Return to skills and labour market size

ABSTRACT Several studies document that skills are strong predictors of earnings; however, less is known about the extent to which labour market size influences the return to skills. Using data from a unique representative survey recording the skill requirements of Hungarian firms, we show that social skills have higher returns in large urban labour markets. Surprisingly, this pattern cannot be observed for cognitive skills, while the return to manual skills slightly decreases with labour market size. Our estimates are robust to different agglomeration measures, additional controls and estimation methods; however, returns to skills seem to vary considerably across worker groups.


INTRODUCTION
Over the last few decades several studies established that skills are strong predictors of individual earnings Deming, 2017;Heckman et al., 2006;Weinberger, 2014) while another strand of research in urban economics focused on the general regularity of higher wages in larger cities, commonly referred to as the urban wage premium (Baum-Snow & Pavan, 2012;De la Roca & Puga, 2017;Glaeser & Maré, 2001). Much less is known, however, about the extent to which labour market thickness contributes to the return to skills. Bacolod et al. (2009) were the first to examine how individual skills are rewarded in cities of different sizes. Relying on the assumption of positive assortative matching between workers and employers, they measured skills by using data on job skill requirements and reported that returns to cognitive and social skills are higher in large cities. Similar conclusions have been drawn by Andersson et al. (2014), and more recently Koster and Ozgen (2021) found that agglomeration affects those who work in nonroutine occupations.
A common feature of these studies is that they use occupation-level data on job skill requirements to approximate individual skills. One considerable limitation of this approach is that skill requirements are assumed to be homogeneous within occupations. Recent evidence, however, suggests that the variation of skill contents or stated requirements within occupations is substantial (Autor & Handel, 2013;Deming & Kahn, 2018), therefore, interpreting higher skill returns in large urban areas as productivity gains from agglomeration is problematic. When skills are measured at the occupational level, the Mincerian approach confounds the benefits from agglomeration with spatial differences in the occupational composition of the labour force.
This paper re-examines the interaction between agglomeration and returns to skills using firm-level data on job skill requirements. We make use of a unique survey recording the skill requirements for more than 1000 Hungarian firms. By matching this dataset to Hungarian wage survey data, we can measure individual skills directly by employers' requirements and estimate wage regressions where returns to skills are allowed to vary by the size of the labour market. The approach of using employers' skill requirements to measure workers' skills builds heavily on the assumption that workers are assigned to firms for which they are well suited (Ingram & Neumann, 2006). Although skill requirements do not reflect the actual capabilities of workers precisely, there are reasons to believe that employer-employee mismatches are rather exceptions than the regular course of things. Several models on search and recruitment predict assortative matching in the labour market even when search frictions are present (Chade et al., 2017).
Our contribution to the literature is twofold. First, we provide evidence for the association between agglomeration and skill returns in the context of a Central European small open economy. Second, we measure worker skills by firm-level job requirements instead of occupational data. The main advantage of measuring skills using firm-byoccupation-level data is that it allows us to control for both occupations and firm characteristics in wage regressions and thus characterize the variation in returns to skills across locations more accurately.
We find that the return to social skills is higher in large urban labour markets even after controlling for firm-level characteristics and occupations. For manual skills, the main result is that the return to these skills decreases with local administrative unit level 1 (LAU-1) population. This suggests that the urban wage premium cannot be associated with manual skills in Hungary. Surprisingly, we find no evidence that labour market size influences the wage return to cognitive skills. We believe this finding reflects the effects of extensive changes in the supply of cognitive skills in Hungary. The massive expansion of enrolment in higher education in the past decades resulted in an increased supply of cognitive skills, especially in large cities. This has recently led to a decrease in the wage returns to higher education as well (Varga, 2020). We suppose that the increased investment in human capital through education has driven down the price of cognitive skills to such an extent that it outweighs the benefits of agglomeration. At the same time, the supply of social skills is probably less affected by rational decisions to invest in human capital and therefore has not increased together with cognitive skills.
Separate estimates for different worker subgroups indicate that the urban premium for social skills is higher for educated male workers and for those who work in nonroutine occupations. When we restrict our sample by sectors, we also find evidence of heterogeneous returns. For service sector workers, social skills pay off better in urban labour markets than for manufacturing workers.
The remainder of the paper is structured as follows. The next section provides a conceptual framework for the analysis. Section 3 presents the empirical model and discusses some the major estimation issues. Section 4 outlines the data. Section 5 presents the results. Section 6 concludes.

