Steven Poelhekke
email: steven.poelhekke@dnb.nl

Anindya Banerjee

Giancarlo Corsetti

Harry Garretsen

Matthias Hertweck

Marko Köthenbürger

John Lewis

Rick Van Der Ploeg

William Strange

Human Capital and Employment Growth in German Metropolitan Areas: New Evidence

Keywords: J24 -Human Capital|Skills|Occupational Choice|Labor Productivity < J2 -Time Allocation, Work Behavior human capital, skills, city employment growth, Germany, GMM estimation human capital, skills, city employment growth, Germany, GMM estimation JEL Classification: J2, O4, R1

German metropolitan areas with highly skilled workers became increasingly skilled between 1975 and 2003, creating faster urban employment growth in both the former East and West. However, using metropolitan areas instead of administrative regions and correcting important biases, we show that the effect of the share of college graduates on growth is at least a third smaller and closer to 0.5% employment growth for a 10% increase in human capital. Moreover, we find positive effects of high school graduates with vocational training, especially if the concentration of technical professionals is high. City success may thus depend on attracting the 'right' combination of skills.

German metropolitan areas with more highly skilled workers became increasingly skilled between 1975 and 2003 as shown in Figure 1. Cities that were very skilled in 1975 (such as Munich) have seen the share of skilled workers increase much more than initially less skilled cities (such as Bremen). This diverging pattern and the estimated effect on city employment growth are both remarkably similar to well known findings for US metropolitan areas (see for example [START_REF] Berry | The Divergence of Human Capital Levels Across Cities[END_REF] and confirms the robustness of the effect of skills on growth in cities. 1 This is good news for Germany's skilled cities but bad news for lagging brownfield cities with fewer skilled workers, such as can be found in the industrial Ruhr area or former East Germany. The size of the skill-growth effect for US metropolitan areas is found to be about 0.8% for every 10% increase in the share of college educated workers [START_REF] Shapiro | Smart Cities: Quality of Life, Productivity, and the Growth Effects of Human Capital[END_REF] and [START_REF] Südekum | Human Capital Externalities and Growth of High-and Low-Skiled Jobs[END_REF][START_REF] Südekum | Human Capital Externalities and Growth of High-and Low-Skilled Jobs[END_REF] finds a similar magnitude for West German counties. 2 If this effect is indeed this large then city mayors should make an effort to attract more skilled workers to boost slow employment growth in some German cities. However, this is subject to several considerations. Is the effect really this large? Does it also hold for metropolitan areas, or only at the county level? Are college graduates the only key to local productivity growth or could cities also improve productivity growth by attracting workers with vocational training, or even only university graduates? These are relevant questions for cities seeking to boost local economic growth. This paper argues that the magnitude of the effect of skills on city growth has been measured with upward bias in the existing literature, because common estimators cannot properly control for the initial employment-size effect when fixed and suggestions, and Matthias Türck, Marc Schramm, John O'Loughlin, Nils Drews and especially Rupert Kawka from the BBR for making their data available to me. The views expressed are those of the author and do not necessarily reflect official positions of De Nederlandsche Bank. effects such as city characteristics correlate with both growth and initial size. We aim to improve these estimates by using recently developed GMM-IV techniques.

These reveal that the effect is at least 30% smaller and that the attenuation of the effect is robust across two separate data sets (see section 4 for details). The source of this bias under severe persistence of the lagged dependent variable is rarely addressed in the context of skills and metropolitan growth. 3 Nickell (1981) proved that regressions in which time-invariant unobserved characteristics affect both growth and initial levels (i.e. initial employment size) lead to a downward bias in the within-estimate of the initial employment size coefficient, and an upward bias in the OLS estimate. The true value should lie in between. Failing to correct for this endogeneity bias places too much weight on the initial size effect and therefore also affects the estimation of other controls, such as human capital. These fixed effects include deeper determinants of human capital concentrations, such as as the presence of historical colleges and compulsory schooling laws as used by [START_REF] Moretti | Workers' Education, Spillovers, and Productivity: Evidence from Plant-Level Production Functions[END_REF] and [START_REF] Shapiro | Smart Cities: Quality of Life, Productivity, and the Growth Effects of Human Capital[END_REF], underscoring the importance of controlling for fixed effects. This paper builds on the previous authors' established work that identifies causality running from human capital to growth and aims to improve estimation by focusing on a neglected separate source of endogeneity. The second contribution is to use an aggregation of counties to improve the geographical definition of cities. German local growth estimates have so far relied on counties (NUTS III level) or other administrative regions which makes direct comparison with US metropolitan areas difficult and may cause measurement error.

Urban growth models typically assume that each city is an 'island' that freely trades with other cities. It is important to have a good definition of what a city is and it should preferably encompass a labor region in which people live and work and the definition should be unrelated to political motives. We will therefore use a definition very similar to US metropolitan areas (an aggregation of counties based on commuting flows) as a unit of observation. The city of Munich for example becomes a metropolitan labor region of 12 counties. Many people commute into the main city which is a county on its own but measures only 20km (12mi) across. Similarly, the cities of Cologne and Bonn really form only one agglomeration because many people commute between the two.

Thirdly, we argue that the share of college graduates is not necessarily the best proxy for local productivity, although it is typically used as such. Other skilled workers such as those with vocational training also contribute significantly to agglomerations' employment growth. 4 Bacolod, Blum and Strange (2009ab) find evidence that cognitive skills rather than motor skills are productivity enhancing in cities, something which many workers with vocational training may also possess in a significant amount. It is therefore not a foregone conclusion that the share of college graduates is the best indication of local productivity. This is also important from a policy perspective. Many cities focus on how to attract as many college graduates as possible although a different mix of skills could also be a successful strategy.

Apart from asking how much human capital is good for growth we want to ask the additional question of which combination of skills is beneficial. For instance, a fast growing city will unlikely depend only on lawyers, doctors, and professors, nor will it benefit most from only mechanics and construction workers. Bacolod, Blum and Strange (2009b) find evidence for a higher variance of worker skills in larger cities, which suggest skill complementarities. If cognitive and manual skills are complements to productivity growth, then a certain combination of skills may well lead to faster growth. We find evidence of positive interaction between workers with vocational training and graduates from technical colleges. The productivity enhancing effect of non-technical college graduates is increasing over time, but their presence was of lesser influence to the productivity effect of workers with vocational skills. Fourthly, our data allows us to explore considerable differences that exist between metropolitan areas in the former East and in West Germany. We show that the evolution of the concentration of skilled workers between East and West Germany has been very different, which may explain why East Germany has not been able to catch up with West Germany. This has not been addressed before since empirical studies on the growth of German cities have replied on data on West German cities (i.e. [START_REF] Blien | Local Employment Growth in West Germany: A Dynamic Panel Approach[END_REF] and [START_REF] Südekum | Human Capital Externalities and Growth of High-and Low-Skilled Jobs[END_REF]). However, we find that the skill effects on growth are stable across the two regions. This suggest on the one hand that other causes are at the root of divergence between the two regions, but also that skilled West German cities who have become increasingly skilled will continue to outpace East German cities who have not increased the concentration of human capital by as much.

