Pierpaolo Parrotta
email: pier-paolo.parrotta@unil.ch.

Dario Pozzoli

Mariola Pytlikova

The Nexus between Labor Diversity and Firm's Innovation

Keywords: JEL Classication: J15, J16, J24, J61, J82, O32 Labor diversity, ethnic diversity, patenting activity, extensive and intensive margins

In this paper we investigate the nexus between rm labor diversity and innovation using data on patent applications led by rms at the European Patent Oce and a linked employer-employee database from Denmark. Exploiting the information retrieved from these comprehensive data sets and implementing proper instrumental variable strategies, we estimate the contribution of workers' diversity in cultural background, education and demographic characteristics to valuable rm's innovation activity. Specically, we nd evidence supporting the hypothesis that ethnic diversity may facilitate rms' patenting activity in several ways by: (a) increasing the propensity to (apply for a) patent, (b) increasing the overall number of patent applications and (c) by enlarging the breadth of patenting technological elds, conditional on patenting. Several robustness checks corroborate the main ndings.

Introduction

Many developed and developing countries have experienced several changes in the workforce composition which has led to an increased heterogeneity of the labor force in terms of age, gender, skills and ethnicity. This is partly the result of policies adopted to counteract the problem of population aging, anti-discrimination measures, immigration and the worldwide globalization process [START_REF] Pedersen | Selection and Network Eects -Migration Flows into OECD Countries 1990-2000[END_REF]). From the demand side, we observe increasing diversity across many workplaces and we often hear about the importance of further internationalization and demographic diversication. The promotion of diversity is often perceived as a chance to improve learning and knowledge management capabilities and then enhance rm productivity [START_REF] Parrotta | Does Labor Diversity Aect Firm Productivity? Norface Migration Discussion Paper[END_REF]). Besides, workforce diversity is believed to be an important source of innovation. For instance, in a relatively recent survey conducted by the European Commission, a large number of respondents identied innovation as a key benet of having diversity policies and practices (European Commission 2005). If this is the case, rms could benet from the growing diverse cultural backgrounds, demographic, and knowledge bases of the workforces. Moreover, since there is a widespread consensus that innovation is crucial for sustainable growth and economic development (as suggested in the new growth theories), understanding the link between workforce diversity and innovation seems to be essential for policy makers.

From a theoretical point of view, a paradox has been recognized: whereas a high degree of heterogeneity among workers can be a source of creativity and therefore foster innovation activity, it can also induce misunderstanding, conicts and uncooperative behaviors within workplaces and in this way hinder innovation (Basset-Jones 2005). There is no general agreement on which eect prevails. Specically, dierences in skills, education and more broadly in knowledge among employees seem to be benecial rather than detrimental (Wat- 2 Some empirical studies 1 have explored the link between labor diversity and rm's inno- vation, and just a few of them have made use of comprehensive matched employer-employee dataset [START_REF] Østergaard | Does a dierent view create something new? The eect of employee diversity on innovation[END_REF](Østergaard et al. , Söllner 2010) ) or have properly addressed endogeneity issues related to the identication of the eects of workforce diversity of rm-level innovation outcomes (Ozgen et al. 2011b). Also our study investigates the nexus between labor diversity and innovation using a rich and register-based linked employer-employee data set from Denmark for the period 1995-2003. However we try to deal with several problems that previous literature studying the impact of workforce diversity on innovation has often not properly addressed. Most importantly, if rms are aware of the importance of labor diversity and leverage it to improve their performance, then the relationship under investigation is very likely to be aected by endogeneity. As an attempt to address these concerns, we implement an instrumental variable (IV) strategy à la [START_REF] Card | Immigrant inows, native outows, and the local labor market impacts of higher immigration[END_REF] based on measures of historical workforce diversity patterns at the commuting area level (where a rm is located) as instruments for the current rm labor diversity. In addition, we use an alternative instrument for the workplace ethnic diversity based on foreign population shares at the commuting areas predicted from a model of migration determinants. Furthermore, rms are characterized by a dierent propensity to innovate. Thus, there exist unobserved and observed rm-specic heterogeneity that should be taken into account to evaluate the eect of any labor diversity dimension on rm's innovation outcome. As we do not have sucient data variation to undertake panel estimations, we use pre-sample information to proxy for unobservable permanent rm characteristics [START_REF] Blundell | Dynamic Count Data Models of Technological Innovation[END_REF]. Finally, we control for the potential role of the external knowledge in favoring rms' patenting activity and compute knowledge spillovers indicators based on geographical and technological distances between rms.

Regarding measures of innovation, we follow previous literature and make use of information on patents to proxy for innovation [START_REF] Griliches | Patent Statistics as Economic Indicators: A Survey[END_REF], [START_REF] Bloom | Patents, real options and rm performance[END_REF]. Specically, we use the following three measures: (1) rm's propensity to apply for a patent, (2) the number of patent applications introduced each year and (3) rm's propensity to apply in more than one technological area, conditional on applying for a patent. We investigate 1 See next section for a brief overview of the literature.

the eect of labor diversity on rm innovation by looking at three dimensions of employee diversity: cultural background, education and demographics. The comprehensive data allows us to dig deeper into the mechanisms by which diverse workforces may aect innovation. In particular, we test whether (a) the benecial eects of diverse problem-solving abilities and creativity would materialize more in terms of innovation for white-collar occupations compared to blue-collar occupations, (b) communication costs associated with ethnic diversity may increase after subtracting out foreigners who are likely to speak Danish or English.

Implementing alternative estimation techniques, we nd evidence of the key role of ethnic diversity in promoting rm's innovation as measured by the number of patent applications, the probability to apply for a patent or to patent in more than one technological eld, conditional on patenting. The contribution of ethnic diversity to start patenting and to the number of rms' patent applications is economically meaningful. Furthermore, the eect of ethnic diversity on extensive margins is very large: conditional on patent application, a standard deviation increase in ethnic diversity almost duplicates the probability to patent in dierent technological elds, according to the most conservative estimates. Eects of diversity in education and demographics turn out to be mostly insignicant when either the full set of controls is included or endogenity is taken care of. These results support the hypothesis that ethnically diverse workers tend to have a wider pool of dierent experiences, knowledge bases and heuristics boosting their problem-solving capacities and creativity, which in turn facilitate innovations.

The structure of the paper is as follows: section 2 reviews related literature and derives hypotheses, section 3 briey describes the data, section 4 provides details on the empirical strategy, section 5 explains all the results of our empirical analyses and section 6 oers some concluding remarks.

2 Literature background and hypotheses development One of the most relevant theoretical contribution, describing the role of workforce diversity in terms of rm's level outcomes, is by [START_REF] Lazear | Globalisation and the Market for Team-Mates[END_REF]. His model predicts positive eects of educational/skill diversity on rm performance as long as workers' information sets are not overlapping but relevant to one another. Thus, being educational diversity a measure of skill complementarity and knowledge spillovers, it is very likely to have a positive inuence on rm's innovation activity. Furthermore, referring to the role of high skilled workers, [START_REF] Berliant | The dynamics of knowledge diversity and economic growth[END_REF] propose a model in which the composition of the research workforce in terms of knowledge heterogeneity positively aects the production of new knowledge as it accelerates the generation of new ideas through individual-level production complementarities.

Conversely, it is less straightforward to predict the directions of the eects of diversity in ethnicity and demographic characteristics, as such dimensions may bring high communication costs and low social ties and trust, which may hinder knowledge spillovers and exchange among diverse employees [START_REF] Lazear | Globalisation and the Market for Team-Mates[END_REF]. Specically, ethnic diversity may create communication barriers, reduce the workforce cohesion and prevent cooperative participation in research activities, bringing high costs of cross-cultural dealing (Williams and O'Reilly 1998, [START_REF] Zajac | New Organizational Forms for Enhancing Innovation: The Case of Internal Corporate Joint Ventures[END_REF][START_REF] Lazear | Globalisation and the Market for Team-Mates[END_REF]). Indeed, demographic heterogeneity among workers may create communication frictions if workers are prejudiced, and therefore bring some cost connected to these frictions [START_REF] Becker | The Economics of Discrimination[END_REF]). On the other hand, diversity in both ethnic and demographic dimension may also bring substantial benets in terms of rm innovation outcomes. Employees of dierent cultural backgrounds may provide diverse perspectives, valuable ideas, problem-solving abilities, and in this way facilitate the achievement of optimal creative solutions and therefore stimulate innovations [START_REF] Watson | Cultural Diversity's Impact on Interaction Process and Performance: Comparing Homogeneous and Diverse Task Groups[END_REF], Drach-Zahavy and Somech 2001, Hong and Page 2004; [START_REF] Berliant | The dynamics of knowledge diversity and economic growth[END_REF]. Given that cultural heterogeneity is often a good proxy for cognitive diversity, ethnically diversied workforces may exploit a larger pool of knowledge. [START_REF] Hong | Problem Solving by Heterogeneous Agents[END_REF] present a model of agents of bounded abilities and analyze their individual and collective performance. Agents are heterogeneous as they dier in their perspectives (internal representations of the problems) and heuristics (algorithms they use to generate solutions). The authors nd that "diversity in either perspectives or heuristics proves sucient for a collection of agents to allocate optimal solutions to dicult problems". Moreover, employees of dierent ethnic backgrounds may stimulate rm to improve or develop new products sold abroad as they also possess knowledge about global markets and customers' tastes [START_REF] Osborne | The Deceptively Simple Economics of Workplace Diversity[END_REF], Kerr and Lincoln 2010, [START_REF] Hatzigeorgiou | Trade and Migration: Firm-Level Evidence[END_REF]Lodefalk 2012, Hiller 2013). Concerning the positive inuence of demographic diversity on rm performance, it seems plausible to assume for instance that age heterogeneity may facilitate innovation because there are complementarities between the human capital of younger and older workers: younger employees have knowledge of new technologies and IT and older employees have a better understanding and experience with the intra-rm structures and the operating process [START_REF] Lazear | Personnel Economics for Managers[END_REF]).

The empirical literature exploring the relationship between labor diversity and rm's innovation consists of (i) business case studies that often look at work-team compositions The limited number of empirical studies at the rm level may be imputed to dierences in research aims and approaches, but also to the lack of more comprehensive employer-employee data, which provide a notable amount of information on the labor force composition at the rm level. To the best of our knowledge, the evidence using more comprehensive data is rather scarce. Only three recent studies analyze the relationship between labor heterogeneity and rm innovation outcomes, using linked employer-employee data (LEED). The rst work the number of foreign restaurants and the historical presence of immigrant communities per municipality as instruments for the immigrant settlement, they nd that whereas rms with large shares of foreigners are less innovative, a more diverse workforce positively aects rm innovativeness. Although Ozgen et al. (2011b) propose an interesting IV strategy, they end up using a relatively small sample of rms to evaluate the impact of cultural diversity on rm propensity to introduce an innovation. Further, they do neither look at other labor diversity dimensions nor take extensively into account rm unobserved heterogeneity as we do in the present study.

