Internal migration, regional labor markets and the role of agglomeration economies

Abstract

We analyze the determinants and regional implications of internal migration flows across Danish municipalities in 2006–2012. Besides assessing the role of labor market and housing market factors in driving a region’s net migration rate, we particularly focus on agglomeration factors identified by “new” migration theories related to regional growth models and the new economic geography. The work contributes to the field in the following way: we extend the scarce literature on the different channels through which agglomeration economies act as an attractor for mobile labor. Moreover, we account for the role of space–time dynamic adjustment processes and simultaneity among migration and labor market variables and finally test for heterogeneity in the migration response to regional labor market disparities among low- and high-skilled migrants. Our results support the view that agglomeration economies are indeed key drivers of internal migration flows in Denmark. That is, while we obtain mixed evidence with regard to the role of traditional labor and housing market variables, most of the included proxies for agglomeration economies such as the region’s population density, patent intensity, endowment with human capital as well as the region’s employment share of knowledge-intensive services are positively correlated with the region’s net in-migration rate. Regarding the regional implications of internal migration flows, the results hint at a process of cumulative causation for the time period of analysis running from agglomeration economies to the inflow of mobile labor and subsequent regional income development.

1 Introduction

The spatial mobility of labor between different regions of a national economic system is typically viewed as an important prerequisite for an efficient labor market allocation and consequently associated with increases in labor productivity. From a national and regional policy perspective, it is thus of vital interest to empirically identify the most relevant causes and consequences of internal labor migration flows. With regard to theoretical priors for an empirical identification approach, however, no clear-cut predictions can be made: on the one hand, the neoclassical migration theory predicts that key labor market signals such as differences in regional wage or income levels as well as disparities in unemployment rates play a major role in canalizing flows of mobile labor (see, e.g., Etzo 2011). The migration response to these initial signals then acts as an equilibrating force in terms of clearing interregional disparities in the adjustment process toward a long-run labor market equilibrium. Modern theories of economic growth and spatial equilibrium, on the other hand, have recently pointed toward the role played by agglomeration economies in attracting mobile labor, which may result in a process of cumulative causation with an advancing regional concentration of economic activities and mobile production factors rather than a balancing of interregional disparities (see Fu and Gabriel 2012). In essence, different hypotheses with regard to the labor market causes for and consequences of labor mobility are offered in the recent literature.

Taking up this discussion, we analyze the migration–income–unemployment nexus for Danish municipalities over the period 2006–2012. Besides assessing the role of traditional labor market factors and general agglomeration measures such as the overall regional population density or the regional concentration of industry employment typically used in empirical studies, we aim at augmenting the current state-of-the-art by focusing on alternative measures of agglomeration economies. Specifically, we consider the region’s innovative and creative capacities proxied by the patent intensity and the regional employment share in knowledge-intensive services (KIS). Denmark can be seen as an interesting case study for investigating these factors underlying the migration–income–unemployment nexus because of two noteworthy characteristics: firstly, the Danish labor market is typically considered to be very flexible in a European perspective. Secondly, the country is one of the most innovative and research-intensive economies in the EU with 3 % of R&D expenditures relative to GDP in 2011 as compared to an EU average of about 2 %.¹

At the heart of the empirical analysis lies the specification of a core migration equation identifying the main determinants of internal labor mobility in Denmark. Additionally, we investigate the feedback linkages running from migration to labor market signals, which leads to the estimation of a three-equation labor market system including separate model equations for regional differences in income levels as well as unemployment rates. In this context, the size and nature of agglomeration economies may play a crucial role as an attractor to human capital through labor mobility. Agglomeration economies may furthermore foster the regional innovation and income performance resulting from this human capital gain through the existence of knowledge spillovers. By adding a broad set of agglomeration economies to each equation of our specified small-scale labor market system, the aim is to identify this dual role played by agglomeration economies. The baseline hypothesis is accordingly that agglomeration economies through urbanization and localization effects attract migration, which is then observed to have a feedback effect on income levels and unemployment rates.

In the course of estimation, we will account for various factors, which are likely to complicate empirical identification and lead to biases in the results if not properly addressed. Firstly, we capture the inherent temporal dynamics in labor market adjustment processes by means of a partial adjustment model approach (Lambert et al. 2014). Secondly, we capture potential estimation biases introduced by underlying spatial dependence among regional labor markets by means of estimating a spatial Durbin model specification (LeSage and Pace 2009). The introduction of spatial dynamics also allows for a richer model interpretation in terms of quantifying spatial neighborhood and spillover effects. Furthermore, in the empirical analysis we will test for potential regime shifts by focusing on the importance of factors driving high-skilled migration vis-à-vis low-skilled migration. Finally, while our baseline modelling approach already includes lagged regressors to resolve issues of reverse causality, throughout the empirical identification strategy, we will also consider the use of instruments adapted from Card (2001) and Fratesi and Percoco (2014). This may allow us to carefully interpret the obtained results as causal effects rather than just conditional correlations.