CONCEPTUAL FRAMEWORK AND THEORETICAL ARGUMENTS
Although skills are central to various areas of social science research and public policy, there is still no consensus among scholars on the meaning of the concept of skill. Economists, sociologists and psychologists all have different interpretations of this concept, and even within these disciplines, no single dominant approach has emerged (e.g., see Green, 2013, for an exhaustive review). Of the many different approaches found in the literature, this paper draws on human capital theory (Becker, 1962;Mincer, 1974), which conceives of skill as a set of personal qualities and capabilities that contribute to the production of economic value (Bowles et al., 2001). In this sense, skills are intangible assets owned by a worker that have potential economic benefits for both the worker and the employer (Green, 2013).
The original theory of human capital investment does not address the question of what constitutes skills: it simply considers everything that is productive as part of human capital. In his seminal paper, Becker (1962) differentiated between skill types solely based on whether they are transferable between firms, since the degree of transferability determines who bears the costs of human capital investments. On this basis, the theoretical and empirical literature on human capital has long distinguished between generic and firm-specific skills. Moving beyond this traditional distinction, Shaw (1984) and Neal (1995) argued that most skills are neither generic nor purely firm specific, but rather occupation and industry specific. Closely related, Gibbons and Waldman (2004) introduced the concept of task-specific skills, while Lazear (2009) has argued that it is not the individual skills that are firm specific, but the demand for different generic skills that is determined by the firm's internal organizational structure and the production technology in use.
The idea that the productive value of skills depends on the nature of work, and the organizational structure of the firm provides a strong rationale for dissecting and categorizing skills. One important way that has proven particularly useful in empirical work is the domain-based classification, whereby skills are categorized according to the domain of tasks in which they are involved (Green, 2013). Task domains can be viewed as groups of job tasks that share similar contents and therefore require similar skills. Such task domains can be constructed in many ways, for example, based on the material content of the work, the methods and tools used to perform the task, or the relationship between the task and new technologies (Fernández-Macías & Bisello, 2022).
One common domain-based classification in occupational psychology distinguishes between cognitive, social and manual skills. This classification builds heavily on the work of psychologist Sydney A. Fine, who argued that each task is directed to some extent towards one of three core activities: dealing with data, people or things (Fine, 1955; for overviews, see, e.g., Kohn & Schooler, 1983;and Fine & Cronshaw, 1999). 'Cognitive skill' is the term used to describe personal capabilities that are useful in intellectual activities that involve processing and combining data and information. Social skills make workers eligible for cooperative work and engagement with others while manual skills include various forms of strength and dexterity that are useful for dealing with material objects (or things). Several studies in labour economics have adopted this tripartite categorization to examine the impact of skills on labour market outcomes. For instance, Bacolod et al. (2009), Abraham and Spletzer (2009), Bacolod and Blum (2010) and Yamaguchi (2010) considered all three skill types, while Weinberger (2014), Deming and Kahn (2018) and Piopiunik et al. (2020) focused on cognitive and social skills only. Combining this categorization scheme with the routinization criterion, Autor et al. (2003) classified tasks into five categories which has proven durable in studying the impact of routine-biased technological change (RBTC) on the labour market (Acemoglu & Autor, 2011;Autor et al., 2003;Spitz-Oener, 2006). In this paper we prefer the above three-piece skill categorization to Autor's fivepiece alternative, because as noted by Fernández-Macías and Bisello (2022) performing non-routine and routine cognitive (and manual) tasks does not necessarily require the use of different skills, but rather the use of the same skills with varying intensities. The distinction between routine and non-routine tasks is not based on the skills involved, but rather on certain features of the work context, for example, the time spent in repetitive work and the importance of accuracy (Acemoglu & Autor, 2011). It should be noted, however, that whatever the criteria used to typify skills, it is never possible to ensure a clear correspondence between skills and tasks. Even the simplest tasks such as cleaning or collecting waste require both cognitive functions and physical strength.