Based on the existing theoretical literature, we derive our hypotheses for the eects of labor diversity on rm's innovation activity. First, we expect to nd a positive contribution of educational diversity to rm's innovation, as soon as workers' information sets are not overlapping but relevant to one another. Second, we don't have any clear prior on the directions of the eects, as benets from diversity in these dimensions may be compensated by potential costs associated with communication and distrust among employees. Finally, given that workforce diversity ought to be translated into larger spectrum of perspectives, heuristics and knowledge (Hong and Page 2001, Berliant and Fujita 2011), we might expect that the workforce diversity may aect not only the scale, but also the scope of innovation.

In other words, we expect workforce diversity to not only aect the probability to innovate and the extent of rm's innovation activity, but also the variety of technological elds, in which rm innovates.

As the comprehensiveness of our data allows us to dig deeper into the mechanisms by which diverse workforces may aect innovation, we test two further hypotheses. Firstly, we test the creativity hypothesis proposed in the theoretical frameworks by [START_REF] Hong | Problem Solving by Heterogeneous Agents[END_REF] and [START_REF] Berliant | The dynamics of knowledge diversity and economic growth[END_REF]. Specically, we expect that the benecial eects of diverse problem-solving abilities and creativity originating from knowledge complementarities would materialize more in terms of innovation for white-collar occupations (high skilled employees) compared to blue-collar occupations (low skilled employees). Secondly, we exclude certain groups of foreigners from the calculation of ethnic diversity measures to test whether the costs of cross-cultural dealing play a role. In particular, we expect that communication costs associated with ethnic diversity may increase after subtracting out foreigners who are likely to speak Danish or English.

Data

Data sources

The data set we use for our analysis is obtained by merging three dierent data sources from Denmark. The rst one is the `Integrated Database for Labor Market Research' (IDA), which is a register-based LEED managed by Statistics Denmark, a Danish governmental institute in charge for creating statistics on the Danish society and economy. IDA contains a broad set of information on individuals and rms for years 1980-2006. In particular, we are interested in gender, age, nationality, education, occupation, tenure, place of work, whether a company is (partially or totally) foreign-owned and a multi-establishment rm.

The second data source is a register of rms' business accounts (REGNSKAB) that provides information on a number of nancial items, which we need in order to construct values of rms' capital stock, information on whether a rm is an exporter and the 3-digit industry, in which the rm operates. This database is also maintained by the Statistics Denmark and reports data for the period 1995-2005. 2 In REGNSKAB it is possible to identify partially and totally imputed values, which we exclude from our nal data set in order to avoid any bias in the estimates. The last data source is a collection of patent applications sent to the European Patent Oce (EPO) by Danish rms.

3 It covers a period of 26 years (1978- 2003) and allows us to account for 2,822 applicants, corresponding to 2,244 unique rms. 4

Unfortunately the patent data, that has been provided to us by the Center for Economic and Business Research and that has been merged to the Danish register data, only cover the number of patent applications and grants, together with a classication of patents in technological areas. Hence our data does not include any variable that has been used by the main literature in this eld to proxy for the quality and traits of innovations [START_REF] Trajtenberg | A penny for your quotes: patent citations and the value of innovations[END_REF], Lanjouw et al. 1998[START_REF] Hall | Market Value and Patent Citations[END_REF]. For instance, both the forward citation weights of patents and measures of originality/generality of inventions are missing. These data limits prevent us from assessing to what extent workforce diversity impacts on the quality and traits of innovations. Furthermore, it is important to underline that patents as a measure of rm innovation, like any other innovation indicators, present both advantages and disadvantages (Archibugi and Planta 1996). On the positive side, patent applications (i) are a direct outcome of the innovation process, (ii) need some eorts to be documented, (iii) are broken down by technical elds (IPC) informing this way on the directions of performed innovation activities. On the other side though not all inventions are necessarily linked to patent applications or technically patentable and rms may present dierent propensity to apply for a patent. All in all, though with some important limitations, we believe that patent applications may represent a plausible and suitable proxy for rm's innovation activity, being somehow a rather conservative and objective measure of innovation.

2 Part of the statistics in REGNSKAB refers to selected rms for direct surveying: all rms with more than 50 employees or prots higher than a given threshold. The rest is recorded in accordance with a stratied sample strategy. The surveyed rms can choose whether to submit their annual accounts and other specications or to ll out a questionnaire. In order to facilitate responding, questions are formulated in the same way as required in the Danish annual accounts legislation.

Therefore the focus of this study is on the following rm innovation outcomes: i) the rm's propensity to apply for a patent, ii) the number of patent applications for each year and iii) the rm's propensity to apply in more than one technological area, conditional on patenting. We disregard industries 5 with no patenting rms during the period covered in our empirical analysis. We also exclude enterprises with less than 10 employees from our sample to allow all investigated rms to reach (potentially) the highest degree of (ethnic) diversity at least when an aggregate specication is used, as outlined in the next section.

Finally we leave out rms that were founded during the estimation period (1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003), given that we use a pre-sample estimator that requires information on rms' patenting behavior prior to 1995. Thus, our nal data set contains information on approximately 12,000 rms per year over a period of 9 years (1995-2003).

Diversity measures

The workforce diversity (heterogeneity) measures used in this article are computed at the workplace level and then aggregated at the rm level and are based on the Herndahl index. The latter combines two important dimensions of diversity: the richness , which refers to the number of dened categories within a rm, and the evenness , which informs on how equally populated such categories are. Specically, our diversity measures represent weighted averages of Herndahl indexes computed at the workplace level:

Index_h it = W w=1 N w N i 1 - S s=1 p 2 wst ,
where Index_h it is the diversity index of rm i at time t for the dimension h, W is the total number of workplaces (w refers to a given workplace) constituting the rm, and therefore N w and N i denote the total number of workers at the workplace and rm levels, respectively.

Thus, the ratio between the last two variables corresponds to the weighting function, while p wst is the proportion of the workplace's employees falling into each category s at time t, with s = 1, 2, ..., S. The diversity index has a minimum value, which takes value on zero if there is only one category represented within the workplace, and a maximum value equal to 1 -1 S if all categories are equally represented. This index can be interpreted as the probability that two randomly drawn individuals in a workplace belong to dierent groups. However, the Herndahl index presents some limitations when it comes to high or low levels of diversity [START_REF] Dawson | Measurement of work group diversity[END_REF]). For such a reason, we perform some sensitivity analysis by measuring diversity using two alternative approaches (the Shannon-Weaver and the richness indexes)

which are proven to be more robust at the extreme tails of the distribution of diversity but may present some aws for intermediate values of diversity [START_REF] Jost | Entropy and diversity[END_REF][START_REF] Dawson | Measurement of work group diversity[END_REF]).

As we distinguish between cultural (ethnic), educational (skill) and demographic diversity, a separate measure is computed along each of the three cited dimensions. 1. First, it is obvious that patenting rms in Denmark have more diverse workforces. In particular there is a clear dierence between patenting and non-patenting rms with respect to the ethnic heterogeneity, which is more than 3 times larger on average in patenting rms. Patenting rms have also larger [START_REF] Bantel | Top Management and Innovations in Banking: Does the Composition of the Top Team Make a Dierence?[END_REF] The linguistic classication is more detailed than the grouping by nationality categories. Specically, we group countries (their major ocial language spoken by the majority in a particular country) by 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 Ethnologue: Languages of the World, see the Appendix section for more details about the list of countries and the linguistic groups included. Furthermore, we adjust the index to take account of the rm size. 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). Further, patenting rms are characterized by notably higher values of capital and labor inputs: the average capital stock is about 9.7 times the value of the non-patenting rms.

Patenting rms are also more likely to be multi-establishment companies and markedly (82 percent) more export-oriented. Regarding the foreign owership status, in general we can observe that the foreign capital penetration is quite low among rms in Denmark, and there is no dierence with respect to foreign ownership status between patenting and nonpatenting rms.

For the purposes of our analyses it appears relevant to take into account the role of external sources of knowledge since they may facilitate rms' innovation activity. Following the approaches suggested by [START_REF] Audretsch | R&D Spillovers and the Geography of Innovation and Production[END_REF] and [START_REF] Adams | Bounding the Eects of R&D: An Investigation Using Linked Establishment and Firm Data[END_REF], we construct two indexes of knowledge spillovers. These are weighted sums of rms' codied knowledge proxied by the discounted stock of patent applications. [START_REF] Basset-Jones | The Paradox of Diversity Management, Creativity and Innovation[END_REF] The weighting function for the rst index refers to the geographical distance between pairs of workplaces' municipalities and is computed by using the rms' latitude and longitude coordinates (the address of their headquarters). The second index is instead based on the technological proximity between pairs of workplaces. Appendix 2 provides a detailed description about how both external knowledge indexes are calculated. Looking at these measures of knowledge spillovers, see Table 1, we nd no evidence of diused clustering behavior or huge dierences in technological distance between the two groups of rms.

Overall, the presented descriptives raise a reasonable interest in evaluating the nexus between workforce diversity in ethnicity, education and demographics and rms' patenting behavior, which is something we are going to investigate in depth in the next sections.

4 Econometric methods

Propensity to innovate

To investigate the eect of labor diversity on rm's propensity to innovate, we employ a 10 Section 4.3 describes how the discounted stock of patent applications is calculated. standard binomial regression technique. Specically, we estimate the following probit model: We also control for the average rm tenure, whether the rm is an exporter, a foreign ownership dummy, a multi-establishment dummy and for possible knowledge spillover eects, by including two external knowledge indexes, as described in the previous section. Whereas Normally the DISCO code reporting to Statistics Denmark takes place directly through the company's electronic salary systems. Over the sample period, the DISCO codes have been updated regularly, with some codes being eliminated and some new codes being created. Of obvious concern is therefore the possibility of spurious changes in the DISCO codes assigned to workers who experience no real change in their occupations.We believe, however, that our analysis is largely free from such spurious changes in the DISCO codes, as we base our main analysis on one-digit classication. As shown in [START_REF] Frederiksen | Human capital and career success: Evidence from linked employer-employee data[END_REF], over the 1992-2002 period, reassuringly at the one-digit level, there was no new code added.

     p it = 1 if p * it > 0 p it =
eect of diversity, holding the shares of dierent worker types constant. The correlation between our diversity measures and the shares of each worker type in terms of ethnicity, education, age and gender in the data turns out to be rather modest 12 , which allows us to control for both variables at the same time and, thus, to separate mix and size eects of the workforce characteristics. Furthermore we think that the inclusion of such shares partly control for the fact that dierent group of foreign labour may have dierent qualities. We nally include a set of regional, year, industry and year times industry dummies in order to capture any business cycle inuences, regional-or industry-specic eects.