On a methodological note, it may also be stated that the period of analysis includes crisis years following the global financial and economic crisis of 2007/2008. The empirical specification considers this “global shock” to the overall Danish labor market in a number of dimensions: one is by including time-fixed effects, and another is by including variables on regional employment structures by NACE one-digit industries controlling for region-specific structural change during a crisis.

Thus, the contribution of the analysis undertaken here accordingly relates to four aspects. One is by contributing to a scarce and recent literature on the importance of agglomeration economies as a pull factor for human capital migration, thereby assessing the empirical validity of the model predictions of the neoclassical migration model and the NEG theory. Another is by allowing such agglomeration economies to arrive from different channels such as relating to urbanization and localization effects. Furthermore, the empirical strategy allows for dynamic adjustment processes of spatial structures, hereby considering the possible importance of regime shifting. Finally, this paper contributes by stressing the effects of internal human capital migration, rather than international migration, which is at the core of most recent empirical studies, when considering a relationship between creativity, innovation and economic development.

Our empirical results support the view that agglomeration economies are key drivers of internal migration processes in Denmark. While we obtain mixed evidence with regard to the role of general labor market and housing market variables in driving internal migration flows, most of the included proxies for agglomeration economies matter: we get positive and statistically significant conditional correlations of the region’s net in-migration rate with the region’s relative population density, the patent intensity, the regional endowment with human capital as well as the employment share of knowledge-intensive services. With regard to the consequences of internal migration flows, the results do not reject the NEG view of a circular process of urbanization and agglomeration, inflow of mobile labor and increasing regional labor market differences. However, given that this analysis has been conducted for a limited time period and a labor market in “crisis,” further research effort is needed to address the complex dynamics between internal migration and regional labor market disparities.

The remainder of the paper is organized as follows: the following section provides a selective literature review on the causes and consequences of migration in a regional labor market context focusing on the role of agglomeration forces. Section 3 outlines the specification of our small-scale labor market system and discusses the empirical estimation strategy. Section 4 provides an overview of the data and presents some stylized facts. The estimation results for the migration–income–unemployment nexus are presented in Sect. 5, while some crucial robustness checks can be found in Sect. 6. Section 7 finally discusses the results with regard to their policy implications and concludes the paper.

2 Literature review: migration in regional labor markets and the role of agglomeration economies

Identifying the causes and consequences of the spatial mobility of labor across the boundaries of a regional labor market has attracted considerably research efforts from scholars in the fields of regional science and economic geography as well as labor economics. Firstly, a large number of theoretical and empirical contributions on interregional labor migration aim at identifying the causes of labor migration from a micro-, meso- or macro-perspective. While studies at the micro- and meso-level are typically concerned with the identification of migration motives for individuals (Sjaastad 1962; Borjas 1987) and among households (Stark 1991), macro theories predominantly focus on analyzing the strength of migration responses to regional labor market disparities as a part of a more general modelling approach to interregional labor market dynamics (Hagen-Zanker 2008). Secondly, there is an extensive literature aiming at assessing the consequences of interregional labor migration on regional economic development (Ozgen et al. 2009).²

Both strands of the literature typically build on the neoclassical migration theory as workhorse model of analysis. The neoclassical model relates migration flows between regions to the locational choice decision of representative agents who seek to maximize their expected income by comparing the underlying labor market characteristics in the origin region and a set of potential destination regions. The latent variable concept of expected income goes back to the seminal contribution of Harris and Todaro (1970) operationalizing expected income as a function of regional differences in observed income or wage levels and the probability of being employed in the origin and destination regions. Hence, under rational behavior an individual will decide to migrate if this decision improves his welfare position in terms of expected income relative to the status quo of not moving net of any transportation costs.

In subsequent theoretical and empirical contributions, this neoclassical labor market model of internal migration has been extended to account for further economic and social factors, which may affect the potential migrant’s utility level (see Napolitano and Bonasia 2012). From an empirical perspective, the main motive for this awareness of modelling migration as a multidimensional phenomenon (Brettel and Hollifield 2000) is associated with the fact that the labor market model may suffer from a severe model misspecification due to omitted variables. Hence, it was found to be useful to analyze interregional migration flows by controlling for further determinants such as house prices (Gabriel et al. 1992; Potepan 1994; Bitter 2008), commuting flows (Evers 1989), public transfer payments (Schmidt 2013), industry structures and structural changes (Saks and Wozniak 2011; Kubis 2005) as well as region-specific amenities (Knapp and Gravest 1989).

Although the neoclassical framework is still the most commonly used vehicle for applied interregional migration studies, it has recently been challenges by advances in theoretical models of the New Economic Geography (NEG), where the core-periphery model of Krugman (1991) is one of the most prominent specifications. Similar to the neoclassical framework, in the core-periphery model migration is assumed to be governed by real income differences (see Brakman et al. 2009). Therefore, potential migrants likewise choose an optimal migration time path in accordance with their lifetime utility maximization. According to Baldwin and Forslid (2000), the law of motion for the migration of mobile workers is therefore driven by the difference in the net present value of utility among the core and periphery. The underlying centripetal forces of the model drive migration flows from the periphery to the core, where the key assumption is that particularly human capital (skilled workers) moves to the core, whereas unskilled labor remains immobile (Forslid 1999).