The rest of the paper is organized as follows. Section two develops an illustrative model. Section three discusses the econometric challenges and solutions after which section four describes the data. Section five presents results on the size of the skill-growth connection and section six expands the college graduate productivity measure to include other skills and interactions. Section seven compares West to East Germany. Section eight concludes. This section briefly outlines how human capital may affect employment growth to motivate the empirical specification. We consider a standard setting similar to [START_REF] Glaeser | Growth in Cities[END_REF] and [START_REF] Simon | Human Capital and Metropolitan Employment Growth[END_REF] in which each metropolitan area i is a separate small open economy. Each i produces one good (which is freely traded nationally under perfect competition). The good is produced using labor L it , and technology A it at time t, using a production function A it (L it ) 1-α , where 0 < α < 1. Firms sell the good for a numéraire price of 1. Following [START_REF] Glaeser | Growth in Cities[END_REF] we abstract from capital or land input because we cannot measure different types of technological process with our data. Firms maximize profits taking technology, prices, and wages w it as given. The wage rate (nominal and real) will thus equal the marginal product of labor:

w it = (1 -α)A it (L it ) -α , (1)
which expressed in terms of growth rates becomes:

ln w it w i,t-1 = ln A it A i,t-1 + α ln L it L i,t-1 . (2)
As in [START_REF] Combes | The dynamics of local employ-23 Page 27 of 43[END_REF] we assume that labor is imperfectly mobile such that labor growth reacts to wage growth with a strictly positive supply elasticity σ:

ln L i,t L i,t-1 = σ ln w it w i,t-1 . (3)
Perfect labor mobility would require wage growth to be a constant across cities, while completely immobile labor would disconnect productivity from employment growth and lead to wage growth instead. 5 We could expand this framework to include quality of life as in [START_REF] Shapiro | Smart Cities: Quality of Life, Productivity, and the Growth Effects of Human Capital[END_REF] and [START_REF] Glaeser | Economic growth in a cross-section of cities[END_REF]. However, we do not observe quality of life and assume implicitly that most of it is captured by the

ln A it A i,t-1 = β 1 H i,t-1 + β 2 X i,t-1 + η i + δ t + v i,t (4)
where unobserved shocks are given by v it . Combining equations 2, 3 and 4 leads to the main relationship of interest:

ln L it L i,t-1 = σ 1 + ασ (β 1 H i,t-1 + β 2 X i,t-1 + η i + δ t + v i,t ) , (5)
where σ/(1 + ασ) is a positive parameter. The functional form of human capital H it is commonly a single variable such as the average or median schooling or the share of workers with a college degree or higher. The common specification for estimating the skill-growth relation is given as follows (reformulating eq. 5):

∆l i,t = λl i,t-1 + βH i,t-1 + η i + δ t + v i,t i = 1, ..., N ; t = 1, ..., T (6)
where lower case l i,t = ln L i,t , the natural logarithm of total employment in city i and year t. [START_REF] Moretti | Workers' Education, Spillovers, and Productivity: Evidence from Plant-Level Production Functions[END_REF][START_REF] Shapiro | Smart Cities: Quality of Life, Productivity, and the Growth Effects of Human Capital[END_REF]. v i,t is an error term which captures i.i.d. shocks to employment growth.

There are three problems in estimating (6). Most importantly, (unobserved) fixed effects such as whether or not a city has a port or whether it used to be a mining town have an effect on employment each year during the sample period. These effects can also include institutions, culture and climate. They mean that employment is not strictly exogenous: E[l i,t-1 , η i ] > 0, and for the same reason:

E[l i,t-1 , v i,t-1 ] > 0.
Even if current shocks are not correlated with previous period employment size we will still estimate a positively biased (OLS) coefficient λ because of the positive correlation between the fixed effects and initial employment. Moreover, this bias does not vanish if the sample size increases in the time dimension, nor if the within transformation is applied to purge the fixed effects.

This problem has not been addressed in earlier papers by [START_REF] Shapiro | Smart Cities: Quality of Life, Productivity, and the Growth Effects of Human Capital[END_REF] and [START_REF] Simon | Human Capital and the Rise of American Cities, 1900-1990[END_REF], nor by [START_REF] Berry | The Divergence of Human Capital Levels Across Cities[END_REF] in the context of urban employment growth and highly skilled labor. A commonly used solution is to use first-differences of the system of equations to remove the η i and use lagged equations as instruments as in [START_REF] Arellano | Some specification tests for panel data: Monte Carlo evidence and an application to employment equations[END_REF]. 7

However, the second problem is that the errors may be serially correlated.

In that case E[v is v it ] = 0 for s = t, but to be able to use lagged equations as instruments we need predetermined initial conditions:

E[l i1 v it ] = 0 for t = 2, ..., T and E[η i ] = E[v it ] = E[η i v it ] = 0. 8
Effectively, the instrumentation strategy uses lags 2 and more of the right-hand-side variables to instrument the current first difference of each variable. In case second order serial correlation is present in the data we use lags 3 and more. Only for time dummies and an East Germany dummy can we safely assume that they are strictly exogenous and for other right-hand-side variables we will make the relatively weak assumption that they are predetermined, such that they can be instrumented by using lags of the predetermined variables as instruments. This method has been used by [START_REF] Blien | Local Employment Growth in West Germany: A Dynamic Panel Approach[END_REF] and [START_REF] Südekum | Convergence of the skill composition across German regions[END_REF] for sector employment growth at the county level and [START_REF] Combes | The dynamics of local employ-23 Page 27 of 43[END_REF] for France.

The third problem is that yearly employment data, such as used in the latter three papers, is very persistent. This creates a serious problem for estimation with this method because λ might be close to zero. A region's employment size does not change much from year to year and is thus very persistent. 9 λ then contains little predictive information about next year's employment size and is too weak as an instruments for employment growth, even if it is exogenous. In finite samples this problem is even more severe and may bias the estimate of the lagged dependent variable's coefficient downward and even below the within estimate (as we will later demonstrate empirically), exacerbating the bias it aims to correct. [START_REF] Blundell | Initial Conditions and Moment Restrictions in Dynamic Panel Data Models[END_REF] proposed to expand the instrument set by including additional moment conditions by using lagged first-differenced equations, allowing consistent and efficient estimation of (5) while dealing with all three challenges. 10 With time dummies this additionally assumes that mean employment evolves in a common way over time for all cities in the sample.

E[∆l i,t-1 , (η i + v it )] = 0 for t = 3, ..., T (7)
All these assumptions can be tested with common Sargan over-identification tests.

A further improvement can be made by applying [START_REF] Windmeijer | A finite sample correction for the variance of linear efficient two-step GMM estimators[END_REF] correction for finite sample bias in the two-step version of System-GMM, which otherwise reports standard errors which are too small. 11

An attractive feature is that many instruments can be used. Strong and valid instruments are rare which makes solving the endogeneity issue difficult in general.

The dynamic panel approach is to assume that lagged levels and lagged first differenced equations are not correlated with the current period disturbances. This means that the past concentration of skilled workers has no influence on the current shock to employment growth after controlling for fixed effects and other controls including the current concentration of skills. Since the time length of our sample is long enough (> 3 periods) we have many instruments and the system is over-identified.

A common Sargan or Hansen test can tell us if the assumption of predetermined initial conditions is valid, where the latter is robust to heteroskedasticity. There is one pitfall with having many instruments. If the set of instruments is much larger than the number of cities (the N dimension) there is a risk of 'over-fitting' the data which decreases the power of the Hansen tests [START_REF] Bowsher | On testing overidentifying restrictions in dynamic panel data models[END_REF]. On the other hand, using more instruments makes more efficient use of the available data. In general, if increasing the number of instruments does not move the lagged dependent's estimated coefficient towards the within-estimate, then over-fitting should not be a problem. Since we want to measure urban human capital and estimate its effect on urban employment growth we need to group the counties into labor regions or agglomerations, because any city may encompass several counties or other administrative regions. 13

By doing so we stay close to the commonly used US statistical metropolitan area definition 14 and circumvent bias from possible spatial dependence. To prevent this bias, the regions capture agglomerations in which people both live and work.

