it does not formally take into account that the labor input is non-homogeneous in the production function, i.e., labor of dierent types is of dierent quality (Hellerstein et al., 1999;[START_REF] Iranzo | Skill Dispersion and Firm Productivity: An Analysis with Employer-Employee Matched Data[END_REF][START_REF] Fox | Does Input Quality Drive Measured Dierences in Firm Productivity?[END_REF] and Irarrazabal et al., 2011). We therefore move toward a richer production function specication, which takes dierent types of labor as inputs and that allows for exible substitution patterns, and possible quality dierences between types. Specically, we proceed by modeling a value-added production function that, as in the reduced-form approach, is Cobb-Douglas in capital and labor but in which the contribution of the labor aggregate also depends on dierent types of labor in a CES specication.

Our results generally show that labor diversity in ethnicity is negatively associated with rm productivity, while the demographic diversity seems not to matter. These ndings are consistent with earlier research by [START_REF] Lazear | Globalisation and the Market for Team-Mates[END_REF], [START_REF] Glaeser | Measuring Trust[END_REF], [START_REF] Alesina | Who Trusts Others?[END_REF], and may provide evidence that the negative eects of the communication and integration costs that are associated with a more demographically and culturally diverse workforce counteract the positive eects of diversity on rm productivity (i.e., the eects of creativity and knowledge spillover). The evidence regarding labor heterogeneity in terms of education is mixed instead. On the one hand, our reduced-form analysis reveals that labor diversity in education is signicantly and positively associated with rm productivity. On the other hand, the estimated parameters of the structural production function, governing the substitutability between labor types, suggest that it is not generally optimal to have dispersion in labor types along the educational dimension. However estimating a modied specication of the structural model separately for each 2-digits industry suggests that, for about half of the sectors, skill diversity arising only among highly educated workers positively associates with rm productivity.

The structure of the article is as follows: section 2 briey describes the data as well as the methods used to calculate labor diversity at the rm level; section 3 describes the main econometric routes we follow to measure rm productivity and its association with labor diversity. Section 4 reports results on the relationship between diversity and productivity using the reduced-form approach. Section 5 includes results from the structural production function estimation which allows for labor heterogeneity. Section 6 oers concluding remarks.

Data

Data description

The data-set for this empirical investigation is created by merging information from three dierent main sources. The rst source is the Integrated Database for Labor Market Research (henceforth IDA), provided by Statistics Denmark. The IDA is a longitudinal employer-employee register that contains valuable information (age, education, other demographic characteristics, labor market experience and earnings) about each individual employed in the recorded population of Danish rms for the period 1980-2005. Only attrition due to death and permanent migration is included in the data-set. The labor market status of each person is his or her status as of the 30th of November of each year. The retrieved information is aggregated at the rm level to obtain variables such as rm size, workforce composition (including average rm tenure; shares of managers, middle managers, men, highly skilled workers, and technicians; and the shares of employees belonging to each age distribution quartile), labor diversity (see the next section for more details) partial/total foreign ownership and whether the rm is multi-establishment.

The second data source (henceforth referred to as REGNSKAB), also compiled by Statistics Denmark, provides information on rms' business accounts. These data cover the construction and manufacturing industries beginning in 1994, manufacturing beginning in 1995, wholesale trade beginning 1998 and the remaining portions of the service industry from 1999 onwards. From REGNSKAB, the following accounting items are used to estimate the production function: value added, 2 materials (intermediates), capital stock (xed assets) and related industries.

3 Furthermore, linking these variables to a third data source, i.e., the Foreign Trade Statistics Register, we can retrieve information on whether the rm engages in export activities. 2 Computed as the dierence between the total sales and the intermediate costs. 3 The following industries are excluded from the empirical analysis: i) agriculture, shing and quarrying; ii) electricity, gas and water supply; and iii) public services.

Firm level labor diversity

This section focuses on employee diversity at the rm level. Labor diversity is quantied using information regarding workers' gender, age, work experience, highest level of education achieved and nationality. We use the Herndahl index to measure the degree of diversity at the rm level. Unlike traditional diversity measures such as the percentage of employees belonging to a specic group, the Herndahl index combines two quantiable measures: the richness (the number of categories represented within the rm or the workplace) and equitability or evenness (how even the numbers are for the individual categories). We calculate three separate indices to measure the cultural, skill and demographic dimensions of diversity.

Cultural diversity is represented either by the employees' nationalities or by the languages they speak. The various nationalities have been grouped into the following categories: North America and Oceania, Central and South America, Africa, West and South Europe, former Communist countries, East Asia, Other Asia, and Muslim countries. 4 It has been argued in the previous literature that linguistic distance serves as a good proxy for cultural distance [START_REF] Guiso | Cultural Biases in Economic Exchange?[END_REF][START_REF] Adsera | The Role of Language in Shaping International Migration: Evidence from OECD Countries 1985-2006[END_REF]. Therefore, we have grouped employees together by the languages spoken in their countries of origin. This linguistic classication is more detailed than the grouping by nationality. We group countries (using the major ocial language spoken by the majority) at the third linguistic tree level, e.g., Germanic West vs. Germanic North vs. Romance languages. The information on languages is drawn from the encyclopedia of languages entitled Ethnologue: Languages of the World [START_REF] Lewis | Ethnologue: Languages of the World[END_REF]; see the Appendix for more details about the list of countries and the linguistic groups included. Education-related diversity is represented by 6 categories based on information concerning the employees' highest educational level completed (tertiary education, secondary and vocational education, or pre-secondary education). We divide tertiary education into 4 categories, making a distinction between Bachelor's, Master's and postgraduate degrees in the social science, the humanities, engineering and the natural sciences. In a more disaggregated specication, we also decompose secondary education into general high school, business high school and short and long vocational education programs. Finally, the demographic index is built from the intersection of gender and age quartiles or quintiles (8 or 9 categories in total, depending on the level of aggregation).

To measure diversity at the rm level for each dimension, we sum the Herndahl indices calculated for each workplace belonging to the same rm, which are weighted by the number of employees employed in each workplace: 4 Second-generation immigrants are not treated as foreigners in the main analysis. However, we employ a specication in which second-generation immigrants are included in the group of foreigners in the section on the mechanisms driving the eect of workforce diversity on rm productivity.

index hit = W w=1 N w N i 1 - S s=1 p 2 swt
where index hit is the Herndahl diversity index of rm i at time t calculated along the h-th dimension (education-related and demographic), W is the total number of workplaces belonging to rm i, S is the total number of categories of the related diversity dimension, and N w and N i are the total number of employees of workplace w and of rm i. The proportion of the workplace's labor force that falls into each category s of the h-th dimension at time t is represented by the term p swt . 5 The diversity index has a minimum value equal to 0 if only one category is represented within the workplace and a maximum value equal to 1 -1

S if

all categories are equally represented. The index is interpreted as the probability that two randomly drawn individuals in a workplace belong to dierent groups.

Descriptive statistics

Before discussing descriptive statistics for the variables included in the main analysis, we should stress that (a) rms with imputed accounting variables and (b) rms with fewer than 10 employees have been omitted from the main sample. [START_REF] Alesina | Who Trusts Others?[END_REF] The former choice was made to reinforce the reliability of our empirical analysis.

The latter was made to allow all of the investigated rms to potentially reach the highest degree of ethnic diversity when an aggregated specication is used.

7 Altogether, we are able to analyze the productivity of approximately 28,000 rms for the years 1995 to 2005. 9 Moreover, 5 For ethnic diversity, the shares of foreign workers of dierent nationalities/linguistic groups in each workplace have been calculated as follows:

pswt = f oreignersswt f oreignerswt .
6 Approximately 9,000 observations corresponding to almost 2,000 rms are lost by limiting the sample to rms with at least ten employees. Descriptive statistics for the excluded rms are reported in Table A1 of Appendix 2. We have also performed the main analysis including rms with fewer than ten employees (Table A2 of Appendix 2) and we found that the results obtained from the unrestricted sample are qualitatively similar to those reported in the paper. 7 When a linguistic classication is adopted, we adjust the ethnic diversity to take rm size into account. Specically, we standardize the index for a maximum value equal to (1-1/N) when the total number of employees (N) is lower than the number of linguistic groups (S). 8 According to the OECD (2005), the population of Danish rms is mainly composed of small and medium-sized companies; rms with fewer than 50 employees account for 97 % of rms and provide 42 % of the total employment in manufacturing and services. 9 Accounting values are reported in thousands of real DKK. Monetary values are deated by using the GDP deator for the base year 2000 retrieved from the World Bank database. whereas small rms feature larger shares of managers, relatively younger employees and personnel with secondary education, rms with more than 50 employees present larger proportions of women, foreigners and employees with longer tenure. The two groups of rms are comparable in terms of share of employees with a tertiary education, a key element in our empirical analysis, and in terms of rm ownership.

[Insert Table 1 and2 around here] Table 2 reports detailed descriptive statistics for all of the diversity indices by industry, by rm size and by year. As mentioned in the previous subsection, we calculate our diversity measures using two dierent aggregation levels for the categories included in the indices. Cultural diversity is represented by the employees' nationalities in the aggregate specication and by the languages they speak in a more disaggregate one.

Education-related diversity is based on the information concerning the employees' highest educational level completed. In the aggregate index, we distinguish between dierent types of tertiary education while in a more disaggregate one, we also make a eld-related distinction at the level of secondary education. Finally, the demographic index is based on gender and age quartiles or quintiles, depending on the level of aggregation. We observe greater diversity for rms within the manufacturing and the nancial and business service industries, whereas small rms present lower diversity in all dimensions no matter the level of aggregation used. Finally, diversity is increasing slightly over time, especially in ethnicity. This result is consistent with the increasing migration to Denmark observed in recent decades.

3 Empirical strategy

Productivity estimation

As highlighted in the literature concerning the identication of the rm production function, the major issue in the estimation of input parameters is the possibility that there are factors inuencing production that are unobserved by the econometrician but observed by the rm. In such a case, rms may use asymmetrically observed shocks to maximize their prots or to minimize their costs. More specically, it is expected that rms respond to positive (negative) productivity shocks by expanding (reducing) their output, which requires a higher quantity and/or quality of production inputs. Thus, the OLS estimates of the coecients of the inputs that are observed by econometricians may be biased and inconsistent, and error terms and regressors may be correlated. Moreover, it is widely acknowledged that whereas xed-eects (FE) estimation techniques [START_REF] Mundlak | Empirical Production Function Free of Management Bias[END_REF] 10 Both OP and LP suggest semiparametric methods based on (i) the identication of a proxy variable, which is assumed to be a function of time-varying productivity shocks (total factor productivity) and (ii) the denition of conditions under which this function is invertible. The aim is to infer the total factor productivity by using the observed rms' input choices [START_REF] Wooldridge | On estimating rm-level production functions using proxy variables to control for unobservables[END_REF].

11 Although OP and LP are broadly used approaches in the structural identication of the production function, they suer from collinearity and even identication problems, as noted by Ackerberg, Caves and Frazer (2006) (henceforth ACF). Given the timing and dynamic implications of input choices, these researchers raise questions about the LP estimation techniques in particular. Therefore, ACF propose an estimation method built on OP and LP approaches that does not suer from potential collinearity problems: the coecient of labor is no longer estimated during the rst stage (in a value added production function).

Gandhi, Navarro and Rivers (2012) (henceforth GNR) have recently expressed some concerns about the fact that the ACF approach may lead to misleading inferences, as the latter is based on the valueadded specication of the production function, which requires fairly specialized assumptions. They therefore propose an alternative method to ACF where the identication problem caused by exible inputs is solved by a transformation of the rm's short run rst-order condition in a gross-output specication.

Methodological approaches

We follow two main methodological routes to investigate the link between workforce diversity and productivity. In the rst one, we estimate a standard Cobb-Douglas function, calculate the implied total factor productivity and relate the latter to our labor diversity indices in a second stage. This reduced-form approach allows us to evaluate which dimensions of workforce diversity seem to descriptively matter but it does not formally account for the fact that labor of dierent types is of dierent quality (Hellerstein et al., 1999;[START_REF] Iranzo | Skill Dispersion and Firm Productivity: An Analysis with Employer-Employee Matched Data[END_REF][START_REF] Fox | Does Input Quality Drive Measured Dierences in Firm Productivity?[END_REF]and Irarrazabal et al., 2013). We therefore move toward 10 See [START_REF] Ackerberg | Structural Identication of Production Functions[END_REF] for a survey. 11 The approach advocated by Olley and Pakes (1996) is a two-step estimation method. In the rst step, semiparametric methods are used to estimate the coecients of the variable inputs along with the nonparametric function linking productivity to capital and investment. In the second step, parameters of capital inputs are identied based on the assumed dynamics of the productivity process (where productivity is assumed to follow a rst-order Markov process, see [START_REF] Wooldridge | On estimating rm-level production functions using proxy variables to control for unobservables[END_REF]. However, the OP estimation method presents two major drawbacks. First, because adjustment costs create lumpiness in the investment levels, these levels may not respond smoothly to productivity shocks. Second, the OP approach excludes rms that report zero investment levels: it induces a de facto truncation bias. To overcome these drawbacks, LP use a measure of intermediate inputs as a proxy for investment levels. This choice has many benets. First, changes in the intermediate inputs do not typically involve adjustment costs, and the intermediate inputs therefore respond better to productivity shocks than investments. Second, the intermediate inputs provide a simple link between the estimation strategy and the economic theory because they do not typically represent state variables. Third, because intermediate inputs are almost always used in production, the LP approach circumvents the above-mentioned data truncation problem. Moreover, the LP approach suggests three specication tests for evaluating the proxy's performance (Petrin et al. 2004). However, the coecient of the proxy is recovered during the second stage rather than the rst (as in the OP approach). a richer production function specication that (i) accounts for dierent types of labor as inputs and (ii) adjusts for both quality dierences and complementarity/substitutability between labor inputs. Specically, we proceed by modeling a value-added production function that is Cobb-Douglas in capital and labor but in which the contribution of the labor aggregate also depends on dierent types of labor in a CES specication.

One of main advantages of the second approach compared to the reduced-form one is that the former is more structurally motivated and theoretically grounded, as it explitly allows for exible substitution patterns and possible quality dierences between labor types. However, the structural estimation approach is computationally demanding and forces us to model labor dispersion with less exibility and with a higher level of aggregation compared to the reduced form approach, which allows us to test a set of hypotheses and the robustness of our main results by attempting several alternative specications as well as by looking at within occupation diversity. The reduced-form approach furthermore allows to simultaneously look at the three dimensions of diversity (ethnic, educational and demographic) within the same equation, while with the structural method we need to make the stronger assumption that each dimension of diversity enters separately into the production function. Given that both approaches have costs and benets, we view their results as complementary.