Identication

If rms aim at labor diversity to improve their innovation performances, then the relationship under investigation is very likely to be aected by endogeneity. To address the potential endogeneity issues, we follow an instrumental variable (IV) strategy in order to obtain a causal eect of workforce diversity on rm innovation activities. More specically, we instrument our diversity variables with indexes of workforce diversity in cultural background, skills and demographic characteristics, computed at the commuting area, 13 where the rm is located. 14 Given that the current geographical location of rms may not be random, we predict the current composition of the labor supply at the commuting area level by using its historical composition and the current population stocks [START_REF] Card | Immigrant inows, native outows, and the local labor market impacts of higher immigration[END_REF]. See also Card In this approach, for example, the predicted share of immigrants from country c and living in a commuting area l at time t, mclt , is computed using the early 90's stock of immigrants from country c living in l and its current population of immigrants:

mclt = stock cl1990 C c=1 stock clt
We believe that diversity at the commuting area level presents a suitable supply driven instrument for workplace level diversity because commuting areas in Denmark (except for the area around Copenhagen) are typically relatively small and therefore rms 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 a clear evidence of low residential mobility among danes, no matter their educational level [START_REF] Deding | Spatial Mobility and Commuting: the Case of Two-Earner Households[END_REF]), which seems to support the properness of our IV strategy. We may be though not able to apply the same argument to high-skilled immigrants, who may be more mobile than the danes themselves. However previous studies have shown that immigrants have generally a tendency to settle down [START_REF] Blundell | Market Share, Market Value and Innovation in a Panel of British Manufacturing Firms[END_REF] We chose 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 eighties and nineties were characterized by rather restrictive immigration policy with respect to economic migrants from countries outside the European Union (EU), which made it rather dicult for rms in Denmark to hire applicants from the international pool of applicants (due to consequences of the Oil Crisis). Immigration to Denmark from those countries during the eighties til mid-nineties was rather 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 a signicant political power, the immigration policy in Denmark became one of the strictest in the world. For rms it meant almost no possibilities to hire international workers from countries outside the EU, which has often been criticized by the Confederation of Danish Industry (DI). Given those historical developments, we decided to use shares of immigrants from 1990 as a base for our predictions.

in areas where there are pre-existing migrants' networks and the presence of individuals with the same cultural and linguistic background as themselves [START_REF] Damm | Ethnic Enclaves and Immigrant Labor Market Outcomes: Quasi-Experimental Evidence[END_REF][START_REF] Pedersen | Selection and Network Eects -Migration Flows into OECD Countries 1990-2000[END_REF]). [START_REF] Blundell | Individual Eects and Dynamics in Count Data Models[END_REF] We can then assume that pre-existing (from 5 to 13 years earlier) immigrant concentrations are unlikely to be correlated with current rm innovation. However, even though our instrument is based on the historical composition of the local labor supply, it may still be the case that our identication strategy is invalidated by the fact that rms choose locations that are rich in local innovation potential and therefore with a higher degree

m clt = α + θ t + (γ l * θ t ) + (σ c * θ t ) + λ cl +
where m clt is a share of foreigners from source country c and living in a commuting area l at time t, θ t are year dummies, γ l and σ c are country of origin and commuting areas xed eects, respectively, and λ cl are time invariant pair of country and commuting areas xed eects, which represent controls for costs of migration and other bilateral historical relationship between the country of origin and commuting areas. We then predict the share of immigrants from country c and living in a commuting area l at time t, mclt , based on the obtained coecients from the empirical model of determinants of migration. Further, we use those predicted shares to compute an ethnic diversity index at the commuting area level and use it as an instrument for the workplace ethnic diversity. We believe that the determinants of migration are likely to be orthogonal with respect to innovation outcomes at the workplace levels. In this robustness check, diversity in the other two dimensions, i.e. educational and demographic, is instrumented as in the main analysis, i.e. by using the historical composition and the current population stocks of the labor supply at the commuting area level.

Intensive margins

Our point of departure for the analysis of the intensive margins, is the patent production function. Following a standard procedure within the literature [START_REF] Blundell | Dynamic Count Data Models of Technological Innovation[END_REF]

P (Y it = y | λ it ) = e -λit λ y y! .
Covariates can be introduced by specifying the individual (rm) mean as

λ it = exp β c Index_ethnic it + β e Index_edu it + β d Index_demo it + w it β w + η i , (1)
where η i stands for the unobserved time-invariant rm-specic heterogeneity term and w it is a vector of patent production determinants, as specied in subsection 3.

disc_stock it-1 = y it-1 + (1 -δ)disc_stock it-2 ,
where y it-1 is the lagged number of patent applications and δ is the depreciation rate set equal to 30 per cent as in [START_REF] Blundell | Dynamic Count Data Models of Technological Innovation[END_REF]. State dependence is hence introduced to the model through the term y it-1 , the lagged number of patent applications.

We also add a dummy variable taking value on zero if the rm had never innovated prior to 1995, to capture persistent dierences between patenting and non-patenting rms [START_REF] Blundell | Dynamic Count Data Models of Technological Innovation[END_REF][START_REF] Blundell | Market Share, Market Value and Innovation in a Panel of British Manufacturing Firms[END_REF]). In addition, this dummy variable represents a remedy for the so-called "zero-ination problem" given that in our data many rms never applied for a single patent. The pre-sample information technique is feasible in a study like ours because we have a long series for the dependent variable (1977)(1978)(1979)(1980)(1981)(1982)(1983)(1984)(1985)(1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994) prior to the starting period (1995) of the nal sample in use.

As described in the identication subsection above, one may argue that the relationship between rm-patenting activity and diversity could be aected by endogeneity. The latter issue might arise because there could be unobserved rm-specic factors inuencing both the number of patent applications and the degree of labor diversity. To address these concerns, we apply a two-stage IV procedure to the Poisson model as suggested by [START_REF] Vuong | Two-Stage Conditional Maximum Likelihood Estimation of Econometric Models[END_REF]. In this case, equation ( 1) is specied as follows:

λ it = exp β c Index_ethnic it + β e Index_edu it + β d Index_demo it + w it β w + η i + u it (2)
where the term u it can be interpreted as unobserved heterogeneity correlated with the diversity indexes but uncorrelated with the vector of patent production determinants w it .17

To model the correlation between the endogenous variables and u it , we specify a system of linear reduced-form equations, one for each diversity index. This is:

           Index_ethnic it = w it γ w + z ct γ z + ε cit Index_edu it = w it γ w + z ct γ z + ε sit Index_demo it = w it γ w + z ct γ z + ε dit
where z ct is the vector of exogenous variables that aects rm level diversity, but does not directly aect the number of patent applications. As in section 3.1, the excluded variables are the diversity indexes computed at the commuting area where the rm is located and the model is just-identied. The error terms ε are assumed to have zero mean and to be correlated across equations for a given rm i, but uncorrelated across observations. Furthermore, we assume that the errors u and ε are related via

u it = ρ c ε cit + ρ s ε sit + ρ d ε dit + ζ it (3)
where 18 Substituting equation (3) in equation ( 2) for u it and taking the expectation with respect to ζ yields

ζ it ∼ 0, σ 2 ζ is independent of ε cit , ε sit and ε cit .
E ζ (λ) = exp(βcIndex_ethnic+βeIndex_edu+β d Index_demo+w β+η+lnE(e ζ )+ρcεc+ρsεs+ρ d ε d ).
The constant term lnE(e ζ ) can be absorbed in the coecient of the intercept as an element of w. It follows that

λ it = exp βcIndex_ethnic + βeIndex_edu + β d Index_demo + w it βw + η i + ρcε cit + ρsε sit + ρ d ε dit ,
where ε cit , ε sit and ε cit are the new additional variables. Given that the former variables are unobservable, we follow a two-step estimation procedure where we rst estimate and generate them and second we estimate parameters of the Poisson model after replacing ε cit , ε sit and ε cit with εcit , εsit and εcit . Obviously, the variance and covariance matrix of the two-step estimator needs to be adjusted for the above replacement by bootstrapping the sequential two-step estimator.

Further, as in the analysis on the propensity to innovate, we also include a set of regional, year, industry and year times industry dummies account for potential business cycle inuences, regional-or industry-specic eects.

Extensive margins

The estimation approach used to evaluate the extensive margins of rms' patenting behavior is similar to the one adopted for the rms' propensity to patent. Although the count data models would be more suitable for the analyses of relationship between workforce diversity and the number of dierent technological areas of patent application, our data and concretely the lack of minimum observations required to run count data models do not allow us to use them. Instead, we evaluate whether more labor diversity increases the probability of a rm to (apply for a) patent in more than one technological area, conditional on patenting.

Results

This section reports ndings for each of the outcome dimensions we look at: propensity to innovate, intensive and extensive margins. [START_REF] Cortes | The Eect of Low-Skilled Immigration on U.S. Prices: Evidence from CPI Data[END_REF] By comparing the results of these two columns, we can see that the marginal eects of diversity along the ethnic, educational and demographic dimensions are robust to the inclusion of an occupational diversity index. We can therefore argue that our main diversity measures are not picking up the eect of having occupational heterogeneity at the workplace. While all the former columns treat the diversity indexes as exogenous variables, column 4 shows the results obtained by implementing an IV method, where the predicted workforce diversity levels at commuting areas are used as instruments for the rm workforce diversity. It is important to note that in all IV models we have augmented the specication of column 3, by adding a linear trend interacted with the initial commuting area diversity, as measured in 1990. The results obtained from the IV estimator imply that a standard deviation increase in the ethnic diversity increases the probability to apply for patent by 0.2 percentage points. This corresponds to a rise in the probability to innovate by about 7 percent.

Results on labor diversity and propensity to innovate

20 On the contrary, the signicance of the eects related to skill/education and demographic diversity vanish. Hypothesis testing also reveals that the marginal eect of ethnic diversity is statistically dierent from the marginal eect of both educational and demographic diversity. Therefore we can conclude that ethnic diversity matters more than the other two dimensions of diversity. Note that the rst stage of our IV approach, reported in 20 These gures are obtained using the average probability of innovating. From the estimates in Table 2, the average probability of innovating is around 0.03. Therefore, the changes in the probability of innovating, in percentage terms, are (0.2/0.03) = 6.66.

dimension of diversity captures the eects associated with other indexes. Ethnic diversity, for example, may pick up some of the skill diversity eects as individuals with the same education but coming from dierent countries may present degrees of educational heterogeneity as well. Both educational and demographic diversity remains insignicant even when they enter the probit model separately while the coecient of ethnic diversity remains stable. We cannot, however, rule out that the ethnic diversity is still capturing heterogeneity in a specic educational level (employees with same degree but coming from dierent universitary systems may still present some degree of heterogeneity).

Turning to the other control variables, rms with higher shares of highly skilled and vocational workers, and exporting rms have higher propensity to patent. Instead, the knowledge spillovers and the average rm tenure do not explain much of such a propensity.