One notable exception in the literature on German regions is [START_REF] Südekum | Human Capital Externalities and Growth of High-and Low-Skilled Jobs[END_REF] who finds that the positive effect of skills on growth at the county level is robust to allowing the employment growth of each county's immediate neighbour to affect local growth. 15 Moreover, [START_REF] Südekum | Human Capital Externalities and Growth of High-and Low-Skilled Jobs[END_REF] finds that the effect of human capital on growth is also positive when the labor market region definition ('Arbeitsmarktregionen') from the 'Institut für Arbeitsmarkt-und Berufsforschung' (IAB) is used. However, according to Eckey et al. (2007) these regions are created on the basis of political motives for the distribution of regional (including EU) subsidies leading them to conclude that they are not suitable for empirical analysis. The IAB uses a shorter inhabitants. This leads to 150 regions consisting of one or more counties that capture the area where people both work and live.

The mean and standard deviation of the ratio of employed workers counted at place of work over place of residence is 0.98 and 0.34 for the German counties, while only 0.96 and 0.07 for the German metropolitan areas, which is clearly an improvement in precision if we rely on employed workers to measure a city's human capital. 16 Single county labor regions are mostly low density rural areas. The labor regions are smaller than the NUTS II ('Bezirke') and NUTS I ('Länder': states) regions: these areas are also administrative rather than economic in nature.

Employment data (see the data appendix for more detail) on the very disaggregated level of counties is provided by two sources. The first is from the German Statistical Agency (DESTATIS), which publishes a 'Statistik Regional' (SR) database ( 2005) providing consistent data on all 439 (East and West) German counties from 1995 to 2003. These include all employed workers, excluding civil servants and the self-employed, subject to social security payments. This data set is supplemented with educational attainment data of workers counted at place of work from the Federal Office for Building and Regional Planning ('Bundesamtes für Bauwesen und Raumordnung', BBR). 17 It distinguishes three levels of human capital where employment of 'highly skilled' labor is defined as those with a degree of a specialized upper secondary school, specialized college of higher education, or institution of higher education. 'medium skilled' workers are those with apprenticeship or training on the job, qualification at a full-time vocational school or at a trade or technical school. 'low skilled' workers are those without occupational qualification. The highly skilled resemble the widely used measure of those with a bachelor degree or higher for US studies, but are likely slightly higher educated than the US highly skilled and form a smaller share of employment.

The second source is the IAB Regional Employment Sample (IABS-R01) of all employees subject to social security payments. OLS estimates λ to be close to zero which means that employment is very persistent, although the within transformation which accounts for city fixed effects finds a rate of convergence of 8.2% per year. The latter is biased downward and seems implausibly large in magnitude. We confirm that a 10% increase in the share of skilled labor leads to 0.8% more employment growth, consistent with [START_REF] Shapiro | Smart Cities: Quality of Life, Productivity, and the Growth Effects of Human Capital[END_REF], while keeping in mind that initial employment size is endogenous. The third column uses lagged level equations as instruments and assumes homoskedastic errors (Difference-GMM, one-step). Also allowing for heteroskedastic errors (two-step, column 4) does not perform well as λ is estimated to be even smaller, while the true value should lie in between the OLS and Within estimate. This is a sign of underidentification and we have to deal with a weak instrument problem. The fifth (one-step) and sixth (two-step) columns therefore employ also lagged differenced equations. These yield a more plausible estimate of λ. The errors in column 6 may suffer from finite sample bias making them too small, but correcting for finite sample bias in column 7 still

L ist L it 2 (8)
where S = 1, ..., 16 is our set of 16 industries in city i at time t. This Herfindahltype index is very similar to the diversity indices used in [START_REF] Glaeser | Growth in Cities[END_REF] and [START_REF] Combes | The dynamics of local employ-23 Page 27 of 43[END_REF], except that we focus on city employment growth rather than industry employment growth. The diversity index reaches its minimum at 0 and its maximum at 2.77 (= -ln(1/16). Unfortunately, the IAB sample does not contain representative information at the county level on the number of firms. We include the average age of employees within a city to account for a possibly negative age effect.

The same basic patterns holds. After correcting for endogeneity of initial employment in columns 3 and 6 (with more controls) we conclude that the effect of highly skilled labor on employment growth is smaller than previously reported. A 10% higher share of skilled labor leads to 0.43% more employment growth. The initial employment size variable now lies between the OLS and Within estimates and the Hansen tests are passed meaning that the GMM estimator is well specified. In particular, we find that for West Germany's increase in the average concentration of human capital, i.e. from 2.4% to 7.7% between 1975 and 2001, the effect on em- Diversity enters with a negative sign, which means that less diverse cities tend to grow faster in Germany, as do cities with an increasing share of manufacturing. 22

As in the SR sample we find that an older work force tends to lead to less employment growth. Recently acquired degrees seem to be more important than experience. We also find evidence that middle skilled workers affect employment growth positively and strongly. However, the data reveals that the average yearly percentage change in each variable is close to 1.0% for medium skilled workers with a standard deviation of 1.5%, while over 4.3% for highly skilled workers with a standard deviation of 9.4%.

This implies that the actual effect of highly skilled workers is still economically most important and critical for city growth. Lastly, we include column 7 where we appeal to the efficiency argument and use all the information available. We include all lags of the variables in the instrument set so that we have 1975 instruments for 150 agglomerations. On the downside, the Hansen test is now uninformative due to over-fitting (the lagged dependent variable's coefficient has moved in the direction of the within estimate), so we cannot test the validity of the instruments. The skill effects are still there but turn out to be slightly smaller.

Growth and skill interactions

This section explores whether or not the share of college graduates is the most appropriate skill definition to capture the effect of education on aggregate productivity. Instead of measuring human capital by the concentration of college graduates (highly skilled, s(5, 6)) and high school graduates (medium skilled, s(2, 3, 4)) we can split these two groups into several distinct levels of educational attainment. The IAB data allows a distinction between six different skill groups. In particular, highly skilled labor consists of workers with degrees from technical colleges (level five, s(5)),

which are engineering schools that also issue Master's degrees, and those with a uni-

∂∆l it ∂s(2, 4) = β 1 + β 2 s(5, 6) (9)
The standard errors follow as:

s.e. = V ar( β1 ) + s(5, 6) 2 + V ar( β2 ) + 2s(5, 6)Cov( β1 , β2 )

where we estimate ∆l it = αl i,t-1 + β 1 s(2, 4) i,t-1 + β 2 (s(5, 6) * s(2, 4)) i,t-1 + controls + η i +v it and β1 = 1.008 and β2 = .25. Using this calculation for all the sample values of s(5, 6) we find that the effect of workers with vocational training is significant across all observed values of the share of highly skilled workers, although it nears insignificance as the share of skilled workers becomes high in the sample. This means that in all cities in our sample, there is a significant positive productivity enhancing effect of highly skilled workers. Workers with vocational skills become more productive in more highly skilled cities, while workers with a high school degree do not benefit from these spillovers. A further qualification is made by columns 3 and 4 where we split highly skilled workers in two groups. They show that the positive interaction between highly skilled workers and workers with vocational training is stronger for graduates of technical colleges than for university graduates. Presumably the former two are closer in terms of knowledge which facilitates better learning and hence larger productivity effects on employment growth. These effects add a new dimension to human capital externalities in the spirit of [START_REF] Lucas | On the mechanics of economics development[END_REF]. The productivity effect of skilled workers may be best captured by a group which is more broadly defined than college graduates alone. Furthermore, skills from different levels of formal education seem to complement each other.