Reduced form approach: the empirical association between diversity and productivity

Referring to the literature concerning the estimation of the production functions, we regard the method suggested by ACF as our main approach. Productivity is obtained from a Cobb-Douglas production function containing the value added, Y , the labor, L, and the capital, K. Because input characteristics dier across industries, the production function parameters are estimated separately for each 1-digit sector j. The loglinear rm i production function is specied as follows:

lnY ijt = cons + αlnL ijt + βlnK ijt + u ijt (1)
with t = 1, 2, ..., T. The error term u ijt consists of a time-varying rm specic eect v ijt (unobserved by econometricians) and an idiosyncratic component ε ijt . Following ACF, we assume that

E (ε ijt | l ijt , k ijt , m ijt , l ijt-1 , k ijt-1, , m ijt-1 , ..., l ij1 , k ij1 , m ij1 ) = 0 (2)
where m refers to our proxy variable (materials) and lower-case letters to log-variables. Because past values of ε ijt are not included in the conditioning set, we allow for serial dependence in the pure shock term. However, we need to restrict the dynamics of the productivity process:

E (v ijt | v ijt-1 , v ijt-2 , ..., v ij1 ) = E (v ijt | v ijt-1 ) = f (v ijt-1 ) (3)
for given functions f (•). As in the ACF approach, we assume that the material input is selected after the labor input. As a result, material demand will be a function not only of capital and productivity but also of l :

m ijt = f (k ijt , v ijt , l ijt ) (4)
and assuming that the material demand function is strictly increasing in productivity shock v ijt , we obtain

v ijt = f -1 (k ijt , m ijt , l ijt ) . ( 5
)
Plugging the inverse material demand into the production function, we obtain the rst-stage equation, which serves here only to separate v ijt from ε ijt ,

y ijt = cons + αl ijt + βk ijt + f -1 (k ijt , m ijt , l ijt ) + ε ijt . (6)
The function f -1 (•) is proxied with a polynomial in materials, capital and labor. Therefore, the estimated net output of the idiosyncratic component is used to identify parameters for the inputs in the second stage.

Recalling that v ijt is a rst-order Markov process, we dene a ijt as an innovation that can be correlated with the current values of the proxy variable m ijt and l ijt :

a ijt = v ijt -g (v ijt-1 ) , (7)
where a ijt is mean independent of all information known at t -1 and g (•, •) is also proxied with a lowdegree polynomial in the dependent variables.

12 Given our timing assumption, we proceed by using the moments:

E [a ijt |k ijt , l ijt-1 ] = 0 (8)
to identify coecients for k and l . Using the estimates of the production function parameters, the total factor productivity (henceforth TFP) for rm i at time t in industry j is dened as

T F P ijt = y ijt -αl ijt -βk ijt (9)
Following the computation of TFP values, the relationship between these and alternative measures of diversity can be estimated with OLS in the following equation separately for each 1-digit sector j:

T F P ijt = ζ 0j + ζ 1j (index_ethnic ijt ) + ζ 2j (index_edu ijt ) + ζ 3j (index_demo ijt )+ +ζ cj (C ijt ) + ζ tj + ζ rj + ζ nj + ζ nj ζ tj + x ijt (10)
where ζ 1j , ζ 2j , and ζ 3j measure the associations between TFP and employees' diversity in terms of ethnicity, education and demographic characteristics, respectively; and C ijt , is a vector including workforce composition characteristics, such as the shares of employees belonging to each category included in our diversity indices. [START_REF] Card | Do Immigrant Inows Lead to Native Outows?[END_REF] We think that the inclusion of such shares partly control for the fact that dierent labor types may have dierent qualities. Failing to control for labor quality, the estimated contribution of diversity in the TFP equation [START_REF] Barrington | Workforce Diversity and Productivity: An Analysis of Employer-Employee Matched Data[END_REF] confounds the direct eects of diversity (ζ 1j , ζ 2j , and ζ 3j ) with such quality dierences. We further and explicitly address the issue of labor quality in the structural estimation approach described in the next sub-section. The same vector C ijt also include the share of managers and middle managers and average rm tenure, whether the rm is foreign-owned, whether the rm exports and a multi-establishment dummy, whereas ζ tj , ζ rj ,ζ nj are time, regional and two-digit industry controls, respectively.

Independent estimations of equation ( 10) by 1-digit industry allow us to rule out the possibility that workplace diversity only reects an industry technology choice. Factor intensities and the mix of capital and labor may vary substantially across industries. For example, some technologies might require a set of highly skilled employees working in concert with a set of mid-level employees and a set of low-skill workers.

Other technologies might only require high-skill or low-skill labor. Considering industry-specic results will therefore ensure that variations in the observed diversity of education levels across rms within the same industry will also reect cross-rm dierences in the makeup of the workforce, rather than merely reecting which type of technology the rm has chosen. 14 13 Specically, in the aggregate specication of diversity we control for the shares of foreigners from North America and Oceania, Central and South America, Africa, Western and Southern Europe, former Communist countries, East Asia, Other Asia, and Muslim countries; the shares of employees with compulsory education, with secondary education, and with tertiary education split into 4 main categories (humanities, natural sciences, social sciences and engineering); and the shares of female and male employees belonging to various age distribution quartiles. In the disaggregate specication of diversity, we include the shares of foreigners belonging to each linguistic group, as described in Appendix 1, and the shares of employees with dierent types of education and belonging to various gender-specic age distribution quintiles, as explained in section 3.2. 14 Prior academic research suggests that diversity leads to economic gains or losses depending on industry characteristics [START_REF] Sparber | Racial Diversity and Aggregate Productivity in US Industries: 1980-2000[END_REF][START_REF] Sparber | Racial Diversity and Macroeconomic Productivity across US States and Cities[END_REF]. More specically, diversity seems to increase productivity in sectors that require creative decision making, problem solving, and customer service, but ethnic diversity may decrease productivity in industries characterized by

Structural estimation approach: production function with dierent types of labor

The reduced-form approach described above allows to identify which types of labor heterogeneity appear to descriptively matter but does not formally recognize that labor input is non-homogeneous, i.e., labor of dierent types is of dierent quality (Hellerstein et al., 1999;[START_REF] Fox | Does Input Quality Drive Measured Dierences in Firm Productivity?[END_REF]Irarrazabal et al., 2013).

Therefore we move toward a richer value-added production function, which continues to be Cobb-Douglas in capital and a labor aggregate, but the contribution of the labor aggregate also depends on dierent types of labor in a CES specication. To account for dierences in rms' labor types, we use the observed shares of labor types within a given dimension, i.e. demographic or educational (for a similar specication see Fox and Smeets, 2011; and Irarrazabal et al., 2013). Specically, we use the following generalized Cobb-Douglas production function in capital and labor:

Y ijt = A ijt • [L ijt • E(H 1ijt .....H W ijt )] α • K β ijt (11)
where W represents the maximum number of labor types in a given dimension and the term E(H 1jt .....H W jt ) represents the overall eciency of the labor force of rm i belonging to industry j depending on the shares of these labor types H wijt . 15 Treating the overall eciency as a CES function of the observed shares of labor types, we can express the term E as:

E(H 1ijt .....H W ijt ) = [(H 1ijt ) γ + (η 2 H 2ijt ) γ + .... + (η W H W ijt ) γ ] 1/γ (12)
where the parameters η 2 , ...., η W model the relative dierence in quality between worker type w and worker type 1, i.e. if workers of type w are more (less) productive than type 1, then η w is greater (less) than one. The parameter γ governs instead the complementarity/substitutability between labor types, as the elasticity of substitution is given by 1/(1-γ). Assuming constant returns to each labor type, a parameter of γ larger than one would imply that the labor types are substitutable, the isoquants are concave, the technology is submodular and exibits a taste for employing workers of dierent types (Grossman and Maggi 2000; [START_REF] Bombardini | Unobservable Skill Dispersion and Comparative Advantage[END_REF]). Put it dierently, if γ is larger than one, then dispersion of labor types increases productivity and it is optimal to combine workers of dierent types along a specic dimension [START_REF] Iranzo | Skill Dispersion and Firm Productivity: An Analysis with Employer-Employee Matched Data[END_REF]. By contrast, if γ is smaller than one, there is complementarity (or imperfect substitutability) between labor types [START_REF] Iranzo | Skill Dispersion and Firm Productivity: An Analysis with Employer-Employee Matched Data[END_REF]. This means that the technology is supermodular, the isoquants are convex and dispersion in labor types has a negative eect on productivity. high levels of group work or teamwork and eciency. Our current industry categorizations, however, are too rough for us to test the hypothesis, as jobs of both types (jobs that require creativity versus eciency) are likely to be in each aggregate industry. 15 We have to make sure that every 0 < H wijt < 1, as H wijt taking the value 0 or 1 is not consistent with the Cobb-Douglas framework. We sort this problem out by adding or subtracting a small to any H wijt = 0 or H wijt = 1 (Irarrazabal et al. 2013).

As in case of the standard production function (1), we estimate equation [START_REF] Berliant | Knowledge Creation as a Square Dance on the Hilbert Cube[END_REF] with the ACF approach.

Specically we use the current value of capital, the lagged values of labor and the shares of workers for each labor type w to form a set of the following moment conditions:

E [ã ijt |k ijt , l ijt-1 , H 1ijt-1 , ..., H W ijt-1 ] = 0 (13)
to identify coecients for k, l and the parameters γ and η 2 , ...., η W . As in section 3.2.1, we assume that the innovation term ãijt to the productivity shock ṽijt = f -1 (k ijt , m ijt , l ijt , H 1ijt , ...., H W ijt ) is mean independent of all information known at t -1.

4 Results from the reduced form approach

Main results

As mentioned in the previous section, in the reduced form approach measures of TFP are computed as residuals from the rst step estimation in which the rms' value added is regressed on their capital and labor stocks. The industry-specic elasticities of capital and labor obtained by implementing the ACF approach are reported in the rst panel of Table 3. In the second and third panel of Table 3, we also report the same elasticities estimated using two alternative approaches to ACF. The rst one (OP) allows for the control of sample selection issues and deals with rm exit. [START_REF] Deding | Spatial Mobility and Commuting: the Case of Two-Earner Households[END_REF] The second method (GNR) employs a gross-output instead of a value-added production function. Comparing the estimated elasticities across these methods, we nd that the OP and GNR estimates of the labor coecients are more often smaller than their ACF counterparts while the capital elasticities obtained from OP (GNR) are larger (smaller). These results are generally in line with what has been found in Ackerberg, Caves and Frazer (2006) and Gandhi, Navarro and Rivers (2012).

The main results for the second step using three alternative measures of TFP (ACF, OP and GNR) are shown separately in the three panels of Table 4. As explained in section 3, we describe the empirical association between labor heterogeneity and rm productivity, using two dierent aggregation levels for the categories included in our diversity indices. The results obtained using the more aggregated level are shown in the rst sub-panel of each TFP panel, whereas the results obtained using the disaggregated categories are presented in the second sub-panel.

17 All of the estimated coecients of our diversity measures are reported in standard deviation units in order to compare the relative contributions of each dimension of diversity, 16 We have also investigated whether rm diversity plays a role in terms of rm survival. In most industries, our diversity indices are not signicantly correlated with rm probability of exiting the market. The results are reported in Table A3 of Appendix 2. 17 The estimated coecients on the share variables used as controls in the aggregate specication of diversity are reported in Table A4_1-4_3 of Appendix 2. thereby easing the comparison across magnitudes.

[Insert Table 4 around here] Ethnic diversity is generally negatively associated with rm TFP, whereas the coecients of educational and demographic diversity are positive. The empirical associations between educational diversity are precisely estimated in all industries but transport, whereas the coecient of ethnic diversity is statistically signicant only in the case of manufacturing, construction and wholesale trade. Demographic diversity is never signicantly correlated with rm productivity. All of these results are qualitatively robust across diversity specications and are not substantially aected by the measure of TFP employed, although the estimated correlations between ethnic diversity and productivity are slightly smaller in the both the OP and GNR specications compared to the ACF counterpart. For the sake of brevity, we proceed by discussing the results for the manufacturing and service industries and those obtained using TFP calculated with ACF approach only.

In the manufacturing sector, a standard deviation increase in ethnic diversity is associated with a decrease in rm TFP by 1.3 %, while a standard deviation increase in educational diversity is associated with an increase in rm TFP by 1 %, when an aggregated index is considered. If we focus on the disaggregated index instead, a standard deviation increase in ethnic diversity is associated with a decrease in rm TFP by 1.6 %, while a standard deviation increase in educational diversity is associated with an increase in rm TFP by 2.9 %.

The magnitudes involved in the wholesale and retail trade are qualitatively similar to those estimated in the manufacturing sector.

Testing alternative hypotheses

In the next steps, we attempt to assess which mechanisms drive our results on employee diversity and rm TFP by exploiting the variation in occupations, nationalities and industry characteristics. While these exercises provide useful information on the channels through which diversity is associated with productivity, it is important to underline that they are not conclusive evidence of a particular mechanism. To simplify the presentation of these exercises, we discuss the results for the manufacturing and the wholesale and retail trade industry only 18 and focus on the disaggregated indices. 19

First, we separately calculate the diversity indices for white-and blue-collar occupations and include them all in the same specication. We use this strategy based on the supposition that diversity could play a dierent role for distinct occupational groups and could consequently have varying eects on rm productivity. In particular, we expect that diverse problem-solving abilities and creativity will generate 18 The results for the other industries are reported in Table A5 of Appendix 2. 19 The results obtained using the aggregate indices are qualitatively similar to those obtained using the detailed categorization and are reported in Table A6 of Appendix 2.

higher productivity for white-collar occupations than for blue-collar occupations.

20 Second, we exclude or include certain groups of foreigners in calculating ethnic diversity to test the importance of communication costs and the costs of cross-cultural dealing. The results regarding the association between diversity and rm productivity, calculated separately for the two occupational groups and included in the same regression are reported in the rst two columns of Table 5. Our results show that the correlation of educational diversity with rm productivity is indeed much larger for white-collar occupations than for blue-collar ones.

Moreover, the negative coecient of ethnic diversity among white-collar workers is lower than the coecient associated with blue-collar occupations. Conversely, the eect of demographic diversity is insignicant for both occupational groups. 21 Therefore, our results are consistent with the creativity and knowledge spillovers hypotheses proposed in the theoretical frameworks developed by Hong and[START_REF] Hong | Problem Solving by Heterogeneous Agents[END_REF]2004) and [START_REF] Berliant | Knowledge Creation as a Square Dance on the Hilbert Cube[END_REF].

To investigate the role of cross-cultural dealing, we exclude either foreigners with tertiary education or foreigners who speak a Germanic language. Alternatively, we include second-generation immigrants in calculating ethnic diversity. All of these groups of foreigners are likely to absorb Danish or English (which is the communication language in many businesses in Denmark) more quickly. Therefore, it is plausible that the communication costs associated with ethnic diversity may increase (decrease) after we remove (include) these foreigners, who are likely to speak Danish or English. [START_REF] Gandhi | On the Identication of Production Functions: How Heterogeneous is Productivity[END_REF] The results presented in Table 5, columns 3, 4 and 5 are obtained by including both the standard ethnic diversity, as calculated in the main analysis, and an alternative one in which the second generation of immigrants is treated as non-native and where foreigners with university education or those who speak a Germanic language are included as natives, respectively.

Interestingly, the coecient of ethnic heterogeneity is larger (smaller) in absolute terms, once we exclude (include) foreigners who most likely speak Danish or English, compared to the coecient estimated on the standard ethnic diversity. 23 These ndings are in line with the hypothesis that the communication costs and the costs of cross-cultural dealing within ethnically heterogeneous workforces play a role in terms of rm productivity. However, the results obtained by excluding second generation immigrants, may also be explained by the fact that the latter generally have stronger labor market networks in addition to lower communication costs compared to other foreigners.

[Insert Table 5 around here] 20 This is grounded on the fact that (i) white-collar workers typically (manage) interact with a larger number of employees than blue-collar ones; (ii) white-collar employees are, on average, more educated than employees in other occupations and are therefore more likely to access and exploit their colleagues' knowledge heterogeneity; and (iii) white-collar employees are typically more inuential in rms business plans and strategies. 21 Hypothesis testing also reveals that the coecients of diversity for white-collar occupations are statistically dierent from the coecients of diversity for blue-collar occupations, especially for the ethnic dimension. 22 According to the existing literature, individuals have an easier time acquiring a foreign language if their mother language is linguistically closer to the foreign language (Isphording and Otten, 2011; [START_REF] Chiswick | The Endogeneity between Language and Earnings: International Analyses[END_REF]. 23 Hypothesis testing reveals that the two estimated coecients are signicantly dierent from one another.

