The urban wage premium and spatial sorting on observed and unobserved ability

Abstract

We estimate static and dynamic agglomeration effects on earnings among university graduates using Swedish longitudinal population register data. The prime interest lies with whether and how the dynamic effects of big city work experience vary by observed ability of workers and whether the effects are portable after relocation. Urban wage premium and spatial sorting of university graduates are analysed by using information on school grades, parental education and university rank. We find that the value of accumulated big city work experience increases with observed ability. The dynamic premium of working in bigger cities is not lost when moving to smaller cities, suggesting that it reflects learning effects and human capital accumulation. Our findings indicate systematic spatial sorting on observed indicators of ability as well as on unobserved productive traits. Sorting on unobserved abilities is driven primarily by graduates in the upper part of the observed ability distribution and is apparent also when taking dynamic learning effects into consideration.

1. Introduction

It is widely documented that wages tend to increase with city size. Broadly speaking, the existence of an urban wage premium (UWP) can be explained either by non-random spatial sorting of workers or by the existence of agglomeration economies, that is, that city size or density stimulates worker productivity. In this study, we estimate the UWP among university graduates in Sweden and provide new evidence on the nature of sorting and on the heterogeneity in the UWP by measures of cognitive ability.

Data for, for example, the USA, France, Norway and Spain indicate a raw UWP ranging from about 20% to 60% (Glaeser and Maré, 2001; Combes et al., 2008; Carlsen et al., 2016; De la Roca and Puga, 2017). Figure 1 shows the relationship between mean annual earnings and population size for 69 travel-to-work areas (TWAs) in Sweden (which we will refer to as ‘cities’). It is clearly the case that workers in bigger cities (in particular, university-educated workers) have higher average earnings. Data for all workers indicate that workers in Stockholm (the largest city) earn 30% more on average than workers in the smallest city and 22% more than workers in the median-sized city. The corresponding figures for university-educated workers are 53% and 30%, respectively.

Figure 1.

Mean annual earnings and city size.

Notes: Data are for employed workers in the private sector aged 25–54 years in 69 TWAs in 2019. Simple ordinary least square estimates of the relationship give the following equations. All workers: log earnings = 0.026 log size + 5.696 (R² = 0.33). Workers with long university education (3 years or more): log earnings = 0.052 log size + 5.576 (R² = 0.43). All estimates are significant at the 1% level.

Duranton and Puga (2004) distinguish three main theoretical micro-foundations of urban agglomeration economies: matching, learning and sharing. Increased knowledge about the underlying mechanisms and effects of geographical concentration on productivity, wages and growth is vital for the design of policies that strengthen prosperous regions and improves the economic potential of lagging areas (OECD, 2018; Iammarino et al., 2019; Faggio et al., 2020).

Our analysis is based on detailed population-wide longitudinal register data for individuals who have graduated from at least 3 years of university education. We focus on university graduates because of the important role of human capital for growth (e.g. Moretti, 2004, 2012) and the relatively high mobility of the highly educated (e.g. Faggian et al., 2007; Haapanen and Tervo, 2012). In addition, both theory (e.g. Venables, 2011) and empirical evidence (see next section) indicate an especially high UWP for this group. The data include several ability-related variables that are unobserved in many empirical studies, such as school grades, parents’ education and earnings and measures of university quality. Unlike many previous studies, our data also include both male and female workers. In many developed countries, women tend to have considerably lower employment rates than men. In Sweden, as well as in the other Nordic countries, the two groups have roughly similar employment rates.

We distinguish between cities at different positions in the urban hierarchy and find that the value of accumulated big city work experience is increasing with observed worker ability. Evaluated at mean experience in the sample (8.8 years), the estimated earnings difference between Stockholm and cities below the top seven is 21.3% for workers in the top decile of the ability distribution (consisting of a static premium of 2.2% and a dynamic premium of 19.1%). For workers in the bottom decile of the ability distribution, the combined static and dynamic premium in Stockholm is 10.7%. The value of work experience accumulated in Stockholm is not lost when moving to smaller cities, indicating that the dynamic premium of working in Stockholm is highly portable and thus likely reflects learning effects and human capital accumulation. In terms of sorting, we find clear evidence of systematic positive sorting of workers into Stockholm on observed indicators of ability as well as on unobserved productive traits. In particular, spatial sorting on unobserved ability is evident after adjusting for big city work experience. This sorting is driven primarily by workers in the upper part of the observed ability distribution.

The following section discusses recent literature on agglomeration economies, with a particular focus on dynamic effects and spatial sorting on unobserved ability. Section 3 describes our data and presents descriptive evidence on spatial sorting on observed indicators of ability. Section 4 reports static wage density estimates, while Sections 5 and 6 present estimates of initial and dynamic wage effects across city types and ability groups. Section 7 analyses spatial sorting on unobserved ability across the observed ability distribution and Section 8 concludes.

2. Relationship to previous literature

Following Glaeser and Maré (2001), many studies have confirmed that labour productivity is higher in agglomerations (see Rosenthal and Strange, 2004; Puga, 2010; Combes and Gobillon, 2015 for summaries of empirical results). In terms of wage elasticities with respect to population size or density, estimates of the UWP with adjustment for residential and other types of self-selectivity, typically based on worker fixed effects estimation, indicate elasticities ranging from about 2% to 6% (e.g. Glaeser and Maré, 2001; Combes et al., 2008; Di Addario and Pattachini, 2008; Mion and Naticchioni, 2009; Lehmer and Möller, 2010; Andersson et al., 2014). Studies focusing on whether agglomeration effects differ between individuals with different human capital generally find that the UWP increases with cognitive skills and worker education (e.g. Wheeler, 2001; Rosenthal and Strange, 2008; Bacolod et al., 2009 on US data; Ahlin et al., 2014; Carlsen et al., 2016; Korpi and Clark, 2019 on data for the Nordic countries).

Recent studies not only look at static agglomeration effects but pay specific attention to the dynamic effects of work experience in different city types.¹ Based on counterfactual simulations of a structural search model, Baum-Snow and Pavan (2012) find that differences in the returns to work experience is the main explanation for the wage gap between large and small metropolitan areas in the USA. This holds for both high school and college graduates, and the authors conclude that the result is consistent with larger cities promoting learning and human capital accumulation. Another recent approach to disentangling the underlying mechanisms of agglomeration economies is based on fixed effects estimations using more or less complete worker location histories. De la Roca and Puga (2017) show that work experience acquired in bigger cities in Spain is more valuable than work experience acquired in smaller cities. Carlsen et al. (2016) report similar results for Norway and, contrary to De la Roca and Puga (2017), also find that the effect of big city experience on wages increases with workers’ educational attainment. De la Roca and Puga (2017) take the analysis a step further and study how the value of experience accumulated in bigger cities is affected when workers move to smaller cities. They show that the value of big city experience is not lost after relocating, suggesting that learning effects are the main explanation behind the dynamic UWP in bigger cities.²

Another strand in recent research is to focus on spatial sorting not only on observed characteristics but also on workers’ unobserved traits. Baum-Snow and Pavan (2012) report that sorting on unobserved ability has, if anything, a small negative impact on the UWP. Another approach to assessing the importance of unobserved worker heterogeneity is to compare distributions of estimated worker fixed effects across locations using a methodology developed by Combes et al. (2012a). While the estimated worker fixed effects capture all dimensions of unobserved time-invariant individual heterogeneity, in this context the fixed effects are typically interpreted as reflecting workers’ ‘unobserved ability’ or ‘unobserved productive traits’. Combes et al. (2012b) report positive sorting on worker fixed effects in bigger cities in France, using a static model. De la Roca and Puga (2017) find no evidence of sorting on unobserved worker effects in a dynamic setting and argue that static models will tend to overestimate sorting on unobserved traits because they confound the value of unmeasured city-specific work experience with innate productive skills. Unlike De la Roca and Puga (2017), Carlsen et al. (2016) report positive sorting on unobserved ability into large labour markets when location-specific work experience is taken into account. Moreover, sorting is found to be driven by the university educated. Comparing bigger cities with the rest of the country, the distribution of worker fixed effects is shifted to the right in bigger cities for the university educated but not for workers with only primary or secondary level education. Although the impact of spatial sorting on unobserved attributes on the UWP is a central question in the most recent literature, it is far from resolved.