In this context, the core-periphery model of the NEG can also be seen as the first attempt to establish a formal link between mobile labor and different types of agglomeration forces. On the one hand, an initially uneven spatial distribution of economic activity is assumed to be a key determinant for interregional migration flows mainly trigged by forward and backward linkages, which are positively affected by market potential (see Brakman et al. 2009). Initial differences may be the result of first- or second-nature agglomeration advantages and their interaction (Chasco Yrigoyen et al. 2012). While first-nature advantages are related to exogenous features of physical geography, second-nature advantages are man-made and may pertain to both localization and urbanization effects (Carlino 1979). With regard to the consequences of labor mobility on the spatial distribution of economic activity, NEG models predict a process of cumulative causation, which may lead to large economic disparities between regions in the long-run. As Capello (2007, p.18) points out: “It is because of agglomeration economies that spatial concentration comes about.”

Challenging the standard neoclassical predictions not only on theoretical but also empirical grounds, Crozet (2004) was among the first to include migration decisions of mobile workers into NEG-type models. Focusing on the role of forward-linkage-type agglomeration force, the author investigates whether access to markets has a significant positive influence on migration choices. The author gets strong statistical support for this linkage based on regional data for different European countries. One important implication of Crozet’s (2004) findings is that these forward linkages do not balance interregional differences in the (real) wage rate, but even amplify them, thereby increasing interregional differences and fostering agglomeration processes.

The potential importance of agglomeration forces in attracting mobile labor, and the likely amplifying feedback effect from migration processes to regional economic disparities, has subsequently attracted further research: Pons et al. (2007) analyze the role of industrial agglomerations in Spain during the early twentieth century on internal migration flows. In line with Crozet (2004), the authors find that access to markets has a significant influence on migration choices of Spanish internal migrants. Focusing on the influence of urban agglomerations, Ritsilä and Ovaskainen (2001) likewise find on the basis of microdata for Finland that individuals are more likely to migrate to centers of economic activity.

Fu and Gabriel (2012) shift the focus from industrial and urban agglomerations to the spatial concentration of knowledge and human capital when analyzing migration flows. They summarize the main arguments, why regional concentrations of human capital can be supposed to influence the migratory incentives for prospective migrants in various ways: firstly, regional differences in human capital concentrations can affect the place-specific demand for skilled labor. Secondly, human capital concentrations support the demand for consumer amenities, and thirdly, a regional concentration of human capital can result in spillover benefits to private investments in human capital and new ideas, which may translate into higher productivity growth rates for these regions. Accordingly, the authors change the focus from an overall or age-specific migration analysis toward the notion of intellectual migration measured by the geographical mobility of highly skilled workers given that this subgroup of migrants can be considered as very mobile. Using data for Chinese provinces, Fu and Gabriel (2012) find that human capital concentrations in China have a positive impact on regional growth trajectories measured by the in-migration balance of highly skilled labor.

Likewise, Faggian and McCann (2009a) study the geography of mobile human capital focusing on student flows in Great Britain. They find that university graduates are highly mobile with respect to geography and that agglomeration processes in British regions are related to interregional flows of graduates. In a related paper, Faggian and McCann (2009b) further explore the link between knowledge agglomerations and skilled migration by estimating a simultaneous equation model for the two-way linkage between interregional graduate migration flows and patent applications in British regions. The authors find a positive two-way relationship among the variables. This supports the cumulative causative process that skilled mobile labor is attracted by innovative and dynamic regions, which are then able to remain highly innovative because of the net inflow of human capital. Again, this interdependent nature of high-skilled mobile labor and knowledge agglomeration is likely to translate into an increased concentration of economic activity in space. Broadening the focus from innovation activity to general economic development, Ozgen et al. (2009) conduct a meta-study concerning the impact of net in-migration on regional growth. The authors find that the impact of net migration is generally more consistent with endogenous self-reinforcing growth than with neoclassical convergence. This result is also supported by a recent study of Fratesi and Percoco (2014), finding that the out-migration of human capital in Italian regions is detrimental to regional growth.

Table 1 Reviewing the link between agglomeration economies and migration in the empirical literature

Similar to the case of agglomeration economies through human capital, most of the recent research work finds positive two-way linkages with regard to the migration–innovation nexus, indicating that a positive correlation of migration decisions and innovation performance can translate into overall productivity gains. However, so far the empirical literature in the latter field has mainly focused on the relationship between international immigration and labor diversity on the innovation performance (Parrotta et al. 2014; Hunt and Gauthier-Loiselle 2012). Empirical analyses assessing the link between internal migration and regional innovation performance are still scarce. Among the few exceptions is Niebuhr (2010) showing that differences in knowledge and capabilities of workers from diverse cultural backgrounds enhance performance of regional R&D sectors for a cross section of German regions. Another exception, which comes closest to the approach taken in this paper, is the above mentioned analysis of Faggian and McCann (2009b).³

To sum up, Table 1 provides an overview of this selective literature review on the different empirical approaches trying to establish a link between agglomeration economies and migration flows. It furthermore summarizes how this relates to regional economic development. The different contributions to the literature consider the importance of agglomeration economies in a set of different contexts over countries and regions. The covered types of agglomeration economies are in general related to urbanization effects and market size, location effects and spillovers among firms, which relates to the spatial structure of knowledge production and possible spillovers relating to this from, e.g., human capital concentration.