Despite its limitations, considering multiple skills is also of particular relevance in understanding the urban wage premium. A considerable body of literature argues that higher earnings in cities can be partly explained by micro-founded agglomeration mechanisms that enhance worker productivity. 1 One such mechanism is the accumulation of human capital which is said to happen faster in large cities. Recent evidence suggests that faster learning increases the return to work experience in cities especially for highly educated workers (Baum-Snow & Pavan, 2012;Carlsen et al., 2016;De la Roca & Puga, 2017). As a theoretical foundation for this finding, Davis and Dingel (2019) developed a spatial equilibrium model with idea exchange that predicts higher skill premia in large cities. An important feature of this model is that interactions between more skilled workers increase productivity to a greater extent. This is consistent with Glaeser's (1999) argument that workers become more productive through random contacts with more skilled colleagues. Since learning is an interactive process that requires various cognitive and social skills on both sides (e.g., active listening, critical thinking or instructing), learning externalities has greater benefits for those who possess these skills.
Another agglomeration mechanism in which intellectual skills (both cognitive and social) might play an important role is the sharing of indivisible resources and local suppliers. Coordinating cooperations that are established for such purposes requires negotiations, contracts and continuous communication between partners (Storper, 2013). Hence, interactive skills are of paramount importance in this process.
Since the benefits of learning and sharing may depend to some extent on the cognitive and social skills of workers, it can be assumed that the productive value of these skills is higher in large urban areas, which could lead to higher labour market returns. However, higher wages for workers with better cognitive and social skills may also be affected by the quality of matching between the employee and the employer. Since tasks entailing high-level decisionmaking, creative work and other forms of non-routine abstract activities tend to concentrate in large urban areas (Barbour & Markusen, 2007;Moretti, 2012;Scott, 2008) one could expect that the quality of matching in cities is better for those who have the skills that enables them to perform these tasks. Although the results of Baum-Snow and Pavan (2012) suggest that lower search frictions in cities has a meagre contribution to the urban wage premium, Koster and Ozgen (2021) recently found that the quality of matching is better for those urban workers who perform non-routine analytical tasks.
RBTC may also amplify the effects of agglomeration mechanisms by driving up the demand for skills required for non-routine jobs in cities. When new technologies become available, they are not applied uniformly across space. Given that computers and information and communication technologies (ICTs) complement both cognitive and social skills (Deming, 2017), those cities get at the forefront of technological adaptation where the supply of such skills is relatively higher (Beaudry et al., 2010;Berger & Frey, 2016). Accordingly, new skill-intensive tasks emerged in response to the adaptation of new technologies shift towards large urban areas further increasing the demand for these skills (Lin, 2011). Moreover, by reducing the cost of transferring information, ICTs provide new possibilities for firm decentralization (Bloom et al., 2009) and offshoring (Robert-Nicoud, 2008) which further accelerates the spatial separation of routine and non-routine production activities.
Consequently, we expect that the return to cognitive and social skills increase with the size of the labour market, more than will the return to manual skills. The main reason is that the return to manual skills is more likely to be affected by localization externalities arising from the spatial concentration of production-related (mostly routine) manufacturing functions that use manual skills more intensively. Since these functions are typically concentrated in small and medium-sized areas and not in large cities (Duranton & Puga, 2005), we expect that the price of manual skills will not increase with the size of the labour market, or even decrease.

EMPIRICAL MODEL AND ESTIMATION ISSUES
Our empirical model is an extended Mincerian wage equation (Mincer, 1974) except that it allows skill returns to vary by urban size as in Bacolod et al. (2009). Considering cognitive (c), social (s) and manual (m) skills the wage equation can be expressed as follows: where w ir represents the wage of individual i working in location r, n r denotes labour market size, z j i denotes the level of skill j ∈ {c, s, m} for individual i and X i is a vector of covariates. Conceptually, the return to skill j for a 802 László Czaller and Zoltán Hermann person working in location r is: where the focus of our attention is d j , a coefficient measuring the association between labour market size and the wage return to skill j. A caution to this approach, however, is that just like the majority of previous studies, it does not provide a convincing analysis of the causal effect of skills on earnings (e.g., Hanushek et al., 2015;Heckman & Kautz, 2012). One of the most extensively discussed concerns comes from unobserved variables such as personality traits and other inherent abilities that might simultaneously affect the level of skills and wages. Consciousnessthe tendency to be perseverant and dedicated to workpredicts educational attainment to a similar extent as cognitive abilities and shows similarly strong correlations with earnings as well. Similarly, emotional stability, often associated with a high internal locus of control and self-esteem, can also be associated with skill formation and later-life labour market outcomes (e.g., see and Heckman & Kautz, 2012, for comprehensive reviews of the evidence).