Columns 5 and 6 show that the effect of highly skilled labor interacts positively with a time trend, indicating that the effect of highly skilled labor is increasing over time. Moreover, the interaction between the trend and the s(5, 6) * s(2, 4) interaction term shows that the spillovers on workers with vocational training decreases over time. This is consistent with our finding that the productivity effect of these workers nears insignificance as the share of skilled workers becomes high. If the size and significance of the effects are different in the former East they should be picked up by interaction effects between an East Germany dummy and each variable. Tables A.8 and A.9 show these effects, based on the preferred specification (6) from Table A.5 and specifications (2) and ( 5) from Table A.6. The columns labeled 'East *' report the coefficients of each variable interacted with the dummy, such that the row-sum equals the net effect for East German metropolitan areas, interpreting insignificant effects as equal to zero. First of all, Table A.8 shows that the conditional effect of highly skilled workers on employment growth is not different in the East. The interaction is negative, but insignificant. At the same time we find strong evidence that an older workforce has a much more negative impact on employment growth in East German cities. In section 5 we argued that degrees acquired longer ago may be a worse match with current technology and business administration practises than more recent degrees. If that is indeed the case, and if no workers migrated from West to East, then one reason for slower growth in the East could be the differential impact of worker age in East Germany. This would imply that workers with older degrees, possibly those obtained before unification, underperform compared to recent degrees. [START_REF] Südekum | Human Capital Externalities and Growth of High-and Low-Skiled Jobs[END_REF][START_REF] Südekum | Convergence of the skill composition across German regions[END_REF] estimates a decline in the coefficient of variation of skill shares, which means that the average skill level rises faster than the standard deviation. [START_REF] Berry | The Divergence of Human Capital Levels Across Cities[END_REF] use US data and define divergence as an increase in the standard deviation, which is the typology followed in this paper.

2 Shearmur and Polese ( 2007) also find positive effects of education on local growth in Canada based on a mix of administrative urban and rural regions of various scale.

3 [START_REF] Blien | Local Employment Growth in West Germany: A Dynamic Panel Approach[END_REF], [START_REF] Südekum | Convergence of the skill composition across German regions[END_REF], and [START_REF] Combes | The dynamics of local employ-23 Page 27 of 43[END_REF] are exceptions although they do not take into account persistence of the lagged dependent variables. This leads to weak identification and may not solve the bias. We come back to this in section 3.

4 Usually the productivity effect of skilled workers is looked upon from the viewpoint of wages (see the debate on the existence of human capital externalities by [START_REF] Rauch | Productivity gains from geographic concentration of human capital: evidence from the cities[END_REF], [START_REF] Moretti | Workers' Education, Spillovers, and Productivity: Evidence from Plant-Level Production Functions[END_REF] and [START_REF] Ciccone | Identifying human capital externalities: theory with an application to US cities[END_REF]) or whether or not workers receive higher wages if they are employed in a city (i.e. [START_REF] Glaeser | Cities and Skills[END_REF]). We will focus on the aggregate city productivity effect on city employment. Employment has been persistently low compared to the labor force in Germany (high unemployment) for some time.

5 Imperfect mobility is supported by the finding that regional labor demand shocks trigger much less migration in Germany than in the US between 1960 and 1987 [START_REF] Decressin | Regional Labor Market Dynamics in Europe[END_REF]. Moreover, the gross migration rate between NUTS 2 regions has declined between 1983 and 1990, down to one percent of the population, below rates for the UK. Also, 60% of migration is between neighboring regions [START_REF] Huber | Inter-Regional Mobility in Europe: A Note on the Cross-Country Evidence[END_REF]).

6 As for example in Glaeser, Scheinkman, Shleifer (1995). 7 We refer to this method as difference-GMM (DGMM).

8 AR(1) is introduced by construction. Note also that we do not require the initial conditions to be strictly exogenous which would require E[l i1 v it ] = 0 ∀t. Strict exogeneity of all variables would result in a consistent within estimate for large N and T . 9 See for example [START_REF] Redfearn | Persistence in urban form: The long-run durability of employment centers in metropolitan areas[END_REF] who shows the degree of persistence of employment density over 20 years even within the Los Angeles Metropolitan Area. 10 We refer to this method as system-GMM (SGMM).

11 Both DGMM and SGMM have one-and two-step versions which refers to the method of estimating the weight matrix for GMM. One-step requires the assumption of homoskedastic v it disturbances, but two-step estimation tends to deflate the standard errors. We use the identity matrix as an initial guess for the covariance matrix of idiosyncratic errors as in [START_REF] Blundell | Initial Conditions and Moment Restrictions in Dynamic Panel Data Models[END_REF]. See [START_REF] Bond | Dynamic Panel Data Models: A Guide to Micro Data Methods and Practice[END_REF] for an overview. 13 The German counties ('Kreise' and 'Kreisfreiestädte' (NUTS III regions)) measure on average a quarter of the surface size of US counties.

14 These are also defined on the basis of counties. See http://www.census.gov/population/www/metroare 15 This approach assumes that neighbouring human capital does not affect local employment growth directly even though a local company can easily employ skilled workers from a neighbouring county.

16 Authors' calculation based on the IAB data set (see further down for a description of the data). 17 These data come from their DUVA database and follow the same definition as the DESTATIS data. 18 We select a cross-section of individuals at date June 30th of each year, which corresponds to the cross-section date of the SR sample, and aggregate (or average) variables within counties, which are then aggregated (or averaged if applicable, with a weight by employment size) to metropolitan areas. Other details: employment is counted as those with main employment (to prevent double counting), with regional observations and those who are not apprentices.

19 Because reporting of skill levels about their workers is done by companies themselves there are some inconsistencies in the IAB data set. We used imputation method IP3 as described in [START_REF] Fitzenberger | Imputation Rules to Improve the Education Variable in the IAB Employment Subsample[END_REF] to make sure that the highest attained degree did not decrease over time for the same worker. This affected 9% of individual cells and mostly changed missing observations into skill level 2 (see Table A.2). Method IP3 may slightly overreport the skill level but it yielded more similar skill levels compared to the SR sample for the years 1995-2001 than other imputation methods or the raw data.

20 Fixed effects regression furthermore control implicitly for density, because the initial employment size coefficient can be interpreted as the effect of a change in employment size relative to its period city average for a constant city surface area. This change is perfectly correlated to a change in density.

21 See [START_REF] Duranton | Micro-Foundations of Urban Agglomeration Economies[END_REF] for an extensive overview of this literature.

22 [START_REF] Blien | Local Employment Growth in West Germany: A Dynamic Panel Approach[END_REF] find a positive effect of diversity on industry employment, and a lagged negative effect. Our negative effect is robust to using their diversity measure (the measures correlate by 0.81; coefficient of -0.12*** in that case, available on request). It appears that employment in metropolitan areas benefits from overall specialization, even though industries may benefit from surrounding diversity on a smaller geographical scale. Since we use metropolitan areas as observations instead of counties and industries these results should be seen as complementary.

23 By the same reasoning the marginal effect of s(5, 6) will now depend on the sample values of the other skill groups and cannot be interpreted directly. to sudden unemployment of many workers. Party members also lost their job, but many of them were highly skilled. 24 The latter presumably had an easier time to find new employment (in the private sector) while medium skilled workers likely moved West or waited for new employment opportunities. If the out-migration of mainly medium skilled workers had been going on for some time prior to 1995, then that might explain the relatively high share of highly skilled workers in the East. The tables also show that manufacturing has continued to be an important employer and has even expanded as a share of employment in the former East. A competition index larger than one means that there is more competition than the national average. The diversity index reaches its minimum at 0 and its maximum at 2.77 (= -ln(1/16), 16 industry groups). Because of these differences we include an East Germany dummy in the pooled data. Furthermore, the agglomerations of Go ẗtingen, Wolfsburg, Coburg, and Hof form agglomerations with an eastern county.

To capture this we also include dummies equal to one from 1992 (the year East German data enters the sample) for each of these four regions. Employment Research (IAB) (see [START_REF] Drews | Variablen der schwach anonymisierten Version der IAB-Beschäftigtenstichprobe 1975-2001 Handbuch-Version 1[END_REF].

Fig. 1 .