We next examine the dierent mechanisms by which diverse workforces are associated with rm productivity by looking at dierent industries and rm categories. 24 First we do not nd that the coecients of the diversity indices dier for rms that are more open to trade.

25 Therefore, our analysis does not support the hypothesis that workforce diversity provides benecial information to rms from other countries and markets and, in this way, creates positive eects on rm productivity [START_REF] Osborne | The Deceptively Simple Economics of Workplace Diversity[END_REF][START_REF] Rauch | Overcoming Informational Barriers to International Resource Allocation: Prices and Ties[END_REF][START_REF] Munshi | Networks in the Modern Economy: Mexican Migrants in the US Labor Market[END_REF]. Second, we look at whether the correlation of diversity and TFP is dierent for rms in high-tech industries, which tend to require higher levels of creative and problem-solving activities. [START_REF] Grund | Age Structure of the Workforce and Firm Performance[END_REF] Our results reveal that the hypothesis on creativity is not supported by this empirical exercise because the coecients of both the education and the ethnic diversity index are not statistically dierent across the two groups of industries, namely those with below and above average R&D intensity. Finally, we nd that the positive (negative) eects of educational (ethnic) diversity are statistically stronger (weaker) in the subsample of industries with increasing employment compared to industries with declining employment. This is in line with the hypothesis that growing rms are more likely to benet from diversity because they hire younger people and foreign individuals more often than do shrinking rms.

Sensitivity analysis

In the next step, as a part of our sensitivity analysis, we evaluate the variations in the coecients estimated on labor diversity that result when diversity is computed in various ways. As in the previous sub-section, we discuss the results for the manufacturing and the wholesale and retail trade industry only and focus on the disaggregated indices.

27 In particular, we use two alternative diversity indices: the Shannon-Weaver entropy index and the richness index. The entropy index is considered to be one of the most profound and useful diversity indices in biology [START_REF] Maignan | Bio-Ecological Diversity vs. Socio-Economic Diversity: A Comparison of Existing Measures[END_REF]. The richness index includes a number of categories observed for each dimension of interest; it does not include the evenness dimension. The results are shown in Table 6, columns 1 and 2, and both sets of results are consistent with our main ndings. Next, we include a Herndhal index for the type of tertiary education (this index now has only 4 categories: engineering, natural sciences, social sciences and humanities) and the standard deviation of the years of education and age. This allows us to treat age as a cardinal variable, and to disentangle the eects associated with the amount of education from those related to the type of tertiary education. Table 6, column 3, reports statistically insignicant coecients on both standard deviations and an estimate on educational diversity (the Herndhal 24 The results of these additiobnal empirical exercises are all reported in Table A7 of Appendix 2. 25 Specically we augment equation ( 2) by including interactions between the export dummy and diversity in ethnic, educational and demographic dimensions and we nd that the interaction terms are not precisely estimated and are not jointly signicantly dierent from zero. 26 Specically, we divide industries into two groups dened by whether their aggregate level of R&D expenditure as a share of employment is above or below the median recorded for the overall economy. 27 The results for the aggregated indices are reported in Tables A8 of Appendix 2.

index for the type of tertiary education) that is in line with the nding discussed in the main analysis. These ndings, together with the results obtained from occupation-specic diversity (Table 5, columns 1 and 2), may suggest that the positive association between educational diversity and rm TFP is mainly driven by the white-collar occupations, who are very likely to have tertiary education, or by workers with dierent types of tertiary education.

We then divide rms by size and evaluate whether there is any change in the coecients of workforce diversity for small rms (those with fewer than 50 employees), medium-sized rms (those with 50-100 employees) and large rms (those with more than 100 employees). [START_REF] Hamilton | Team Incentives and Worker Heterogeneity: An Empirical Analysis of the Impact of Teams on Productivity and Participation[END_REF] The eects of diversity could be more benecial to larger rms because the organizational and diversity management practices of such rms are well established and formalized, and thus, they are more likely to introduce policies that can help to sustain a diversied workforce and to counteract the potential costs associated with diversity. On the one hand, the coecients on the ethnic diversity index are negative for dierently sized rms, with the largest coecient associated with large rms, as reported in columns 4, 5 and 6 of Table 6. On the other hand, educational diversity is more important for large than for medium-sized rms. We can therefore conclude that larger rms are more likely to benet from educational diversity but the latter are not necessarily more successful in counteracting the costs of ethnic diversity compared to smaller rms.

Given that large cities usually host many immigrants and highly skilled workers and also house a high percentage of productive rms, we conduct an additional sensitivity check by removing the only real agglomeration area in Denmark, namely Copenhagen and its environs. The results concerning this robustness check are reported in column 7 of Table 6 and do not qualitatively dier from the main results.

Furthermore, because labor diversity has been computed at the rm level (by weighting the average of the Herndahl indices computed at the workplace level), we evaluate how the results change if multi-establishment rms are excluded from the sample. The last column of Table 6 reports the results. These ndings do not signicantly dier from the main results.

[Insert Table 6 around here] 28 It is important to clarify that the scope for diversity is not mechanically increasing in rm size. This can be explained with a simple example. Let's assume that there are 5 possible categories of employees, and let's compare two rms with 10 and 100 employees, respectively. The two rms would feature exactly the same level of diversity, if their workforces equally represented all possible categories, i.e. if there were 2 and 20 employees for each category in the rst and second rm, respectively. For both rms the diversity index would equal (1 -((0.2) 2 * 5)).

Endogeneity

Even if it is not clear whether rms always have control over their workforce diversity, 29 we cannot completely rule out that rms endogenously choose the level of labor diversity in order to improve their productivity. This would imply that the ndings in the previous section are likely to be biased estimates. We therefore attempt a causal eect analysis by using an instrumental variable (IV) strategy to address these potential endogeneity issues. More specically, we instrument our diversity variables with indices of workforce diversity in cultural background, education and demographic characteristics, computed at the commuting area, 30 where the rm is located. [START_REF] Hong | Problem Solving by Heterogeneous Agents[END_REF] Given that diversity in a given commuting area may be a function of the current rms' demand for diversity, we predict the current composition of the labor supply at the commuting area level by using its historical composition and the current population stocks (for similarly computed instruments see [START_REF] Hong | Groups of Diverse Problem Solvers Can Outperform Groups of High-Ability Problem Solvers[END_REF] In particular we use workforce composition at the commuting areas from the year 1990. [START_REF] Iranzo | Skill Dispersion and Firm Productivity: An Analysis with Employer-Employee Matched Data[END_REF] In this approach, for example, the instrument for ethnic diversity is calculated using the predicted share of immigrants from country c and living in a commuting area l at time t, mclt . The latter is computed using the early 1990's stock of immigrants from country c living in l and its current population of immigrants at time t : 29 It seems reasonable to assume that the hiring and ring costs for labor or the xed costs of changing the workforce characteristics can generally last longer than a period. This suggests that the workforce composition and diversity are very likely to be persistent over time. Therefore, rms may not promptly respond to TFP shocks with immediate changes to their diversity mix. 30 The so-called functional economic regions or commuting areas are identied using a specic algorithm based on the following two criteria: rstly, a group of municipalities constitutes a commuting area if the interaction within the group of municipalities is high compared to the interaction with other areas; second, at least one municipality in the area must be a center, i.e., a certain share of the employees living in the municipality must also work in the municipality [START_REF] Andersen | Commuting Areas in Denmark[END_REF]. In total, 104 commuting areas are identied. 31 Unfortunately, in our data-set, it is not possible to observe in which area each establishment of a multi-establishment rm is located. For multi-establishments rms, location information is only provided at the headquarter level. However, we do not think this represents a serious problem as multi-establishment rms constitute only 11 % of our sample. This is also conrmed by the fact that estimating our IV models on the sub-sample of mono-establishment rms provide qualitatively similar results to the ones obtained from the full sample. These additional results are reported in Table A9 of Appendix 2. Note that the estimation of the parameters on diversity cannot be carried out for transport sector because of the low number of observations. 32 Reverse causality however may be still an issue for big rms employing a large fraction of the local labor force. However, running our IV models on the subsample of rms with fewer than 50 employees provides qualitatively similar results to those obtained from the full sample, as shown in Table A9 of Appendix 2. Note that the estimation of the parameters on diversity cannot be carried out for transport sector because of the low number of observations. 33 We choose the year 1990 as a historical base for our predictions because we believe that the lag of 5-13 years should be a sucient lag for the purposes of our IV construction. In addition, the development in immigration to Denmark also supports the choice. The 1980s and 1990s were characterized by rather restrictive immigration policy with respect to economic migrants from countries outside the European Union (EU), which made it dicult for rms in Denmark to hire applicants from the international pool of applicants (due to the consequences of the oil crisis). Immigration to Denmark from those countries from the 1980s to the mid-1990s was characterized by immigration on the basis of humanitarian reasons and family reunion. However, since then, Denmark has further tightened its immigration policy (even laws concerning family reunication and asylum). In particular since the 2001 election, in which the right-wing Danish People's Party (DF) with its anti-immigration agenda acquired signicant political power, Denmark's immigration policy became one of the strictest in the world. For rms, it meant almost zero possibilities to hire international workers from countries outside the EU, which has often been criticized by the Confederation of Danish Industry (DI). Given these historical developments, we decided to use shares of immigrants from 1990 as a base for our predictions.

mclt = stock cl1990 C c=1 stock clt (14)
We believe that diversity at the commuting area level may represent a suitable supply driven instrument for workplace level diversity 34 because commuting areas in Denmark (except for the area around Copenhagen) 35 are typically relatively small, and are therefore very likely recruit workers from a given local supply of labor, which is characterized by a certain degree of heterogeneity. This argument is further reinforced by the role of networks in the employment process [START_REF] Montgomery | Social Networks and Labor Market Outcomes: Toward an Economic Analysis[END_REF][START_REF] Munshi | Networks in the Modern Economy: Mexican Migrants in the US Labor Market[END_REF]. Thus, rms placed in areas with high labor diversity are also more likely to employ a more diverse workforce. It is important to emphasize that although the commuting areas are not closed economies, in the sense that workers are free to move in and out, there is clear evidence of low residential mobility [START_REF] Deding | Spatial Mobility and Commuting: the Case of Two-Earner Households[END_REF], which seems to support the appropriateness of our IV strategy.

The results of the rst and the second stage of this IV exercise are shown in Table 7 and8, respectively. In addition to the economic motivation for the instruments presented above, their statistical validity is largely conrmed by the F-statistics reported in Table 7.

[Insert Table 7 around here] The estimation adopting the IV strategy yields qualitatively similar results to those reported in the main analysis (Table 4) and are in line with the conclusions drawn in the previous sub-sections. Table 8 reveals a statistically signicant and positive (negative) relationship between educational (ethnic) diversity and rm productivity, especially within the manufacturing and the wholesale and retail trade sectors. However, the estimated parameters on diversity and their standard errors are generally larger compared to the results, in which diversity is treated as exogenous.

[Insert Table 8 around here] Although our instrument is based on the historical composition of the local labor supply, however, it may still be the case that our identication strategy is invalidated by the fact that rms choose locations that are historically richer in population diversity. [START_REF] Kurtulus | What Types of Diversity Benet Workers? Empirical Evidence on the Eects of Co-Worker Dissimilarity on the Performance of Employees[END_REF] To indirectly assess the extent to which the endogeneity 34 Summary statistics of our supply driven instruments reveal that they are persistent over time, i.e. most of the variation is between commuting areas and that the overtime within variation is modest. Specically, the overall, between, and within variations of the commuting area ethnic diversity are 0.163, 0.161, and 0.026, respectively. The same statistics are 0.072, 0.071, and 0.012 for the commuting area educational diversity and 0.045, 0.043, and 0.01 for the commuting area demographic diversity. Similar descriptive statistics are obtained by excluding Copenhagen and its environs. 35 Excluding rms located in Copenhagen and its environs from the IV estimations provides similar results to those obtained from the main sample, as shown in Table A9 of Appendix 2. 36 Previous studies on rm localization (Krugman 1991, Audretsch and Feldman 1996, Adams and Jae 1996, Alcacer and Chung 2010, Delgado et al. 2010), however, have shown that the location choices are mainly driven by the access to local innovation potential and knowledge spillovers and also by the size of the local demand, the proximity to customers and suppliers and the quality of local physical infrastructure.

of location aects our results, we have also estimated the IV models on a sub-sample of rms, for which this issue may be less important, i.e. rms which enter the market before the reference year used to predict diversity at the commuting area level (1990). Unfortunately the information about the establishment year is available only for about 30 percent of the total sample. Findings obtained from this additional robustness check are reported in Table A9 of Appendix 2 and they are qualitatively in line with those reported in Table 8, but they are generally less precisely estimated due to the fact that the sample size considerably shrinks.

Note that the estimation of the parameters on diversity cannot be carried out for construction and transport sectors because of the low number of observations. All in all, we think that, although our IV strategy presents some potential aws and we should interpret our IV results with caution, this additional analysis provides us with a useful tool to assess the robustness of the directions of the associations between diversity and productivity in terms of the methodology used to estimate them. Moreover, the fact that the results are qualitatively similar whether or not instruments are used, supports the initial assumption that the estimated TFP represents an exogenous rst-order Markov process, i.e. these results support the assumption for the rst stage of the reduce-form approach (see equations 1-8) to be valid.

Results from the structural estimation approach

The previous section has explored the empirical associations between labor diversity and TFP in a reducedform fashion and have served to identify which types of labor heterogeneity appear to descriptively matter.

On the basis of these results, it seems that labor diversity in ethnicity and education are strongly correlated with rm productivity with opposite signs, while demographic diversity is not signicantly associated with rm TFP.

While our results show that diversity in both the ethnic and the educational dimensions plays an important role, we immediately recognize that labor input is non-homogeneous (Hellerstein et al., 1999;[START_REF] Fox | Does Input Quality Drive Measured Dierences in Firm Productivity?[END_REF]and Irarrazabal et al., 2011) and that dispersion in these labor types may have an impact on rm output [START_REF] Iranzo | Skill Dispersion and Firm Productivity: An Analysis with Employer-Employee Matched Data[END_REF]. Therefore in this section we discuss the results obtained by estimating a richer production function specication that takes dierent types of labor as inputs and directly models a set of parameters adjusting for quality dierences and governing complementarity/substitutability between these dierent labor inputs. Specically, we show the results obtained from two alternative specications. In the rst one, we include in the overall eciency term E (see equation 12) the shares of workers belonging to each ethnic group used in the aggregate specication of our ethnic diversity index, including natives. In this case we can re-write E as follows:

E(N ijt .....F 8ijt ) = [(N ijt ) γ + (η 1 F 1ijt ) γ + .... + (η 8 F 8ijt ) γ ] 1/γ (15)
where N ijt is the share of natives, while F 1ijt , ...., F 8ijt are the share of foreigners belonging to the eight categories used to construct the ethnic diversity index in the aggregate specication. Table 9 shows the estimated coecients of the production function [START_REF] Berliant | Knowledge Creation as a Square Dance on the Hilbert Cube[END_REF], where the overall eciency of the labor force, E, is expressed by equation [START_REF] Chiswick | The Endogeneity between Language and Earnings: International Analyses[END_REF]. As in the reduced form approach, production function ( 11) is estimated with ACF. [START_REF] Kremer | The O-Ring Theory of Economic Development[END_REF] The coecients on labor (capital) are slightly larger (smaller) but in line with those obtained from a standard specication of the production function, as reported in Table 3. These ndings are consistent with [START_REF] Hellerstein | Production Function and Wage Equation Estimation with Heterogeneous Labor: Evidence from a New Matched Employer-Employee Data Set[END_REF], who state that rms' labor heterogeneity and quality is not a necessary component to the estimation of the rest of the production function. We also investigate how the introduction of the term E in the production function aects the measurement of TFP, by comparing TFP calculated from a standard production function (see equation 9) with TFP calculated from the non-homogenous production function [START_REF] Berliant | Knowledge Creation as a Square Dance on the Hilbert Cube[END_REF]. Standard TFP estimates have a tendency to be larger than the non-standard TFP measures. This is clearly shown by plotting the kernel densities of standard and non-standard TFP measures (see Figure 1). Applying Kolmogorov-Smirnov (KS) tests conrm that the distribution of standard TFP stochastically dominates the distribution of non-standard TFP. [START_REF] Krugman | Geography and Trade[END_REF] The fact that standard TFP may constitute an up-ward biased measure of productivity can be explained by the fact that standard TFP measures do not take into account the term E, which allows for exible substitution patterns and quality dierences between labor types.