As mentioned in section 2.2, we additionally estimate probit models using diversity indexes based on a more detailed category specication; the results are shown in the Table 2, columns 8, 9 and 10. As in the aggregate specication, also in this one we nd that our measures of diversity are robust to the inclusion of an occupational diversity index and that applying our IV strategy only ethnic diversity seems to matter in terms of the propensity to innovate. A standard deviation change in the ethnic diversity produces an increase in the probability to apply for a patent by 0.1 percentage points which correspond to a rise in the probability to innovate by 3 percent, whereas the eects of education and demographic diversity appear negligible. 21 not include proxies for rm unobservables and don't control for the workforce composition; furthermore they do not deal with potential endogeneity issues.

Results on labor diversity and intensive margins

In the next step, we analyze how workforce diversity contributes to the number of patent application. Tables 3 reports the results of the intensive margins analyses, here the estimated coecients represent elasticities. The rst column in Table 3 shows the output of a Poisson regression 22 having only the diversity measures as regressors: the coecients to all diversity indexes are large, positive and signicant. Once more, after including all the other control variables (column 2) their dimension and statistical signicance decreases but are robust to the inclusion of an occupational diversity (column 3). Both in columns 2 and 3, hypothesis testing does not allow us to conclude that the estimated elasticities to our measures of diversity are statistically dierent from each other. In our preferred specication (column 4) though we nd that only the eect of ethnic diversity is precisely estimated and that a ten percent increase in the latter index leads to 4 percent increase in the number of patent applications for the aggregated diversity measures. This eect is quite sizable given that the elasticity associated with an important production input, like human capital (proxied by the share of highly skilled workers) is of comparable magnitude. Similar conclusions are drawn when all the diversity indexes enter separately the Poisson equation. As in the previous section, our rst stage results conrm that our instruments are very good predictors of the rm level diversity.

23

In line with previous literature, we nd important eects of the shares of highly skilled workers, capital and labor stock on the number of patent applications, whereas knowledge spillovers do not seem to have signicant contributions to the overall number of patent applications. As in the case of patenting propensity, exporters benet from the knowledge gained on the international markets.

Columns 7 and 8 in Table 3 report results for models using the labor diversity indexes 22 Negative binomial models provide very similar results which are available on request from the authors. [START_REF] Deding | Spatial Mobility and Commuting: the Case of Two-Earner Households[END_REF] The results from the rst stage are reported in Table A2 of Appendix 3.

based on disaggregate groupings. The results are similar to those using aggregate diversity specications, although the coecients to our diversity variables are slightly smaller in size.

Specically, the IV Poisson estimations (column 10) reveal that only the coecient to ethnic diversity is precisely estimated and that a ten percent increase in this index implies a 2.2 percent increase in the number of patent applications. [START_REF] Delgado | Clusters and Entrepreneurship[END_REF]

Results on labor diversity and extensive margins

Table 4 reports the eects of labor diversity on the probability of patenting in dierent technological areas in a given year, conditional on patent application. The structure of this table is similar to the previous one and all the marginal eects of diversity measures are reported in standard deviation units, to ease the comparison across magnitudes. Regarding the variables of interest, we nd that the diversity indexes alone explain 7 percent of the overall variation in the dependent variable and that the coecients to both ethnic and educational diversity indexes are positive and statistically signicant and robust to the inclusion of all the other controls (column 2) and of an occupational diversity index (column 3). However, the signicance of the diversity in skill/education vanishes when endogeneity is taken care of and hypothesis testing indicates that ethnic diversity matters more than educational diversity in terms of patenting in dierent technological areas (column 4). More specically, our IV results indicate that a standard deviation increase in ethnic diversity is associated with a raise of about 14 [START_REF] Griliches | Patent Statistics as Economic Indicators: A Survey[END_REF] percent points in the probability to patent in dierent technological elds for the aggregate (disaggregate) diversity, conditional on patent application. Or alternatively, a standard deviation increase in ethnic diversity almost duplicates the probability to patent in dierent technological elds, according to the most conservative estimates. 25 Thus, the fact that cultural diversity is much more relevant for [START_REF] Delgado | Clusters and Entrepreneurship[END_REF] We have also investigated whether the eects of a particular dimension of diversity can be inuenced by other forms of labor heterogeneity by inclusion of all possible interaction couples between the diversity indexes. Furthermore, driven by the hypothesis that there might be complementarities among dierent skills and demographic groups, in particular young and educated workers together with a more diverse workforce can stimulate innovation and creativity, we have augmented our models with interactions between diversity indexes and shares of highly skilled and younger workers. Nevertheless, none of the interactions turned out to be statistically signicant. Figures showing marginal eects of the interactions are available from the authors upon request.

25 From the estimates in Table 4, the average probability of patenting in dierent technological areas is patenting in dierent technological areas rather than for the patenting per se is somehow plausible as a diversied portfolio of patent applications might reect a substantial degree of knowledge heterogeneity and hence skill complementarity.

Turning to the other control variables, rms with higher shares of highly skilled and young workers, and larger capital stock have higher probability of patenting in dierent technological areas.

Results -mechanisms involved

Our rich dataset allows us to uncover the role of dierent mechanisms by which diverse workforces aect rms' innovation outcomes as proposed by the theory and thus we test a number of hypotheses. Firstly, we calculate our diversity indexes for white-and blue-collar occupations separately. This is driven by the idea that diversity could play a dierent role for distinct occupational groups and consequently have diverse eects on rm innovation. In particular, we expect that the benecial eects of diverse problem-solving abilities and creativity would materialize more in terms of innovation for white-collar occupations compared to blue-collar occupations. Second, we exclude certain groups of foreigners from calculation of ethnic diversity measures to test how important are the communication costs and costs of cross-cultural dealing. In these analysis and those reported in the next section, we use disaggregate indexes only, as we think that the indexes based on a detailed categorization may be more adequate to represent workforce diversity.

26 Moreover, all results are obtained by estimating the full IV specication described in the previous section.

The results of the eect of diversity indexes calculated separately for the two occupational groups on rm probability to innovate, number of patent applications and rm probability of applying for a patent in dierent technological areas are presented in the rst two columns of Table 5. Our results show that that workforce ethnic diversity is indeed much more important for white-collar than for blue-collar occupations. Hypothesis testing around 0.18. Therefore, the changes in the corresponding probability, in percentage terms, are (14/0.18) = 77.

26 The results using the aggregate indexes are qualitatively similar to the detailed categorization and are reported in Tables A3-A5 of Appendix 3.

always reveal that the coecient of ethnic diversity calculated for white-collar workers is statistically dierent than the corresponding coecient for blue collar workers. [START_REF]The Business Case for Diversity: Good Practices in the Workplace[END_REF] The eect of ethnic diversity on both the intensive and extensive margins of innovation is positive and statistically signicant for the group of white-collar workers only. Conversely, the eect of education and demographic diversity is insignicant for both white-and blue-collar occupations. Thus, our results support the creativity hypothesis proposed by the theoretical frameworks by Hong and Page (2001) and Berliant and Fujita (2011), at least for ethnic diversity.

To test the role of cross-cultural dealing we exclude from the calculation of ethnic diversity alternative groups of foreigners: (1) the second generation immigrants, who are very likely to be uent in Danish and who are almost perfectly integrated into the Danish society and culture; (2) foreigners with tertiary education and (3) foreigners speaking one of the language belonging to the germanic group. The last two groups are likely to absorb Danish or English (which is the communication language in many businesses in Denmark) more quickly. It is plausible to expect that communication costs associated with ethnic diversity may increase after subtracting out foreigners who are likely to speak Danish or English.

The results are shown in Table 5, columns 3, 4 and 5 for measures treating the second generation of immigrants, foreigners with a language belonging to the Germanic group of languages and foreingers with university education as natives, respectively. Interestingly, the role of ethnic heterogeneity on innovation weakens once we exclude foreigners who probably speak English or Danish, conrming the idea that the communication costs and costs of cross-cultural dealing are likely to be more important when foreigners don't speak the same language. This is shown by results of analyses from all innovation outcomes under consideration. Furthermore, the fact that the eect of ethnic diversity on the number of patent applications remains positive and signicant even when we exclude university graduates may also indicate that the latter eects are not merely driven by the recruitment of talented high skilled workers from abroad.

Sensitivity analyses

In this section, we examine whether the eects of labor diversity on patenting activity of rms hold across alternative diversity measures and samples. All results are again based on the full IV specication described in the previous section and they are shown in Tables 6 and7.

First, as a part of the sensitivity analysis we evaluate eventual variations in the eects of labor diversity when the diversity measure is dierently computed. In particular, we use two alternative diversity indexes: the Shannon-Weaver entropy and the richness indexes.

The entropy index is considered as one of the most profound and useful diversity indexes in biology [START_REF] Maignan | Bio-Ecological Diversity vs. Socio-Economic Diversity: A Comparison of Existing Measures[END_REF], whereas the richness index is dened as a number of categories observed for each dimension of interest (it does not account for the evenness dimension). The results are shown in Table 6, columns 1 and 2, respectively, and both measures support the results from our main analyses using our preferred Herndhal index and show that ethnic diversity has signicant positive eect on all considered innovation outcomes.

Next, we include an Herndhal index for the type of tertiary education (this index has now only 4 categories: engineering, natural sciences, social sciences and humanities) and the standard deviation for the years of education and age. This allows us, on one hand, to treat age as a cardinal variable and, on the other, to disantangle the eects associated with the amount of education from those related to the type of tertiary education. The results from Table 6, column 3, show that the eects of both education and demographic diversity are never signicant.

Next, we run our analyses using an alternative instrument for the workplace ethnic diversity based on shares of immigrants at the commuting areas predicted from a model of migration determinants, as described in section 4.2 above. Specically, we use the model of migration determinants to predict shares of immigrants from a particular source country living in a particular commuting area. We then use the predicted shares of immigrants to construct ethnic diversity levels at commuting areas, which we then use as an instrument for ethnic diversity on the workplace level. Diversity in the other two dimensions, i.e. educational and demographic, is instrumented as in the main analysis, i.e. by using the historical composition and the current population stocks of the labor supply at the commuting area level. The results using the alternative IV shown in column 4, Table 6, conrm our main ndings. For all three studied innovation outcomes we observe that the ethnic diversity has a signicantly positive eect, whereas the eects of educational and demographic diversity are statistically insignicant.

We also look at whether there is any dierence in the eect of diversity on innovation for rms with or without pre-sample patents. Not surprisingly, the last two columns of Table 6 show that the impact of ethnic diversity is stronger for rms with pre-sample patents, especially in the regressions where the probability to innovate is the outcome variable.

As big cities have usually a lot of immigrants and at the same time a high percentage of innovative rms, in the next robustness check we drop Copenhagen (the only real agglomeration area in Denmark) and environs from the analysis. Results from this robustness check are reported in column 1 of Table 7, and do not qualitatively dier from the main results.

In the main analysis our labor diversity measures have been obtained as weighted averages of Herndahl indexes computed at the workplace level. Given that 11 percent of rms are multi-establishment companies, we test the robustness of our results: i) by constructing a single-rm level metric rather than using the weighted approach to measure diversity as described in section 3.2, ii) by excluding multi-establishment enterprises from the sample.