We make five contributions to the existing literature on agglomeration economies. First, given that our data contain a number of ability-related variables that are typically unobserved—such as school grades, parents’ education and earnings and indicators of university quality—we can present comprehensive descriptive evidence on spatial sorting among university-educated workers (who already are a selective group). Secondly, given the unusually rich data, we can test how adding ability-related controls and other observed covariates changes the magnitude of the estimated UWP. To facilitate comparison with previous studies, we use a standard log wage–log density specification. Thirdly, we analyse how the dynamic effects of work experience at different levels of the urban hierarchy vary depending on the observed ability of workers. Our assumption is that, if positive agglomeration effects on earnings from matching and/or learning mechanisms increase with individual ability, this should be evident not only across levels of educational attainment but also within groups, for example, among university graduates. Fourthly, we study whether the dynamic effects of big city work experience are portable after relocation for a highly skilled group with a high capacity to learn from their urban peers. Fifthly, we add to the existing evidence on spatial sorting on unobserved productive skills by analysing how sorting on unobserved traits varies across observed indicators of ability.

3. Data, city classification and spatial sorting on ability

We use detailed population-wide longitudinal register data administered by Statistics Sweden. The data cover all individuals who graduated from at least 3 years of university education during the period 2001–2010 and who were aged 22–33 years in the year of graduation.³ We track each graduation cohort throughout the first 9 years of their post-graduation labour market career.⁴ Using matched employer–employee data, we can combine information on individuals’ school achievements, parental background and various demographic attributes with information on workplace and job characteristics. In total, 99,326 workers and 634,572 yearly observations are included in the data (see  Appendix A and Table A1 therein for details on sample restrictions and variable definitions).

The data include several ability-related variables. Among these are grade point average (GPA) at the end of compulsory school and high school (typically at the age of 16 and 19 years, respectively). The data also contain information on parents’ level of education, annual earnings and other socio-economic attributes. A number of studies show that measures such as cognitive test scores, school grades and parents’ educational attainment are strong predictors of wages and other socio-economic outcomes (e.g. Heckman et al., 2006; Björklund and Jäntti, 2012; Grönqvist et al., 2017).⁵ We will use these variables as indicators of latent ability and various personality traits (e.g. ambition, motivation and persistence) that are valued in the labour market. The data also include an indicator of college quality, measured in terms of enrolment selectivity of the degree-awarding university. Bacolod et al. (2009) use college quality in an UWP context and argue that measures of college quality may pick up effects on earnings of individual heterogeneity in ability, since more able (and potentially more productive) individuals are more likely to apply to, and be accepted by, more selective institutions. Studies also show that college quality has a positive effect on earnings (e.g. Black and Smith, 2006 on US data, Eliasson, 2006 on Swedish data).

The data further contain information on the number of years of university education, field of university education (two-digit level) and basic demographic attributes such as gender, country of birth and various family characteristics. For employed individuals, we use annual information on sector (two-digit level), occupation (three-digit level), employment at a multinational firm, establishment size and the geographical location of the workplace.

Importantly, based on the information on employment status and workplace location, we calculate accumulated overall work experience as well as accumulated city-specific work experience for each individual.

The dependent variable in the analysis is annual gross labour earnings.⁶ The earnings measure excludes income transfers such as unemployment and social security benefits. We follow previous agglomeration literature and focus our attention on nominal earnings (e.g. Bacolod et al., 2009; Andersson et al., 2016; De la Roca and Puga, 2017). Economists tend to prefer hourly earnings over annual earnings because the former is presumed to better reflect the productivity of the individual worker. Unfortunately, Swedish register data do not include information on the number of hours worked per year. Lacking information on working time, we draw on Antelius and Björklund (2000) and drop observations with annual earnings below SEK 140,000 (corresponding to the bottom 7% of the earnings distribution).⁷ This reduces the influence of labour supply on annual earnings. As a robustness check, we will apply alternative earnings restrictions (including using all observations). Moreover, given that earnings increase with city size, applying a single, country-wide restriction on annual earnings could lead to downward bias in the estimated UWP. An alternative approach is to use the same percentile cut-off across different cities. When we apply both strategies, it turns out that using city-specific earnings restrictions tends to give slightly higher estimates of the UWP. We will nevertheless stick with the more conservative estimates based on a country-wide restriction on earnings. All main results based on city-specific earnings restrictions are reported in Supplementary Appendix Tables A1–A5.

Since we are focusing on effects on labour earnings, we exclude job spells as self-employed. We also exclude job spells in the public sector because earnings in this sector are less influenced by market conditions. However, these spells are still counted when calculating accumulated experience (both overall experience and city-specific experience).

The spatial dimension in the analysis starts out with 69 TWAs that are defined by Statistics Sweden on the basis of commuting flows between municipalities in 2015. A TWA is a functionally integrated local labour market within which most people both live and work (i.e. commuting flows across the border is minimised).⁸ For simplicity, we will refer to these local labour markets as cities. We group the cities into four categories based on their position in the urban hierarchy. At the top of the urban hierarchy, we have Stockholm, with a population of about 2.6 million (about 25% of the Swedish population). At the next level, we find Göteborg and Malmö, with populations of 1.3 and 1.1 million, respectively. After that follows a group of four cities referred to as large regional centres, with a population above 200,000 (average population 258,000). Finally, there is a large group of smaller cities with a population below 200,000 (average population 60,000). We believe that the applied classification of cities in the Swedish urban hierarchy captures important spatial differences in terms of labour market diversity and human capital endowments that potentially affect the probability and quality of job matching, as well as the potential for knowledge accumulation through learning (see Table A2 in  Appendix A). As a robustness check, we will consider alternative classifications of cities. Many studies report UWP estimates in terms of wage elasticities with respect to population density or size. To facilitate comparisons with this literature, we will also present UWP estimates using continuous measures of population density or size based on all 69 cities in the urban system. Note that we assign workers to cities based on the location of their workplace.

The UWP literature generally confirms that highly skilled workers, typically measured in terms of educational attainment or occupational skill level, tend to concentrate in bigger cities (see e.g. Glaeser and Maré, 2001; Bacolod et al., 2009; Andersson et al., 2014; De la Roca and Puga, 2017). But there are few studies analysing the spatial sorting process based on more detailed observed indicators of productive traits. We complement the existing research by presenting evidence on spatial sorting using our different ability-related variables.

Table 1 reports the location pattern of the workers in the sample in terms of workplace location across the different city types and by indicated ability. The first row shows that, on average over the workers’ 9-year post-graduation labour market career, 43% are working in Stockholm, 28% in Göteborg/Malmö, 9% in large regional centres and 20% in smaller cities. The following rows show corresponding percentages for workers in the bottom and top of the ability distribution. The numbers reveal consistent positive sorting of workers into Stockholm on the different ability-related attributes. For instance, 49% (53) of the workers in the top decile of the compulsory school (high school) GPA distribution are working in Stockholm, compared to only 38% (37) of the workers in the bottom decile. Similarly, 52% of the workers who graduated from top-ranked universities are working in Stockholm, compared to only 28% of workers who graduated from low-ranked universities. We find similar patterns of positive sorting of workers into Stockholm with regard to parents’ earnings and level of education. At the other end of the urban hierarchy, the data reveal consistent negative sorting of workers into smaller cities based on the various ability-related variables. We can thus conclude that, within the group of highly skilled workers, bigger cities tend to attract the best workers in terms of observed indicators of latent ability and productive traits. Two recent studies focusing on migration patterns of college graduates report similar findings of systematic spatial sorting on some of the ability-related variables discussed above (Ahlin et al., 2018 on data for Sweden, Eliasson et al., 2020 on data for Finland and Sweden).