The estimates of η 1 , ...., η W parameters governing relative quality dierence between native and each types of foreign workers reveal that only a few groups of foreigner workers are relatively more productive than native workers, i.e. foreign workers from West/South Europe, Other Asia and North America/Oceania. The other groups are generally less productive instead. The industry-specic estimates of the parameter γ are precisely estimated in the wholesale and retail trade, and nancial and business sector only, and are lower than one in all industries. Note that we always reject at reasonable signicance levels the null hypothesis that the coecients γ is greater than one, implying between labor types imperfect substitutability or complementarity. This is consistent with the hypothesis that dispersion in labor types along the ethnic dimension has a negative association with rm output, in line with the results found in the previous section with the reduced form approach.

In a second specication, we categorize workers according to their education as we did in the construction 37 Note that the estimation of production function [START_REF] Berliant | Knowledge Creation as a Square Dance on the Hilbert Cube[END_REF] cannot be carried out for construction and transport sectors due to non-convergence of the estimation algorithm. 38 The p-values associated with the null hypothesis for the equality of the distributions take value 0.000 in all cases.

of our educational diversity index using the aggregate specication. In this case E can be re-written as:

E(C ijt , S ijt , T 1ijt , ...., T 4ijt ) = [(C ijt ) γ + (η 0 S 1ijt ) γ + (η 1 T 1ijt ) γ + .... + (η 4 T 4ijt ) γ ] 1/γ (16)
where C ijt is the share of workers with compulsory education, S ijt the share of workers with secondary education, while T 1ijt , ...., T 4ijt are the share of workers with dierent types of tertiary education, as described in the aggregate specication of education diversity. Table 10 shows the result obtained by estimating production function [START_REF] Berliant | Knowledge Creation as a Square Dance on the Hilbert Cube[END_REF], in which the overall eciency of the labor force is expressed by equation ( 16).

39

As in the previous table the coecients on labor and capital are in line with those obtained from a standard specication of the production function, as reported in Table 3, and standard TFP estimates are larger than non standard TFP measures (see Figure 2). The η parameters show that workers with either secondary or tertiary education are much more productive than workers with compulsory education, especially workers with an engineering or a scientic tertiary education. We nd that the parameter γ governing substitutability among employees with dierent educational levels is below one in all industries, suggesting a supermodular technology with a distaste for dispersion in types along the educational dimension. We therefore interpret these results as evidence that highly-educated workers and low-skilled workers are imperfect substitutes and that dispersion of labor types along the educational dimension has not a positive impact on productivity in line with what has been found in [START_REF] Iranzo | Skill Dispersion and Firm Productivity: An Analysis with Employer-Employee Matched Data[END_REF].

[Insert Table 10 around here]

The latter result is starkly contradictory with the descriptive analysis reported above in section 4, where we nd that our education diversity statistic is positively related with productivity. This inconsistency can be partly explained by the fact that in the descriptive analysis we do not appropriately control for quality dierences between labor types, which seem to play an important role in the production function, as indicated by the estimates on the η parameters. Furthermore in the reduced-form analysis we show that by calculating occupation-specic diversity (Table 5, columns 1 and 2) or the Herndhal index based only on the type of tertiary education (Table 6, column 3), the positive association between educational diversity and rm TFP is largely driven by the white-collar workers, who are very likely to be highly educated, or by workers with dierent types of tertiary education. These results may therefore suggest that the contribution of educational diversity is most likely due to the combination of skills of highly educated employees rather than by combining the overall skills of workers with dierent levels of education. A possible test for the latter conjecture is to estimate a modied version of the structural production function [START_REF] Berliant | Knowledge Creation as a Square Dance on the Hilbert Cube[END_REF], that splits labor aggregate L into two groups, i.e. employees with compulsory education L 1 , and workers with more than compulsory education L 2 , and that estimates the role of skill dispersion only among L 2 types. Treating L 1 as a standard Cobb-Douglas input with unit elasticity of substitution to the L 2 types, we can re-write production function [START_REF] Berliant | Knowledge Creation as a Square Dance on the Hilbert Cube[END_REF] as follows:

Y ijt = A ijt L α1 1ijt • [L 2ijt • [(η 0 S 1ijt ) γ + (T 1ijt ) γ + (η 1 T 2ijt ) γ + (η 2 T 3ijt ) γ + (η 4 T 4ijt ) γ ] 1/γ ] α2 • K β ijt ( 17
)
where S ijt is the share of workers with secondary education, T 1ijt , ...., T 4ijt are the share of workers with dierent types of tertiary education, as in equation ( 16), and γ governs the complementarity/substitutability only arising among workers with more than compulsory education, i.e. L 2 . Table 11 shows the estimates of production function [START_REF] Mercedes | Clusters and Entrepreneurship[END_REF], using the LP approach. 40 The estimates of the parameter γ slightly increase compared to those reported in Table 10, but they never exceed the threshold of one, suggesting imperfect substitutability or complementarity also when we focus on dispersion in labor types within highly educated workers.

[Insert Table 11 around here] A possible explanation behind the latter result may be that the industrial classication used to separately estimate production function ( 17) is very aggregate and may group industries with a super-modular technology together with those with a sub-modular technology under the same 1-digit industry. Estimating equation [START_REF] Mercedes | Clusters and Entrepreneurship[END_REF] separately for each 2-digits sector in fact reveals that for about half of the industries the γ coecient is estimated to be larger than one.

41 This is the case for the following industries: i) food, beverages and tobacco, ii) sales and repair of motor vehicles, iii) retail trade, iv) hotels and restaurants and v) nancial intermediation. However the γ coecient is precisely estimated only for 3 industries (food, beverages and tobacco; sales and repair of motor vehicles; hotels and restaurants).

[Insert Table 12 around here]

By taking together all these results, we cannot thus conclude that dispersion in labor types in terms of education for the overall workforce is positively correlated with productivity. However estimating a modied specication of the structural model separately for each 2-digits industry suggests that, for about half of the sectors, skill diversity arising only among highly educated workers positively associates with rm productivity, in line with the descriptive evidence on the role of diversity among white-collar or tertiary education employees.

Conclusions

Using a comprehensive linked employer-employee data-set, this article primarily investigates the empirical relationship of diversity in workers' ethnic-cultural, educational and demographic characteristics with rm productivity in Denmark. Unlike the majority of previous empirical studies, which focused on single aspects of labor diversity, we provide a number of ndings that extensively explore the overall consequences of rm workforce heterogeneity for rm performance. Specically, we follow two main methodological routes to investigate the link between workforce diversity and productivity. In the rst one, we estimate a standard Cobb-Douglas function, calculate the implied total factor productivity and relate the latter to our labor diversity indices in a second stage. The results from this reduced-form approach allow us to identify which types of labor heterogeneity appear to descriptively matter and suggest that labor diversity in ethnicity (education) is negatively (positively) associated with rm productivity, whereas the demographic diversity seems not to matter. Several robustness checks and the results obtained by implementing the IV method are in line with these descriptive ndings. The main limit of the reduced-form approach is that it does not formally take into account that the labor input is non-homogeneous in the production function, i.e., labor ). We therefore move toward a richer production function specication, which takes dierent types of labor as inputs and that allows for exible substitution patterns, and possible quality dierences between types. The results obtained from this structural estimation approach suggest that labor heterogeneity in terms of ethnicity decreases rm output and that it is not optimal to have dispersion in terms of employees' education.

of
Thus, we nd evidence that the negative eects of the communication and integration costs associated with a more culturally diverse workforce seem to counteract the positive eects of ethnic diversity (e.g., better problem-solving abilities, more creativity, and knowledge spillover). These ndings are consistent with those of previous studies by Lazear (1999), [START_REF] Glaeser | Measuring Trust[END_REF], and Alesina and La Ferrara (2002).

Instead, the results concerning labor heterogeneity in terms of education are mixed. On the one hand, the reduced-form analysis provides descriptive evidence of a positive association between education diversity and productivity, consistently with Lazear (1999). On the other hand, the structural estimation approach reveals that the overall dispersion of labor types in terms of education decreases rm output, i.e. high-educated and low-educated workers' skills are imperfect substitutes, in line with what has been found in [START_REF] Iranzo | Skill Dispersion and Firm Productivity: An Analysis with Employer-Employee Matched Data[END_REF]. However estimating a modied specication of the structural model separately for each 2-digits industry suggests that, for about half of the sectors, skill diversity arising only among highly educated workers positively associates with rm productivity. Note: The dependent variable is the log of total factor productivity estimated by using the ACF approach. Index ethnic disaggr ( 1) is calculated as in the main analysis whereas index ethnic disaggr ( 2) is separately calculated for white-and blue-collar workers in columns 1 and 2, or by excluding/including a specific group of employees, as described in the column head, in columns 3 and 4. All regressions include the shares of employees belonging to each category considered in the diversity indices; shares of managers and middle-managers; average firm tenure; whether the firm is foreign owned, multi-establishment, and exports; a full set of 2-digit industry, year, size, and county dummies; and industry-year interactions. Note: The dependent variable is the log of total factor productivity estimated by using the ACF approach. Firm level diversity is instrumented by using the predicted level of diversity at the commuting area, where the firm is located. All regressions include the shares of employees belonging to each category considered in the diversity indices; shares of managers and middle-managers; average firm tenure; whether the firm is foreign owned, multi-establishment, and exports; a full set of 2-digit industry, year, size, and county dummies; and industry-year interactions. Standard errors are clustered at the commuting area level. Significance levels: ***1%, **5%, *10%.

viii Table 9: Production function estimates with shares of labor types along the ethnic dimension Note: The dependent variable is the log of total factor productivity estimated by using the ACF approach. Index ethnic disaggr (1) is calculated as in the main analysis whereas index ethnic disaggr ( 2) is separately calculated for white-and blue-collar workers in columns Note: The dependent variable is the log of total factor productivity estimated by using the ACF approach. Firm level diversity is instrumented by using the predicted level of diversity at the commuting area, where the firm is located. All regressions include the shares of employees belonging to each category considered in the diversity indices; shares of managers and middle-managers; average firm tenure; whether the firm is foreign owned, multi-establishment, and exports; a full set of 2-digit industry, year, size, and county dummies; and industry-year interactions. Standard errors are clustered at the commuting area level. Significance levels: ***1%, **5%, *10%.

xxx

Food

  The dependent variable is the log of value added. Input elasticities are estimated by using the LP approach. The estimates of η parameters governing relative quality difference between labor types are not reported in the

  employees from Muslim countries, as a proportion of foreign employees 0employees from East Asia, as a proportion of foreign employees 0employees from Other Asia, as a proportion of foreign employees 0employees from formerly communist countries, as a proportion of foreign employees 0employees from West/South Europe, as a proportion of foreign employees 0employees from North America/Oceania, as a proportion of foreign employees 0employees from Central/South America, as a proportion of foreign employees 0secondary/ post-secondary education, as a proportion of all employees 0social sciences tertiary education, as a proportion of all employees 0

Financial

  Hypothesis tests (chi2, p-value)Interactions of diversity indices and export =0

Table 1

 1

provides basic descriptive statistics for all of the variables used in our analysis for the main sample by rm size. We split the sample into two main groups: rms above and below 50 employees. Consistent with the overall character of the Danish private sector, 78 % of the observations corresponds to rms with fewer than 50 employees. 8 Compared with larger rms, smaller companies are engaged in export activities to a lesser extent and are characterized by lower levels of value added, materials and capital stock.

  Card and Di Nardo, 2000;[START_REF] Dustmann | The impact of immigration on the British labor market[END_REF][START_REF] Cortes | The Eect of Low-Skilled Immigration on U.S. Prices: Evidence from CPI Data[END_REF] and Foley and Kerr, 2012). Pre-existing workforce diversity at the commuting area level may be not correlated with a rm's current labor demand and productivity, if measured with a sucient time lag.

Table 1 :