 1 Fig. 1. Change in % Highly Skilled Labor (IAB Sample)

4

  German metropolitan employment dataA different source of measurement error, apart from the issues raised in the previous section, comes from the fact that several German employment studies have used NUTS level III administrative boundaries rather than economic agglomerations. 12 Statistical offices do not readily provide data on the level of agglomerations.

  commuting time cut-off yielding on average smaller labor market regions (270 in IAB case versus 150 in theEckey et al. (2007) case) and they separate cities from their district. For example, in the IAB definition the city of Berlin is an isolated region which does not allow for commuting in or out of Berlin. Because this precludes the analysis of metropolitan areas we follow the definition of[START_REF] Eckey | Abgrenzung deutscher Arbeitsmarktregionen[END_REF]. They define German labor market regions using cluster analysis on the basis of commuting data from the Ministry for Transport, Construction and Urban Planning (using a maximum commuting time of 45 to 60 minutes) and have a size of at least 50,000

  been +13.8%, instead of +25.7% (using the older estimate of 0.08).

12

  See for example Su dekum (2008) and[START_REF] Blien | Local Employment Growth in West Germany: A Dynamic Panel Approach[END_REF].

  Access to the factually anonymous IAB Employment Sample (IABS) (years 1975 -2001) was provided via a Scientific Use File supplied by the Research Data Centre (FDZ) of the German Federal Employment Agency (BA) at the Institute for

  Common shocks across cities for a given year, such as general technological progress, policy changes, EU enlargement, etc, are captured by the δ t . The η i are

	(unobserved) city characteristics that do not change over time, such as for example
	access to a river (geography) or other inputs in production which do not vary over our
	sample period, such as the existence of an airport. These may correlate strongly with
	employment growth. Moreover, they include time-invariant deeper determinants of
	human capital concentrations, such as historical colleges or different compulsory
	schooling laws

  of employees subject to social security payments. 1819 It provides a long time series from 1975 to 2001 and distinguishes between more distinct levels of human capital, as described in TableA.2. The sum of levels 5 and 6 corresponds to highly skilled workers in the SR data, while the sum of levels 2, 3 and 4 corresponds to medium skilled workers. Level 1 corresponds to low skilled workers. Appendix B provides more details and descriptive statistics for both data sets.

	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y

It comprises a 2% random sample 5 The overestimated effect of skills on metropolitan growth

We start the analysis with the Statistik Regional (SR) sample with population data on all German metropolitan areas from 1995 to 2003. Table

A

.3 estimates the effect of the concentration of highly skilled labor on total employment growth with controls for initial employment (the lagged dependent variable with coefficient λ), a dummy for the former Eastern agglomerations, and time dummies, as in equation (

5

).

20

  yields significant estimates. The Sargan test for exogeneity shows irregular performance and the test fails in columns 6 and 7 so we cannot properly identify λ. This means that also the coefficient on highly skilled labor will still be biased. Moreover, this regression does not capture other possible determinants of employment growth, such as the industrial mix. Next, we control for such omitted variable bias.TableA.4 adds more controls (and hence also more instruments). Centers of manufacturing may have had a different growth experience while possibly attracting less highly skilled labor. Manufacturing in Germany has on average employed less highly skilled workers and has grown slower throughout the sample period. Com-have the expected effect that cities with a higher share of persons between 45 and 60 years of age tend to grow more slowly. Omitting the age variables would have given a high skilled workers effect of 0.46%, which is very similar.

	Page 17 of 43	Regional Studies
	Table A.5 repeats the exercise for the longer IAB sample, covering the years
	1975-2001. s(5, 6) refers to the natural logarithm of skill levels 5 and 6 as a share
	F o r of employment (see Table A.2 in the previous section) which is equivalent to highly F skilled labor in the SR sample. s(2, 3, 4) refers to middle skilled labor. The IAB o r sample allows us to add a measure of local industry diversity as a control to account
	P for the possibility of diversity or specialization being beneficial to growth. We define P diversity as minus the natural logarithm of the sum of 16 squared industry shares
	in each city.	e e
		e r e diversity = -ln r	S s=1
		R R
		e e
		v i e v i e
			w w
			O n l O n l
			y y
	tification as column 3 shows. We find a plausible rate of conditional employment
	convergence of 1.3%, and a positive effect of highly skilled labor, which is however
	now smaller at 0.43% for a 10% increase in the concentration skilled workers. Since

http://mc.manuscriptcentral.com/cres Email: regional.studies@fm.ru.nl petition is added to capture the effect of the local industry structure. There is a long-standing debate fueled by

[START_REF] Glaeser | Growth in Cities[END_REF]

and

[START_REF] Henderson | Industrial development in cities[END_REF]

as to whether an industry grows faster if the local environment is competitive, diverse, specialized, or a combination of those three.

21

We do not observe enough industry information in the SR sample to include diversity or specialization save for the share of manufacturing. We measure competition as the local average number of employees per firm divided by the national average number of employees per firm. A competition index larger than one means that there is more competition than the national average. The age distribution of employees (relative to the national average) might be relevant because the education level reported is based on the highest acquired degree. With progressive advancement of technology it might be that a worker with a recent degree is actually more skilled than a worker with a degree from 30 years earlier. Young employees might thus be more productive. Medium skilled workers contain workers with a level of education that could be considered of equivalent to college level in the US (trade and technical schooling). These controls improve idenwe find some weak evidence for AR(2) we only use lags 3 and up as instruments.

Controlling for the effects of competition does not affect our results. Demographics

  (which provides other disciplines and awards PhDs). Within the group of medium skilled workers we can distinguish between three different schooling types. However, there is no clear difference in educational level between levels two and four, except that 'Abitur' allows a student to enter schools of levels five and six. We therefore group levels two and four together because both list vocational training as tertiary education. Effectively, we split medium skilled workers in those with, s(2, 4), and those without vocational training, s(3). Figure 2 graphs the average share of skilled workers across all agglomerations over time, for 6 different skill groups. By far the largest shares are taken up byFig. 2. Change in Skill Concentration Over Time (IAB Sample, West Germany)the lowest two schooling levels (upper two lines in the graph), of which the share of workers without a degree is trending and steadily decreasing over time. The left scale is in logs, so the fastest relative increase in education was among level four: high school + vocational training (dotted line). We will use unskilled labor as the reference skill level since it is the only level that has decreased over time. All other shares have increased but unequally so across cities, leading to various rates of employment growth over time.Table A.6 differentiates between more than two skill levels. Regressions one to four include time dummies to account for common shocks such as from technological progress and for example policy changes, while five and six include a time trend to account for a common trend in employment growth and to investigate whether the effect of skills changes over time. In the first column middle skilled workers are split into two groups, showing that vocational training, s(2, 4), has no significant effect, while a higher concentration of workers with only a high school degree actually decreases growth. This finding changes somewhat in column 2, which considers the possibility that spillovers exist between different skill levels. If workers from different skill levels complement and learn from each other than cities may also benefit from a suitable combination of skills. Highly skilled workers could for example increase the productivity of workers with vocational training by enabling more efficient use of

	Page 21 of 43	Regional Studies
		F o r P e e r R e v i e F o r P versity degree s(6) 1% 5% 20% 40% 60% 80% e e r R e Share of Total Employment (log scale) 1975 1980 1985 1990 Year v i e	1995	2000
		Level 6 Level 4	w Level 5 Level 3 w
		Level 2		Level 1
				O n l O n l
				y y

http://mc.manuscriptcentral.com/cres Email: regional.studies@fm.ru.nl their specific skills. Column 2 finds a positive interaction effect between high skilled labor and workers with vocational training, s(5, 6) * s(2, 4), and no interaction effect with high school graduates. To interpret the size and significance of the marginal effect of vocationally trained workers on employment growth we need to calculate how it depends on the share of skilled workers in a city:

23

Table A

 A on-the-job training programs. This fits well into the story that a certain level of attained education is needed to benefit from the knowledge of others.