Table 1

Location of workers by city types and ability-related attributes (average over the 9-year post-graduation labour market career)

Sample	Stockholm	Göteborg/Malmö	Large regional centres	Smaller cities
All	0.43	0.28	0.09	0.20
Compulsory school GPA
≤P(10)	0.38	0.26	0.09	0.28
≥P(90)	0.49	0.31	0.07	0.13
High school GPA
≤P(10)	0.37	0.27	0.10	0.26
≥P(90)	0.53	0.29	0.07	0.11
University quality ranking
Lowest (Q1)	0.28	0.27	0.04	0.41
Highest (Q5)	0.52	0.36	0.03	0.08
Parents' earnings
≤P(10)	0.40	0.29	0.09	0.22
≥P(90)	0.64	0.22	0.05	0.09
Parents’ education
Low	0.37	0.29	0.10	0.25
High	0.56	0.27	0.06	0.11

Notes: University quality ranking is a measure of the quality of the degree-awarding university in terms of enrolment selectivity. If neither of the parents has long university education (3 years or more), they are classified as having low education. If both parents have long university education, they are classified as having high education.

4. Static city population density and size wage premiums

Many studies report estimates of UWPs with respect to continuous measures of population density or size. We follow this literature and begin with a reduced-form empirical model where the log wage of worker $i$ is expressed as a function of log city density, work experience, other observed characteristics, worker-fixed effects and year-fixed effects: where $w_{\mathrm{ict}}$ is the wage of worker $i$ in city $c$ at year $t$⁠, ${\mathrm{den}}_{\mathrm{ct}}$ is the population density in city $c$ at year $t$⁠, ${\exp }_{\mathrm{it}}$ is aggregated post-graduation work experience acquired by worker $i$ up until year $t$ (we allow experience to have a non-linear effect, but only include the linear term here for simplicity), $X_{\mathrm{it}}$ is a vector of observed demographic, ability, parental, college and job-related characteristics of worker $i$ at year $t$⁠, ${\mu }_i$ is a worker-fixed effect, ${\gamma }_t$ is year-fixed effects, and ${\epsilon }_{\mathrm{ict}}$ is an error term. In this specification, population density is used as a measure of urban scale, but as an alternative we will also use population size.⁹

$${\log w}_{\mathit{ict}}=\alpha \log {\mathrm{den}}_{\mathrm{ct}}+\delta {\exp }_{\mathrm{it}}+X_{\mathrm{it}}\beta +{\mu }_i+{\gamma }_t+{\epsilon }_{\mathrm{ict}}$$

(1)

Table 2, Columns (1)–(5), report simple pooled ordinary least square estimates of Equation (1). The raw UWP with respect to city density is 7.7%, shown in Column (1).¹⁰ Controlling for work experience and basic demographic characteristics reduces the premium slightly to 7.4% (Column (3)). The estimates in Column (4) are from an augmented specification including observed indicators of ability. When controlling for school grades, parental background and field/level/quality of university education, the estimated elasticity of wage with regard to city density drops by more than two percentage points, down to 5.2% (Column (4)). This suggests that spatial sorting of graduates on these attributes is a quantitatively important source of the raw UWP. The specification in Column (5) includes controls for job characteristics in terms of sector (two-digit level), occupation (three-digit level), establishment size and a dummy variable indicating employment at a multinational firm. Introducing these controls lowers the wage premium to 4.3%.

Table 2

Estimation of static city density earnings premium

	(1)	(2)	(3)	(4)	(5)	(6)
Dependent variable	Log earnings	Log earnings	Log earnings	Log earnings	Log earnings	Log earnings
Log population density	0.0772***	0.0776***	0.0735***	0.0521***	0.0428***	0.0217***
	(0.0005)	(0.0005)	(0.0005)	(0.0005)	(0.0005)	(0.0013)
Experience		0.1418***	0.1338***	0.1200***	0.1032***	0.0914***
		(0.0023)	(0.0022)	(0.0021)	(0.0019)	(0.0035)
Experience2		−0.0025***	−0.0022***	−0.0022***	−0.0017***	−0.0022***
		(0.0001)	(0.0001)	(0.0001)	(0.0001)	(0.0001)
Year fixed effects	Yes	Yes	Yes	Yes	Yes	Yes
Graduate cohort fixed effects	Yes	Yes	Yes	Yes	Yes	–
Demographic controls	No	No	Yes	Yes	Yes	Yes
Grades, parental, and college controls	No	No	No	Yes	Yes	–
Job controls	No	No	No	No	Yes	Yes
Worker fixed effects	No	No	No	No	No	Yes
Observations	634,572	634,572	634,572	634,572	634,572	634,572
Workers	99,326	99,326	99,326	99,326	99,326	99,326
R2	0.10	0.11	0.24	0.31	0.38	0.26

Notes: Demographic controls include indicators for gender, married/cohabiting, having children, country of birth and a measure of potential pre-university work experience. Grade controls include GPA from compulsory school and high school and indicators for field of education in high school. Parental controls include indicators for parents’ country of birth, level of education, homeownership and a variable measuring the parents’ annual gross labour earnings (all parental controls are defined when the individual is 17 years of age). College controls include indicators for number of years of university education, field of university education (ISCED two-digit level) and a measure of the quality of the degree-awarding university. Job controls include indicators for sector (NACE two-digit level), occupation (ISCO three-digit level), employment at a multinational firm and a variable measuring establishment size. See Table A1 in the  Appendix for additional variable definitions. Graduate cohort and grades/parental/college controls are time-invariant and thus not included in the fixed effects specification. All specifications include a constant term. The reported R² value in Column (6) is within workers. Robust standard errors (clustered by workers) are given in parentheses.

***

Indicates significance at the 1% level.

To account for sorting across cities on unobserved characteristics, we follow Glaeser and Maré (2001) and introduce worker-fixed effects in the regression model (Column (6)). This removes bias in the estimates due to unobserved time-invariant worker heterogeneity. The within transformation of the fixed effect model implies that the parameter of the density variable is identified primarily on the basis of movers between cities of varying densities, while all other parameters in the model are identified from changes over time for both movers and stayers.¹¹ The introduction of fixed effects leads to a sharp reduction in the estimated elasticity of wage with respect to city density, from 4.3% (Column (5)) to 2.2% (Column (6)). This corresponds to a drop of 49%, which is close to what De la Roca and Puga (2017) report for Spain, and falls in between the results reported by Combes et al. (2010) and Mion and Naticchioni (2009) for France and Italy, respectively. The fixed effect estimate indicates that a doubling of city density is associated with 2.2% higher wages. This result is at the lower end of previously reported elasticities based on worker fixed effects. Carlsen et al. (2016) find an elasticity of 3.0% for college-educated workers in Norway. The somewhat lower estimate found here might be explained by less spatial variation in entry level wages for our sample of workers entering the labour market just after completing college. As expected, the effect of overall experience on wages is non-linear. In the regression model including worker fixed effects, one additional year of experience raises wages by 5.1% (evaluated at mean experience in the sample, 8.8 years).

Based on the reported estimates, we can calculate how much of the raw UWP with respect to city density that is explained by observed and unobserved characteristics. The raw UWP is 7.7% (Column (1)). The premium drops to 4.3% when all observed attributes are considered (Column (5)), and further to 2.2% when worker fixed effects are taken into account (Column (6)). From this, it follows that the raw UWP is explained primarily by observed worker characteristics (45%) and to a lesser extent by unobserved attributes (27%). This finding reflects the unusually rich data available for this study.

As a robustness check, we have estimated the fixed effects model in Table 2 with population density fixed at the mean values in the 9-year post-graduation time window during which we follow the graduates. With this approach, the parameter of the density variable is identified exclusively on the basis of movers between cities of different densities (thus eliminating the effect of changes over time in city density for stayers). The estimated elasticity is similar (1.9% compared to 2.2%) when using this approach.

De la Roca and Puga (2017) argue that population size is preferable to density as a measure of urban scale because density can be affected by the degree of spatial tightness applied when determining the boundaries around urban areas. If we replace log population density with log population size and use the same fixed effects specification as in Column (6), the estimated UWP with respect to city size is 1.4% (not reported in Table 2). De la Roca and Puga (2017) find an elasticity of wage with respect to city size of 2.4% for workers in Spain.¹² Their sample includes both low- and high-skilled workers. Papers focusing on the elasticity of wage with respect to city size for workers at the upper end of the educational distribution tend to report higher premiums (e.g. Wheeler, 2001; Rosenthal and Strange, 2008; Bacolod et al., 2009).¹³ As discussed above, the comparatively low estimate found here might be related to our sample of workers entering the labour market just after college graduation.