 1 Descriptive statistics, main sample and by size

	Variables Definition Total Size1 Size2	IDA Variables: Mean Median Sd Mean Median Sd Mean Median Sd	foreigners1 non-Danish employees from Muslim countries, as a proportion of foreign employees 0.079 0 0.228 0.065 0 0.221 0.127 0 0.243	foreigners2 non-Danish employees from East Asia, as a proportion of foreign employees 0.037 0 0.156 0.031 0 0.153 0.06 0 0.166	foreigners3 non-Danish employees from Other Asia, as a proportion of foreign employees 0.024 0 0.123 0.018 0 0.118 0.044 0 0.152	foreigners4 non-Danish employees from formerly communist countries, as a proportion of foreign employees 0.037 0 0.156 0.031 0 0.154 0.059 0 0.164	foreigners5 non-Danish employees from West/South Europe, as a proportion of foreign employees 0.257 0 0.395 0.212 0 0.384 0.41 0.344 0.391	foreigners6 non-Danish employees from Africa, as a proportion of foreign employees 0.010 0 0.069 0.006 0 0.067 0.013 0 0.075	foreigners7 non-Danish employees from North America/Oceania, as a proportion of foreign employees 0.014 0 0.098 0.012 0 0.096 0.013 0 0.077	foreigners8 non-Danish employees from Central/South America, as a proportion of foreign employees 0.008 0 0.075 0.007 0 0.074 0.013 0 0.075	males men, as a proportion of all employees 0.715 0.785 0.232 0.722 0.8 0.237 0.692 0.736 0.21	age1 employees aged 15-32, as a proportion of all employees 0.243 0.2 0.191 0.254 0.214 0.195 0.204 0.157 0.169	age2 employees aged 33-41, as a proportion of all employees 0.238 0.231 0.123 0.234 0.222 0.131 0.253 0.245 0.095	age3 employees aged 42-50, as a proportion of all employees 0.192 0.187 0.107 0.186 0.176 0.113 0.21 0.214 0.077	age4 employees aged 51-65, as a proportion of all employees 0.181 0.211 0.178 0.201 0.198 0.165 0.229 0.213 0.191	skill0 employees with compulsory education, as a proportion of all employees 0.331 0.307 0.191 0.33 0.305 0.193 0.329 0.321 0.178	skill1 employees with a secondary/ post-secondary education, as a proportion of all employees 0.632 0.653 0.178 0.635 0.666 0.184 0.621 0.628 0.157	skill2 1 employees with a humanities tertiary education, as a proportion of all employees 0.01 0 0.031 0.011 0 0.031 0.009 0 0.025	skill2 2 employees with a scientific tertiary education, as a proportion of all employees 0.003 0 0.021 0.003 0 0.018 0.005 0 0.024	skill2 3 employees with a social sciences tertiary education, as a proportion of all employees 0.016 0 0.052 0.015 0 0.051 0.021 0 0.055	skill2 4 employees with a engineering tertiary education, as a proportion of all employees 0.01 0 0.047 0.01 0 0.047 0.012 0 0.046	tenure average tenure 4.541 4.91 0.49 4.363 4.627 0.501 5.153 5.752 4.507	managers managers, as a proportion of all employees 0.045 0.021 0.058 0.045 0 0.063 0.037 0.025 0.039	middle managers middle managers, as a proportion of all employees 0.166 0.087 0.208 0.153 0.076 0.204 0.211 0.138 0.214	bluecoll blue-collars, as a proportion of all employees 0.741 0.829 0.276 0.739 0.811 0.265 0.75 0.832 0.289	Index ethnic aggr diversity index based on employees' nationality (8 categories) 0.102 0 0.207 0.054 0 0.159 0.265 0.244 0.263	Index edu aggr diversity index based on employees' education (6 categories) 0.415 0.444 0.111 0.407 0.436 0.115 0.442 0.468 0.090	Index demo aggr diversity index based on employees' demographic characteristics (8 categories) 0.742 0.759 0.088 0.731 0.75 0.090 0.779 0.790 0.068	Index ethnic disaggr diversity index based on employees' language (40 categories) 0.121 0 0.407 0.058 0 0.374 0.336 0.432 0.440	Index edu disaggr diversity index based on employees' education (9 categories) 0.573 0.578 0.131 0.558 0.562 0.134 0.622 0.624 0.109	Index demo disaggr diversity index based on employees' demographic characteristics (10 categories) 0.868 0.886 0.086 0.857 0.876 0.088 0.907 0.919 0.066	Accounting Variables:	total sales (1000 kr.) 106,455.6 24,424.69 773,081 33,501.14 17,806.29 102,538 357,089 119,981.1 1,591,768	intermediates (1000 kr.) 77,091.01 14,369.88 626,067.9 24,598.44 10,012.36 96,835.73 257,427.8 73,243.01 1,290,107	capital (1000 kr.) 45,632.38 3,661.496 978,689.2 11,263 2,516.854 543,658 163,708 21,980.64 1,793,078	0.467 export 1, if the firm export 0.418 0 0.493 0.343 0 0.475 0.676 0.761	0.058 foreign ownership 1, if the firm is foreign owned 0.004 0 0.059 0.004 0 0.06 0.003 0	0.492 multi 1, if the firm is multi-establishment 0.118 0 0.323 0.032 0 0.178 0.413 0	Observations 126,788 98,203 28,585	Note: All IDA and accounting variables are expressed as time averages from 1995 to 2005. The industrial sectors included in the	empirical analysis are the following: food, beverages and tobacco (3.43 %); textiles (1.81 %), wood products (5.82 %), chemicals	(3.08 %), other non-metallic mineral products (1.28 %), basic metals (16.68 %), furniture (3.11 %), construction (19.69 %), sale	and repair of motor vehicles (4.16 %), wholesale trade (14.11 %), retail trade (8.92 %), hotels and restaurants (3.10 %), transport	(4.59 %), financial intermediation (1 %) and business activities (9.22 %). Small size (Size 1): Employees ≤ 49; Middle and big size	(Size 2): Employees ≥ 50.

i

Table 2 :

 2 Descriptive statistics of diversity indices by industry, by size and by year

				Aggregate specification
		Manufacturing Construction Wholesale and retail trade Transport Financial and business services
	Index ethnic	0.154	0.031	0.077	0.080	0.138
	Index edu	0.430	0.387	0.402	0.437	0.449
	Index demo	0.766	0.716	0.730	0.738	0.751
	Observations	45,766	24,605	37,991	5,841	12,667
		Small size	Middle size	Big size	1995	2005
	Index ethnic	0.030	0.080	0.259	0.081	0.121
	Index edu	0.399	0.417	0.441	0.427	0.414
	Index demo	0.717	0.747	0.777	0.735	0.739
	Observations	50,564	46,630	29,676	7,461	13,819
				Disaggregate specification
		Manufacturing Construction Wholesale and retail trade Transport Financial and business services
	Index ethnic	0.191	0.046	0.080	0.083	0.156
	Index edu	0.578	0.503	0.573	0.567	0.698
	Index demo	0.891	0.847	0.854	0.865	0.877
	Observations	45766	24605	37991	5841	12667
		Small size	Middle size	Big size	1995	2005
	Index ethnic	0.028	0.090	0.328	0.081	0.137
	Index edu	0.545	0.573	0.622	0.546	0.588
	Index demo	0.841	0.876	0.906	0.862	0.866
	Observations	50,564	46,630	29,676	7,461	13,819

Note: Small size: Employees ≤ 49; Middle size: 50 ≤ Employees ≤ 99; Big size: Employees ≥ 100.

ii

Table 3 :

 3 Production function estimatesThe dependent variable is the log of value added in the first two sub-panels (ACF, OP). In the last sub-panel (GNR), the dependent variable is the log of total sales. Standard errors are computed by using a block bootstrap procedure with 300 replications and are robust against heteroskedasticity and intra-firm correlation. Significance levels: ***1%, **5%, *10%.

	ACF	Manufacturing Construction Wholesale and retail trade Transport Financial and business services	0.913*** 0.928*** 0.984*** 0.842*** 0.906***	(0.020) (0.024) (0.209) (0.104) (0.114)	0.102*** 0.115*** 0.089*** 0.140*** 0.156***	(0.005) (0.024) (0.032) (0.020) (0.009)	36,079 18,095 26,604 4,041 8,097	0.865 0.836 0.711 0.797 0.713	OP	Manufacturing Construction Wholesale and retail trade Transport Financial and business services	0.828*** 0.955*** 0.809*** 0.697*** 0.792***	(0.014) (0.006) (0.009) (0.020) (0.014)	0.123*** 0.157*** 0.161*** 0.243*** 0.029	(0.029) (0.012) (0.036) (0.037) (0.078)	10,684 6,589 9,225 1,528 2,985	0.812 0.805 0.698 0.783 0.694	GNR	Manufacturing Construction Wholesale and retail trade Transport Financial and business services	0.487*** 0.467*** 0.246*** 0.528*** 0.538***	(0.032) (0.020) (0.015) (0.013) (0.047)	0.096*** 0.047*** 0.055*** 0.092*** 0.069***	(0.023) (0.014) (0.017) (0.014) (0.034)	0.441*** 0.491*** 0.546*** 0.383*** 0.182***	(0.001) (0.001) (0.001) (0.001) (0.001)	35,387 17,823 26,016 3,928 7,626	0.852 0.905 0.848 0.883 0.848
			Log(L)		Log(K)		Observations	R2			Log(L)		Log(K)		Observations	R2			Log(L)		Log(K)		Log(Intermediates)		Observations	R2

Note:

iii

Table 4 :

 4 Labor diversity and firm total factor productivity, main results The dependent variable is the log of total factor productivity estimated by using the ACF, OP and GNR approach, alternatively. All regressions include the shares of employees belonging to each category considered in the diversity indices; shares of managers and middle-managers; average firm tenure; whether the firm is foreign owned, multi-establishment, and exports; a full set of 2-digit industry, year, size, and county dummies; and industry-year interactions. Standard errors are clustered at the firm level. Significance levels:

	TFP (ACF)	Manufacturing Construction Wholesale and retail trade Transport Financial and business services	-0.013*** -0.012** -0.033*** -0.009 -0.011	(0.003) (0.005) (0.006) (0.018) (0.008)	0.014** 0.010* 0.010** 0.048 0.017**	(0.006) (0.006) (0.004) (0.027) (0.008)	0.023 -0.026 -0.004 0.035 0.018	(0.013) (0.015) (0.005) (0.022) (0.012)	35,887 18,024 26,418 4,007 7,931	0.281 0.235 0.553 0.185 0.347	-0.016*** -0.012** -0.015*** -0.008 0.001	(0.003) (0.005) (0.004) (0.008) (0.006)	0.029*** 0.012* 0.053*** 0.007 0.054***	(0.007) (0.007) (0.006) (0.022) (0.013)	0.021 -0.027 -0.016 0.032 -0.010	(0.011) (0.015) (0.009) (0.019) (0.012)	35,887 18,024 26,418 4,007 7,931	0.290 0.247 0.558 0.203 0.361	TFP (OP)	Manufacturing Construction Wholesale and retail trade Transport Financial and business services	-0.008* -0.007* -0.015** -0.038 -0.005	(0.005) (0.004) (0.008) (0.024) (0.014)	0.012* 0.011* 0.031*** 0.063* 0.032**	(0.007) (0.007) (0.008) (0.029) (0.013)	0.030 -0.020 0.010 0.080 0.014	(0.018) (0.016) (0.007) (0.042) (0.014)	10,662 6,572 9,199 1,526 2,985	0.268 0.230 0.432 0.253 0.351	-0.014*** -0.008** -0.012*** -0.003 -0.001	(0.005) (0.003) (0.005) (0.011) (0.014)	0.029*** 0.014* 0.053*** 0.033 0.051**	(0.008) (0.008) (0.008) (0.025) (0.016)	0.028 -0.018 0.009 0.076 -0.002	(0.018) (0.011) (0.007) (0.046) (0.016)	10,662 6,572 9,199 1,526 2,985	0.271 0.245 0.444 0.271 0.364	TFP (GNR)	Manufacturing Construction Wholesale and retail trade Transport Financial and business services	-0.007*** -0.008** -0.011** -0.012 -0.004	(0.002) (0.003) (0.004) (0.014) (0.009)	0.008** 0.009** 0.015*** 0.027 0.028**	(0.004) (0.003) (0.003) (0.018) (0.011)	0.007 -0.017 -0.006 0.040 0.003	(0.004) (0.013) (0.004) (0.029) (0.012)	35,477 17,769 26,086 3,954 7,818	0.262 0.262 0.513 0.331 0.265	-0.009*** -0.008** -0.010*** -0.008 -0.001	(0.002) (0.003) (0.002) (0.008) (0.006)	0.007* 0.010** 0.031*** 0.017 0.067***	(0.004) (0.004) (0.004) (0.019) (0.015)	0.009 -0.016 0.008 0.039 -0.020	(0.006) (0.010) (0.007) (0.023) (0.013)	35,477 17,769 26,086 3,954 7,818	0.279 0.252 0.52 0.344 0.278
			Index ethnic aggr		Index edu aggr		Index demo aggr		Observations	R2	Index ethnic disaggr		Index edu disaggr		Index demo disaggr		Observations	R2			Index ethnic aggr		Index edu aggr		Index demo aggr		Observations	R2	Index ethnic disaggr		Index edu disaggr		Index demo disaggr		Observations	R2			Index ethnic aggr		Index edu aggr		Index demo aggr		Observations	R2	Index ethnic disaggr		Index edu disaggr		Index demo disaggr		Observations	R2

Note: ***1%, **5%, *10%. iv

Table 5 :

 5 Testing alternative hypotheses: estimates by using occupation-specific diversity, alternative index definitions, and

	"subtract-out" groups

Table 6 :

 6 Standard errors are clustered at the firm level. Robustness checks: estimates by size, under alternative samples and index definitions The dependent variable is the log of total factor productivity estimated by using the ACF approach. All regressions include the shares of employees belonging to each category considered in the diversity indices; shares of managers and middle-managers; average firm tenure; whether the firm is foreign owned, multi-establishment, and exports; a full set of 2-digit industry, year, size, and county dummies; and industry-year interactions. Standard errors are clustered at the firm level. Significance levels: ***1%, **5%, *10%.

	Significance levels: ***1%, **5%,

v Note: vi

Table 7 :

 7 IV results: first stage regressions The dependent variable is diversity at the firm level. All regressions include the shares of employees belonging to each category considered in the diversity indices; shares of managers and middle-managers; average firm tenure; whether the firm is foreign owned, multi-establishment, and exports; a full set of 2-digit industry, year, size, and county dummies; and industry-year interactions. Standard errors are clustered at the commuting area level. Significance levels: ***1%, **5%, *10%.

			Manufacturing
		Index ethnic disaggr Index edu disaggr Index demo disaggr
	index ethnic com	1.601***	-0.120**	-0.056**
		(0.177)	(0.051)	(0.028)
	index edu com	-0.884***	0.273***	-0.190***
		(0.234)	(0.066)	(0.051)
	index demo com	-2.134***	-0.039	1.009***
		(0.342)	(0.196)	(0.097)
	F test (excluded instruments); p-value	36.83; 0.000	18.14; 0.000	29.44; 0.000
	Observations	48,238	48,238	48,238
	R2	0.227	0.594	0.385
			Construction
		Index ethnic disaggr Index edu disaggr Index demo disaggr
	index ethnic com	0.351***	-0.243***	-0.038
		(0.082)	(0.062)	(0.030)
	index edu com	0.336**	0.314***	-0.035
		(0.113)	(0.077)	(0.060)
	index demo com	-0.494	0.542**	0.585**
		(0.327)	(0.173)	(0.173)
	F test (excluded instruments); p-value	26.69; 0.000	38.90; 0.000	6.08; 0.011
	Observations	26,969	26,969	26,969
	R2	0.131	0.574	0.348
		Wholesale and retail trade
		Index ethnic disaggr Index edu disaggr Index demo disaggr
	index ethnic com	0.909***	-0.342***	0.166***
		(0.112)	(0.060)	(0.046)
	index edu com	0.431**	0.938***	-0.496***
		(0.135)	(0.102)	(0.057)
	index demo com	-0.192	-0.256**	1.238***
		(0.195)	(0.078)	(0.086)
	F test (excluded instruments); p-value	19.77; 0.000	37.81; 0.000	90.43; 0.000
	Observations	41,493	41,493	41,493
	R2	0.187	0.570	0.481
			Transport
		Index ethnic disaggr Index edu disaggr Index demo disaggr
	index ethnic com	0.212***	0.022	-0.187**
		(0.023)	(0.236)	(0.062)
	index edu com	0.510	0.017**	0.158
		(0.486)	(0.008)	(0.126)
	index demo com	-0.389	0.202	0.576**
		(2.076)	(0.280)	(0.245)
	F test (excluded instruments); p-value	16.70; 0.000	9.89; 0.000	25.78; 0.000
	Observations	6,287	6,287	6,287
	R2	0.261	0.635	0.285
		Financial and business services
		Index ethnic disaggr Index edu disaggr Index demo disaggr
	index ethnic com	1.585***	-0.407***	-0.076
		(0.230)	(0.081)	(0.058)
	index edu com	-0.021	0.903***	0.080
		(0.224)	(0.074)	(0.063)
	index demo com	-0.319	-0.225	1.027***
		(0.366)	(0.206)	(0.097)
	F test (excluded instruments); p-value	16.81; 0.000	37.02; 0.000	25.87; 0.000
	Observations	14,008	14,008	14,008
	R2	0.396	0.468	0.353
		vii

Note:

Table 8 :

 8 Labor diversity and productivity, IV results: second stage regressions

		Manufacturing Construction Wholesale and retail trade Transport Financial and business services
	index ethnic disaggr	-0.026*	-0.038*	-0.028**	-0.031	0.009
		(0.014)	(0.019)	(0.014)	(0.084)	(0.012)
	index edu disaggr	0.061**	0.037	0.095**	0.047	0.078*
		(0.028)	(0.019)	(0.040)	(0.149)	(0.038)
	index demo disaggr	0.093	-0.048	-0.056	-0.085	-0.048
		(0.086)	(0.049)	(0.033)	(0.070)	(0.033)
	Observations	35,887	18,024	26,418	4,007	7,931
	R2	0.310	0.123	0.252	0.189	0.200

Table 10 :

 10 The dependent variable is the log of value added. Input elasticities are estimated by using the ACF approach. Standard errors are computed by using a block bootstrap procedure with 300 replications and are robust against heteroskedasticity and intra-firm correlation. Significance levels: ***1%, **5%, *10%. Production function estimates with shares of labor types along the educational dimension The dependent variable is the log of value added. Input elasticities are estimated by using the ACF approach. Standard errors are computed by using a block bootstrap procedure with 300 replications and are robust against heteroskedasticity and intra-firm correlation. Significance levels: ***1%, **5%, *10%.