		Regional Studies		Page 24 of 43
	6%			München
	F o r 7 East and West Germany So far we have pooled East and West data and assumed that the effect of human capital on growth is similar in the two regions. However, there are considerable differences in the evolution of the concentration of skilled workers between East and F Hamburg Wolfsburg Bremen Köln/Bonn Frankfurt am Main Wiesbaden Stuttgart Bodenseekreis Dingolfing Berlin Potsdam Elbe-Elster Dresden Leipzig Erfurt Jena Eisenach -2% 0% 2% 4% Change in % highly skilled labor 92-01 o 0% 5% 10% 15% 20% r % highly skilled labor in 1992
	P West Germany. Figures 3 and 4 show that the divergence of human capital levels West East P Fitted values Fitted values
	e e r e r e Fig. 4. Change in % Highly Skilled Labor (IAB Sample)
		R R
		e e
		v i e v i e
	As a second robustness test we exclude those workers that are in training. Many of the vocational training schools include 'on the job' training which might increase the measured share of this human capital group while their effect on productivity might be lower in reality. Comparing Table A.2 and Table C.1 shows that some w O n l y Hamburg Wolfsburg Bremen Köln/Bonn Frankfurt a.M. Wiesbaden Stuttgart Bodenseekreis München Dingolfing Berlin Potsdam Elbe-Elster Rügen Dresden Leipzig Erfurt Jena Eisenach -2% 0% 2% 4% 6% w O n l Change in % highly skilled labor 95-03 y
	0%	5%	10%	15%	20%
	workers without formal education (level 1) and those with only high school (level % highly skilled labor in 1995
	West 3) were in training while at their job. Table C.2 in the appendix does not find East Fitted values Fitted values
	Fig. 3. Change in % Highly Skilled Labor (SR Sample)
			20

.7 shows the robustness of these findings, where we control for the local industry structure and age of the work force using the same set of interactions as in columns three to six in Table

A

.6. In this case the interactions are even stronger, reinforcing the findings. qualitatively different results. On the other hand, the size of the spillovers is now larger for full time employed workers and therefore slightly weaker for workers in is observed in both data sources, but also that this has only taken place in West Germany. Another fact is that formal education levels were initially higher in the East while the growth of employment has at the same time been much slower, as shown in the data appendix. This is unexpected if the effect of skilled workers on growth is the same across regions, although it may also be due to other factors such as the (unobserved) quality of the stock of capital. Our data allows us to add to the literature by looking into the differences between the former East and West specifically.

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  We interact the skill complementarities between skill levels with the East Germany dummy in TableA.9. The regressions find little evidence that the match within cities between the college educated and workers with vocational training is any different in the former East, nor is the increased importance over time of college educated workers different in the East. A notable difference however, is that the regressions find that while West German cities have conditionally converged in terms of employment size, this has been the other way around among East German cities. Conditional on initial skill levels and abstracting from worker age effects, the East German cities have grown further apart. Together with the fact that human capital has a similar positive impact on East German city growth this means that employment will concentrate in skilled cities such as Jena and Berlin and lagging East German areas will not be able to catch up. This results in greater inequality decreasing over time however, while non-technical university graduates are becoming more important. Thirdly, we find no evidence that these effects are any different between West and East German metropolitan areas. City success may depend on the right combination of skills and not only on the percentage of college graduates.Micro-data at the firm level may shed more light on this link in the future.

	Page 25 of 43 Page 29 of 43	Regional Studies Regional Studies
	Notes
	1 Using a slightly different dataset and West German administrative regions (counties)
	F o r F o r F o r F o r F o r
	P P P P P
	e e e e e
	e r e r e r e r e r
		R R R R R
		e e e e e
	8 Conclusion	v i e w v i e v i e v i e v i e w w w w
	O n l This paper shows that well known estimates of the size of the effect of skills on metropolitan area growth are biased because endogeneity of the initial employment size is not sufficiently accounted for when fixed effects matter for both growth and O n l O n l O n l O n l
	y initial city characteristics. Adjusting the estimates using two data-sets on German y y y y
	metropolitan areas and recently improved dynamic panel GMM techniques shows
	that the effect is significant but at least 30% smaller than previously estimated in
	the literature. Secondly, we demonstrate that other skill groups matter for growth,
	namely those with vocational training. We find robust evidence that technical college
	graduates such as engineers interact positively with workers with vocational training
	and reinforce the latter's positive effect on employment growth. This effect is slightly
		22

http://mc.manuscriptcentral.com/cres Email: regional.studies@fm.ru.nl between Eastern agglomerations. At the same time we observe in the data that, unlike in West German metropolitan areas, skilled workers do not increasingly concentrate in skilled cities in the former East, leading to additional inequality between skilled cities in the West and cities in the former East.

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  significant at 10%; * * significant at 5%; * * * significant at 1%. Time dummies included. Column 7 uses the[START_REF] Windmeijer | A finite sample correction for the variance of linear efficient two-step GMM estimators[END_REF] robust standard errors and the last digit in the column names refers to 1-and 2-step estimation. Over-id. test is the Sargan test for one-step and the robust Hansen test for two-step estimation. significant at 10%; * * significant at 5%; * * * significant at 1%. Time dummies included. Columns 3 and 6 use the[START_REF] Windmeijer | A finite sample correction for the variance of linear efficient two-step GMM estimators[END_REF] robust standard errors and 2-step estimation. Column 7 uses all available instruments. Preferred estimate in bold. * significant at 5%; * * * significant at 1%. East Germany dummy included, and time dummies in columns 1 to 4. Preferred estimate in bold. denotes the ln of the sum of share of workers of skill level(s) x. The second column represents the effects of each variable interacted with the East Germany dummy.[START_REF] Windmeijer | A finite sample correction for the variance of linear efficient two-step GMM estimators[END_REF] robust standard errors in parentheses (two-step GMM estimation). * significant at 10%; * * significant at 5%; * * * significant at 1%. Time dummies included.Tables B.1 to B.3 provide descriptive statistics for the German metropolitan areas from the two data sources. Employment growth since 1995 has been distinctly lower than before and even negative on average. TableB.2 shows that skill levels were very high in East Germany in 1995 compared to the West. Part of the anomaly might be due to data quality, but an alternative explanation comes from specific labor market characteristics of the former DDR. Before unification it was standard to acquire at least medium skills in the former East and unemployment did not exist because each worker was assigned a job by the government. The resulting over-employment and subsequent closure of inefficient plants after unification led