3 Model specification and estimation: a small-scale labor market system

We specify a small-scale regional labor market system to analyze the causes and consequences of interregional migration in the presence of agglomeration economies. At the core of this system lies a functional equation for a region’s net migration balance. As outlined above, the workhorse model in most applied studies is the neoclassical migration framework, which views the migration decision as a rational choice process in terms of maximizing the potential migrant’s expected utility level. While both the neoclassical theory and NEG-type models concordantly predict that migration flows are driven by (expected) interregional income differences, the consequences of migration are viewed as diametrically different in these theories. This difference will be of importance when modelling the feedback effects of migration to regional differences in income levels and unemployment rates as separate equations of the small-scale labor market system.

The neoclassical theory of interregional migration and income growth assumes that migration flows act as a balancing factor to interregional labor market disparities. Since migrants are attracted by positive interregional income differences, migratory moves to a destination region j with a higher relative income level compared to the origin destination i will increase the labor supply in this region. This in turn puts a downward pressure on income levels received by workers in j due to a changing capital–labor ratio, while the reduced labor supply in the origin region i will shift income levels in the opposite direction (Coulombe 2006). In long-run equilibrium, interregional differences in income levels and the unemployment rate will cancel out. The core-periphery model, in contrast, predicts a fortification of interregional income differences due to migratory behavior. This is mainly driven by agglomeration economies including increasing economies of scale at the firm level, a home market effect (backward linkage) due to increasing manufacturing demand of larger agglomerations in the presence of transportation costs as well as an associated forward-linkage stemming from price index changes (for details, see Brakman et al. 2009).

The purpose of our small-scale labor market system is to assess the empirical validity of these model predictions. We start with the specification of a model equation for interregional migration flows to study the determinants of (high-skilled) labor mobility and then extend the model by two auxiliary equations to model the potential consequences of migration on interregional income disparities and differences in the unemployment rate. In specifying the migration equation based on a flexible model framework, we draw on Puhani (2001) and model the aggregate regional net in-migration rate for skill group s in region i over time t as

$$\begin{aligned} {\textit{MIG}}_{s,i,t} =\frac{{\textit{NM}}_{s,i,t} +Pop_{s,i,t-1} }{{\textit{Pop}}_{s,i,t-1}}=A_{s,i,t} \frac{U_{i,t-k}^{\gamma _1 } Y_{i,t-k}^{\gamma _3 } \mathbf{X}_{i,t-k}^{\Omega ^{\prime }} }{U_{j,t-k}^{\gamma _2 } Y_{j,t-k}^{\gamma _4} \mathbf{X}_{j,t-k}^{\sigma ^{\prime }}}. \end{aligned}$$

(1)

In Eq. (1), the net in-migration rate (MIG) is defined as a net in-migration-induced population growth for skill group s in region i, where net migration (${\textit{NM}}_{s,i,t} )$ is defined as the difference between in-migration and out-migration for region i and skill group s at time t. Pop, U and Y denote the population, unemployment rate and disposable income level, respectively. As indicated by the term “$t-k$,” we impose a lag structure of up to a maximum of k lags for the migration model assuming that time lags account for the delays in the course of dissemination of labor market signals to migration (see Puhani 2001).⁴ The use of stratifying the dependent variable into skill groups is mainly motivated from the NEG literature assuming potential regime changes among high- and low-skilled migrants.

The regression coefficients $\gamma _1$ and $\gamma _2$ are the associated elasticities for the net in-migration with respect to changes in the unemployment rate in region i and the rest of the country (region j), respectively. In similar veins, $\gamma _3$ and $\gamma _4$ are the elasticities with respect to changes in regional income differences in region i and the rest of the country, respectively, while $\Omega ^{\prime }$ and ${\sigma }^{\prime }$ are coefficient vectors for the set of further control variables in region i and j. “A” is a constant term. The log-linear transformation of the specification in Eq. (1) together with the introduction of a stochastic term ($\nu _{s,i,t})$ can be written as

$$\begin{aligned} mig_{s,i,t}= & {} A_{s,i,t} +\gamma _1 u_{i,t-k} -\gamma _2 u_{j,t-k} +\gamma _3 y_{i,t-k} -\gamma _4 y_{j,t-k} +\Omega ^{\prime }\mathbf{X}_{i,t-k}\nonumber \\&-\sigma ^{\prime }\mathbf{X}_{j,t-k}+\nu _{s,i,t}. \end{aligned}$$