	2.333***	(0.630)	0.634***	(0.280)	0.464	(0.763)	3.611***	(1.424)	0.343	(0.600)	1.314***	(0.548)	6.78; 0.022	8,097	0.779
	1.431***	(0.378)	0.675***	(0.260)	0.648	(0.690)	2.776**	(1.119)	0.944	(0.718)	0.856*	(0.444)	6.27; 0.031	26,604	0.737
	1.010***	(0.188)	0.797***	(0.270)	0.966	(1.037)	1.016	(0.937)	0.998	(0.818)	1.040**	(0.501)	6.57; 0.029	36,079	0.891
			η Af rica		η Central/South America		η N orth America/Oceania		η F ormerly communist countries		η Asia	Hypothesis testing (chi2, p-value)	γ > 1	Observations	R2

Note:

ix Note:

x

Table 11 :

 11 Production function estimates with shares of labor types along the educational dimension, labor aggregate splitted The dependent variable is the log of value added. Input elasticities are estimated by using the LP approach. Standard errors are computed by using a block bootstrap procedure with 300 replications and are robust against heteroskedasticity and intra-firm correlation. Significance levels: ***1%, **5%, *10%.

	Manufacturing Wholesale and retail trade Financial and business services	0.266*** 0.211*** 0.193***	(0.006) (0.007) (0.009)	0.339*** 0.428*** 0.493***	(0.006) (0.009) (0.016)	0.124*** 0.074*** 0.050***	(0.004) (0.005) (0.009)	0.737*** 0.768*** 0.926***	(0.225) (0.103) (0.073)	4.198 1.590* 2.266**	(2.533) (0.938) (0.983)	3.313 4.810** 3.366	(2.097) (1.912) (3.015)	1.165 1.056** 3.275***	(1.097) (0.431) (1.820)	3.773** 4.923*** 4.657**	(1.643) (1.014) (2.825)	6.22; 0.032 6.21; 0.032 5.20; 0.025	36,079 26,604 8,097	0.895 0.779 0.777
		Log(L 1 )		Log(L 2 )		Log(K)		γ		η secondary/postsecondary		η scientif ic tertiary		η social sciences tertiary		η engineering tertiary	Hypothesis testing (chi2, p-value)	γ > 1	Observations	R2
	into two groups

Note:

xi

Table 12 :

 12 Production function estimates with shares of labor types along the educational dimension, labor aggregate splitted into two groups and estimates by 2 digits industry

Table A1 :

 A1 Table anbd are available on request from the authors. Standard errors are computed by using a block bootstrap procedure with 300 replications and are robust against heteroskedasticity and intra-firm correlation. Significance levels: ***1%, **5%, *10%. Descriptive statistics, sample including firms with less than 10 employees

	Figure 1: Kernel density of firm TFP, calculated with or without worker heterogeneity Figure 2: Kernel density of firm TFP, calculated with or without worker heterogeneity
	in terms of nationality in terms of education
			Manufacturing Manufacturing					Wholesale and retail trade Wholesale and retail trade
	.2 .4 .6 .8 1 .2 .4 .6 .8 1					.2 .4 .6 .8 .2 .4 .6 .8
	0 0					0 0
	4 4	5 5	6 Etimated tfp 6 Estimated tfp	7 7	8	8	4 4	6 6	Estimated tfp Estimated tfp	8 8	10 10
			standard standard						standard standard
			non standard non standard					non standard non standard
		Financial and business Financial and business
	.2 .4 .6 .8 .2 .4 .6 .8 1
	0 0
	4 4	6 6	8 Estimated tfp Estimated tfp	8	10	10
			standard standard
			non standard non standard
	Note: TFP is estimated by using the ACF approach. Note: TFP is estimated by using the ACF approach.
					xii xiii xiv

Table A2 :

 A2 All IDA and Accounting variables are expressed as time averages from 1995 to 2005. Labor diversity and firm total factor productivity, sample including firms with fewer than 10 employees The dependent variable is the log of total factor productivity estimated b using the ACF approach. All regressions include the shares of employees belonging to each category considered in the diversity indices; shares of managers and middle-managers; average firm tenure; whether the firm is foreign owned, multi-establishment, and exports; a full set of 2-digit industry, year, size, and county dummies; and industry-year interactions. Standard errors are clustered at the firm level. Significance levels: ***1%, **5%, *10%.

									TFP (ACF)
		Manufacturing Construction Wholesale and retail trade Transport Financial and business services
	Index ethnic aggr	-0.021***	-0.014**				-0.016**					-0.024	-0.045***
		(0.004)	(0.005)					(0.006)					(0.020)	(0.010)
	Index edu aggr	0.011**	-0.015**				-0.013**					0.057	0.019**
		(0.005)	(0.005)					(0.006)					(0.029)	(0.009)
	Index demo aggr	0.034	0.021					0.005						0.066	0.005
		(0.018)	(0.016)					(0.007)					(0.041)	(0.010)
	Observations	36,855	20,298					28,192						4,335	8,233
	R2 Index ethnic disaggr	0.261 -0.022*** (0.004)	0.222 -0.014** (0.005)	0.276	0.09	0.137	0.268 -0.010** 0.102 0.124 0.129 0.479 (0.003)	49,583.6	48,335.78	28,779.17	0.417	0.049	0.190 0 -0.006 (0.006)	0.344 -0.012* (0.007)
	Index edu disaggr	0.036***	0.008				0.048***					0.007	0.062***
	Index demo disaggr Observations R2	(0.007) 0.022 (0.013) 36,855 0.271	(0.006) -0.021 (0.015) 20,298 0.230	829	0.045 0	0.386 0.42	0.694 0.72	0.074 0 (0.006) 0.379 0.406 0.701 0.739 -0.011 (0.010) 28,192 0.490	14,114.76 8,048.458	10,310.94 4,495	3,329.596 1,142.857	0 0.224	0 0.001	0 (0.018) 9,405 0.049 (0.027) 4,335 0 0.210	(0.013) -0.019 (0.012) 8,233 0.357
					diversity index based on employees' nationality (8 categories)	diversity index based on employees' education (6 categories)	diversity index based on employees' demographic characteristics (8 categories)	diversity index based on employees' language (40 categories)	diversity index based on employees' education (9 categories)	diversity index based on employees' demographic characteristics (10 categories)		(1000 kr.)	(1000 kr.)	(1000 kr.)	1, if the firm export	1, if the firm is foreign owned	1, if the firm is multi-establishment
					Index ethnic aggr	Index edu aggr	Index demo aggr	Index ethnic disaggr	Index edu disaggr	Index demo disaggr	Accounting Variables:	total sales	intermediates	capital	export	foreign ownership	multi	N
					Note: xviii xix

Note:

Table A3 :

 A3 Labor diversity and firm exit The dependent variable is a dummy variable equal to 1 if the firm exits the market. All regressions include the shares of employees belonging to each category considered in the diversity indices; shares of managers and middle-managers; average firm tenure; whether the firm is foreign owned, multi-establishment, and exports; a full set of 2-digit industry, year, size, and county dummies; and industry-year interactions. Standard errors are clustered at the firm level. Significance levels: ***1%, **5%, *10%. The dependent variable is the log of total factor productivity estimated by using the ACF approach. All regressions include average firm tenure; whether the firm is foreign owned, multi-establishment, and exports; a full set of 2-digit industry, year, size, and county dummies; and industry-year interactions. Standard errors are clustered at the firm level. The dependent variable is the log of total factor productivity estimated by using the OP approach. All regressions include average firm tenure; whether the firm is foreign owned, multi-establishment, and exports; a full set of 2-digit industry, year, size, and county dummies; and industry-year interactions. Standard errors are clustered at the firm level. Significance levels: ***1%, **5%, *10%. The dependent variable is the log of total factor productivity estimated by using the GNR approach. All regressions include average firm tenure; whether the firm is foreign owned, multi-establishment, and exports; a full set of 2-digit industry, year, size, and county dummies; and industry-year interactions. Standard errors are clustered at the firm level.

	Table A4 1: Additional results of Table 4, workforce composition characteristics and firm total factor productivity (aggregate Table A4 2: Additional results of Table 4, workforce composition characteristics and firm total factor productivity (aggregate Table A4 3: Additional results of Table 4, workforce composition characteristics and firm total factor productivity (aggregate	specification) specification) specification)	Index ethnic aggr Index edu aggr Index demo aggr Observations R2 Index ethnic disaggr Index edu disaggr Index demo disaggr Observations R2 TFP (ACF) Manufacturing Construction Wholesale and retail trade Transport Financial and business services age1 female -0.686 0.031 0.163 2.204*** 0.025 (0.522) (0.588) (0.396) (0.627) (0.169) age2 female -0.472 0.370 0.698* 2.469*** 0.651*** TFP (OP) Manufacturing Construction Wholesale and retail trade Transport Financial and business services age1 female -0.634 1.135 0.128 0.559 0.071 (0.965) (0.859) (0.594) (1.230) (0.191) age2 female -0.466 1.374* 0.409 2.233* 0.591*** TFP (GNR) Manufacturing Construction Wholesale and retail trade Transport Financial and business services age1 female -1.073*** -0.950** 0.152 0.268 -0.347 (0.295) (0.433) (0.245) (0.548) (0.286) age2 female -0.920*** -0.698* 0.133 0.334 0.146	Manufacturing Construction Wholesale and retail trade Transport Financial and business services 0.001 -0.006 -0.007* -0.010 -0.008 (0.003) (0.004) (0.003) (0.012) (0.006) -0.004 -0.014 -0.008* -0.009 0.003 (0.004) (0.009) (0.004) (0.007) (0.003) -0.011* -0.025* -0.016 -0.009 -0.022 (0.006) (0.013) (0.009) (0.007) (0.014) 35,887 18,024 26,418 4,007 7,931 0.034 0.04 0.047 0.055 0.065 -0.002 -0.006 -0.002 -0.012 -0.002 (0.003) (0.004) (0.001) (0.008) (0.002) -0.003 -0.012 -0.004 -0.003 0.002 (0.003) (0.008) (0.003) (0.010) (0.003) -0.010* -0.024** -0.016 -0.011 -0.023 (0.006) (0.012) (0.008) (0.008) (0.017) 48,238 26,969 41,493 6,287 14,008 0.035 0.042 0.048 0.057 0.068 (0.520) (0.586) (0.395) (0.601) (0.169) age3 female -0.801 0.210 0.381 2.443*** 0.277* (0.520) (0.587) (0.395) (0.618) (0.161) age4 female -1.347*** -0.185 -0.141 1.002 -0.429*** (0.520) (0.588) (0.399) (0.626) (0.166) age1 male 1.199** 0.003 0.187*** 1.683** 0.291* (0.525) (0.589) (0.398) (0.671) (0.180) age2 male -0.623 0.145 0.610 0.234 0.341** (0.519) (0.593) (0.393) (0.657) (0.168) age3 male 0.883* 0.258 0.309 2.067*** 0.096 (0.524) (0.596) (0.396) (0.658) (0.172) age4 male -1.201** -0.075 -0.012 0.606 -0.245 (0.521) (0.595) (0.399) (0.679) (0.183) skill0 -0.225 0.324 -1.487*** -2.205** -0.042 (0.431) (0.501) (0.264) (1.017) (0.195) skill1 0.092 0.315 -1.039*** -1.861* 0.313 (0.433) (0.504) (0.265) (1.010) (0.199) skill2 1 0.513* -0.663* 2.339** 0.428* (0.278) -(0.362) (1.107) (0.236) skill2 2 -0.618** -1.866 --(0.207) -(2.163) -skill2 3 0.472* 0.707 -0.273 1.619 0.933*** (0.235) (0.625) (0.314) (1.264) (0.190) skill2 4 0.101 0.687 1.127*** -0.472** (0.492) (0.620) (0.392) -(0.200) foreigners1 -0.023* -0.020 -0.025 -0.065 -0.033 (0.012) (0.014) (0.016) (0.045) (0.034) foreigners2 0.010 0.004 0.038* 0.095 0.032 (0.017) (0.029) (0.023) (0.119) (0.057) foreigners3 0.001 -0.002 0.018* 0.092*** 0.059*** (0.008) (0.008) (0.011) (0.027) (0.023) foreigners4 -0.025 0.042 0.141*** 0.201* 0.032 (0.033) (0.058) (0.044) (0.107) (0.089) foreigners5 0.021 -0.081* 0.059 0.138 -0.044 (0.041) (0.045) (0.052) (0.141) (0.057) foreigners6 0.024 0.037 0.116** 0.169* 0.058 (0.032) (0.035) (0.050) (0.100) (0.041) foreigners7 0.037* -0.024 0.015 0.073 -0.007 (0.022) (0.026) (0.022) (0.053) (0.041) foreigners8 -0.009 -0.083** -0.017 -0.230 -0.097 (0.018) (0.035) (0.034) (0.233) (0.069) manager 0.250*** 0.468*** 0.304*** -0.071 -0.000 (0.067) (0.082) (0.068) (0.258) (0.106) (0.964) (0.857) (0.591) (1.227) (0.198) age3 female -0.713 1.277 0.019 1.300 0.500*** (0.957) (0.860) (0.594) (1.227) (0.191) age4 female -1.231 0.846 -0.421 -1.791 -0.343* (0.960) (0.860) (0.592) (1.218) (0.199) age1 male 1.078 1.056 1.124* 3.061** 1.291*** (0.974) (0.858) (0.597) (1.252) (0.215) age2 male -0.668 1.257 0.349 1.131 0.406* (0.961) (0.855) (0.594) (1.246) (0.209) age3 male 0.695 1.276 1.051* 2.936** 0.139 (0.957) (0.864) (0.591) (1.265) (0.204) age4 male -1.159 1.036 -0.323 -1.903 -0.344 (0.960) (0.867) (0.593) (1.277) (0.216) skill0 0.536 0.668 -0.723* -0.947 -0.248 (0.461) (0.965) (0.389) (2.121) (0.215) skill1 0.863* 0.686 -0.319 -0.533 0.109 (0.465) (0.966) (0.392) (2.118) (0.203) skill2 1 1.137* -1.274** -2.225 -(0.609) -(0.481) (2.189) -skill2 2 -0.796 0.276 --0.074 -(1.371) (0.528) -(0.366) skill2 3 1.230** 1.880* 1.085** 1.574* 0.691*** (0.578) (0.998) (0.456) (0.792) (0.244) skill2 4 0.906* 0.330 -1.659** 0.163 (0.549) (1.177) -(0.701) (0.194) foreigners1 -0.008 -0.011 -0.026 -0.156** -0.024 (0.018) (0.028) (0.026) (0.071) (0.053) foreigners2 0.032 -0.011 0.053 -0.045 0.003 (0.026) (0.037) (0.033) (0.118) (0.087) foreigners3 0.018 -0.001 0.032** 0.035 0.064* (0.011) (0.011) (0.014) (0.037) (0.033) foreigners4 0.012 0.094 0.139** 0.477** -0.025 (0.044) (0.065) (0.057) (0.227) (0.118) foreigners5 -0.062 -0.128* -0.001 0.241 0.030 (0.070) (0.067) (0.085) (0.251) (0.088) foreigners6 0.001 0.066* 0.059 0.051 0.167** (0.053) (0.041) (0.063) (0.103) (0.069) foreigners7 0.019 -0.018 -0.016 -0.021 -0.035 (0.034) (0.043) (0.030) (0.065) (0.063) foreigners8 -0.015 -0.106* -0.034 -0.011 -0.174 (0.023) (0.058) (0.053) (0.121) (0.149) manager 0.177* 0.589*** 0.293*** -0.257 0.356** (0.094) (0.096) (0.084) (0.358) (0.158) (0.293) (0.431) (0.245) (0.536) (0.271) age3 female -1.092*** -0.718* -0.052 0.366 -0.031 (0.293) (0.431) (0.245) (0.533) (0.269) age4 female -1.354*** -0.872** -0.258 0.135 -0.722** (0.295) (0.430) (0.245) (0.540) (0.282) age1 male 1.460*** 0.816* 1.048*** 1.546** 0.660** (0.295) (0.434) (0.246) (0.569) (0.295) age2 male -0.898*** -0.703* 0.170 0.989* -0.038 (0.294) (0.434) (0.245) (0.573) (0.280) age3 male 1.117*** 0.759* 1.031*** 0.685 0.550* (0.296) (0.433) (0.246) (0.554) (0.315) age4 male -1.382*** -1.005** -0.303 -0.121 -0.752*** (0.294) (0.430) (0.246) (0.576) (0.287) skill0 0.350 0.121 -0.390** -1.077 1.435*** (0.263) (0.306) (0.164) (0.983) (0.371) skill1 0.500* 0.171 -0.320* -0.655 1.681*** (0.265) (0.307) (0.164) (0.977) (0.379) skill2 1 1.053*** -1.136*** -1.200 1.773*** (0.315) -(0.214) (1.114) (0.402) skill2 2 -1.830* -1.189* --(0.934) -(0.613) -skill2 3 0.803*** 0.819* 0.612*** -1.034 1.972*** (0.281) (0.375) (0.201) (1.120) (0.366) skill2 4 0.454 0.319 0.635*** -1.535*** (0.298) (0.440) (0.235) -(0.379) foreigners1 0.002 -0.001 0.002 -0.065* -0.077* (0.008) (0.010) (0.009) (0.039) (0.040) foreigners2 0.006 0.005 0.024 0.104 -0.007 (0.010) (0.017) (0.016) (0.084) (0.049) foreigners3 0.007 0.000 0.024*** 0.062*** 0.078*** (0.005) (0.005) (0.007) (0.022) (0.024) foreigners4 0.001 0.010 0.035 0.007 0.048 (0.025) (0.037) (0.033) (0.117) (0.093) foreigners5 0.021 -0.041* 0.029 0.172 -0.116** (0.024) (0.024) (0.034) (0.157) (0.056) foreigners6 0.008 0.005 0.027 0.143* 0.142** (0.018) (0.018) (0.030) (0.084) (0.061) foreigners7 0.016 -0.028 0.004 0.050 0.042 (0.013) (0.019) (0.016) (0.041) (0.049) foreigners8 -0.013 -0.032* -0.011 -0.082 -0.018 (0.011) (0.017) (0.023) (0.127) (0.065) manager 0.120*** 0.295*** 0.253*** -0.123 0.092 (0.040) (0.065) (0.048) (0.226) (0.108)	middle managers 0.195*** 0.492*** 0.229*** 0.271*** 0.229*** middle managers 0.290*** 0.501*** 0.293*** 0.375*** 0.273*** middle managers 0.215*** 0.353*** 0.176*** 0.192** 0.212***	(0.035) (0.069) (0.031) (0.082) (0.035) (0.048) (0.075) (0.039) (0.115) (0.052) (0.022) (0.047) (0.022) (0.078) (0.038)	Observations 35,887 18,024 26,418 4,007 7,931 Observations 10,662 6,572 9,199 1,526 2,985 Observations 35,387 17,823 26,016 3,928 7,626	R2 0.281 0.235 0.553 0.185 0.347 R2 0.268 0.230 0.432 0.253 0.351 R2 0.852 0.905 0.848 0.883 0.848	Significance levels: ***1%, **5%, Significance levels: ***1%, **5%,	*10%. *10%.
				xx xxi xxii xxiii