	Table A.1 Number of Counties Versus Labor Regions Labor Regions Counties Germany 150 439 West 112 326 East 38 113 Table A.2 Skill definitions (IAB Sample) Level Definition 6 University Degree ('Hochschule') 5 Technical college degree ('Fachhochschule') 4 High school degree and vocational training ('Abitur mit Berufsausbildung') 3 High school degree ('Abitur') 2 Vocational training ('Volks-,Haupt-,Realschule mit Berufsausbildung') 1 no degree ('ohne Berufsausbildung') Regional Studies F o r P e e r R e v i e w O n l y Table A.3 SR Sample, 1995-2003 Dependent variable: Yearly % total employment growth Nickell-biased Weak-IV OLS Within DGMM1 DGMM2 SGMM1 SGMM2 At t-1 (1) (2) (3) (4) (5) (6) ln % highly skilled labor .006 .084 .239 .223 .160 .175 (.003) * (.015) * * * (.065) * * * (.020) * * * (.050) * * * (.018) * * * ln total employment -.0009 -.082 -.283 -.269 -.065 -.077 (.001) (.017) * * * (.085) * * * (.021) * * * (.022) * * * (.009) * * * East Germany Dummy -.029 -.126 -.130 (.002) * * * (.032) * * * (.012) * * * Obs. 1200 1200 1050 1050 1200 1200 AR(1) test, p-value .0007 3.85e-07 .001 2.05e-07 AR(2) test, p-value .506 .748 .194 .043 AR(3) test, p-value .489 .366 .592 .228 Over-id. test, p-val. .84 .0008 .999 .0001 # instruments 42 42 63 49 # Metropolitan Areas 150 150 150 150 150 150 Adj. R2 .561 .503 Heteroskedasticity robust and (city) clustered standard errors in parentheses. F o r P e e r R e v i e w O n l y Table A.4 Robustness SR Sample, 1995-2003 Dependent variable: Yearly % total employment growth Nickell-biased OLS Within At t-1 (1) (2) log % highly skilled labor 0.005 0.083 (0.003) (0.015)*** log % medium skilled labor -0.019 0.114 (0.017) (0.049)** log total employment -0.001 -0.084 (0.001) (0.016)*** ln % manufacturing 0.001 0.002 (0.002) (0.001)** Competition Rel. Pop. 25 < % < 35yr. Rel. Pop. 35< % <45yr. Rel. Pop. 45< % <60yr. East Germany Dummy -0.025 0.000 (0.003)*** (0.000) Observations 1187 1187 AR(1) test, p-value AR(2) test, p-value AR(3) test, p-value Hansen over-id. test, p-val. # instruments # Metropolitan Areas 150 150 Adj. R2 .565 .506 Robust and (city) clustered standard errors in parentheses. * significant at 10%; * * significant at 5%; * * * significant SGMM2r (7) .175 (.071) * * -.077 (.032) * * -.130 (.044) * * * 1200 3.25e-07 .067 .235 .0001 49 150 SGMM2r (3) 0.043 (0.012)*** 0.009 (0.084) -0.013 (0.006)** 0.023 (0.011)** -0.012 (0.011) 0.005 (0.028) -0.044 (0.053) -0.149 (0.053)*** -0.024 (0.014)* 1187 .001 .066 .093 .223 145 150 at 1%. Time dummies included. Column 3 uses the Windmeijer (2005) robust standard errors and 2-step estimation. Preferred estimate in bold. F o r P e e r R e v i e w O n l y Table A.5 IAB Sample, 1975-2001 Dependent variable: Yearly % total employment growth Nickell-biased Nickell-biased OLS Within SGMM2r OLS Within SGMM2r SGMM2r At t-1 (1) (2) (3) (4) (5) (6) (7) s 5,6 -.0008 .003 .059 .002 .006 .043 .025 (.002) (.004) (.017) * * * (.001) (.004) (.018) * * (.013) * * ln total employment -.003 -.035 -.030 -.0009 -.042 -.003 -.019 (.0007) * * * (.008) * * * (.007) * * * (.0005) (.008) * * * (.006) (.017) s 2,3,4 .008 .036 .236 .106 (.008) (.020) * (.061) * * * (.051) * * ln % manufacturing .004 -.012 .033 .008 (.002) * * (.012) (.013) * * (.031) Diversity index -.0007 -.027 -.076 -.012 (.002) (.008) * * * (.024) * * * (.017) Average worker age -.005 .002 -.016 .0003 (.0005) * * * (.001) (.004) * * * (.004) East Germany Dummy -.028 -.061 -.024 -.030 -.045 (.002) * * * (.011) * * * (.002) * * * (.013) * * (.025) * Obs. 3252 3252 3252 3252 3252 3252 3252 AR(1) test, p-value 3.61e-20 1.42e-19 1.24e-19 AR(2) test, p-value .415 .773 .69 Hansen over-id. test, p-val. .419 .593 -# instruments 167 175 1975 # Metropolitan Areas 150 150 150 150 150 150 150 Adj. R2 .721 .729 .729 .731 Robust and (city) clustered standard errors in parentheses. Page 35 of 43 Regional Studies F o r P e e r R e v i e w O n l y Table A.6 Skill interactions (IAB Sample, 1975-2001) Dependent variable: Yearly % total employment growth (SGMM2r estimator) Interactions with: S 5,6 s 5 s 6 s 5,6 & time trend At t-1 (1) (2) (3) (4) (5) (6) s 5,6 .063 .160 -.025 .013 (.014) * * * (.042) * * * (.019) (.038) s 5 .060 .013 (.045) (.010) s 6 .017 .077 (.008) * * (.032) * * s 2,4 .073 1.008 1.119 .928 .143 -.015 (.048) (.235) * * * (.284) * * * (.219) * * * (.064) * * (.308) s 3 -.017 -.018 -.046 -.027 .037 .038 (.005) * * * (.020) (.030) (.019) (.007) * * * (.007) * * * ln total employment -.023 -.025 -.014 -.015 -.038 -.037 (.006) * * * (.005) * * * (.005) * * * (.005) * * * (.009) * * * (.009) * * * s 5,6 * s 2,4 .250 .007 (.060) * * * (.080) s 5,6 * s 3 -.001 (.007) s 5 * s 2,4 .240 (.063) * * * s 5 * s 3 -.009 (.007) s 6 * s 2,4 .190 (.048) * * * s 6 * s 3 -.003 (.005) s 5,6 * time trend .003 (.0007) * * * s 5,6 * s 2,4 * time trend -.003 (.0009) * * * time trend .007 .0003 (.002) * * * (.001) Obs. 3207 3207 3204 3204 3207 3207 AR(1) test, p-value 5.19e-19 9.84e-18 4.59e-19 1.30e-18 2.82e-18 3.35e-18 AR(2) test, p-value .72 .666 .839 .791 .063 .055 Hansen over-id. test, p-val. .407 .332 .34 .361 .227 .215 # instruments 169 169 169 169 150 150 # Metropolitan Areas 150 150 150 150 150 150 s x denotes the ln of the sum of share of workers of skill level(s) x. Windmeijer (2005) robust standard errors in parentheses (two-step estimation). F o r P e e r R e v i e w O n l y Table A.7 Skill interactions with additional controls (IAB Sample, 1975-2001) Dependent variable: Yearly % total employment growth (SGMM2r estimator) Interactions with: s 5 s 6 s 5,6 & time trend At t-1 (3) (4) (5) (6) s 5,6 -.074 -.059 (.018) * * * (.040) s 5 .043 .025 (.055) (.013) * s 6 .023 .072 (.010) * * (.039) * s 2,4 1.932 1.418 .324 -.454 (.398) * * * (.300) * * * (.075) * * * (.352) s 3 -.096 -.048 .038 .036 (.033) * * * (.025) * (.007) * * * (.006) * * * ln total employment -.013 -.017 -.031 -.030 (.007) * (.006) * * * (.009) * * * (.009) * * * s 5 * s 2,4 .390 (.086) * * * s 5 * s 3 -.025 (.008) * * * s 6 * s 2,4 .265 (.059) * * * s 6 * s 3 -.012 (.007) * s 5,6 * time trend .006 (.001) * * * time trend .015 .005 (.002) * * * (.002) * * * s 5,6 * s 2,4 * time trend -.007 (.001) * * * s 5,6 * s 2,4 -.122 (.091) ln % manufacturing -.010 .012 .087 .073 (.023) (.023) (.026) * * * (.022) * * * Diversity index -.106 -.082 -.032 -.049 (.030) * * * (.027) * * * (.030) (.030) * Average worker age -.015 -.010 .0005 -.0003 (.005) * * * (.004) * * * (.003) (.003) Obs. 3204 3204 3207 3207 AR(1) test, p-value 5.86e-19 3.87e-18 1.58e-17 1.46e-17 AR(2) test, p-value .739 .819 .075 .068 Hansen over-id. test, p-val. .374 .371 .177 .167 # instruments 169 169 150 150 # Metropolitan Areas 150 150 150 150 F o r P e e r R e v i e w O n l y Table A.8 East and West Germany (IAB Sample) Dependent variable: Yearly % total employment growth At t-1 East * s(5, 6) (highly skilled) 0.045*** -0.007 (0.014) (0.057) s(2, 3, 4) (medium skilled) 0.089** 0.733* (0.040) (0.419) ln total employment -0.015** 0.028* (0.006) (0.016) ln % manufacturing 0.033** -0.007 (0.015) (0.030) Diversity index -0.005 -0.170* (0.016) (0.097) Average worker age -0.007** -0.031*** (0.003) (0.006) East Germany Dummy 1.502** (0.599) Observations 3252 AR(1) test, p-value 0.345 AR(2) test, p-value 0.472 # instruments 403 # Metropolitan Areas 150 Hansen over-id. test, p-val. 1.000 s(x) F o r P e e r R e v i e w O n l y Table A.9 Skill Complementarities in East and West Germany (IAB Sample) Dependent variable: Yearly % total employment growth (1) (2) At t-1 East * East * s(5, 6) (highly skilled) 0.221*** -0.830 -0.032* -0.254 (0.061) (0.528) (0.018) (0.485) s(2, 4) (vocational) 1.171*** -1.893 0.121* 1.203 (0.318) (4.614) (0.061) (1.553) s(3) (high school) -0.003 -0.069 0.029*** 0.115*** (0.031) (0.092) (0.007) (0.038) ln total employment -0.043*** 0.125*** -0.038*** 0.126*** (0.009) (0.024) (0.010) (0.048) s(5, 6) * s(2, 4) 0.297*** -1.261 (0.082) (2.026) s(5, 6) * s(3) 0.001 -0.041 (0.010) (0.041) s(5, 6) * time trend 0.004*** -0.006 (0.001) (0.022) time trend 0.010*** -0.031 (0.002) (0.050) East Germany Dummy -2.634** 60.598 (1.264) (99.294) Constant 1.156*** -18.438*** (0.280) (3.696) Observations 3207 3207 AR(1) test, p-value 0.658 9.37e-09 AR(2) test, p-value 0.793 0.679 Hansen over-id. test, p-val. 0.892 0.919 # instruments 205 191 # Metropolitan Areas 150 150 s(x) denotes the ln of the sum of share of workers of skill level(s) x. The second and fourth columns represent the effects of each variable interacted with the East Germany dummy. Windmeijer (2005) robust standard errors in parentheses (two-step GMM estimation). * significant at 10%; * * significant at 5%; * * * significant at 1%. Time dummies included in regression (1). Page 39 of 43 Regional Studies F o r P e e r R e v i e w O n l y s Regional Studies B Data appendix and descriptive statistics