(2)

Here, lower case letters denote logarithmic transformations of the variables. For estimation purposes, the constant term can be decomposed into $A_{s,i,t} =c_0 +\mu _{s,i} +\lambda _t$, where $c_0$ is the overall constant term, $\mu _{s,i}$ denotes skill group-specific region fixed effects and $\lambda _t$ are time-fixed effects. Since the number of variables can become quite large in Eq. (2), applied research typically uses a restricted version based on regional differences for each variable (see, for instance, Alecke et al. 2010), where the regional difference for each log-transformed variable “x” can be defined as $\tilde{x}_{i,t-k} =\left( {x_{i,t-k} -x_{j,t-k} } \right)$.⁵ Eq. (2) can then be rewritten as

$$\begin{aligned} mig_{s,i,t} =c_0 +\omega _1 {\tilde{u}}_{i,t-k} +\omega _2 {\tilde{y}}_{i,t-k} +{\theta }^{\prime }\tilde{\mathbf{X}}_{i,t-k}+\mu _{s,i}+\lambda _{t}+\nu _{s,i,t}, \end{aligned}$$

(3)

where $\omega _1 =\gamma _1 -\gamma _2 ,\omega _2 =\gamma _3 -\gamma _4$ and $\theta ={\Omega }-\sigma$. In the recent empirical interregional migration literature, it is a common assumption that migration flows react sluggishly to interregional labor market disparities (see Etzo 2011), and the inclusion of a time lagged endogenous variable has proven to be an important factor in the adjustment path of interregional migration flows. This temporal dynamics of interregional migration flows allows us to rewrite Eq. (3) in the form of a partial adjustment model, which has recently received growing interest in the regional science literature (see, for instance, Lambert et al. 2014). For ease of presentation, we can formulate Eq. (3) in matrix notation stacked over the dimensions ${s=1,{\ldots },S}$, ${i=1,{\ldots },N}$ and ${t=1,{\ldots },T}$ as

$$\begin{aligned} mig^{*}=\iota +L.\mathbf{Z}{\Theta }+\mu +\lambda +\nu \end{aligned}$$

(4)

where $mig^{*}$ is the long-run level of the dependent migration variable, the matrix $\mathbf{Z}$ contains the set of exogenous variables as $\mathbf{Z}=\left[ {\tilde{u}},{\tilde{y}},{\tilde{\mathbf{X}}} \right]$, $\iota$ is a vector of ones and L. indicates the use of a time lag operator. Partial equilibrium models then assume that only a constant proportion ($\alpha )$ of the adjustment process toward long-run levels is achievable in a given time period as

$$\begin{aligned} \left( {mig-L.mig} \right) =\alpha \left( {mig^{*}-L.mig} \right) . \end{aligned}$$

(5)

Substitution Eq. (5) in the long-run specification of Eq. (4) finally yields

$$\begin{aligned} mig=\iota +\alpha \left( {L.mig} \right) +L.\mathbf{Z}\beta +\mu +\lambda +\varepsilon , \end{aligned}$$

(6)

where $\beta =\alpha \Theta$ and $\varepsilon =\alpha \nu$. Equation (6) will be taken as the benchmark specification for the estimation of the migration equation in the small-scale labor market system. When operationalizing the matrix of exogenous variables included in Eq. (6), $\mathbf{Z}$ can be decomposed into two submatrices of regressors $\mathbf{Z}1$ and $\mathbf{Z}2$. The submatrix $\mathbf{Z}1$ contains an extended set of labor market and housing market characteristics as $\mathbf{Z}1=\left[ {{\widetilde{u}},{\widetilde{y}}, {\widetilde{com}},{\widetilde{house}} ,{\widetilde{crime}}} \right]$, where ${\widetilde{com}} ,{\widetilde{house}}$ and ${\widetilde{crime}}$ are interregional differences in net commuting rates, house prices and crime rates, respectively. The second submatrix $\mathbf{Z}2$ contains variables proxying agglomeration economies as $\mathbf{Z}2=\left[ {\widetilde{popd} ,\widetilde{pat,} \widetilde{hk} ,\widetilde{hitec} ,\widetilde{kis}} \right]$, where $\widetilde{popd} , \widetilde{pat,} \widetilde{hk} , \widetilde{hitec}$ and $\widetilde{kis}$ are interregional differences in the population density, the patent intensity, the share of human capital, the employment share in manufacturing high-tech sectors and the employment share in knowledge-intensive services, respectively.