Note:

Note: Note: Note:

Table A5 :

 A5 Testing alternative hypotheses: estimates by using occupation-specific diversity, alternative index definitions, and "subtract-out" groups (results for all the other industries)

	Construction	Occupation specific diversity 2nd gen. Imm. included in the ethnic diversity University graduates excluded from the ethnic diversity Germanic group excluded from the ethnic diversity	white-collar blue-collar	-0.015** -0.007 -0.005	(0.007) (0.006) (0.005)	-0.011** -0.012** -0.006 -0.016** -0.015**	(0.005) (0.006) (0.006) (0.006) (0.006)	0.016** 0.004 0.012* 0.012* 0.012*	(0.005) (0.003) (0.007) (0.007) (0.007)	-0.021 -0.008* -0.027 -0.027 -0.027	(0.014) (0.004) (0.015) (0.015) (0.016)	0.68; 0.041	7.67; 0.005	6.07; 0.013	5.99; 0.013 6.01; 0.013 6.1; 0.012	18,024 18,024 18,024 18,024	0.247 0.247 0.247 0.247	Transport	Occupation specific diversity 2nd gen. Imm. included in the ethnic diversity University graduates excluded from the ethnic diversity Germanic group excluded from the ethnic diversity	white-collar blue-collar	-0.007 -0.005 -0.005	(0.008) (0.018) (0.007)	-0.008 -0.008 -0.003 -0.009 -0.013	(0.014) (0.020) (0.019) (0.008) (0.017)	0.008 -0.004 0.007 0.007 0.007	(0.017) (0.008) (0.022) (0.022) (0.022)	0.029 -0.003 0.032 0.033 0.032	(0.019) (0.006) (0.019) (0.019) (0.019)	0.00; 0.99	0.33; 0.56	0.50; 0.48	0.05; 0.83 0.01; 0.94 0.14; 0.70	4,007 4,007 4,007 4,007	0.201 0.203 0.203 0.203	Financial and Business services	Occupation specific diversity 2nd gen. Imm. included in the ethnic diversity University graduates excluded from the ethnic diversity Germanic group excluded from the ethnic diversity	white-collar blue-collar	-0.032** 0.010 0.007	(0.010) (0.006) (0.006)	0.007 -0.014* -0.013** -0.025** -0.017**	(0.008) (0.008) (0.006) (0.010) (0.009)	0.033** 0.017* 0.055*** 0.055*** 0.055***	(0.010) (0.009) (0.013) (0.013) (0.013)	-0.025 -0.008 -0.010 -0.009 -0.009	(0.019) (0.010) (0.011) (0.011) (0.011)	0.39; 0.53	1.39; 0.23	1.88; 0.17	9.51; 0.002 6.34; 0.012 3.90; 0.05	7,931 7,931 7,931 7,931	0.361 0.361 0.361 0.361
				Index ethnic disaggr (1)		Index ethnic disaggr (2)		Index edu disaggr		Index demo disaggr	Hypothesis tests (chi2, p-value)	Index ethnic (white-collar)=index ethnic (blue-collar)	Index edu (white-collar)=index edu (blue-collar)	Index demo (white-collar)=index demo (blue-collar)	Index ethnic (1)=index ethnic (2)	Observations	R2				Index ethnic disaggr (1)		Index ethnic disaggr (2)		Index edu disaggr		Index demo disaggr	Hypothesis tests (chi2, p-value)	Index ethnic (white-collar)=index ethnic (blue-collar)	Index edu (white-collar)=index edu (blue-collar)	Index demo (white-collar)=index demo (blue-collar)	Index ethnic (1)=index ethnic (2)	Observations	R2				Index ethnic disaggr (1)		Index ethnic disaggr (2)		Index edu disaggr		Index demo disaggr	Hypothesis tests (chi2, p-value)	Index ethnic (white-collar)=index ethnic (blue-collar)	Index edu (white-collar)=index edu (blue-collar)	Index demo (white-collar)=index demo (blue-collar)	Index ethnic (1)=index ethnic (2)	Observations	R2

Table A6 :

 A6 1 and 2, or by excluding/including a specific group of employees, as described in the column head, in columns 3 and 4. All regressions include the shares of employees belonging to each category considered in the diversity indices; shares of managers and middle-managers; average firm tenure; whether the firm is foreign owned, multi-establishment, and exports; a full set of 2-digit industry, year, size, and county dummies; and industry-year interactions. Standard errors are clustered at the firm level. Testing alternative hypotheses: estimates by using occupation-specific diversity, alternative index definitions, and "subtract-out" groups (aggregate specification of diversity) The dependent variable is the log of total factor productivity estimated by using the ACF approach. Index ethnic disaggr (1) is calculated as in the main analysis whereas index ethnic disaggr (2) is separately calculated for white-and blue-collar workers in columns 1 and 2, or by excluding/including a specific group of employees, as described in the column head, in columns 3 and 4. All regressions include the shares of employees belonging to each category considered in the diversity indices; shares of managers and middle-managers; average firm tenure; whether the firm is foreign owned, multi-establishment, and exports; a full set of 2-digit industry, year, size, and county dummies; and industry-year interactions. Standard errors are clustered at the firm level.

	Manufacturing	Occupation specific diversity 2nd gen. Imm. included in the ethnic diversity University graduates excluded from the ethnic diversity	white-collar blue-collar	-0.018** -0.008	(0.009) (0.009)	-0.005* -0.013*** -0.006 -0.026***	(0.003) (0.003) (0.009) (0.007)	0.027*** 0.009** 0.014** 0.014**	(0.005) (0.003) (0.006) (0.006)	-0.008 -0.002 0.024 0.024	(0.005) (0.003) (0.016) (0.016)	4.57; 0.057	8.53; 0.003	2.52; 0.133	9.78; 0.000 8.71; 0.002	35,887 35,887 35,887	0.21 0.291 0.281	Wholesale and retail trade	Occupation specific diversity 2nd gen. Imm. included in the ethnic diversity University graduates excluded from the ethnic diversity	white-collar blue-collar	-0.024** -0.007	(0.009) (0.010)	-0.010** -0.037*** -0.010 -0.027**	(0.004) (0.006) (0.009) (0.010)	0.036*** 0.007** 0.012** 0.010*	(0.005) (0.003) (0.006) (0.006)	-0.015 -0.014 -0.004 -0.004	(0.014) (0.015) (0.005) (0.005)	19.61; 0.000	20.07; 0.000	0.75; 0.381	17.91; 0.000 19.33; 0.000	26,418 26,418 26,418	0.555 0.553 0.553	Significance levels: ***1%, **5%, Significance levels: ***1%, **5%,
		Germanic group excluded from the ethnic diversity		Index ethnic aggr (1)		Index ethnic aggr (2)		Index edu aggr		Index demo aggr	Hypothesis tests (chi2, p-value)	index ethnic (white-collar)=index ethnic (blue-collar)	index edu (white-collar)=index edu (blue-collar)	index demo (white-collar)=index demo (blue-collar)	index ethnic (1)=index ethnic (2)	Observations	R2		Germanic group excluded from the ethnic diversity		Index ethnic aggr (1)		Index ethnic aggr (2)		Index edu aggr		Index demo aggr	Hypothesis tests (chi2, p-value)	index ethnic (white-collar)=index ethnic (blue-collar)	index edu (white-collar)=index edu (blue-collar)	index demo (white-collar)=index demo (blue-collar)	index ethnic (1)=index ethnic (2)	Observations	R2	*10%. *10%.
																	xxiv xxv

Note:

Table A7 :

 A7 Testing alternative hypotheses: the role of export and estimates by relevant industrial aggregations Interactions with export dummy Estimates by Industry R&D intensity Estimates by Industrial employment development Manufacturing Construction Wholesale and retail trade Transport

Table A8 :

 A8 The dependent variable is the log of total factor productivity estimated by using the ACF approach. All regressions include the shares of employees belonging to each category considered in the diversity indices; shares of managers and middle-managers; average firm tenure; whether the firm is foreign owned, multi-establishment, and exports; a full set of 2-digit industry, year, size, and county dummies; and industry-year interactions. Standard errors are clustered at the firm level. Significance levels: ***1%, **5%, *10%. Robustness checks: estimates by size, under alternative samples, and index definitions (aggregate specification of diversity) The dependent variable is the log of total factor productivity estimated by using the ACF approach. All regressions include the shares of employees belonging to each category considered in the diversity indices; shares of managers and middle-managers; average firm tenure; whether the firm is foreign owned, multi-establishment, and exports; a full set of 2-digit industry, year, size, and county dummies; and industry-year interactions. Standard errors are clustered at the firm level. Significance levels: ***1%, **5%, *10%.

	Manufacturing	Estimates by Firm Size "Copenhagen" county is excluded Mono-establishment firms	Small Firms Medium Firms Large Firms	-0.019** -0.014** -0.020*** -0.014*** -0.009**	(0.008) (0.005) (0.004) (0.003) (0.003)	0.005 0.026** 0.048*** 0.016*** 0.013**	(0.008) (0.009) (0.012) (0.006) (0.006)			0.012 0.010 0.011 0.015 0.009	(0.007) (0.009) (0.014) (0.009) (0.006)							9,727 13,446 12,714 34,763 31,279	0.287 0.293 0.290 0.283 0.277	Wholesale and retail trade	Estimates by Firm Size "Copenhagen" county is excluded Mono-establishment firms	Small Firms Medium Firms Large Firms	1.65; 0.21 -0.005* -0.015* -0.062*** (0.003) 0.33; 0.56 2.56; 0.09 (0.008) (0.010) -0.027*** (0.006) -0.021*** (0.006)	0.01; 0.92 6.08; 0.03 0.004** 0.009* 0.017** 0.013** 0.019**	0.10; 0.75 0.58; 0.63 (0.002) (0.005) (0.007) (0.005) (0.006)	7,931 6,506 85761 35157 57110	0.363 0.190 0.673 0.665 0.654	-0.002 0.009 -0.026 -0.003 0.001	(0.007) (0.009) (0.014) (0.005) (0.006)				10,042 10,492 5,884 24,329 21,720	0.473 0.505 0.509 0.560 0.518
		Shannon entropy index Richness Edu and demo diversity as sd		-0.015*** -0.014** -0.014***	(0.003) (0.005) (0.003)	0.023** 0.014** 0.012**	(0.007) (0.005) (0.004)	0.006	(0.004)	0.024 -0.002	(0.015) (0.005)	-0.001	(0.005)	0.203***	(0.025)	5.67; 0.036	64.92; 0.000	35,887 35,887 35,887	0.282 0.279 0.286		Shannon entropy index Richness Edu and demo diversity as sd		1.70; 0.18 1.01; 0.45 1.47; 0.22 2.12; 0.14 -0.040*** -0.042*** (0.007) (0.009) -0.015*** (0.004)	0.018** 0.023** 0.033***	(0.008) (0.008) (0.006)	35,887 18,024 26,418 4,007 0.007 0.292 0.249 0.56 0.204 (0.004)	-0.002 -0.001	(0.006) (0.005)	-0.010	(0.007)	0.142***	(0.025)	8.88; 0.000	22.50; 0.000	26,418 26,418 26,418	0.554 0.554 0.56
				Index ethnic aggr		Index edu aggr		Sd(years of education)		Index demo aggr		Sd(age)		Share of men	Hypothesis tests (chi2, p-value)	index edu=sd(years of education)	Sd (age)=share of men	Index ethnic (above)=index ethnic (below) Note: xxvi Index edu (above)=index ethnic (below) Index demo (above)=index demo (below) Observations R2 Observations R2 Index ethnic aggr Index edu aggr Sd(years of education) Index demo aggr xxvii		Sd(age)		Share of men	Hypothesis tests (chi2, p-value)	index edu=sd(years of education)	Sd (age)=share of men	Observations	R2

Note:

Table A9 :

 A9 Labor diversity and productivity, IV results: additional second stage regressions Manufacturing Construction Wholesale and retail trade Transport Financial and business services The dependent variable is the log of total factor productivity estimated by using the ACF approach. Firm level diversity is instrumented by using the predicted level of diversity at the commuting area, where the firm is located. All regressions include the shares of employees belonging to each category considered in the diversity indices; shares of managers and middle-managers; average firm tenure; whether the firm is foreign owned, multi-establishment, and exports; a full set of 2-digit industry, year, size, and county dummies. Standard errors are clustered at the commuting area level. Significance levels: ***1%, **5%, *10%.