Recognizing this issue, Bacolod et al. (2009) included worker fixed effects to the wage models in order to eliminate these unobserved factors. However, even in cross-sectional settings where the inclusion of fixed effects is not feasible, there are good reasons to believe that the extent of ability bias can be minimized by including employer characteristics and occupations in X i . As shown by Heckman et al. (2006), personality traits prevail through various channels including education and occupational choice. If workers with certain unobserved traits find positions at productive firms and self-select into prestigious occupationsas the literature suggestscontrolling for these factors will capture the unobserved individual component and thus partly correct for the omitted variable bias. Since it is likely that some of the unobserved abilities considered above are also correlated with urban size (e.g., Combes et al., 2012), controlling for employers and occupations may help mitigate spatial sorting. Since our analysis is based on cross-sectional data, we include a large variety of controls into the regression models to control for unobservables. By doing so, it is also possible to infer on the economic conduits through which skills affect earnings (e.g., through education, occupational choice or selection to firms).
Another issue is that measurement error in skills could give rise to attenuation bias implying that the estimated coefficients will be biased toward zero. Moreover, when skills are measured using information on skill requirements, it is possible that the actual skill level of some workers will differ from observed values. If unmeasured skill components are correlated with either of our key variables, estimates on returns to skills will be biased.
Since the rate of return to skills is assumed to vary with the size of the labour market, it is not enough to mitigate the endogeneity issues associated with skills, because the potential endogeneity of log n r may also bias the estimates of wage returns through the interaction terms. The endogeneity of labour market size can be caused by several factors. For instance, educated workers with better skills may be willing to pay more for housing in order to enjoy the consumption amenities offered by cities. Moreover, there may be demand shocks that increase the wages of certain groups of workers, which are overrepresented in cities (e.g., as a result of specific governmental policies). Without addressing these threats, there is a high risk of overestimating the role of labour market size in determining the value of skills.
Apart from these technical issues there is another limitation to be mentioned. As is generally the case in the literature, our approach does not provide a full characterization of the rate of returns to skills because it does not account for the costs of living and a series of other factors that might affect the actual rate of return (e.g., the costs of achieving a certain level of skills). Ideally, a structural model on the location choice of workers with different combinations of skills would be required to properly allow for the whole spectrum of equilibrium effects that might affect the actual rate of return to skills. Nevertheless, even in the absence of any structural underpinning, wage regressions provide a strong indication of the relative importance of skills in local labour markets and help unravel the mechanisms behind urban wage premium.

DATA AND MEASUREMENT
We draw on multiple data sources. First, we extract data from a detailed survey carried out by the Institution of Economics, Hungarian Academy of Sciences (IE-HAS) in the fall of 2012. A sample of Hungarian firms were asked about the skill requirements of 10 occupations performed within the firm (the five most important occupations in terms of employment and another five randomly selected occupations), 2 using a standardized list of queries similar to the O*NET Skills Questionnaire. All occupations were graded on a set of skill descriptors, in terms of two separate dimensions: first, on a scale of 1-7 according to the 'level' of skill needed to perform the occupation; and second, on a scale of 1-5 corresponding the 'importance' of the skill descriptor to the occupation in terms of frequency of use. Scores assigned to the descriptors are provided by the human resource manager, or the executive manager of the firm. Throughout the survey a unique occupational classification consisting of 200 elements was used. Each of these elements are small groups of four-digit International Standard Classification of Occupations (ISCO)-88 occupations. Sample firms were selected by stratified sampling, and then, the respondent sample was weighted to the known distribution of the sampling frame (firm size, industry, occupation and location). The final sample consists of 1029 firms and the total number of filled questionnaires is 8568 covering 194 occupations.
We matched this dataset to the 2010 and 2011 waves of the National Employment Office's annual wage survey using both firm identifiers and four-digit ISCO-88 codes as matching variables. The Wage Survey includes the entire public sector, all firms with more than 20 employees and a 20% random sample of firms employing fewer than 20 workers. Firms with fewer than 50 employees provide data on all workers, while larger firms report only a 10% random sample of their employees. This dataset includes a wide range of individual characteristics such as wages, sex, age, hours of work, educational attainment, occupation and also detailed information on employers. By combining the two surveys, employers' skills requirements for occupations can be directly linked to the workers in those occupations. Removing observations with missing values we obtained a dataset containing 14,990 private sector employees.