Including population density into $\mathbf{Z}2$ relates to urbanization effects from larger and dense markets as, e.g., reflected in corresponding measures used by Ritsilä and Ovaskainen (2001) and Faggian and McCann (2009a) and outlined in Table 1. The share of human capital in terms of a higher pool of skilled labor may, e.g., lead to Marshallian forces that result in a co-location of firms similar to Faggian and McCann (2009a) and Fu and Gabriel (2012). Patent intensities, the share of high-tech manufacturing and the share of knowledge-intensive services relate to the mechanisms outlined in, e.g., Faggian and McCann (2009b), Hunt and Gauthier-Loiselle (2012) and Parrotta et al. (2014). As such, the analysis includes a set of agglomeration economies relating to urbanization effects from market size, localization effects from production and knowledge spillovers among firms generating a cumulative learning process in a region. More generally, this renders a spatial dependence of knowledge production and spillovers including inputs in the form of human capital and business structures and outputs in terms of patent intensities.

Given that the migration equation in Eq. (6) is specified as a dynamic panel data models, the inclusion of the lagged endogenous variable among the set of regressors results in a built-in correlation between this variable and the error term, which, in turn, may bias the estimation results (see, e.g., Nickell 1981; Baltagi 2008). We thus use a bias-corrected estimator in the spirit of Kiviet (1995) for the estimation of the dynamic model in Eq. (6). Moreover, we will sequentially extend the baseline migration specification from Eq. (6) from two further modelling perspectives. Firstly, we will allow for the possibility of a regime change in the determinants of in-migration-induced population growth among high- and low-skilled migrants. The use of regime-switching models in the field of regional science is rather new (see, for instance, Lambert et al. 2014). There are different classes of regime-switching models, which can be classified according to the smoothness of the underlying transition process as well as whether the state determining variable G can be observed or has to be estimated. In our case, we use a simple approach based on observable differences in the skill level of migrations, which can be estimated by means of a linear regression model with dummy variables $D_{edu}$ as outlined in Eq. (7)

$$\begin{aligned} mig=\iota +\alpha \left( {L.mig} \right) +L.\mathbf{Z}1\beta _1 +L.\mathbf{Z}2\beta _2 +D_{edu} \cdot L.\mathbf{Z}1\delta _1 +D_{edu} \cdot L.\mathbf{Z}2\delta _2 +\mu +\lambda +\varepsilon . \end{aligned}$$

(7)

Here, the main difference compared to Eq. (6) is that we interact each variable in the two variable matrices Z1 and Z2, with a binary dummy variable for two high-skilled education strata ($D_{edu}$) representing the transition process. The dummy takes values of one if we are observing the net in-migration rate for high-skilled education groups and is zero otherwise. The coefficient vectors $\delta _1$ and $\delta _2$ then measure the extra migration response of high-skilled education groups on top of the overall migration response measured by $\beta _1$ and $\beta _2$. Thus, if the null hypothesis of joint statistical insignificance of $\delta _1 =0$ and $\delta _2 =0$ cannot be rejected, we can interpret the results as no observable regime change in the behavioral response of high and low-skilled migrants. Due to the multi-level structure of our data arrangement, we computed clustered standard errors across education strata and municipalities.

Secondly, since spatial dynamics may be an important source of estimation bias, in addition to the included time lags according to the partial adjustment model, we also include spatial lags of the regressand and regressors. This can be motivated by potential knowledge spillovers or other mechanisms generating spatial dependence across municipalities. As Eq. (8) shows, our model thus takes the form of a spatial Durbin model (SDM), which allows for different spatial patterns among the variables. Since the model in Eq. (8) only includes a contemporaneous spatial lag of the dependent variable ($\mathbf{W}mig)$, it is also referred to as space–time simultaneous model (see Anselin et al. 2007). The spatial weighting matrix $\mathbf{W}$ is specified as a queen-type first-order contiguity matrix. The SDM is estimated by means of a bias-corrected ML approach as proposed in Lee and Yu (2010) for fixed effects panel data models. Including spatial lags, Eq. (7) becomes

$$\begin{aligned} mig= & {} \iota +\rho \left( {\mathbf{W}mig} \right) +\alpha \left( {L.mig} \right) +L.\mathbf{Z}1\beta _1 +L.\mathbf{Z}2\beta _2 +D_{edu} \cdot L.\mathbf{Z}1\delta _1 \nonumber \\&+\,D_{edu} \cdot L.\mathbf{Z}2\delta _2+L.\mathbf{W}\left( {\mathbf{Z}1} \right) \beta _3+L.\mathbf{W}\left( {\mathbf{Z}2} \right) \beta _4 +D_{edu} \cdot L.\mathbf{W}\left( {\mathbf{Z}1} \right) \delta _3\nonumber \\&+\,D_{edu} \cdot L.\mathbf{W}\left( {\mathbf{Z}2} \right) \delta _4 +\mu +\lambda +\varepsilon . \end{aligned}$$

(8)