				All sample
	index ethnic disaggr	-0.026*	-0.038*	-0.028**	-0.031	0.009
		(0.014)	(0.019)	(0.014)	(0.084)	(0.012)
	index edu disaggr	0.061**	0.037	0.095**	0.047	0.078*
		(0.028)	(0.019)	(0.040)	(0.149)	(0.038)
	index demo disaggr	0.093	-0.048	-0.056	-0.085	-0.048
		(0.086)	(0.049)	(0.033)	(0.070)	(0.033)
	Observations	35,887	18,024	26,418	4,007	7,931
	R2	0.310	0.123	0.252	0.189	0.200
				Mono-establishment firms
	index ethnic disaggr	-0.017	-0.062	-0.024	-	0.017
		(0.093)	(0.035)	(0.016)	-	(0.079)
	index edu disaggr	0.057*	0.028	0.082**	-	0.074
		(0.029)	(0.021)	(0.061)	-	(0.037)
	index demo disaggr	0.143	-0.046	-0.027	-	-0.066
		(0.088)	(0.085)	(0.033)	-	(0.157)
	Observations	31,279	17,118	21,720	-	6,479
	R2	0.260	0.108	0.277	-	0.114
				Small firms with fewer than 50 employees
	index ethnic disaggr	-0.015*	-0.075	-0.033**	-	0.027
		(0.008)	(0.049)	(0.014)	-	(0.019)
	index edu disaggr	0.032*	0.055	0.123*	-	0.082
		(0.017)	(0.037)	(0.069)	-	(0.049)
	index demo disaggr	0.170	-0.084	-0.055	-	-0.041
		(0.161)	(0.079)	(0.046)	-	(0.035)
	Observations	23,173	15,423	20,534	-	5,536
	R2	0.435	0.096	0.188	-	0.109
				Copenhagen county is excluded
	index ethnic disaggr	-0.034	-0.047	-0.013	-0.027	0.025
		(0.023)	(0.030)	(0.016)	(0.068)	(0.012)
	index edu disaggr	0.053**	0.025*	0.060**	0.022	0.080*
		(0.022)	(0.013)	(0.021)	(0.123)	(0.042)
	index demo disaggr	0.144	-0.057*	-0.028	-0.127	-0.102
		(0.213)	(0.029)	(0.041)	(0.099)	(0.094)
	Observations	34,763	17,302	24,329	3,619	6,149
	R2	0.263	0.145	0.365	0.128	0.255
				Firms established before 1990
	index ethnic disaggr	-0.038	-	-0.045**	-	0.016
		(0.084)	-	(0.022)	-	(0.014)
	index edu disaggr	0.023*	-	0.186	-	0.142
		(0.014)	-	(0.269)	-	(0.089)
	index demo disaggr	0.105	-	-0.107	-	-0.029
		(0.180)	-	(0.139)	-	(0.142)
	Observations	8,962	-	5,447	-	1,717
	R2	0.231	-	0.281	-	0.198
				xxviii

Note:

Table A10 :

 A10 IV results: first stage regressions (aggregate specification of diversity) The dependent variable is diversity at the firm level. All regressions include the shares of employees belonging to each category considered in the diversity indices; shares of managers and middle-managers; average firm tenure; whether the firm is foreign owned, multi-establishment, and exports; a full set of 2-digit industry, year, size, and county dummies; and industry-year interactions. Standard errors are clustered at the commuting area level. Significance levels: ***1%, **5%, *10%.

			Manufacturing
		Index ethnic aggr Index edu aggr Index demo aggr
	index ethnic com	0.949***	-0.064	-0.060**
		(0.080)	(0.045)	(0.027)
	index edu com	-0.348**	0.072***	-0.172***
		(0.110)	(0.028)	(0.041)
	index demo com	-1.181***	0.024	1.054***
		(0.246)	(0.182)	(0.093)
	F test (excluded instruments); p-value	48.51; 0.000	11.67; 0.000	30.61; 0.000
	Observations	48,238	48,238	48,238
	R2	0.404	0.462	0.371
			Construction
		Index ethnic aggr Index edu aggr Index demo aggr
	index ethnic com	0.247***	-0.301***	-0.041
		(0.063)	(0.062)	(0.032)
	index edu com	0.079	0.241**	-0.076
		(0.051)	(0.092)	(0.061)
	index demo com	-0.119	0.685***	0.590***
		(0.252)	(0.173)	(0.140)
	F test (excluded instruments); p-value	9.19; 0.000	7.93; 0.003	7.12; 0.004
	Observations	26,969	26,969	26,969
	R2	0.223	0.513	0.397
		Wholesale and retail trade
		Index ethnic aggr Index edu aggr Index demo aggr
	index ethnic com	0.463***	-0.411***	0.234***
		(0.099)	(0.050)	(0.049)
	index edu com	0.101	0.902***	-0.655***
		(0.190)	(0.092)	(0.058)
	index demo com	0.147*	-0.281***	1.392***
		(0.086)	(0.079)	(0.096)
	F test (excluded instruments); p-value	30.82; 0.000	28.42; 0.000	81.58; 0.000
	Observations	41,493	41,493	41,493
	R2	0.331	0.487	0.47
			Transport
		Index ethnic aggr Index edu aggr Index demo aggr
	index ethnic com	0.407***	0.157	-0.168**
		(0.106)	(0.239)	(0.067)
	index edu com	0.060	0.507**	0.155
		(0.166)	(0.231)	(0.145)
	index demo com	-1.030**	0.135	0.589**
		(0.326)	(0.249)	(0.188)
	F test (excluded instruments); p-value	11.97; 0.000	6.94; 0.000	9.48; 0.000
	Observations	6,285	6,285	6,285
	R2	0.393	0.327	0.294
		Financial and business services
		Index ethnic aggr Index edu aggr Index demo aggr
	index ethnic com	0.678***	-0.037	-0.139**
		(0.186)	(0.093)	(0.060)
	index edu com	-0.041	0.297***	0.070
		(0.133)	(0.086)	(0.072)
	index demo com	-0.018	-0.336*	1.004***
		(0.157)	(0.183)	(0.111)
	F test (excluded instruments); p-value	10.35; 0.000	5.12; 0.002	51.19; 0.000
	Observations	14,008	14,008	14,008
	R2	0.43	0.593	0.441
		xxix

Note:

Table A11 :

 A11 Labor diversity and productivity, IV results: second stage regressions (aggregate specification of diversity) Manufacturing Construction Wholesale and retail trade Transport Financial and business services

	-0.027	(0.036)	0.058*	(0.029)	-0.048	(0.033)	7,931	0.159
	-0.051	(0.058)	0.092	(0.069)	-0.068	(0.070)	4,007	0.165
	-0.069**	(0.025)	0.048**	(0.013)	-0.012	(0.027)	26,418	0.329
	-0.037*	(0.018)	0.026*	(0.014)	0.070	(0.096)	18,024	0.114
	-0.049**	(0.016)	0.029*	(0.016)	0.027	(0.022)	35,887	0.312
	index ethnic aggr		index edu aggr		index demo aggr		Observations	R2

To keep the number of regressors manageable, we always use a fourth-degree polynomial (with interactions) in the rst stage and a third-degree polynomial in v ijt to compute g(.).

Note that the estimation of the production function[START_REF] Berliant | Knowledge Creation as a Square Dance on the Hilbert Cube[END_REF] cannot be carried out for construction and transport sectors due to non-convergence of the estimation algorithm.

Note that the estimation of production function (17) cannot be carried out with either ACF or OP due to non-convergence of the estimation algorithm.

Note that the estimation of production function[START_REF] Mercedes | Clusters and Entrepreneurship[END_REF] cannot be carried out for textiles, other-non metallic mineral products, construction and transport due to non-convergence of the estimation algorithm.

Acknowledgments

We thank Sandra E. Black, Holger Bonin, Tor Eriksson, Luca Merlino, Andreas Moxnes, Jozef Konings, Jennifer Poole, Michael Rosholm, Fabiano Schivardi, Vanormelingen Stijn, Chad Syverson, Kenneth L. Sørensen, and Frederic Warzynski (alphabetical order) for their helpful comments and suggestions. Additionally, we appreciate the comments from participants at seminars organized by the Copenhagen Business School, University of Bergamo, Aarhus School of Business, University of Lausanne and ZEW (Mannheim) and from participants at the following conferences: ESPE 2010, the 5th Nordic Summer Institute in Labor Economics, the 2010 Ratio Young Scientist Colloquium, ESEM 2010 and CAED/COST 2010 in London. Pierpaolo Parrotta acknowledges nancial support from the Graduate School for Integration, Production and Welfare, and the Swiss National Centres of Competence in Research LIVES. Mariola Pytlikova gratefully acknowledges funding from the NORFACE Migration Programme. The usual disclaimer applies.

Appendix 1: Groups included in the measure of ethnic diversity 1) The citizens in the different nationality groups are: Danish: Danish native including second generation immigrants; North America and Oceania: United States, Canada, Australia, New Zealand; Central and South America, Guatemala, Belize, Costa Rica, Honduras, Panama, El Salvador, Nicaragua, Venezuela, Ecuador, Peru, Bolivia, Chile, Argentina, Brazil; Formerly Communist Countries: Armenia, Belarus, Estonia, Georgia, Latvia, Lithuania, Moldova, Russia, Tajikistan, Ukraine, Bulgaria, Czech Republic, Hungary, Poland, Romania, Slovakia, Albania, Bosnia and Herzegovina, Croatia, Rep. of Macedonia, Montenegro, Serbia, and Slovenia; Muslim Countries: Afghanistan, Algeria, Arab Emirates, Azerbaijan, Bahrain, Bangladesh, Brunei Darussalem, Burkina Faso, Camoros, Chad, Djibouti, Egypt, Eritrea, Gambia, Guinea, Indonesia, Iran, Iraq, Jordan, Kazakstan, Kirgizstan, Kuwait, Lebanon, Libyan Arab Jamahiriya, Malaysia, Maldives, Mali, Mauritania, Morocco, Nigeria, Oman, Pakistan, Palestine, Qatar, Saudi Arabia, Senegal, Sierra Leone, Somalia, Sudan, Syria, Tadzhikstan, Tunisia, Turkey, Turkmenistan, Uzbekistan, Yemen; East Asia: China, Hong Kong, Japan, Korea, Korea Dem. People's Rep. Of, Macao, Mongolia, Taiwan; Other Asia: all the other Asian countries non included in both East Asia and Muslim Countries categories and Africa, all the other African countries not included in the Muslim Country; Western and Southern Europe: all the other European countries not included in the Formerly Communist Countries category.

2) The linguistic groups are: Germanic West (Antigua Barbuda, Aruba, Australia, Austria, Bahamas, Barbados, Belgium, Belize, Bermuda, Botswana, Brunei, Cameroon, Canada, Cook Islands, Dominican Republic, Eritrea, Gambia, Germany, Ghana, Grenada, Guyana, Haiti, Ireland, Jamaica, Liberia, Liechtenstein, Luxemburg, Mauritius, Namibia, Netherlands, Netherlands Antilles, New Zealand, Saint Kitts and Nevis, Saint Lucia, Saint Vincent and Grenadines, Seychelles, Sierra Leone, Solomon Islands, South Africa, St. Helena, Suriname, Switzerland, Trinidad and Tobago, Uganda, United Kingdom, United States, Zambia, Zimbabwe); Slavic West (Czech Republic, Poland, Slovakia); Germanic Nord (Denmark, Iceland, Norway, Sweden); Finno-Permic (Finland, Estonia); Romance (Andorra, Angola, Argentina, Benin, Bolivia, Brazil, Burkina Faso, Cape Verde, Chile, Colombia, Costa Rica, Cote D'Ivoire, Cuba, Djibouti, Dominican Republic, Ecuador, El Salvador, Equatorial Guinea, France, French Guyana, Gabon, Guadeloupe, Guatemala, Guinea, Guinea Bissau, Holy See, Honduras, Italy, Macau, Martinique, Mexico, Moldova, Mozambique, Nicaragua, Panama, Peru, Portugal, Puerto Rico, Reunion, Romania, San Marino, Sao Tome, Senegal, Spain, Uruguay, Venezuela); Attic (Cyprus, Greece); Ugric (Hungary); Turkic South (Azerbaijan, Turkey, Turkmenistan); Gheg (Albania, Kosovo, Republic of Macedonia, Montenegro); Semitic Central (Algeria, Bahrain, Comoros, Chad, Egypt, Irak, Israel, Jordan, Kuwait, Lebanon, Lybian Arab Jamahiria, Malta, Mauritiania, Morocco, Oman, Qatar, Saudi Arabia, Sudan, Syrian Arab Republic, Tunisia, Yemen, United Arabs Emirates); Indo-Aryan (Bangladesh, Fiji, India, Maldives, Nepal, Pakistan, Sri Lanka); Slavic South (Bosnia and Herzegovina, Croatia, Serbia, Slovenia); Mon-Khmer East (Cambodia); Semitic South (Ethiopia); Slavic East (Belarus, Bulxv garia, Georgia, Mongolia, Russian Federation, Ukraine); Malayo-Polynesian West (Indonesia, Philippines); Malayo-Polynesian Central East (Kiribati, Marshall Islands, Nauru, Samoa, Tonga); Iranian (Afghanistan, Iran, Tajikistan); Betai (Laos, Thailand); Malayic (Malasya); Cushitic East (Somalia); Turkic East (Uzbekistan); Viet-Muong (Vietnam); Volta-Congo (Burundi, Congo, Kenya, Lesotho, Malawi, Nigeria, Rwanda, Swaziland, Tanzania, Togo); Turkic West (Kazakhstan, Kyrgystan); Baltic East (Latvia, Lithuania); Barito (Madagascar); Mande West (Mali); Lolo-Burmese (Burma); Chadic West (Niger); Guarani (Paraguay); Himalayish (Buthan); Armenian (Armenia); Sino Tibetan (China, Hong Kong, Singapore, Taiwan); Japonic (Japan, Republic of Korea, Korea D.P.R.O.). xvi