Note: A high school degree of the 'Abitur' level qualifies for university and technical college, while a high school degree from the 'Volks-,Haupt-,Realschule' does not.

Page 32 of 43 http://mc.manuscriptcentral.com/cres Email: regional.studies@fm.ru.nl * * http://mc.manuscriptcentral.com/cres Email: regional.studies@fm.ru.nl * significant at 10%; * x denotes the ln of the sum of share of workers of skill level(s) x.

[START_REF] Windmeijer | A finite sample correction for the variance of linear efficient two-step GMM estimators[END_REF]

robust standard errors in parentheses (two-step estimation). * significant at 10%; * * significant at 5%; * * * significant at 1%. East Germany dummy included, and time dummies in columns 1 and 2.. Page 37 of 43 http://mc.manuscriptcentral.com/cres Email: regional.studies@fm.ru.nl http://mc.manuscriptcentral.com/cres Email: regional.studies@fm.ru.nl

Table B

 B (consumer) goods manufacturing, steel, machines, metal, transportation manufacturing, processed foods. Total employment is a sample of individuals. Age is averaged over metropolitan areas. Table C.2 Without workers in training(IAB Sample, 1975[START_REF] Glaeser | Cities and Skills[END_REF]

	.3 IAB 2% Sample Descriptive Statistics 1975 (West) 2001 (West) mean sd mean sd % level 6 1.2% 0.8% 4.6% 2.2% % level 5 1.2% 0.5% 3.1% 0.9% % level 4 0.6% 0.3% 5.5% 1.9% % level 3 0.3% 0.2% 1.3% 0.7% % level 2 57.0% 5.1% 69.4% 4.8% 75.5% mean 7.1% 4.7% 4.5% 1.0% % level 1 39.7% 5.8% 16.1% 2.8% 7.2% Total employment 3183 4056 4378 5261 3414 % Manufacturing 46.2% 10.4% 32.9% 9.0% 19.9% Diversity 2.36 0.27 2.45 0.14 2.51 Average Age 34.1 1.1 39.2 0.5 40.0 Note: Manufacturing includes WZWG 2 to 6 ('Wirtschaftszweig', Industrial classi-2001 (East) sd 2.3% 0.9% 0.9% 0.5% 4.3% 1.2% 4586 6.2% 0.10 0.4 Regional Studies F o r P e e r R e v i e w O n l y C Robustness Table C.1 Skill shares without workers in training (IAB Sample) Level Av. share in 1975 Av. share in 2001 6 1.3% 5.4% 5 1.3% 3.6% 4 0.6% 5.4% 3 0.3% 0.8% 2 60.1% 74.0% 1 36.4% 10.7% Note: 2001 includes East Germany. Regional Studies F o r P e e r R e v i e w O n l y Dependent variable: Yearly % total employment growth (SGMM2r estimator) Interactions with: s 5 s 6 s 5,6 & time trend (1) (2) (3) (4) (5) s 5,6 .052 -.057 .043 (.017) * * * (.024) * * (.048) s 5 .374 .046 (.071) * * * (.019) * * s 6 .040 .227 (.016) * * (.045) * * * s 2,3,4 .202 (.073) * * * s 2,4 1.815 1.118 .521 .572 (.456) * * * (.288) * * * (.102) * * * (.407) s 3 .144 .094 .064 .070 (.035) * * * (.024) * * * (.007) * * * (.008) * * * ln total employment -.005 -.025 -.025 -.035 -.041 (.006) (.009) * * * (.008) * * * (.012) * * * (.012) * * * s 5,6 * s 2,4 .092 (.106) s 5 * s 2,4 .353 (.100) * * * s 5 * s 3 .034 (.009) * * * s 6 * s 2,4 .193 (.058) * * * s 6 * s 3 .022 (.006) * * * s 5,6 * time trend .006 (.001) * * * time trend .013 .0007 (.003) * * * (.002) s 5,6 * s 2,4 * time trend -.006 (.002) * * * ln % manufacturing .033 .037 .055 .091 .089 (.014) * * (.024) (.022) * * (.026) * * * (.025) * * * Diversity index -.072 -.077 -.056 -.045 -.060 (.026) * * * (.041) * (.036) (.035) (.040) Average worker age -.016 -.012 -.009 -.006 -.005 fication): Page 41 of 43 (.003) * * * (.007) * (.007) (.004) (.004)	Page 42 of 43
	Obs.	3250	3115	3115	3117	3117
	AR(1) test, p-value	3.43e-15	1.57e-16	5.32e-07	1.53e-15	7.20e-15
	AR(2) test, p-value	.670	.943	.671	.077	.068
	Hansen over-id. test, p-val.	.605	.481	.695	.186	.165
	# instruments	175	173	173	150	150
	# Metropolitan Areas s	150	150 38	150	150	150

http://mc.manuscriptcentral.com/cres Email: regional.studies@fm.ru.nl http://mc.manuscriptcentral.com/cres Email: regional.studies@fm.ru.nl x denotes the ln of the sum of share of workers of skill level(s) x.

[START_REF] Windmeijer | A finite sample correction for the variance of linear efficient two-step GMM estimators[END_REF]

robust standard errors in parentheses (two-step estimation). * significant at 10%; * * significant at 5%; * * * significant at 1%. East Germany dummy included, and also time dummies in column 1.

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Regional

Regional Studies