We have also investigated results with different sample restrictions. First, we repeat the fixed effects estimations including all sectors of the economy. As expected, when also considering job spells in the public sector, where wage formation is more regulated, the estimated elasticity of wage with respect to city density drops somewhat, from 2.2% to 1.6% (see Table A3 in  Appendix A). This indicates that the UWP is higher in the private sector. Secondly, we have experimented with different restrictions on annual earnings (see Table A4 in  Appendix A). When including all observations with positive earnings, the estimated elasticity becomes slightly lower (1.7%). For restrictions above SEK 100,000, the estimates are fairly stable. Finally, we have analysed separate results for men and women, again applying different earnings restrictions (see Table A5 in  Appendix A). For men, the estimated elasticity turns out to be around 2.5% regardless of which earnings restriction we impose. For women, the estimated elasticity is between 1.4% and 1.7% for restrictions above SEK 100,000. When including all observations with positive earnings, the estimate is 0.4% but statistically insignificant.

5. Initial wage premium across city types

We continue by investigating how the wage premium differs between cities at different positions in the urban system. With this approach, we relax the implicit assumption that the effect of density/size is linear across the urban hierarchy. We start by considering an urban system consisting of four categories of cities and estimate the following equation: where $c_{1,\mathrm{it}}$⁠, $c_{2,\mathrm{it}}$ and $c_{3,\mathrm{it}}$ are dummies for Stockholm, Göteborg/Malmö and a group of four cities referred to as large regional centres (having above 200,000 inhabitants). The excluded reference group consists of smaller cities in the urban hierarchy. As a robustness check, we will consider alternative classifications of the urban system.

$${\log w}_{\mathrm{ict}}={\alpha }_1{c}_{1,\mathrm{it}}+{\alpha }_2{c}_{2,\mathrm{it}}+{\alpha }_3{c}_{3,\mathrm{it}}+\delta {\exp }_{\mathrm{it}}+X_{\mathrm{it}}\beta +{\mu }_i+{\gamma }_t+{\epsilon }_{\mathrm{ict}}$$

(2)

Table 3 reports the results. The raw UWP (Column (1)) is 19.5% for Stockholm, 8.5% for Göteborg/Malmö and 5.4% for large regional centres. When controlling for all observed factors (Column (2)), the premium is reduced to 11.6% for Stockholm, 3.4% for Göteborg/Malmö and 1.4% for large regional centres. When also controlling for unobserved characteristics using worker fixed effects (Column (3)), the premium drops to about 5% for Stockholm and slightly above 1% for the other two groups of cities. In this case, the estimated city effects are exclusively identified on the basis of migrants between the different city types.¹⁴ Using a similar fixed effects specification, Carlsen et al. (2016) find a premium of 7.6% for college-educated workers in Oslo. Ahlin et al. (2014) and Korpi and Clark (2019) report premiums of about 6–8% for college-educated workers in cities at the top of the urban hierarchy in Sweden. Both papers use identification strategies that differ from the one applied here and do not distinguish Stockholm from Göteborg and Malmö but group these three cities into a single category of metropolitan regions.

Table 3

Estimation of static earnings premium by city type

	(1)	(2)	(3)
Dependent variable	Log earnings	Log earnings	Log earnings
Stockholm	0.1945***	0.1164***	0.0495***
(1st)	(0.0012)	(0.0011)	(0.0030)
Göteborg/Malmö	0.0853***	0.0338***	0.0151***
(2nd–3rd)	(0.0012)	(0.0010)	(0.0029)
Large regional centres	0.0540***	0.0139***	0.0115***
(4th–7th)	(0.0016)	(0.0014)	(0.0034)
Experience		0.1021***	0.0914***
		(0.0019)	(0.0035)
Experience2		−0.0017***	−0.0022***
		(0.0001)	(0.0001)
Year fixed effects	Yes	Yes	Yes
Graduate cohort fixed effects	Yes	Yes	–
Demographic controls	No	Yes	Yes
Grades, parental and college controls	No	Yes	–
Job controls	No	Yes	Yes
Worker fixed effects	No	No	Yes
Observations	634,572	634,572	634,572
Workers	99,326	99,326	99,326
R2	0.11	0.39	0.26

Notes: See notes to Table 2 for variable definitions. All specifications include a constant term. The reported R² value in Column (3) is within workers. Robust standard errors (clustered by workers) are given in parentheses.

***

Indicates significance at the 1% level.

If we calculate the contribution from observed and unobserved characteristics in explaining the raw UWP for the different city types, we find that unobserved worker attributes play a relatively larger role at the top of the urban hierarchy. For Stockholm, 40% of the raw UWP is explained by observed factors and 34% by unobserved characteristics. For large regional centres, only 4% of the raw UWP is explained by unobserved worker attributes, while as much as 74% is explained by observed characteristics. In Section 7, we present a more formal analysis of sorting on unobserved worker heterogeneity across city types and observed indicators of ability.

The classification with four categories of cities attempts to capture the most relevant levels in the Swedish urban system. As a robustness check, Table A6 in  Appendix A presents estimates based on a more detailed classification. We find no differences in the estimated premiums for Göteborg and Malmö when including these two cities as separate categories (about 1.4% for both) and we find no extra premium for a group consisting of 15 cities referred to as small regional centres (with between 100,000 and 200,000 inhabitants) compared to the reference group that includes smaller cities (with a population below 100,000). We draw two main conclusions from this complementary analysis. First, we can stick with the original regional classification. Secondly, the results based on the more detailed classification show that agglomeration effects are not linear across city size. As for the latter point, despite considerable differences in city size, the estimated premiums for Göteborg and Malmö (average population 1.2 million) and large regional centres (average population 260,000) are similar, and practically identical for small regional centres (average population 160,000) and the reference group with smaller cities (average population 30,000).¹⁵

6. Dynamic wage effects across city types and ability groups

An important explanation as to why earnings are higher at the top of the urban hierarchy is that bigger cities may allow workers to accumulate more valuable experience (Carlsen et al., 2016; De la Roca and Puga, 2017). Both papers demonstrate that dynamic effects in terms of city-specific work experience over time generate a widening gap between the earnings profiles of larger and smaller cities. An interesting question is whether the dynamic effect of big city experience varies depending on the observed ability of workers. While De la Roca and Puga (2017) report no differences for workers with different levels of education or occupational skills, Carlsen et al. (2016) find that the effect of big city experience on wages increases with workers’ educational attainment. We address the question of whether ability-related heterogeneity in UWP also can be detected within a group of highly skilled individuals. For this purpose, we divide our sample of university graduates based on an observed indicator of ability, namely high school GPA. To allow for experience to have a different impact on earnings depending on where the experience is acquired, we estimate the following dynamic version of the fixed effects model: where ${\exp \_c}_{1,\mathrm{it}}$⁠, ${\exp \_c}_{2,\mathrm{it}}$ and ${\exp \_c}_{3,\mathrm{it}}$ are post-graduation work experience accumulated by worker $i$ up until year $t$ in Stockholm, Göteborg/Malmö and large regional centres (quadratics of city-specific work experience are also included but left out of the equation for simplicity). Given that overall work experience (⁠${\exp }_{\mathrm{it}}$⁠) is included in the model, the parameters ${\tau }_1$⁠, ${\tau }_2$ and ${\tau }_3$ indicate whether work experience acquired in bigger cities is more valuable than experience accumulated in the reference group consisting of smaller cities in the urban hierarchy. For instance, if ${\tau }_1>0,$ then work experience acquired in Stockholm is more valuable than experience accumulated in smaller cities. Note that, while the initial city effects (⁠${\alpha }_1$⁠, ${\alpha }_2$ and ${\alpha }_3$⁠) are identified by migrants between the different city types, as before, the city-specific value of experience is identified based on both migrants and stayers.