The SDM specification in Eq. (8) captures the mutual dimensions of spatial dependence in the migration equation through spatial lag terms for both the regressand and the set of regressors, which are defined as weighted averages of values in the immediately neighboring of region i for variable x at time t. The spatial lags are accordingly defined as $\mathbf{W}x_i =\sum \nolimits _{j=1}^N w_{ij} x_j$ with N being the total number of regions and $w_{ij}$ are the elements of the spatial weighting matrix $\mathbf{W}$ with a value of 1 if region i and j are contiguous and 0 otherwise. We use row standardization of $\mathbf{W}$ in the calculation of the spatial lag terms.⁶ Since the SDM specified in Eq. (8) is typically characterized by a high degree of simultaneity and complexity, the corresponding regression output cannot be straightforwardly interpreted. Instead, meaningful marginal effects have to be computed. LeSage and Pace (2009) propose a set of reduced-form summary measures for calculating the average direct $\left( {\partial y_i /\partial x_i } \right)$ and spatial indirect $\left( {\partial y_i /\partial x_j } \right)$ marginal effect on the model’s dependent variable $\left( y \right)$ for changes in different locations (i, j) of each regressor $\left( x \right)$ calculated as

$$\begin{aligned} {\bar{M}}_{direct}= & {} \frac{1}{N}tr\left( {S_r \left( \mathbf{W} \right) } \right) \end{aligned}$$

(9)

$$\begin{aligned} {\bar{M}}_{indirect}= & {} \left[ {\frac{1}{N}z^{\prime }S_r \left( \mathbf{W} \right) z} \right] -\left[ {\frac{1}{N}tr\left( {S_r \left( \mathbf{W} \right) } \right) } \right] \end{aligned}$$

(10)

where $S_r =\left[ {\left( {1-\alpha } \right) \mathbf{I}_N -\rho \mathbf{W}} \right] ^{-1}\left( {\epsilon \mathbf{I}_N +\tau \mathbf{W}} \right)$, $\epsilon$ is a vector of parameter estimates stacking $\beta _{1}, \beta _{2,} \delta _{1}, \delta _{2 }$ and $\theta , \tau$ is a vector stacking $\beta _{3}, \beta _{4}, \delta _{3}, \delta _{4}$, while z is a ($N \times 1$)-vector of ones and $\mathbf{I}_N$ is an identity matrix of dimension N. Since the standard errors cannot be calculated from standard regression output of the SDM, we follow Elhorst (2014) in simulating the standard errors of direct, indirect and total marginal effects based on the variance–covariance matrix from estimating Eq. (8). In the simulations, for a draw f, a particular combination of $\rho , \epsilon , \tau$ and $\sigma ^{2}$ is obtained from the variance–covariance matrix given by⁷

$$\begin{aligned} \left[ {\rho _{f} ,\epsilon _{f} ,\tau _{f} ,\sigma _{f}^{2} } \right] = P^{\prime }\vartheta + [\hat{\rho } ,\hat{\epsilon } , \hat{\tau } ,\widehat{\sigma ^{2}}] \end{aligned}$$

(11)

where “hats” indicates that parameters arrive from the SDM estimation, P is an upper triangle Cholesky decomposition of $Var\left( {\hat{\rho } ,\hat{\epsilon } ,\hat{\tau } ,\widehat{\sigma ^{2}}} \right)$ and $\vartheta$ is vector containing random numbers from a normal distribution with $\vartheta =\hbox {N}(0,1)$. With $f=1,{\ldots },F$ parameter combinations being drawn from the SDM estimation of $\left( {\hat{\rho } ,\hat{\epsilon } ,\hat{\tau } ,\hat{\sigma ^{2}}} \right)$ and plugging in the resulting outcomes using Eq. (8) into Eqs. (9), (10) and (11) render F values of ${\bar{M}}_{direct}$ and ${\bar{M}}_{indirect}$. The simulated effect can be calculated by the mean value over these F draws of ${\bar{M}}_{direct}$ and ${\bar{M}}_{indirect}$ and the significance level (t-statistic) is obtained from dividing this mean with its corresponding standard variation (Elhorst 2014). This is the empirical strategy followed in estimating Eq. (8), which has the advantage of rendering both direct (local) and spatial indirect marginal effects allowing for an assessment of whether effects are purely local by nature or run through wider neighborhood sets of macro regions as specified in the contiguity matrix. Again, we test for the joint significance of $\delta _3$ and $\delta _4$ in order to check for a regime change in the spatially indirect migration effects between high- and low-skilled net migrants.

Finally, in order to assess the importance of feedback effects of the migration response to interregional income differences and disparities in unemployment rates, we add two separate equations for these variables as

$$\begin{aligned} {\tilde{y}}= & {} \iota +\rho _y \left( {\mathbf{W}{\tilde{y}}} \right) +\alpha _y \left( {L.{\tilde{y}}} \right) +L.\mathbf{Z}1\beta _{1,y} +L.\mathbf{Z}2\beta _{2,y} +L.\mathbf{W}\left( {\mathbf{Z}1} \right) \beta _{3,y} \nonumber \\&+\,L.\mathbf{W}\left( {\mathbf{Z}2} \right) \beta _{4,y}+D_{edu} \cdot \left( {L.mig} \right) \delta _{1,y} +D_{edu} \cdot \left( {\mathbf{W}L.mig} \right) \delta _{3,y} +\mu +\lambda +e, \nonumber \\ \end{aligned}$$