Columns 2 and 3 of Table 7 report information on these robustness checks: the interpretation of these ndings does not substantially dier from the main results.

Finally as our diversity measures are likely to have some mechanical link to rm size, we have divided 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).

As reported in Table 7, columns (4)-( 6), the coecients of the ethnic diversity index are signicantly positive for all size categories, with the largest coecient associated with large rms. As in the main analysis, diversity in the other two dimensions is never statistically signicant.

Conclusions

In this paper we provide evidence of the nexus between labor diversity and rms' patenting behavior. Our study represents an attempt to generalize the relationship between labor diversity and innovation by using detailed information on rms' workforce composition. In fact, our nal sample is the result of a merge of the Danish linked employer-employee data with the register of rms' business accounts and a collection of patent applications sent to the European Patent Oce (EPO) by Danish rms.

In our empirical analysis, we (a) control for a large number of rm-specic characteristics duplicates the rms' probability to apply for a patent in dierent technological areas. Thus, in order to widen the patent technological spectrum it seems to be fundamental to increase the heterogeneity in the workers' knowledge stemming from diverse cultural backgrounds.

This comes as no surprise as a diversied portfolio of patent applications most likely reects a variety of perspectives, heuristics, skills and ideas that complement each other.

Regarding the results of education and demographic diversity on innovation, their eects typically vanish when we include the full set of controls or once we instrument the diversity measures. Finally, we nd that the benecial eect of ethnic diversity on innovation materializes for white-collar occupations only, whereas the eect for the group of blue-collar workers is negligible. These results support the hypothesis that more educated workers tend to have a wider pool of dierent experiences, knowledge bases and heuristics boosting their problem-solving capacities and creativity, which in turn facilitate innovations. In this regard, our ndings are consistent with the theoretical frameworks proposed by [START_REF] Hong | Problem Solving by Heterogeneous Agents[END_REF] and [START_REF] Berliant | The dynamics of knowledge diversity and economic growth[END_REF].

The overall picture coming out from our empirical analyses seems to be particularly relevant not only for the design of rms' innovation and hiring strategies but also for public policies aimed at fostering innovation. Our results give an important insight into the technological process, a driver of productivity growth and hence of the economic growth. We nd that an increase in rm labor diversity in terms of ethnicity has a positive eect on the rm innovation process. Thus, governmental policies aimed to promote an employment of workers with dierent cultural backgrounds can be benecial in terms of improvements in rms' patenting activities, increasing both private returns, directly, and social gains, i Table 2: The effects of labor diversity on firm probability to innovate. Main results.

Model (1) Model ( 2) Model ( 3) Model ( 4)

Model ( 5)

Model ( 6) Model ( 7) Model ( 8) Model ( 9) Model ( 10

Model ( 6) Model ( 7) Model ( 8) Model ( 9) Model ( 10 Notes: The dependent variable in all estimations is the number of patent applications. Elasticities are reported. Model1-Model7: diversity based on the aggregate specification. Model8-Model10: diversity based on the disaggregate specification. Model4-Model7 and Model10 report results from IV estimation. In all IV models we augment the specification by adding a linear trend interacted with the initial commuting area diversity, as measured in 1990. Significance levels: ***1%, **5%, *10%.

Standard errors clustered at the firm level in model1-model3 and model8-model9.

Standard errors clustered at the commuting area level and bootstrapped using a sequential two step bootstrapping procedure with 200 replications in Model4-Model7 and Model10.

iii Table 4: The effects of labor diversity on the probability of applying in different technological areas. Main results.

Model (1) Model ( 2) Model (3) Model ( 4)

Model ( 5)

Model ( 6) Model ( 7) Model ( 8) Model ( 9) Model ( 10

Appendix 2: External knowledge indexes

The main literature on agglomeration economies emphasizes the importance of firm's local environment, which may reflect information advantages, labor or other inputs pooling and further beneficial network effects aimed at alleviating the burden represented by fixed costs. A seminal contribution in this field is due to [START_REF] Audretsch | R&D Spillovers and the Geography of Innovation and Production[END_REF], who find that industries characterized by elevated R&D intensity or particularly skilled labor forces present a greater degree of geographic concentration of production. Other relevant studies like [START_REF] Wallsten | An Empirical Test of Geographic Knowledge Spillovers Using Geographic Information Systems and Firm-Level Data[END_REF] and Adams and Jaffe (1996) provide evidence of the geographic extent of knowledge spillovers by computing the distance in miles between each firm-pair. However, the geography is not the only dimension of the external knowledge. In fact, there exists at least another approach which focuses on the concept of technological proximity (Jaffe 1986, Adams 1990). Specifically, the idea that the technology developed by a firm can affect other firms, even though they are not geographically close or no transactions of goods occur between them, has led to the definition of technological proximity as closeness between firm-pairs' technological profiles.

Following both the cited approaches, we construct two indexes of knowledge spillovers. These are weighted sums of firms' codified knowledge proxied by the discounted stock of patent applications. The weighting function for the first index refers to the geographical distance between pairs of workplaces' municipalities and is computed by using the firms' latitude and longitude coordinates (the address of their headquarters). Specifically, assuming a spherical earth of actual earth volume, this method allows us to measure the distance in kilometers between any pair of firms i and j. 1 The first knowledge spillover index is then computed as follows:

K geo it = 1 e dist ij I j =i disc stock jt . (1)
The second index is instead based on the technological proximity. Following Adams (1990), we use the shares of differently skilled workers to define our alternative weighting function ψ ij that is the uncentered correlation:

ψ ij = f i f j f i f i f j f j 1/2 . ( 2
)
The components of the generator vector f reflects firm's workforce composition in terms of skills using the disaggregated categorization as described in section 3.1. The second measure of knowledge spillover pool is therefore defined as x

K tech it = ψ ij I j =i disc stock jt . (3)
Thus, both K geo it and K tech ij contain weighting functions that might capture the so-called firm's absorptive capacity, which is the ability to identify and exploit the knowledge externally produced [START_REF] Cohen | Absorptive Capacity: A New Perspective on Learning and Innovation[END_REF] xv Table A5: The effects of labor diversity on firm innovation, further robustness checks.

Probability to innovate

Copenhagen is excluded Mono-establishment firms Firm level diversity Less than 50 employees 50-100 employees more than 100 employees xvi

  son et al. 1993, Drach-Zahavy and Somech 2001, Lazear 1999, Osborne 2000, Hong and Page 2001, Berliant and Fujita 2011). Ambiguity instead persists for diversity in ethnic and demographic characteristics of employees (Becker 1957, Williams and O'Reilly 1998, Zajac et al. 1991, Lazear 1999).

(

  Horwitz and Horwitz 2007, and Harrison and Klein 2007), (ii) works focusing on diversity in top management teams only (Bantel and Jackson 1989, Knight et al. 1999, Pitcher and Smith 2001), (iii) analyses linking workforce heterogeneity -typically ethnic diversity -to innovation using aggregate regional or industry data (Kelley and Helper 1999, Feldman and Audretsch 1999, Anderson et al. 2005, Niebuhr 2010, Kerr and Lincoln 2010, Ozgen et al. 2011a, Nathan 2012), (iv) a few rm level studies using linked employer-employee data (Østergaard et. al. 2011, Söllner 2010, Ozgen et al. 2011b).

is

  Østergaard et. al. (2011), which merges the Danish LEED for the year 2002 with a survey that refers to the period 2003-2005 (Danish Innovation System: Comparative analyses, strength and bottlenecks, DISKO) and analyzes a cross-section of 1,648 rms. This study nds evidence of (a) positive eect of diversity in education and gender, (b) no signicant eects of ethnic diversity and (c) negative eects of age diversity on rm's innovation. The second study by Söllner (2010) evaluates how occupational diversity, considered as a proxy of human capital heterogeneity, is linked to the rm's likelihood to introduce a product innovation. Controlling for age and tenure diversity among other covariates, Söllner (2010) nds that occupational diversity is positively related to the propensity to innovate. However, none of these studies addresses endogeneity issues related to the identication of the eects of diversity on rm innovation, which we take into account in the present article. Ozgen et al. (2011b) is the third study. It investigates the impact cultural diversity on innovation by matching information from the Dutch Labor Force Survey to Community Innovation Survey 3.5. Their nal sample consists of 4,638 rms over the period 2000-2002. Using

  educational and demographic diversity compared to non-patenting rms.

  the inclusion of spillover measures and foreign ownership status captures eects related to external knowledge production, controls on the workforce composition allow estimating the 11 The Ministerial Order on the Statistics Denmark Act requires every employer in Denmark to report annually an occupational classication code for each of its full-time employees, following the DISCO. The DISCO is the Danish version of the ILO's ISCO (International Standard Classication of Occupations).

  and Di Nardo (2000), Dustmann et al. (2005), Cortes (2008),Foley and Kerr (2012) for similarly computed instruments. Pre-existing workforce diversity at the commuting area level is unlikely to be correlated with a current rm' s innovation, if measured with a sucient time lag. In particular we use workforce composition at the commuting areas from year 1990.[START_REF] Blundell | Market Share, Market Value and Innovation in a Panel of British Manufacturing Firms[END_REF]

  of diversity. Nonetheless previous studies on rm localization (Krugman 1991, Audretsch and Feldman 1996, Adams and Jae 1996, Alcacer and Chung 2010, Delgado et al. 2010)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. We believe that our measures of rms' knowledge spillovers, described in the previous section, should be able to partly address the potential endogeneity of rm location decisions in terms of knowledge spillovers. We use the described IV strategy for analyses of all three dimensions of innovation: propensity to innovate, intensive and extensive margins.As a part of our robustness analyses, we also use an alternative instrument for ethnic diversity, in which our ethnic diversity levels at commuting areas are computed on the basis of the shares of foreign population predicted by an empirical model of determinants of migration. Specically we run the following empirical specication, which is based on time variant push and pull factors, and costs of migration[START_REF] Pedersen | Selection and Network Eects -Migration Flows into OECD Countries 1990-2000[END_REF], Ortega and Peri 2009):

  Further, we dig deeper into the analyses and we test three main hypotheses, which help us to uncover the role of the mechanisms by which diverse workforces aect rms' innovation outcomes. First, we test the creativity hypothesis proposed by the theoretical frameworks in Hong and Page (2001) and Berliant and Fujita (2011) by distinguishing between diversity among white-and blue-collar workers.Second, we exclude certain groups of foreigners from calculation of ethnic diversity measures to investigate the role of the costs of cross-cultural dealing as suggested by Williams and O'Reilly (1998),[START_REF] Zajac | New Organizational Forms for Enhancing Innovation: The Case of Internal Corporate Joint Ventures[END_REF] and[START_REF] Lazear | Globalisation and the Market for Team-Mates[END_REF]. Finally, in the sensitivity analyses subsection we examine whether the results dier across alternative diversity measures and samples.