Similar to previous studies a subset of the available skill items is used to construct interpretable indices for different skill types. As a first step the product of the 'level ' and the 'importance' scales are calculated for each item to increase variance. Cognitive skills are defined as the average of the following items: reading, active learning, critical thinking, monitoring and decision-making. Social skills are measured by the average of social perceptiveness, coordination, persuasion, negotiation and service orientation. Finally, to capture manual skills, the following items are selected and averaged out: operation and control, installation, repairing and equipment selection. For ease of interpretation, we standardized the skill indices to have a mean of 0 and a standard deviation (SD) of 1. Criteria for the selection of skills items are further described in Appendix A in the supplemental data online. 3 Although the annual wage survey provides information on job sites at the municipality level, labour market size is measured as the log of LAU-1 population (LAU-1 was formerly NUTS-4). The main reason is that the LAU-1 regions provide a reasonable approximation to local labour markets in which agglomeration mechanisms are expected to operate. In Appendix B in the supplemental data online, we check whether the results are sensitive to how the size of the local labour market is measured. Similar to Koster et al. (2014), we consider kernel-based agglomeration measures that take into account the distance-weighted population of nearby locations as well. The results of these models do not differ from those reported below. The data used to measure labour market size come from the 2011 Census.
All other variables used in the analysis are from the Wage Survey. The dependent variable is the gross average monthly wage containing the basic wage and other remuneration benefits such as overtime pay, and commissions. Individual control variables include sex, work experience (and its square), educational attainment, occupation and a dummy for part-time work, while firm-level controls include dummies on firm size, ownership and collective agreements. Work experience is measured as age minus years of schooling minus 6 and those who work fewer than 36 hours per week are considered as part-time workers. To control for education, we define four educational dummies such that they correspond to the following International Standard Classification of Education (ISCED) categories: (1) primary education or less (ISCED 0 and 1), (2) lower secondary education (ISCED 2), (3) upper secondary education (ISCED 3) and (4) tertiary education or more (ISCED 5 and 6). Firms are classified into five categories by the number of employees, and two dummies are introduced to control for ownership: the first indicates whether at least 50% of the firm is owned by foreigners, and the second takes a value of 1 if the majority of the firm is owned by the state or a local government. Some of the regression models include dummies for two-digit NACE Rev. 2. industries as well. Table 1 presents some descriptive statistics on the variables used in the analysis. The mean monthly wage in the sample is 211,437 HUF with significant variation (with a SD of almost 260,000 HUF). There are three orders of magnitude differences between the extremes. By construction, the mean of the skill indices is 0 and the SD is 1, with all three skills having similar ranges. Our measure of labour market size (LAU-1 population) ranges from 10,000 (in the western border region) to 1.7 million in Budapest. The proportion of men is slightly higher than their employment share, because the sample covers firms with more than five employees and excludes the public sector, self-employed persons and small firms. Two-thirds of the workers in the sample (68%) have secondary education, 15% have elementary education and 17% have a college degree or more. Almost a quarter of workers are covered by collective agreements and 44% work in small and medium-sized enterprises. Figure 1 reports the kernel densities of skills for different LAU-1 size categories. Regions are partitioned into four categories using population quartiles. Although the distribution of skills appears similar across size categories as in Bacolod et al. (2009), the larger the size of the local labour market, the lower the proportion of workers with low cognitive and social skills while the prevalence of above-average cognitive and social skills is slightly higher in the top two quarters. Interestingly, in the case of manual skills, it can be seen that the third quartile has the highest proportion of above average skills. The reason for this pattern is that manufacturing activities are often located on the outskirts of middle-sized cities and cities with county rights, therefore the share of productionrelated jobs (e.g., machine operators, assemblers) that require more manual skills is somewhat higher in these areas. Table 2 presents the baseline results of our regression analysis. Column 1 contains the cognitive skill index, the log of LAU-1 population and their interaction as explanatory variables. It shows that the return to cognitive skills as imputed from the employers' skill requirements grows with labour market size. Columns 2 and 3 include individual and firm-level characteristics into the model. While

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László Czaller and Zoltán Hermann worker characteristics seem to have a smaller impact on the interaction term (d C ), it drops considerably after the inclusion of firm-level controls in column 3. These results suggest that cognitive skills affect wages mostly through worker selection into firms with different attributes. Results for social skills are reported in columns 4-6. The key result is that the return to social skills increases with urban size. However, unlike in the case of cognitive skills, this result persists even if we control for worker and firm-level characteristics. Consistent with the idea that agglomeration effects enhance the productive value of social skills, we continue to find that the interaction of social skills and LAU-1 population has a positive and significant effect on wages. Based on the estimates reported in column 6, the elasticity of wage with respect to population is 4.2%, which means that a doubling of LAU-1 population increases the wage by 2.9% (ln(2) × 0.042 ¼ 0.029) for a worker with average skill levels. However, for a worker whose social skills are 1 SD above the average, the elasticity is 2.5 percentage points higher (6.7%).