$$\begin{array}{c}\hspace{0.17em}\text{log}\hspace{0.17em}{w}_{\mathit{ict}}={\alpha }_1{c}_{1,it}+{\alpha }_2{c}_{2,it}+{\alpha }_3{c}_{3,it}+\delta ex{p}_{it}+X_{it}\beta +{\mu }_i+{\gamma }_t\\ +{\tau }_1\cdot \hspace{0.17em}\text{exp}\_c_{1,it}+{\tau }_2\cdot \hspace{0.17em}\text{exp}\_c_{2,it}+{\tau }_3\cdot \hspace{0.17em}\text{exp}\_c_{3,it}+{\epsilon }_{\mathit{ict}}\end{array}$$

(3)

Table 4 reports the results. If we compare with the previous specification that does not control for city-specific experience (Table 3, Column (3)), the initial earnings premium for all workers (Column (1)) is slightly lower for Stockholm and Göteborg/Malmö (3.5% and 1.2%) and somewhat higher for large regional centres (1.4%). When it comes to the dynamic effects of city experience, the results indicate economically significant effects for Stockholm. A first year of experience in Stockholm increases earnings by 2.2% compared to having worked that same year in a city below the top seven. Over time, this gap widens considerably. Evaluated at mean experience in the sample (8.8 years), the earnings difference between Stockholm and cities below the top seven is 15.6% (consisting of a static premium of 3.5% and a dynamic premium of 12.1%). This result is consistent with the findings in Carlsen et al. (2016) and De la Roca and Puga (2017), who find considerable dynamic effects of work experience at the top of the urban hierarchy in Norway and Spain. In particular, Carlsen et al. (2016) report a total premium of 14% for college-educated workers in Oslo (evaluated at 8.1 years of experience). Our results also indicate modest dynamic effects of work experience in Göteborg/Malmö (a total effect of 3.3%, up from an initial effect of 1.2%).

Table 4

Estimation of static and dynamic earnings premium by city type and ability group

	(1)	(2)	(3)	(4)	(5)
Dependent variable	Log earnings	Log earnings	Log earnings	Log earnings	Log earnings
High school GPA percentile	All	≤P(10)	≤P(25)	≥P(75)	≥P(90)
Stockholm	0.0351***	0.0377***	0.0386***	0.0305***	0.0218**
(1st)	(0.0030)	(0.0088)	(0.0058)	(0.0066)	(0.0109)
Göteborg/Malmö	0.0115***	0.0159*	0.0168***	0.0090	−0.0021
(2nd–3rd)	(0.0029)	(0.0086)	(0.0057)	(0.0065)	(0.0106)
Large regional centres	0.0135***	0.0110	0.0201***	0.0128	0.0148
(4th–7th)	(0.0036)	(0.0101)	(0.0066)	(0.0079)	(0.0127)
Experience	0.0813***	0.1046***	0.0863***	0.0927***	0.0871***
	(0.0036)	(0.0099)	(0.0067)	(0.0077)	(0.0120)
Experience2	−0.0016***	−0.0012***	−0.0014***	−0.0022***	−0.0023***
	(0.0001)	(0.0002)	(0.0002)	(0.0002)	(0.0003)
Experience in Stockholm	0.0233***	0.0169***	0.0185***	0.0252***	0.0277***
	(0.0012)	(0.0036)	(0.0023)	(0.0025)	(0.0041)
Experience in Stockholm2	−0.0011***	−0.0010***	−0.0010***	−0.0007***	−0.0007*
	(0.0001)	(0.0003)	(0.0002)	(0.0002)	(0.0004)
Experience in Göteborg/Malmö	0.0069***	0.0054	0.0073***	0.0016	0.0044
	(0.0012)	(0.0036)	(0.0024)	(0.0027)	(0.0044)
Experience in Göteborg/Malmö2	−0.0005***	−0.0004	−0.0007***	0.0003	0.0001
	(0.0001)	(0.0003)	(0.0002)	(0.0003)	(0.0004)
Experience in large regional centres	−0.0025	0.0031	0.0002	−0.0057	−0.0133**
	(0.0017)	(0.0048)	(0.0032)	(0.0036)	(0.0057)
Experience in large regional centres2	0.0001	−0.0003	0.0000	0.0003	0.0011*
	(0.0002)	(0.0005)	(0.0003)	(0.0004)	(0.0006)
Year fixed effects	Yes	Yes	Yes	Yes	Yes
Graduate cohort fixed effects	–	–	–	–	–
Demographic controls	Yes	Yes	Yes	Yes	Yes
Grades, parental and college controls	–	–	–	–	–
Job controls	Yes	Yes	Yes	Yes	Yes
Worker fixed effects	Yes	Yes	Yes	Yes	Yes
Observations	634,572	65,683	159,285	167,221	74,082
Workers	99,326	10,779	25,632	25,556	11,201
R2	0.27	0.28	0.28	0.27	0.27

Notes: See notes to Table 2 for variable definitions. All specifications include a constant term. The reported R² values are within workers. Robust standard errors (clustered by workers) are given in parentheses. ***, ** and * indicate significance at the 1%, 5% and 10% level, respectively.

Columns (2)–(5) report results for university graduates with different levels of observed ability approximated by high school GPA. The estimated dynamic effect of work experience in Stockholm increases monotonically with observed worker ability. If we again evaluate the earnings premium at mean experience in the sample, the total Stockholm effect for workers in the bottom decile of the ability distribution (Column (2)) is 10.7% (3.8% initial premium plus 6.9% dynamic premium). The corresponding effect for workers in the top decile (Column (5)) is 21.3% (2.2% initial premium plus 19.1% dynamic premium). Carlsen et al. (2016) find that the value of experience in large cities in Norway increases with the level of education. Our estimates also indicate that, among a group of highly skilled workers (with 3 years or more of university education), the value of accumulated big city work experience is increasing with observed worker ability.

If we assume a positive correlation between learning capacity and ability, the finding that high-ability workers benefit most from working in big cities is consistent with a learning hypothesis. But the result may also reflect better matching opportunities for highly specialised workers in larger/thicker labour markets. To learn more about potential mechanisms, we follow De la Roca and Puga (2017) and study how the value of experience acquired in big cities is affected if a worker migrates to work in cities at lower levels in the urban hierarchy. We focus on the dynamic effect in Stockholm and estimate a version of Equation (3) that includes overall work experience, work experience accumulated in Stockholm, and interactions between years of experience acquired in Stockholm and indicators for currently working in Göteborg/Malmö, large regional centres, or cities below the top seven. In this case, the parameter on work experience in Stockholm indicates whether work experience there is more valuable than in the rest of the country. The parameters on the interaction variables indicate whether the dynamic effect of work experience in Stockholm remains uneffaced, decreases, or increases when moving to cities at lower levels in the urban hierarchy.

Table 5 presents the results. The estimated static city effects and the effect of overall experience are about the same as for all workers in Table 4 (Column (1)). A first year of experience in Stockholm raises earnings by 2.0% compared to having worked that same year in other parts of the country. The parameters for the interactions between work experience in Stockholm and indicators for currently working in other cities are small in magnitude and statistically insignificant in the case of large regional centres and smaller cities. These findings suggest that the value of work experience accumulated in Stockholm is either fully retained or only marginally depreciated when moving away from Stockholm. Our results thus confirm the conclusion in De la Roca and Puga (2017) that the dynamic premiums of working in big cities are highly portable.

Table 5

Estimation of portability of accumulated work experience in Stockholm

Dependent variable	Log earnings
Stockholm	0.0393***
(1st)	(0.0037)
Göteborg/Malmö	0.0104***
(2nd–3rd)	(0.0030)
Large regional centres	0.0106***
(4th–7th)	(0.0037)
Experience	0.0838***
	(0.0035)
Experience2	−0.0018***
	(0.0001)
Experience in Stockholm	0.0203***
	(0.0011)
Experience in Stockholm2	−0.0009***
	(0.0001)
Experience in Stockholm*Now in Göteborg/Malmö	0.0063***
	(0.0017)
Experience in Stockholm*Now in Large regional centres	0.0015
	(0.0020)
Experience in Stockholm*Now in Smaller cities	−0.0012
	(0.0016)
Year fixed effects	Yes
Graduate cohort fixed effects	–
Demographic controls	Yes
Grades, parental and college controls	–
Job controls	Yes
Worker fixed effects	Yes
Observations	634,572
Workers	99,326
R2	0.27

Notes: See notes to Table 2 for variable definitions. The specification includes a constant term. The reported R² value is within workers. Robust standard errors (clustered by workers) are given in parentheses.