  referring to the workforce (average rm tenure, shares of foreigners from dierent group of countries or languages, males, workers with either tertiary or secondary education, workers with dierent occupation, employees belonging to dierent age groups) or to whether the rm is exporter, foreign owned and multi-plant; (b) add at least to the equation of intensive margins the discounted patent stock and a dummy for past patenting rm status to proxy for rm time-invariant unobservables and hence to deal with rm heterogeneity[START_REF] Blundell | Dynamic Count Data Models of Technological Innovation[END_REF][START_REF] Blundell | Market Share, Market Value and Innovation in a Panel of British Manufacturing Firms[END_REF]); (c) include reasonable measures of knowledge spillovers based on geographical and technological proximity between rms to take into account the inuence of external sources of knowledge in rm innovation outcome (Audretsch and Feldman 1996, Adams and Jae 1996); (d) implement an IV strategy grounded on the historical composition of the labor force at the commuting area level (Card and Di Nardo 2000, Dustmann et al. 2005, Cortes 2008, Foley and Kerr 2012); (e) adopt alternative categorizations (aggregate and disaggregate) and dierent measures (Herndahl, Shannon-Weaver and richness) of diversity as sensitivity tests.However, our study presents some limitations that further research may address. Most importantly, we could not implement panel estimation approaches, that would have better controlled for rm time-invariant unobservables, due to insucient data variation. Furthermore, the lack of detailed information on the traits of innovations prevent us from investigating whether ethnic diversity plays an important role in terms of the quality of innovation.Our results broadly support the hypothesis that ethnic diversity of the labor force is an important source of innovation. Ethnic diversity seems to facilitate rms' patenting activity in several ways by: (a) increasing the propensity to (apply for a) patent; (b) increasing the overall number of patent applications and (c) enlarging the breadth of patenting technological elds, conditional on patenting. Being prudent in the quantication of ethnic heterogeneity eects on all these aspects of patenting activities, we nd that a 10 percentage change in ethnic diversity increases the number of rms' patent applications by approximately 2.2 percent, according to the most conservative estimates. The contribution of ethnic diversity in terms of general propensity to send at least one patent application in a given year is economically sound: a standard deviation change in its value turns to raise such a probability by 3-7 percent. Conditional on patenting, the eect of ethnic diversity on extensive margins is very large, a standard deviation change in skill diversity almost

  through knowledge diusion mechanisms. Such policies might help to invert the general decline in patenting activity recorded during the recent economic crisis among the OECD countries (OECD 2009 and 2011).

  In the first and last panel marginal effects are reported and all diversity measures have been standardized. In the middle panel elasticities are reported. All regressions are estimated with the same IV approach as the one used in the previous tables and include a linear trend interacted with the initial commuting area diversity, all firm specific characteristics, year and two-digit industry dummies plus year-industry interactions. Significance levels: ***1%, **5%, *10%. Standard errors clustered at the commuting area level. Probability of applying in different technological areas: convergence is not achieved for size specific sub-samples.

  Probability of applying in different technological areasShannon entropy index Richness Edu and demo diversity as sd IV migration determinants Firms without pre-sample patents Firms with pre-sample patents In the first and last panel marginal effects are reported and all diversity measures have been standardized. In the middle panel elasticities are reported. All regressions are estimated with the same IV approach used in the previous tables and include all firm specific characteristics, year and two-digit industry dummies plus year-industry interactions. Significance levels: ***1%, **5%, *10%. Standard errors clustered at the commuting area level. Probability of applying in different technological areas: convergence is not achieved for the sub-sample of firms with pre-sample patents.

  Copenhagen is excluded Mono-establishment firms Firm level diversity Less than 50 employees 50-100 employees more than 100 employeesProbability of applying in different technological areasCopenhagen is excluded Mono-establishment firms Firm level diversity Less than 50 employees 50-100 employees more than 100 employees In the first and last panel marginal effects are reported and all diversity measures have been standardized. In the middle panel elasticities are reported. All regressions are estimated with the same IV approach used in the previous tables and include all firm specific characteristics, year and two-digit industry dummies plus year-industry interactions. Significance levels: ***1%, **5%, *10%. Standard errors clustered at the commuting area level. Probability of applying in different technological areas: convergence is not achieved for size specific sub-samples.

  Index_ethnic it + γ e Index_edu it + γ d Index_demo it + x it β + v it where p * it denotes the unobservable variable inducing rm i to apply at least once for a patent at time t; p it indicates whether rm i concretely has applied at time t; the rst three terms at the right-hand side are diversity in ethnic background, education/skills and demographics respectively and v it is the error term. The vector x it includes an extensive set

	0 otherwise
	with p * it = γ c of observable characteristics that might aect rms' innovation outcomes. More specically,
	we include detailed workforce composition characteristics such as shares of foreigners coming
	from a given group of countries under the aggregate diversity specication (e.g. shares of
	foreigners from North America and Oceania, Central and South America, Africa, Western
	and Southern Europe, Formerly Communist Countries, East Asia, Other Asia, and Muslim
	Countries), shares of males, of workers with either tertiary or secondary education, shares of
	dierently aged workers belonging to the employees' age distribution quartiles and shares of
	workers for each occupation, according to the rst digit classication code of occupation. 11

Table 2

 2 reports estimated marginal eects concerning the propensity to apply for a patent in a given year. All the marginal eects of our diversity measures are reported in standard deviation units, to be able to compare the relative contributions of each dimension of diversity, thereby easing the comparison across magnitudes. Moreover, statistical tests of the equality of the marginal eects across dimensions of diversity are included at the bottom of Table2. In column 1, we show a model with the three workforce diversity indexes as the only regressors. The workforce diversity can explain about 14% of the overall variation in the dependent variable and is associated with sizable and signicantly positive eects. Columns 2 show the results from a probit model with all other covariates as described in section 3.1, while columns 3 extends the specication in column 2, by adding an occupational diversity index among the control variables.

  Table A1 of Appendix 3, clearly shows that our instruments are strongly correlated with the rm level diversity. Their statistical validity is also conrmed by the F-statistics, as the latter are always above 70, which allows us to dismiss the null hypothesis of weak instrument (Stock and Yogo 2005).

	Columns 4 to 6 report models with single diversity dimensions to check whether one
	19 The index of occupational diversity is constructed on the rst digit classication code of occupation
	(DISCO) and is based on the Herndahl index. Its sample mean and standard deviation are 0.692 and
	0.229.

  Our ndings dier fromØstergaard et al. (2011), which also investigates the relationship between labor diversity and rm's innovation in the Danish context, because of dierences in data and estimation methods employed. AlthoughØstergaard et al. (2011) use the same employer-employee data set, they focus only on the year 2002 for the computation of diversity indexes. Whereas our dependent variable is whether the rm applies for a patent at EPO, theirs is dened as the introduction of a new product or service, which is retrieved from survey data. This implies that the sample sizes in the two studies are too far to be comparable: 96,636 versus 1,648. Compared to our study,Østergaard et al. (2011) do

21 Results obtained from the specications with single diversity dimensions are very similar to the ones reported in columns 5, 6 and 7 and are available on request from the authors.

  The dependent variable in all estimations is the probability to have at least one patent application. Marginal effects are reported. All diversity measures have been standardized. Model1-Model7: diversity based on the aggregate specification. Model8-Model10: diversity based on the disaggregate specification. Model4-Model7 and Model10 report results from IV estimation. In all IV models we augment the specification by adding a linear trend interacted with the initial commuting area diversity, as measured in 1990. Significance levels: ***1%, **5%, *10%. Standard errors clustered at the firm level in model1-model3 and model8-model9. Standard errors clustered at the commuting area level in Model4-Model7 and Model10.

	(0.0000) (0.0000) (0.0004)	19.48; 0.000 19.48; 0.000 19.53; 0.000	18.87; 0.000 18.87; 0.000 25.126; 0.000	1.67; 0.267 1.67; 0.267 3.75; 0.111	yes yes yes	yes yes yes	yes yes yes	96,636 96,636 96,636	0.383 0.383 0.386
	(0.0001)				yes	yes	yes	96,636	0.371
	(0.0001)				yes	yes	yes	96,636	0.370
					yes	yes	yes	96,636	0.372
		25.78; 0.000 17.65; 0.000 16.78; 0.000 36.76; 0.000	11.24; 0.000 19.57; 0.000 23.12; 0.000 32.786; 0.000	3.24; 0.0720 1.13; 0.281 2.02; 0.151 2.75; 0.141	no yes yes yes	no yes yes yes	no yes yes yes	96,636 96,636 96,636 96,636	0.136 0.370 0.374 0.372
	hypothesis tests (chi2, p-value)	index ethnic=index edu	index ethnic=index demo	index demo=index edu	size/industry/year/industry*year dummies	shares of foreigners by group of countries	shares of employees by occupation	N	pseudo R-sq	Notes:

Table 3 :

 3 The effects of labor diversity on firm patent applications. Main results.

Model (1) Model (

2

) Model (

Table 5 :

 5 The effects of labor diversity on firm innovation, the mechanisms involved.Occupation specific diversity 2nd gen. Imm. as as natives Germanic group as natives University graduates as natives In the first and last panel marginal effects are reported and all diversity measures have been standardized. In the middle panel elasticities are reported. All regressions are estimated with the same IV approach as the one used in the pre-

	Probability to innovate	Occupation specific diversity 2nd gen. Imm. as natives Germanic group as natives University graduates as natives	White collar Blue collar	0.0025** 0.0014*** 0.0009*** 0.0001** 0.0002*	(0.0004) (0.0005) (0.0003) (0.0000) (0.0001)	0.0001 -0.0009 0.0004 0.0004 0.0006	(0.0001) (0.0009) (0.0002) (0.0002) (0.0004)	0.0009 0.0027 0.0002 0.0003 0.0002	(0.0007) (0.0021) (0.0003) (0.0002) (0.0001)	96,636 96,636 96,636 96,636 96,636	0.382 0.381 0.389 0.386 0.389	Number of firm patents	White collar Blue collar	0.5788** 0.2109 0.0319** 0.0231 0.2401*	(0.2110) (0.2127) (0.0142) (0.0152) (0.1310)	0.7501 0.9545 0.3910 0.3268 0.2710	(0.8027) (1.8809) (0.6377) (0.6452) (0.6545)	1.9155 1.7520 1.6321 1.4488 1.4861	(5.4810) (4.5561) (4.4462) (4.2869) (4.3082)	96,636 96,636 96,636 96,636 96,636	33730.0 27768.3 26982.2 27186.8 24934.8	Probability of applying in different technological areas	Occupation specific diversity 2nd gen. Imm. as natives Germanic group as natives University graduates as natives	White collar Blue collar	0.0588 0.4537*** 0.0212 0.0527** 0.0222*	(0.3052) (0.0810) (0.0469) (0.0188) (0.0121)	-0.0177 -0.0677 -0.1012 -0.0280 -0.0337	(0.0521) (0.0653) (0.0537) (0.0482) (0.0491)	0.0327 0.0669 0.0610 0.0537 0.0580	(0.0691) (0.0810) (0.0562) (0.0727) (0.0712)	1,086 1,086 1,086 1,086 1,086	0.297 0.292 0.289 0.235 0.298	Notes: vious tables and include a linear trend interacted with the initial commuting area	diversity, all firm specific characteristics, year and two-digit industry dummies plus	year-industry interactions. Significance levels: ***1%, **5%, *10%. Standard errors	clustered at the commuting area level.
				index ethnic disaggr		index edu disaggr		index demo disaggr		N	pseudo R2			index ethnic disaggr		index edu disaggr		index demo disaggr		N	Chi2				index ethnic disaggr		index edu disaggr		index demo disaggr		N	pseudo R2

v

Table 6 :