The next three columns present the results for manual skills, which are quite different from those for social skills. In the absence of any controls, the manual skills index is positively related to wages, and its interaction term with population is insignificant. However, after extending the model with individual and firm-level controls, we find that the return to manual skills decreases with urban size (column 9). Comparing a worker with average skills to one with a manual skill level exactly 1 SD higher, the average workers' population elasticity to wages is 1.7 percentage points higher.
When all skill indices are included (column 10), these results remain unchanged which suggest that neither skill index acts as a proxy for another. The same results hold even if we look at the skill variation across workers within the same occupation (column 11). Although the joint contribution of occupational dummies to the predictive performance of the model seems to be important (joint F-statistic is 76.38 with p < 0.01), it does not have a large influence on any of the key coefficients. Based on the last column of Table 2, the elasticity of wage with respect to LAU-1 population is 2.8 percentage points higher for those with social skill levels 1 SD higher than the average (7.4%). However, an increase of 1 SD from the mean in manual skills reduces the population elasticity of wage by roughly one-third. Surprisingly, the return to cognitive skills remains unaffected by labour market thickness. 4

Endogeneity issues
As noted in section 2, the Mincerian approach might be exposed to endogeneity issues caused by unobserved worker heterogeneity, measurement error in skills and omitted variables correlated with both labour market size Return to skills and labour market size 805 and wages. In this section we pursue several approaches designed to address these issues. The first problem we consider is related to unobserved worker heterogeneity. If skill indices capture the effects of personality traits and other unobserved characteristics, the interaction terms in equation (1) will be biased (Combes et al., 2012). Moreover, if workers self-select across locations according to these characteristics, the role of labour market size will be overstated in the interaction terms. To examine the possible extent of omitted variable bias we follow Oster (2019) who proposes a simple procedure to calculate bounding values for unbiased coefficients. This test relies on the assumption that selection on observable covariates from a basic towards a full model is proportional to the selection on unobserved variables (Altonji et al., 2005;Oster, 2019). Assuming that selection in unobservables is equal to selection on observable covariates, and taking columns 4 and 11 of Table 1 as the basic and full models for social skills, Oster's bias-adjusted coefficient for the interaction between social skills and agglomeration is 0.0249. This suggest that after controlling for firm-level variables and occupations any remaining bias related to omitted variables is relatively small, as the biasadjusted coefficient is close to our prior estimates. For the interaction of manual skills and LAU-1 population Oster's procedure yields −0.0168 while for cognitive skills the biascorrected coefficient is virtually zero (−0.002).
Although this simple heuristic provides some circumstantial evidence that omitted variables bias is not a critical issue, it cannot be ruled out entirely. For example, prior estimates might be biased due to unobserved amenities and location-specific demand shocks as discussed earlier.
To overcome this issue, we follow the common approach of using historical data on the distribution of population as an instrument for the agglomeration metric. The underlying idea of such historical instruments is that the late nineteenth century distribution of population is by no means correlated with the recent distribution of amenities and local demand shocks but it still predicts current population levels quite well. However, if the LAU-1 population is endogenous, then we also expect its interactions to be endogenous as well. For the interaction of LAU-1 population and skill j, the historical population multiplied by skill j can be used a natural instrument (Wooldridge, 2002).
Column 1 of Table 3 reports two-stage least squares (2SLS) estimates where LAU-1 population and its interaction with cognitive skills are treated as endogenous. As it is shown at the bottom panel the first stage Sanderson-Windmeijer F-statistic rejects the null-hypothesis of weak instruments. The second stage estimates are consistent with those obtained using ordinary least squares (OLS) in the corresponding column of Table 2. As expected, the point estimate for labour market size is slightly smaller   (0.040 compared with 0.053), but the coefficient of the interaction term is unchanged. Columns 2 and 3 interact social and manual skills with the LAU-1 population, respectively. For both skills, we obtain similar results as in Table 1. Again, the coefficient of our labour market size measure is lower, but the point estimates of the interaction terms do not differ from those obtained by OLS. These results suggest that endogeneity of labour market size at most only slightly distorts our baseline estimates. Another concern regarding our prior results is attenuation bias arising from measurement errors in skills. It is possible that the finding of no urban cognitive premium is due to such errors. Probably, the most straightforward way to address this issue is to use an alternative measure of the same skill type as an instrumental variable (Hanushek et al., 2015). This approach essentially extracts the variation that is common to both the skill index and the instrument in the first stage of a 2SLS model, and uses this variation to estimate skill returns in the second stage. Since speaking skills are presumably associated with all the items that constitute our social skill index, the standardized item of speaking skills can be used as an instrument for social skills. On the same basis, problem-solving and equipment maintenance skills might be reasonable instruments for cognitive and manual skill indices. Again, the interaction between these instruments and LAU-1 population can be used as instruments for the interaction terms.