***

Indicates significance at the 1% level.

As an illustration, we can use the estimated parameters in Table 5 and calculate the earnings profile for a worker with no prior experience who starts by working for 5 years in Stockholm and then migrates to work for 5 additional years in smaller cities. The initial earnings premium compared to working in smaller cities is 3.9%. The earnings gap widens over time due to the more valuable experience accumulated in Stockholm and reaches a total of 11.9% by Year 5 (3.9% initial effect plus 8.0% dynamic effect). When moving from Stockholm, the earnings premium immediately drops to 8.0% (because the static Stockholm effect is replaced by the smaller cities static effect). During the 5 years in the new location, the value of work experience acquired in Stockholm only depreciates slightly. By Year 10, the remaining premium amounts to 7.4%.

Overall, the results in Tables 4 and 5 indicate that work experience in Stockholm is associated with an economically significant dynamic premium that is highly portable and only marginally depreciates when migrating to smaller cities in the urban hierarchy. Workers accumulate more valuable experience in Stockholm and to a large extent retain the value of this experience when relocating. This latter result lines up with the evidence in De la Roca and Puga (2017) for Spain, suggesting that human capital accumulation and learning effects are the main explanations behind dynamic agglomeration effects in big cities.

7. Spatial sorting on unobserved ability across the observed ability distribution

In the descriptive analysis in Section 3, we found consistent positive sorting of workers into Stockholm on observed indicators of ability. In this section, we provide a more formal analysis of spatial sorting on unobserved ability and how it relates to our observed indicators of ability. Do bigger cities also tend to attract the best workers among those in the upper part of the observed ability distribution? To answer this question, we compare distributions of estimated worker fixed effects using the quantile approach developed by Combes et al. (2012a). As previously discussed, worker fixed effects are assumed to be closely related to workers’ unobserved and time-invariant productive traits. Given how Stockholm stands out in terms of estimated UWP, it seems reasonable to contrast the fixed effects distribution of workers in Stockholm to the corresponding distribution of workers in the rest of the country. According to the proposed methodology, we can approximate the distribution of fixed effects in Stockholm by taking the distribution of fixed effects in the rest of the country, shifting it by an amount $A$⁠, and dilating it by a factor $D$⁠.¹⁶ The fixed effects are attributed to the location of the workplace at the end of the 9-year follow-up period.

We exploit information on high school GPA, university quality rank, and parents’ level of education to examine heterogeneity in sorting on estimated unobserved ability. Table 6 reports results. The first row in Panel A compares worker fixed effects estimated from a static model using all workers (model specification as in Table 3, Column (3)). The estimated shift parameter is 9.5%, indicating positive sorting on unobserved ability into Stockholm. This is in line with Combes et al. (2012b), Carlsen et al. (2016) and De la Roca and Puga (2017). The second row compares worker fixed effects estimated from a dynamic model, allowing the value of work experience to vary depending on where it is acquired (model specification as in Table 4, Column (1)). The estimated shift parameter is smaller, 3.5%, but remains statistically significant, signalling that positive sorting on unobserved ability into Stockholm also exists when considering dynamic effects. This is in accordance with Carlsen et al. (2016) but contrary to De la Roca and Puga (2017), who find no evidence of sorting on unobserved ability when allowing homogeneous or heterogeneous dynamic effects.

Table 6

Comparison of worker fixed effects distributions, Stockholm versus rest of country

Worker fixed effects specification	Shift	Dilation
	(⁠$\widehat{A}$⁠)	(⁠$\widehat{D}$⁠)	R2	Obs.
Panel A: Aggregate
Static premium (Table 3, Column (3))	0.0954***	1.2584***	0.90	69,059
	(0.0026)	(0.0099)
Static and dynamic premium (Table 4, Column (1))	0.0354***	1.2681***	0.81	69,059
	(0.0024)	(0.0103)
Panel B: Across high school GPA percentiles
≤P(10): Static and dynamic premium (Table 4, Column (2))	0.0277***	1.1235***	0.92	7310
	(0.0071)	(0.0257)
≤P(25): Static and dynamic premium (Table 4, Column (3))	0.0138***	1.1508***	0.83	17,553
	(0.0042)	(0.0148)
≥P(75): Static and dynamic premium (Table 4, Column (4))	0.0646***	1.3545***	0.88	17,984
	(0.0061)	(0.0193)
≥P(90): Static and dynamic premium (Table 4, Column (5))	0.0714***	1.4253***	0.91	7965
	(0.0097)	(0.0311)
Panel C: Across university quality ranking (quintiles)
Lowest (Q1): Static and dynamic premium	−0.0024	1.0930***	0.78	6146
	(0.0086)	(0.0265)
Highest (Q5): Static and dynamic premium	0.0267***	1.3580***	0.83	24,387
	(0.0040)	(0.0171)
Panel D: Across parents’ level of education
Low: Static and dynamic premium	0.0245***	1.2173***	0.78	41,965
	(0.0033)	(0.0133)
High: Static and dynamic premium	0.0439***	1.2989***	0.90	10,307
	(0.0066)	(0.0257)

Notes: University quality ranking is a measure of the quality of the degree-awarding university in terms of enrolment selectivity. If neither of the parents has long university education (3 years or more), they are classified as having low education. If both parents have long university education, they are classified as having high education. Bootstrapped standard errors are given in parentheses (100 replications based on 100% random samples with replacement).

***

Indicates significance at the 1% level (different from the null hypotheses $\widehat{A}=0$ and $\widehat{D}=1$⁠).

Panel B gives estimates by segments of the high school GPA distribution, allowing for dynamic effects (model specifications as in Table 4, Columns (2)–(5)). The shift for Stockholm is positive and statistically significant for all subsamples and the shift parameter increases with the worker’s rank in the school grade distribution. The estimated shift is 2.8% in the first decile and 7.1% in the top decile.

The dispersion of worker fixed effects is greater among workers in Stockholm for all examined segments of the high school GPA distribution, indicating that unobserved abilities are more dispersed in Stockholm. The largest dilation coefficients are found for samples with school grades above the median. The fixed effects distribution for Stockholm is amplified by a factor of 1.43 for workers in the top decile as compared with 1.12 for workers in the first decile of the school grade distribution. Figure 2 shows the estimated fixed effects distributions for the subsamples in panel B.

Figure 2.

Comparison of worker fixed effects distributions across high school GPA percentiles, Stockholm versus rest of country.

Notes: Formal tests of shift and dilation are reported in Table 6.

Panels C and D in Table 6 present estimates by university quality rank and by parents’ level of education. The shift estimates indicate larger positive shifts for Stockholm among workers who have graduated from universities of higher rank and among workers who have parents with a high education level. Again, the dilation parameters indicate greater dispersion of worker fixed effects for Stockholm.

In sum, we find significant positive sorting on unobserved productive traits into the largest and most dense labour market in Sweden. Spatial sorting on unobserved ability is also evident after adjusting for city-specific work experience, suggesting that workers who are inherently more productive choose to locate in bigger cities. This result corroborates the findings for college-educated workers in Carlsen et al. (2016). We contribute by showing that, within a group of highly skilled workers, the magnitude of sorting on unobserved ability increases with workers’ high school grades and our two other indicators of observed ability. Not only does Stockholm seem to attract university-educated workers at the upper part of the observed ability distribution, but, within this group, there is also positive sorting on unobserved productive traits into the Stockholm labour market.

8. Summary and discussion

This study has estimated static and dynamic agglomeration effects on earnings among Swedish university graduates, using detailed population-wide longitudinal register data, including indicators of individual ability such as school grades, parental background and university quality. We estimate the static UWP of employment in a particular location; the dynamic effects of working in large labour markets; the variation of these dynamic effects by observed ability of workers; and the portability of the UWP. We further analyse how systematic spatial sorting on observed and unobserved ability affects earnings. Our indicators of individual ability seem to carry valuable information for analysing the static and dynamic agglomeration effects, as well as spatial sorting by ability.