 6 The effects of labor diversity on firm innovation, robustness checks.Shannon entropy index Richness Edu and demo diversity as sd IV migration determinants Firms without pre-sample patents Firms with pre-sample patents Shannon entropy index Richness Edu and demo diversity as sd IV migration determinants Firms without pre-sample patents Firms with pre-sample patentsProbability of applying in different technological areasShannon entropy index Richness Edu and demo diversity as sd IV migration determinants Firms without pre-sample patents Firms with pre-sample patents In the first and last panel marginal effects are reported and all diversity measures have been standardized. In the middle panel elasticities are reported. All regressions are estimated with the same IV approach as the one used in the pre-

	Probability to innovate

Table 7 :

 7 The effects of labor diversity on firm innovation, further robustness checks.Probability of applying in different technological areasCopenhagen is excluded Mono-establishment firms Firm level diversity Less than 50 employees 50-100 employees more than 100 employees

	Probability to innovate	Copenhagen is excluded Mono-establishment firms Firm level diversity Less than 50 employees 50-100 employees more than 100 employees	0.0009** 0.0009** 0.0009** 0.0014*** 0.0036*** 0.0150***	(0.0004) (0.0004) (0.0004) (0.0006) (0.0015) (0.0032)	0.0004 0.0005 0.0006 0.0001 0.0021 0.0101	(0.0003) (0.0003) (0.0004) (0.0001) (0.0014) (0.0062)	0.0002 0.0001 0.0002 0.0001 -0.0012 0.0006	(0.0002) (0.0002) (0.0002) (0.0001) (0.0010) (0.0004)	85,555 78,964 96,636 73,879 11,776 8,453	0.386 0.335 0.387 0.247 0.221 0.296	Number of firm patents	Copenhagen is excluded Mono-establishment firms Firm level diversity Less than 50 employees 50-100 employees more than 100 employees	0.8357*** 1.2569*** 0.2819** 0.5410*** 1.4577** 2.0149***	(0.2050) (0.1712) (0.0919) (0.0821) (0.5161) (0.3761)	1.0069 0.7801 0.2012 0.1269 0.5527 0.7610	(0.8171) (0.5027) (0.7669) (0.5819) (1.1058) (1.2602)	3.9877 1.6377 1.3577 1.3950 1.2546 1.5182	(6.3270) (1.7610) (4.7345) (8.3637) (3.7071) (6.6242)	85,555 78,964 96,636 73,879 11,776 8,453	21235.1 20541.1 25848.4 23402.3 18687.0 10741.4
			index ethnic disaggr		index edu disaggr		index demo disaggr		N	pseudo R2			index ethnic disaggr		index edu disaggr		index demo disaggr		N	Chi2

1

  We use the following formula d ij = 6378.7 * acos{sin(lat i /57.2958) * sin(lat j /57.2958) + +cos(lat i /57.2958) * cos(lat j /57.2958) * cos(lon j /57.2958 -lon i /57.2958).

Table A1 :

 A1 . SUR estimates of the IV first step for the probability to innovate

	Appendix 3: Additional results
			Aggregate			Disaggregate
		Index ethnic Index edu Index demo Index ethnic Index edu Index demo
	index ethnic com	0.2712***	-0.0884***	-0.0339***	0.2623***	-0.0096**	-0.0204***
		(0.0068)	(0.0040)	(0.0024)	(0.0064)	(0.0029)	(0.0019)
	index edu com	-0.0927***	0.8169***	-0.0491***	-0.1429***	0.5207***	-0.0736***
		(0.0127)	(0.0075)	(0.0046)	(0.0132)	(0.0060)	(0.0039)
	index demo com	-0.0583**	-0.0331**	0.6209***	-0.0464**	-0.0272**	0.5926***
		(0.0194)	(0.0114)	(0.0070)	(0.0223)	(0.0102)	(0.0066)
	index ethnic 1990* linear trend	0.0104***	-0.0055***	-0.0007*	0.0099*	0.0060**	0.0009
		(0.0010)	(0.0006)	(0.0004)	(0.0060)	(0.0027)	(0.0018)
	index edu 1990*linear trend	0.0488***	0.0889***	-0.0321***	0.0395***	0.0057**	-0.0036**
		(0.0145)	(0.0085)	(0.0052)	(0.0054)	(0.0025)	(0.0016)
	index demo 1990*linear trend	0.1068	0.0611	0.1936***	-0.1670***	-0.0316***	0.0158**
		(0.1451)	(0.0854)	(0.0521)	(0.0199)	(0.0091)	(0.0059)
	log(K)	0.0012*	0.0037***	0.0019***	-0.0015*	0.0062***	0.0014***
		(0.0007)	(0.0004)	(0.0002)	(0.0008)	(0.0004)	(0.0002)
	log(L)	0.0793***	0.0193***	0.0216***	0.1160***	0.0073***	0.0254***
		(0.0015)	(0.0009)	(0.0005)	(0.0017)	(0.0008)	(0.0005)
	age1	-0.0021	0.0645***	-0.0966***	0.0050	0.1141***	-0.1041***
		(0.0051)	(0.0030)	(0.0018)	(0.0061)	(0.0028)	(0.0018)
	age2	-0.0273***	-0.0136***	-0.0451***	-0.0158**	0.0558***	-0.0242***
		(0.0053)	(0.0031)	(0.0019)	(0.0065)	(0.0030)	(0.0019)
	age3	-0.0187**	0.0137***	0.0287***	-0.0065	0.0259***	0.0380***
		(0.0065)	(0.0038)	(0.0023)	(0.0078)	(0.0036)	(0.0023)
	males	-0.0361***	-0.0342***	-0.0822***	-0.0377***	-0.0415***	-0.0784***
		(0.0033)	(0.0019)	(0.0012)	(0.0039)	(0.0018)	(0.0012)
	exp	0.0026**	0.0044***	0.0067***	0.0051***	0.0125***	0.0066***
		(0.0013)	(0.0007)	(0.0004)	(0.0015)	(0.0007)	(0.0004)
	skill1	-0.0001**	0.0008***	-0.0000	-0.0228***	-0.0808***	0.0095***
		(0.0000)	(0.0000)	(0.0000)	(0.0050)	(0.0023)	(0.0015)
	skill2	0.0002***	-0.0006***	-0.0000***	0.1265***	0.4702***	0.0173***
		(0.0000)	(0.0000)	(0.0000)	(0.0111)	(0.0051)	(0.0033)
	tenure	-0.0026***	0.0001	0.0016***	-0.0033***	-0.0016***	0.0016***
		(0.0003)	(0.0002)	(0.0001)	(0.0004)	(0.0002)	(0.0001)
	multi	-0.0730***	-0.0210***	-0.0271***	-0.1452***	-0.0248***	-0.0291***
		(0.0021)	(0.0013)	(0.0008)	(0.0025)	(0.0011)	(0.0007)
	geo spillover	0.0001***	0.0001***	0.0001***	0.0001***	0.0004***	0.0001***
		(0.000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)
	tech spillover	0.0001***	0.0001***	0.0001***	0.0001***	0.0000***	0.0001***
		(0.000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)
	size/industry/year/industry*year dummies	yes	yes	yes	yes	yes	yes
	shares of foreigners by group of countries	yes	yes	yes	yes	yes	yes
	shares of employees by occupation	yes	yes	yes	yes	yes	yes
	F test (excluded instruments); p-value	185.81; 0.000			165.79; 0.000
	N		96,636			96,636
	R2		0.509			0.555
			xi

Notes:

The dependent variables are all diversity indexes. Significance levels: ***1%, **5%, *10%. Standard errors clustered at the commuting area level.

xii

Table A2 :

 A2 estimates of the IV first step for the number of patent applications The dependent variables are all diversity indexes. Significance levels: ***1%, **5%, *10%. Standard errors clustered at the firm level.

			Aggregate			Disaggregate
		Index ethnic Index edu Index demo Index ethnic Index edu Index demo
	index ethnic com	0.2762***	-0.0192***	-0.0346***	0.2519***	-0.0067**	-0.0177***
		(0.0073)	(0.0030)	(0.0022)	(0.0062)	(0.0032)	(0.0036)
	index edu com	-0.1446***	0.2608***	-0.0468***	-0.1303***	0.5346***	-0.0162***
		(0.0130)	(0.0063)	(0.0053)	(0.0122)	(0.0062)	(0.0036)
	index demo com	-0.0221	0.0956***	0.6177***	-0.0489**	-0.0355***	0.0729***
		(0.0188)	(0.0082)	(0.0073)	(0.0213)	(0.0102)	(0.0062)
	index ethnic 1990* linear trend	0.0103***	-0.0046	-0.0012*	0.0102*	0.0056**	0.0010
		(0.0008)	(0.0012)	(0.0000)	(0.0056)	(0.0027)	(0.0022)
	index edu 1990*linear trend	0.0493***	0.0893***	-0.0319***	0.0389***	0.0057**	-0.0036**
		(0.014)	(0.0088)	(0.0053)	(0.0046)	(0.0022)	(0.0016)
	index demo 1990*linear trend	0.1068	0.0608	0.1937***	-0.1666***	-0.0319***	0.0160**
		(0.1453)	(0.0852)	(0.0524)	(0.0202)	(0.0088)	(0.0056)
	log(K)	0.0008	0.0035***	0.0020***	-0.0021**	0.0061***	0.0016***
		(0.0007)	(0.0004)	(0.0002)	(0.0008)	(0.0004)	(0.0002)
	log(L)	0.0789***	0.0189***	0.0218***	0.1151***	0.0075***	0.0258***
		(0.0015)	(0.0009)	(0.0005)	(0.0017)	(0.0008)	(0.0005)
	discounted stock of applications	-0.0007**	0.0005**	-0.0001	-0.0015***	-0.0006***	-0.0002*
		(0.0003)	(0.0002)	(0.0001)	(0.0004)	(0.0002)	(0.0001)
	log(fixed effects)	0.0112	0.0297***	-0.0130**	0.0684***	-0.0148*	-0.0162**
		(0.0140)	(0.0082)	(0.0050)	(0.0166)	(0.0076)	(0.0050)
	fixed effect dummy	0.0284***	0.0006	0.0009	0.0227***	0.0125***	-0.0002
		(0.0036)	(0.0021)	(0.0013)	(0.0043)	(0.0019)	(0.0013)
	age1	-0.0016	0.0647***	-0.0966***	0.0060	0.1141***	-0.1043***
		(0.0051)	(0.0030)	(0.0018)	(0.0061)	(0.0028)	(0.0018)
	age2	-0.0273***	-0.0132***	-0.0452***	-0.0151**	0.0557***	-0.0244***
		(0.0053)	(0.0031)	(0.0019)	(0.0065)	(0.0030)	(0.0019)
	age3	-0.0189**	0.0137***	0.0287***	-0.0063	0.0257***	0.0379***
		(0.0065)	(0.0038)	(0.0023)	(0.0078)	(0.0036)	(0.0023)
	males	-0.0353***	-0.0337***	-0.0824***	-0.0367***	-0.0414***	-0.0786***
		(0.0033)	(0.0019)	(0.0012)	(0.0039)	(0.0018)	(0.0012)
	exp	0.0023*	0.0044***	0.0067***	0.0049**	0.0123***	0.0066***
		(0.0013)	(0.0007)	(0.0004)	(0.0015)	(0.0007)	(0.0004)
	skill1	-0.0001**	0.0009***	-0.0000	-0.0229***	-0.0808***	0.0096***
		(0.0000)	(0.0000)	(0.0000)	(0.0050)	(0.0023)	(0.0015)
	skill2	0.0002***	-0.0006***	-0.0000***	0.1240***	0.4703***	0.0181***
		(0.0000)	(0.0000)	(0.0000)	(0.0111)	(0.0051)	(0.0033)
	tenure	-0.0027***	0.0001	0.0016***	-0.0033***	-0.0017***	0.0016***
		(0.0003)	(0.0002)	(0.0001)	(0.0004)	(0.0002)	(0.0001)
	multi	-0.0728***	-0.0213***	-0.0270***	-0.1446***	-0.0247***	-0.0291***
		(0.0021)	(0.0013)	(0.0008)	(0.0025)	(0.0011)	(0.0007)
	geo spillover	0.0001***	0.0001***	0.0001***	0.0001***	0.0004***	0.0001***
		(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)
	tech spillover	0.0001***	0.0001**	-0.0001***	0.0001***	0.0000***	-0.0001***
		(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)
	size/industry/year/industry*year dummies	yes	yes	yes	yes	yes	yes
	shares of foreigners by group of countries	yes	yes	yes	yes	yes	yes
	shares of employees by occupation	yes	yes	yes	yes	yes	yes
	F test (excluded instruments); p-value		179.22; 0.000			163.64; 0.000
	N		96,636			96,636
	R2		0.509			0.552
	Notes: xiii