Column 4 shows that the instruments based on the standardized skill item of problem-solving are strong predictors of the endogenous variables (Sanderson-Windmeijer F-statistic ¼ 164.5 with p < 0.001). In the second stage, the point estimate of δ C is similar to the reference estimate in column 3 in Table 2. Columns 5 and 6 repeat the same exercise for social and manual skills. The excluded instruments seem to be quite strong, which means that any bias arising from weak identification is not likely in either model. Second-stage results are almost exactly similar to previous models. The fact that the estimates in columns 4-6 do not change compared with the baseline indicates that attenuation bias from measurement error is only a minor issue in our setting and the lack of a significant urban cognitive premium cannot be attributed entirely to measurement error.
Of course, none of the models reported in Table 3 is able to deal with the entire spectrum of endogeneity issues, but the consistency across different models supports the robustness of our baseline results.

Heterogeneous returns by worker groups
We continue by looking at different worker groups to examine the heterogeneity in returns to skills along multiple dimensions. As often shown in the literature, the task content of jobs substantially varies between female and male workers, which may result in different skill returns (Bacolod & Blum, 2010;Borghans et al., 2014). While women predominate in care work occupations such as nursing and child care as well as in other service jobs involving human interactions, the share of male workers is higher in production-related occupations. Table B2 in Appendix B in the supplemental data online shows that in our sample women have somewhat higher social skills, and lower cognitive and manual skills than men. Two-sample t-tests based on group means show significant differences for cognitive skills at the 10% level, while for the other two skills differences are highly significant (cognitive skills ¼ −1.48, p ¼ 0.069; social skills ¼ 6.34, p ¼ 0.000; manual skills ¼ 29.34, p ¼ 0.00).
Columns 1 and 2 of Table 4 show significant gender differences in the returns to manual and social skills. While for male workers the interaction of the social skill index and LAU-1 population is positive and significant at the 5% level, for females the same coefficient is almost zero and insignificant. For a male worker, a 1 SD increase from the mean in social skills increases the elasticity of wage with respect to labour market size by 4.4%. These results suggest that even though women are well-endowed with social skills, they benefit less from their skills in cities compared with men. One reason for this pattern might be that women face barriers that limit their access to professional networks which does not allow them to exploit their social potentials and harness the benefits of agglomeration (Rosenthal & Strange, 2012). For instance, due to the unequal division of labour within the household, women cannot devote as much time to learning and networking as men. Moreover, having preschool-age children is shown to discourage women from making job changes that would result in higher wages and more productive matches (Looze, 2017).
With regard to manual skills, we find that point estimates for the interaction term are almost exactly the same for women and men, but its standard error is much lower for men. In fact, having excellent manual skills does not seem to affect the wage of women at all.
Another variable along which returns to skills might vary is educational attainment. To analyse heterogeneity between education groups we split the sample into two parts: one for individuals without a high-school graduation (corresponding to fewer than 12 years of schooling) and another for those with a high-school graduation or more. Columns 3 and 4 of Table 4 report separate estimates for educational subsamples. These results suggest that the urban wage premium tends to be higher when social skills are coupled with high educational attainment. For educated workers the interaction between labour market size and the social skill index is somewhat larger than the corresponding full-sample estimate (0.032 as opposed to 0.028 reported in the last column of Table 2), while for the less educated the same interaction term is virtually to zero. These results are in line with our expectations as more educated workers are more likely to perform nonroutine tasks that involve different types of human interactions. Surprisingly, cognitive skills have no effect in either group when we control for firm characteristics and occupations. Manual skills contribute significantly to the wage of low educated workers.