The value of accumulated big city work experience is increasing with observed worker ability. Evaluated at the sample mean for employment experience (8.8 years), the estimated earnings difference between the largest local labour market Stockholm and cities below the top seven is 21.3% for workers in the top decile of the ability distribution (consisting of a static premium of 2.2% and a dynamic premium of 19.1%). For workers in the bottom decile of the ability distribution, the combined static and dynamic premium in Stockholm is 10.7%.

Consistent with the hypothesis of positive learning and human capital accumulation effects of working in large and dense labour markets, our estimates suggest that the dynamic premium of working in Stockholm is highly portable. The premium of work experience accumulated in Stockholm is not lost when moving to smaller cities.

We find clear evidence of systematic positive sorting of workers into Stockholm on observed indicators of ability as well as on unobserved productive traits. Sorting on unobserved ability also is evident after adjusting for big city work experience. This form of self-selectivity is driven by graduates in the upper part of the observed ability distribution.

Throughout the article, we have kept returning to the special position of Stockholm, by far the largest local labour market in Sweden. Stockholm is a major driver of the estimated overall log wage–log density relationship. Learning effects from work experience in Stockholm generate an economically significant dynamic earnings premium that increases with observed ability. Stockholm also stands out in terms of positive sorting of workers on observed ability as well as on unobserved productive traits. Similarly to the other Nordic countries, the urban system in Sweden is characterised by a large capital region (with roughly a quarter of the country’s total population) but few other large and densely populated metropolitan areas. One avenue in future empirical work could be to further analyse the extent to which cities at the very top of the urban hierarchy drive observed static and dynamic agglomeration effects in countries with different urban structures.

Supplementary material

Supplementary data for this paper are available at Journal of Economic Geography online.

Footnotes

1

Glaeser and Maré (2001) find a positive wage growth effect over time for rural-to-urban area migrants in the USA. However, their results are not based on city-specific work experience but instead on migrants observed at different times before and after a move to a metropolitan area.

2

Glaeser and Maré (2001) and Andersson et al. (2014) also find that workers who move away from metropolitan regions do not experience wage declines. However, neither of the studies explicitly analyses how accumulated city-specific work experience is affected when leaving a metropolitan area.

3

In 2010, about 20% of the working-age population (20–64 years) in Sweden had university education for 3 years or longer as the highest level of education. The flow of university graduates during the period 2001–2010 that is included in the data correspond to about 23% of the stock of graduates in 2010. We focus on individuals that are 22–33 years of age in the year of graduation because for this age group we have information on GPA from compulsory school and high school.

4

The cohort graduating in 2001 is followed annually during 2002–2010, the 2002 cohort is followed during 2003–2011, and so forth until the 2010 cohort, which is followed during 2011–2019.

5

Strenze (2007) reviews and analyses previous research on intelligence, academic achievement and parental background as predictors of socioeconomic outcomes. Intelligence is found to be a powerful predictor but not overwhelmingly better than school grades or parents’ socioeconomic status. Intelligence is shown to correlate with school grades, but noncognitive skills may also contribute to variance in school grades (e.g., Spinath et al. 2006; Roth et al. 2015). Graetz et al. (2020) find that compulsory school and high school grades, as well as parental education, are strong predictors of performance on the Swedish scholastic aptitude test.

6

Earnings are expressed in 2019 prices using the national CPI as deflator.

7

When comparing estimates of the returns to education based on different data sets, Antelius and Björklund (2000) show that using a restriction of SEK 100,000 (about SEK 140,000 in 2015 prices) of annual earnings (available in register data) gives estimates that are close to those obtained using hourly earnings (available in survey data).

8

For 93% of the employed population, the residence and the workplace are located in the same TWA.

9

Instead of including the log population density variable directly into Equation (1), Combes et al. (2008) and De la Roca and Puga (2017) use a two-stage estimation procedure. Since they find that the single-step and two-step approach give qualitatively similar results, we stick with the single-step specification.

10

For simplicity, we interpret the estimates as approximate percentage premiums.

11

By movers, we refer to workers taking a job at a workplace located in a different travel-to-work area. In the 9-year post-graduation time window during which we follow the workers, our sample of 99,326 workers make a total of 22,014 moves between the 69 travel-to-work areas.

12

When using the same type of single-step estimation as we use, De la Roca and Puga (2017) find an elasticity of 1.6%.

13

Wheeler (2001) reports an elasticity of wage with respect to population size of about 2.7% for all workers. The urban wage premium increases monotonically with worker education; for workers at the top end of the educational distribution (16+ years of schooling), the elasticity of wage with regard to population size is about 4.0%. Rosenthal and Strange (2008) find an elasticity of wage with respect to population size of about 5.2% for college-educated workers and 4.7% for workers without a college degree. Bacolod et al. (2009) report that the elasticity of wage with respect to population size is about 7.0% for college-educated workers and 3.6% for workers without a high school degree. The papers in question are based on data for the USA. Since they use methods other than fixed effects to handle potential bias due to unobserved worker heterogeneity, it is difficult to directly compare the results.

14

Our sample of 99,326 workers make a total of 17,766 moves between the different city types in the 9-year post-graduation time window during which we follow them. The number of moves to/from each city type reveal that the migration flows are fairly balanced: Stockholm (5,642/5,161), Göteborg/Malmö (4,953/4,911), large regional centres (2,461/2,667), and smaller cities (4,710/5,027).

15

That agglomeration effects are not linear across the urban scale is also supported by using a log wage–log density specification including cities at different levels of the urban hierarchy. If we repeat the fixed effect specification of Column (6) in Table 2 but exclude Stockholm from the sample, the estimated elasticity of wage with respect to city density drops from 2.2% to 1.0%. The estimated elasticity remains at 1.0% if Göteborg and Malmö (second and third largest cities) are also excluded (results reported in Table A7 in  Appendix A). This indicates that the overall elasticity of wage with respect to city density is driven by Stockholm to a large extent.

16

The methodology also allows for truncation, but since we find no significant truncation when comparing the two distributions, we restrict the analysis to the shift and dilation parameters.

Acknowledgements

We would like to thank editor Frédéric Robert-Nicoud and the anonymous referees for their valuable comments and suggestions. We also would like to thank participants at the labour economics seminar at the Department of Economics, Umeå University, for helpful comments. The usual disclaimer applies.

Funding

This work was supported by the Swedish Research Council (Grant no. 2015-01706).

Conflict of interest statement

The authors have no conflicts of interest to report.

Appendix A

Sample restrictions

The initial data include approximately 1.7 million worker–year observations. About 10% of the observations are excluded due to missing information on grades from compulsory school or high school and another 5% are dropped due to missing information on other covariates. This reduces the data to approximately 1.4 million worker–year observations. We exclude job spells as self-employed and job spells workers spend in the public sector. These restrictions reduce the data to approximately 680,000 worker–year observations. Finally, we drop observations when annual earnings are below SEK 140,000. The final data include 99,326 workers and 634,572 yearly observations.

Table A1

Variable definitions

Variable	Definition
Earnings	Annual gross labour earnings (in logs). Expressed in 2019 prices using the national CPI as deflator
Experience	The number of years the individual has been registered as employed (after graduation)
Gender	Dummy coded as 1 if female
Married/cohabiting	Dummy coded as 1 if married or cohabiting
Children	Dummy coded as 1 if having children under 18 years of age
Country of birth	Dummy coded as 1 if born in Sweden
Pre-university work experience	Age at university enrolment minus 18
Compulsory school GPA	Cohort specific percentile rank of the GPA from compulsory school
High school GPA	Cohort specific percentile rank of the GPA from high school
Field of education in high school	Dummies for high school programme (11 different fields)
Parents’ country of birth	Dummy coded as 1 if both parents are born outside of Sweden
Parents’ level of educationa	Dummies for having parents with long university education (3 years or more) (one of the parents, both parents)
Parents homeownersa	Dummies for homeownership (single-family home, tenant-owned apartment)
Parents’ earningsa	Sum of parents’ annual gross labour earnings (in 2019 prices)
Years of university education	Dummies for length of university education (4 years, 5 years or more)
Field of university education	Dummies for field of university education (International Standard Classification of Education (ISCED 1997), two-digit level)
University quality	Dummies for five quintiles of university quality, proxied by enrolment selectivity at the degree-awarding university. The enrolment selectivity of each university is measured in terms of the average high school GPA among all graduates from at least 3 years of university education during the period 2001–2010
Sector	Dummies for establishment sector (Statistical classification of economic activities (NACE Rev. 1.1), two-digit level)
Occupation	Dummies for occupation (International Standard Classification of Occupations (ISCO-88), three-digit level)
Multinational firm	Dummy coded as 1 if working at a multinational firm
Establishment size	Size of the establishment in terms of the number of employees (in logs)

^a

Measured when the individual is 17 years of age.