Table A3 :

 A3 The effects of labor diversity on firm innovation, the mechanisms involved.Occupation specific diversity 2nd gen. Imm. as as natives University graduates as natives In the first and last panel marginal effects are reported and all diversity measures have been standardized. In the middle panel elasticities are reported. All regressions are estimated with the same IV approach used in the previous tables and include all firm specific characteristics, year and two-digit industry dummies plus year-industry interactions. Significance levels: ***1%, **5%, *10%. Standard errors clustered at the commuting area level.

	Probability to innovate	Occupation specific diversity 2nd gen. Imm. as natives University graduates as natives	White collar Blue collar	index ethnic aggr 0.0009*** 0.0027*** 0.0001 0.0005***	(0.0003) (0.0009) (0.0001) (0.0001)	index edu aggr 0.0001 0.0002 0.0001 0.0001	(0.0001) (0.0001) (0.0001) (0.0001)	index demo aggr 0.0008 0.0029* 0.0001 0.0001	(0.0012) (0.0015) (0.0001) (0.0001)	N 96,636 96,636 96,636 96,636	pseudo R2 0.372 0.371 0.389 0.389	Number of firm patents	White collar Blue collar	index ethnic aggr 0.5677*** 0.2577* 0.1980** 0.2991*	(0.1922) (0.1043) (0.0562) (0.1550) Notes: xiv index edu aggr 0.7270* 0.8909 0.2166 0.1819 (0.4403) (0.9272) (0.5523) (0.5563) index demo aggr 0.9746 0.5577 0.4136 0.6546 (2.1803) (3.7982) (2.7813) (2.7992) N 96,636 96,636 96,636 96,636 pseudo R2 33730.0 27768.3 26982.2 24934.8 2nd gen. Imm. as natives University graduates as natives 0.0152* 0.0683** (0.0077) (0.0312) -0.0262 -0.0288 (0.0303) (0.0283) 0.0389 0.0242 (0.0682) 1,086 0.297 (0.0610) 1,086 0.296 Probability of applying in different technological areas Blue collar 0.0127* (0.0069) -0.0037 (0.0077) 0.0138 (0.0173) 1,086 0.289 Occupation specific diversity White collar index ethnic aggr 0.1954** (0.0718) index edu aggr -0.0322 (0.0877) index demo aggr 0.0320 1,086 0.292 (0.1088) N pseudo R2

Table A4 :

 A4 The effects of labor diversity on firm innovation, robustness checks.Shannon entropy index Richness Edu and demo diversity as sd IV migration determinants Firms without pre-sample patents Firms with pre-sample patentsNumber of firm patentsShannon entropy index Richness Edu and demo diversity as sd IV migration determinants Firms without pre-sample patents Firms with pre-sample patents

		0.0160***	(0.0061)	0.0027	(0.0017)		-0.0801	(0.0602)				3,368	329.7	1.5491**	(0.7479)	0.8436	(0.5751)		0.6539	(1.2921)				3,368
		0.0009***	(0.0003)	0.0001	(0.0001)		0.0007	(0.0004)				93,268	0.293	0.4177***	(0.4671)	0.4688	(0.3870)		0.9042	(2.9191)				93,268
	Probability to innovate	0.0010***	(0.0001)	0.0001	(0.0001)		0.0001	(0.0001)				96,636	0.390	0.4746**	(0.1746)	0.6218	(0.5420)		0.7077	(1.7151)				96,636
		0.0009***	(0.0003)	0.0009	(0.0010)	-0.0021	(0.0022)	0.0011	(0.0012)	-0.0001	(0.0001)	96,636	0.379	0.3551***	(0.1219)	0.6012	(1.8341)	1.3546	(2.3561)	0.1052	(1.0042)	0.2227	(0.3688)	96,636	6035.7
		0.0077***	(0.0004)	0.0021	(0.0020)		-0.0009	(0.0010)				96,636	0.338	0.7342***	(0.1901)	0.7381	(0.6662)		1.2272	(1.4921)				96,636	5932.8
		0.0009***	(0.0003)	0.0001	(0.0001)		0.0007	(0.0004)				96,636	0.377	0.7827**	(0.2131)	0.6502	(1.2852)		0.8601	(1.5032)				96,636	42368.8
		index ethnic aggr		index edu aggr		Sd(years of education)	index demo aggr	Sd(age)		Male		N	pseudo R2	index ethnic aggr		index edu aggr		Sd(years of education)	index demo aggr	Sd(age)		Male		N	pseudo R2

The access to these data has been made possible thanks to the Center for Economic and Business Research (CEBR), an independent research center aliated with the Copenhagen Business School (CBS).

More details concerning the construction and composition of the data set can be found in Kaiser, Kongsted and Rønde (2008).

Agriculture, shing and quarrying; electricity, gas and water supply; sale and repair of motor vehicles; hotels and restaurants; transports; and public services.

See Appendix1 for more details about the countries belonging to each ethnic category.

Previous literature argues that linguistic distance serves also as a proxy for cultural distance (Guiso et al. 2009; Adsera and Pytlikova 2012).

Specically, we use the ocial language spoken by majority in a given country of origin to link the country into groups by family of languages.

In the aggregate specication, for example, the correlations between ethnic (demographic) diversity and the shares of workers from each ethnic (demographic) group are always below 0.30. The correlations between educational diversity and the shares of workers with either tertiary or secondary education are below 0.20.

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 constitute a commuting area if the interaction within the group of municipalities is high compared to the interaction with other areas; secondly, at least one municipality in the area must be a center, i.e. a certain share of the employees living in the municipality must work in the municipality, too[START_REF] Andersen | Commuting Areas in Denmark[END_REF]. In total 104 commuting areas are identied.

Unfortunately in our dataset it is not possible to observe in which area each establishment of a multi- establishment rm is located. For multi-establishments rms, the information about the location is only provided at the headquarter level. However, we do not think this represents a serious problem as multiestablishments rms constitute only 11% of our sample. It is also important to note that most of rms included in our estimation sample remain in the same commuting area over the estimation period(1995- 2003).

In the case of Denmark, there was also a special dispersal policy implemented for refugees between years 1986 and 1998 by the Danish authorities. The dispersal policy implied that new refugees were randomly distributed across locations in Denmark, see e.g.[START_REF] Damm | Ethnic Enclaves and Immigrant Labor Market Outcomes: Quasi-Experimental Evidence[END_REF]. This fact as well supports the validity of our instrument because the refugees, as a part of international migrants to Denmark, were not driven by the rm innovation outcomes when settling, but by those dispersal policies or by the migrant networks. In addition, the inows of economic migrants are driven by push and pull factors of destination and origin countries, costs of migration and other bilateral relationships between the origins and destinations(Pedersen et al. 2008, Ortega and[START_REF] Ortega | The Causes and Eects of International Migrations: Evidence from OECD Countries 1980-2005[END_REF]. We believe that those migration determinants are unlikely to be correlated with a rm' s innovation outcomes.

The error term u it is added to allow for endogeneity. It also induces overdispersion, so that the Poisson model and the Negative binomial model are empirically equivalent.

This assumption means that ε is a common latent factor that aects both diversity and patent applications and is the only source of dependence between them, after controlling for the inuence of the observed variables.

The chi2 (p-value) are respecitvely 29.64 (0.000), 4.79; 0.047: 34.78 (0.000) in the regressions for rm probability to innovate, number of patent applications and rm probability of applying for a patent in dierent technological areas.

Acknowledgments

We thank Guglielmo Barone, Tor Eriksson, Hideo Owan, Pekka Ilmakunnas, Michael Rosholm, Chad Syverson and Måns Soderbom (alphabetical order) for helpful suggestions. In addition, we appreciate comments from participants at seminars organized by the Copenhagen Business School, University of Bergamo, Aarhus School of Business, University of Lausanne, 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, CAED/COST 2010 in London, the 2010 International Symposium on Contemporary Labor Economics at WISE, Xiamen, and EALE 2011 in Paphos. We also thank Ulrich Kaiser and Cedric Schneider for graciously providing us the data on patent applications. Pierpaolo Parrotta acknowledges the nancial support from the Swiss National Centre of Competence in Research LIVES and Graduate School for Integration, Production and Welfare. Mariola Pytlikova gratefully acknowledges funding from the NORFACE programme on Migration in Europe Social, Economic, Cultural and Policy Dynamics (project MI3, Migration: Integration, Impact and Interaction ). 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, Bulgaria, 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; Asia: all the other Asian countries non included in both East Asia and Muslim Countries categories; 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.