Columns 5 and 6 of Table 4 report that there is a sharp gap in urban social skills premium between routine and Return to skills and labour market size 809 non-routine occupations. 5 When we restrict our sample to workers in routine occupations, we find no sign of higher returns in urban labour markets (0.015 with SE ¼ 0.017) while for non-routine workers we find a strong association between the hedonic price of social skills and labour market size. By contrast, manual skills show a significant correlation only for routine workers, mostly in rural areas and small towns. In line with Koster and Ozgen (2021), these results highlight that the urban skill premium stems in part from cities' greater appreciation of non-routine activities.
The remaining columns report estimates for manufacturing and service sectors. Although estimates for both sectors show that the returns to social skills are positively influenced by the size of the local labour market, the correlation is stronger for services. While in the manufacturing sector, a 1 SD increase from the mean in social skills increases the size elasticity to wages by 2.9%, in the service sector the increase is 4.7%. A reasonable explanation for this finding is that localized competition in non-tradable services drives urban firms to customize services to the needs of clients, maintain customer relationships and resolve complaints in order to prevent customer attrition or expand their client base (Storper, 2013). Since these activities require skills such as persuasion, service orientation and social perceptiveness , when local competition is fierce, it becomes important for the firm to hire employees with better social skills and incentivise their effort with higher wages. In the manufacturing sector, however, this incentive is of lesser importance as firms producing tradable goods can sell to larger markets and thus face more similar product market competition, irrespective of their location.
Another important difference between sectors is that in the service sector, the price of manual skills decreases much more sharply with the size of the labour market. This can be explained by the fact that while the service sector of small and medium-sized urban areas is dominated by personal services and industry support tasks requiring higher manual skills, in large cities there is a higher proportion of financial, technical and information technology (IT) services that do not require the intensive use of manual skills. Similarly, manufacturing firms tend to locate management, sales and creative functions in cities, which also do not rely on manual skills (Duranton & Puga, 2005).
Overall, there are considerable heterogeneities across worker groups and sectors in the return to social skills, however cognitive skills are not predictive of earnings in any of the worker groups considered.

CONCLUSIONS
This paper examines whether returns to cognitive and social skills are greater in dense urban settings. The novelty of the paper is that it draws on a representative survey containing detailed information on the skill requirements of Hungarian firms which allows us to rule out the possibility that spatial differences in skill returns are driven by firm selection or the 'functional specialization' of locations. Although we cannot neutralize every econometric issue that might bias our results, the consistency of estimates across different model specifications provides some support for the underlying importance of social skills in urban labour markets. This result is consistent with the arguments that emphasize the role of knowledge exchange and learning as possible sources of agglomeration economies (e.g., Davis & Dingel, 2019). Moreover, it is also consistent with the idea that fierce competition in cities raises demand for social skills especially in non-traded services and innovative activities. Surprisingly, despite its theoretical underpinning we do not find any relationship between returns to cognitive skills and the degree of agglomeration. In fact, cognitive are not predictive of wages which might be the result of the educational expansion that increased the supply of cognitive skills in the last two decades in Hungary. Since cognitive skills can be more easily developed through education and informal human capital investment than social skills (Cawley et al., 2001), access to tertiary education plays a major role in driving down the price of cognitive skills.
Another important conclusion of the paper is that the size of the labour market negatively affects the returns to manual skills, and this is independent of the sector we are talking about. The productive value of manual skills is not extended by agglomeration mechanisms associated with large urban labour markets, but rather by localization economies stemming from the concentration of routine manufacturing activities in small and mediumsized cities.
The results of this paper contribute to a number of other related literatures as well. For example, previous research has shown that early childhood interventions may have long-term benefits for several adult outcomes (Chetty et al., 2011). Although this paper does not examine where skills come from, our results suggest that social skills acquired at an early age may have positive effects on lifetime earnings which makes a case for focusing more on the development of interpersonal skills at every stage of education. As shown in section 5, even high-school graduates can benefit from their social capabilities, thus building these skills should be started earlier than higher education.
Another strand of the literature investigates the sources of urban wage premium. Social skills might play an important role in explaining higher individual earnings in big cities. First, workers with better social capabilities may choose to locate in dense urban and self-select into well-paid occupations. Second, since all sorts of agglomeration economies involve some kind of human interaction, social skills might help harness the external benefits of agglomeration and facilitate specialization by reducing coordination costs within firms (Becker & Murphy, 1992;Deming, 2017). An interesting followup would be to formalize the mechanisms underlying these ideas in a spatial equilibrium framework. The results of this paper provide a strong empirical rationale for such theoretical investigations.