Table A2

Characteristics of cities in the Swedish urban hierarchy

City category	Number of cities in category	Populationa (in 1000s)	Share of high-skilled workersa	Industrial Diversitya	Workplace Diversitya	Types of jobsa
Stockholm (1st)	1	2633	0.33	743	27	427
Göteborg/Malmö (2nd–3rd)	2	1228	0.28	698	20	419
Large regional centres (4th–7th)	4	258	0.23	498	15	374
Smaller cities (8th–69th)	62	60	0.17	226	15	221

Notes: Based on data for 2015. Highly skilled workers refers to workers with long university education (3 years or more). Industrial diversity is measured as the number of industries at the five-digit level (NACE Rev. 2) with at least one highly skilled worker. Workplace diversity is measured as the number of workplaces with at least one highly skilled worker per 1000 residents. Types of jobs are measured as the number of occupations at the four-digit level (ISCO-88) with at least one highly skilled worker.

^a

Average across the TWA: s in the respective region type.

Table A3

Estimation of static city density earnings premium including different sectors of the economy

	(1)	(2)
Dependent variable	Log earnings	Log earnings
Included sectors	Private sector	All sectors
Log population density	0.0217***	0.0155***
	(0.0013)	(0.0007)
Experience	0.0914***	0.0762***
	(0.0035)	(0.0020)
Experience2	−0.0022***	−0.0012***
	(0.0001)	(0.0000)
Year fixed effects	Yes	Yes
Graduate cohort fixed effects	–	–
Demographic controls	Yes	Yes
Grades, parental and college controls	–	–
Job controls	Yes	Yes
Worker fixed effects	Yes	Yes
Observations	634,572	1,439,295
Workers	99,326	191,400
R2	0.26	0.26

Notes: Specifications as in Column (6) in Table 2. The reported R² values are within workers. Robust standard errors (clustered by workers) are given in parentheses.

***

Indicates significance at the 1% level.

Table A4

Estimation of static city density earnings premium using different earnings restrictions

	(1)	(2)	(3)	(4)
Dependent variable	Log earnings	Log earnings	Log earnings	Log earnings
Earnings restriction (in SEK 1,000)	>0	>100	>140	>180
Log population density	0.0165***	0.0211***	0.0217***	0.0228***
	(0.0023)	(0.0015)	(0.0013)	(0.0012)
Experience	0.0926***	0.0987***	0.0914***	0.0837***
	(0.0060)	(0.0037)	(0.0035)	(0.0033)
Experience2	−0.0004***	−0.0019***	−0.0022***	−0.0024***
	(0.0001)	(0.0001)	(0.0001)	(0.0001)
Year fixed effects	Yes	Yes	Yes	Yes
Graduate cohort fixed effects	–	–	–	–
Demographic controls	Yes	Yes	Yes	Yes
Grades, parental and college controls	–	–	–	–
Job controls	Yes	Yes	Yes	Yes
Worker fixed effects	Yes	Yes	Yes	Yes
Observations	679,461	651,991	634,572	614,383
Workers	101,874	100,366	99,326	98,057
R2	0.13	0.23	0.26	0.30

Notes: Specifications as in Column (6) in Table 2. The reported R² values are within workers. Robust standard errors (clustered by workers) are given in parentheses.

***

Indicates significance at the 1% level.

Table A5

Estimation of static city density earnings premium for men and women using different earnings restrictions

Dependent variable	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	Log earnings	Log earnings	Log earnings	Log earnings	Log earnings	Log earnings	Log earnings	Log earnings
Gender/earnings restriction (in SEK 1000)	Men >0	>100	>140	>180	Women >0	>100	>140	>180
Log population density	0.0257***	0.0248***	0.0245***	0.0252***	0.0037	0.0143***	0.0159***	0.0174***
	(0.0021)	(0.0018)	(0.0016)	(0.0015)	(0.0044)	(0.0025)	(0.0021)	(0.0019)
Experience	0.1230***	0.1124***	0.0990***	0.0824***	0.0470***	0.0716***	0.0713***	0.0733***
	(0.0070)	(0.0055)	(0.0052)	(0.0049)	(0.0091)	(0.0050)	(0.0046)	(0.0043)
Experience2	−0.0035***	−0.0033***	−0.0031***	−0.0029***	0.0020***	−0.0009***	−0.0015***	−0.0019***
	(0.0001)	(0.0001)	(0.0001)	(0.0001)	(0.0002)	(0.0001)	(0.0001)	(0.0001)
Year fixed effects	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Graduate cohort fixed effects	–	–	–	–	–	–	–	–
Demographic controls	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Grades, parental and college controls	–	–	–	–	–	–	–	–
Job controls	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Worker fixed effects	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Observations	358,016	355,743	352,940	348,594	321,445	296,248	281,632	265,789
Workers	49,518	49,346	49,136	48,884	52,356	51,020	50,190	49,173
R2	0.25	0.30	0.32	0.35	0.18	0.26	0.28	0.30

Notes: Specifications as in Column (6) in Table 2. The reported R² values are within workers. Robust standard errors (clustered by workers) are given in parentheses.

***

Indicates significance at the 1% level.

Table A6

Estimation of static earnings premium by detailed city classification

Dependent variable	Log earnings
Stockholm	0.0487***
(1st)	(0.0040)
Göteborg	0.0141***
(2nd)	(0.0043)
Malmö	0.0145***
(3rd)	(0.0047)
Large regional centres	0.0107**
(4th–7th)	(0.0043)
Small regional centres	−0.0011
(8th–22nd)	(0.0037)
Experience	0.0914***
	(0.0035)
Experience2	−0.0022***
	(0.0001)
Year fixed effects	Yes
Graduate cohort fixed effects	–
Demographic controls	Yes
Grades, parental and college controls	–
Job controls	Yes
Worker fixed effects	Yes
Observations	634,572
Workers	99,326
R2	0.26

Notes: See notes to Table 2 for variable definitions. All specifications include a constant term. The reported R² value is within workers. Robust standard errors (clustered by workers) are given in parentheses. *** and ** indicate significance at the 1% and 5% level, respectively.

Table A7

Estimation of static city density earnings premium based on different set of cities

	(1)	(2)	(3)
Dependent variable	Log earnings	Log earnings	Log earnings
Included cities	All cities	Stockholm excluded	Stockholm, Göteborg and Malmö excluded
Log population density	0.0217***	0.0097***	0.0100***
	(0.0013)	(0.0019)	(0.0035)
Experience	0.0914***	0.0792***	0.1021***
	(0.0035)	(0.0046)	(0.0072)
Experience2	−0.0022***	−0.0017***	−0.0015***
	(0.0001)	(0.0001)	(0.0001)
Year fixed effects	Yes	Yes	Yes
Graduate cohort fixed effects	–	–	–
Demographic controls	Yes	Yes	Yes
Grades, parental and college controls	–	–	–
Job controls	Yes	Yes	Yes
Worker fixed effects	Yes	Yes	Yes
Observations	634,572	364,586	184,270
Workers	99,326	62,693	35,551
R2	0.26	0.26	0.26

Notes: See notes to Table 2 for variable definitions. All specifications include a constant term. The reported R² values are within workers. Robust standard errors (clustered by workers) are given in parentheses.

***

Indicate significance at the 1% level.