(12)

$$\begin{aligned} {\tilde{u}}= & {} \iota +\rho _u \left( {\mathbf{W}{\tilde{u}}} \right) +\alpha _u \left( {L.{\tilde{u}}} \right) +L.\mathbf{Z}1\beta _{1,u} +L.\mathbf{Z}2\beta _{2,u} +L.\mathbf{W}\left( {\mathbf{Z}1} \right) \beta _{3,u} \nonumber \\&+\,L.\mathbf{W}\left( {\mathbf{Z}2} \right) \beta _{4,u}+D_{edu} \cdot \left( {L.mig} \right) \delta _{1,u} +D_{edu} \cdot \left( {\mathbf{W}L.mig} \right) \delta _{3,u} +\mu +\lambda +\omega ,\nonumber \\ \end{aligned}$$

(13)

where e and $\omega$ are the error terms for the two equations. As for the case of the migration equation, the income and unemployment equations are estimated as partial adjustment specifications in an SDM framework in order to allow for spatial and time dynamics of the variables in focus and account for omitted variables and latent neighborhood effects. Again, direct, indirect and total simulated marginal effects are computed. The resulting three-equation model consisting of Eqs. (8), (12) and (13) is estimated in an equation-by-equation manner using limited information ML. As shown above, in Eqs. (12) and (13), we can only test for a regime change in the response of income and unemployment differences to the skill-specific migration variable and its spatial lag.

The simultaneity of migration, income and unemployment dynamics in the above labor market system may induce an endogeneity problem and hence prevent us from interpreting the regression results in a meaningful way. To give an example, the decision on whether and where to migrate is based on expectations regarding the regional distribution of income levels, which, in the case of selective migration, may be self-fulfilling (see Fratesi and Percoco 2014). While the use of one-period lagged regressors may not be sufficient to solve the underlying reverse causality issue, the use of instrumental variables can solve this estimation problem. For the purpose of this analysis, we make use of an IV strategy in the spirit of Card (2001) and Fratesi and Percoco (2014) based on instruments for each endogenous variable ($mig,{\tilde{y}},{\tilde{u}})$ as

$$\begin{aligned} \widehat{mig}_{s,i,t}= & {} mig_{s,i,t=0} \times I_{s,t}^m \end{aligned}$$

(14)

$$\begin{aligned} {\hat{{\tilde{y}}}}_{i,t}= & {} {\tilde{y}}_{i,t=0} \times I_t^y \end{aligned}$$

(15)

$$\begin{aligned} {\hat{{\tilde{u}}}} _{i,t}= & {} {\tilde{u}}_{i,t=0} \times I_t^u . \end{aligned}$$

(16)

where the time index $t=0$ indicates that interregional differences in migration, income and unemployment are taken from the initial sample period and kept fixed over time, which are then multiplied with aggregate/national time-varying indices in (skill-specific) gross mobility ($I_{s,t}^m )$, income evolution ($I_t^y)$ and unemployment ($I_t^u )$. The rationale for using these “natural” instruments as regressors in Eqs. (8), (12) and (13) of the labor market system is that they may represent overall trends in the variables while keeping the relative performance of regions unchanged at the initial sample year level. This restriction, in fact, should reduce the above-mentioned reverse causality issue, for instance, related to selective migration decisions. As Fratesi and Percoco (2014) point out, this type of instrument does not account for the potential endogeneity of the individual migration decision, but rather accounts for the exogenous spatial distribution of migrants. It is particularly of importance to consider the latter spatial distribution in order to study how regional labor market disparities affect and react to (selective) migration and vice versa.

4 Data and stylized facts

We use data for 95 Danish municipalities⁸ over the period 2006–2012 to estimate the above-sketched migration–income–unemployment nexus in a small-scale labor market model. The data are a unique combination derived from three types of sources. A first source is the official statistics for Danish municipalities produced by Statistics Denmark. These data include a broad range of socioeconomic indicators at the municipal level needed for the construction of the subsets of labor and housing market variables (Z1) as well as measures of agglomeration economies (Z2). Detailed information on the construction for each individual variable together with summary statistics is provided in Table 2. One restriction is, however, that no information is available prior to the year 2006 due to a large administrative reform consolidation 270 Danish municipalities into 98 larger units with at least 20,000 inhabitants.⁹

The second data source concerns micro level information on skill-specific migration flows across Danish municipalities. While aggregate migration rates among municipalities can be calculated on the basis of official statistics, skill-specific migration rates cannot be calculated on the basis of publically available data. To allow for such measures, we have accordingly turned to register data. Based on this type of data, we have calculated the “net in-migration rate” for each municipality by four different skill levels.¹⁰ These skill levels are (1) basic primary and secondary education, (2) vocational education, (3) shorter and intermediate further education and (4) university education. As such, these education levels reflect gradually longer educations and higher skill levels. We calculate the net in-migration rate for each municipality by skill level as

$$\begin{aligned} mig_{s,i,t} =\frac{nm_{s,i,t} +pop_{s,i,t-1} }{pop_{s,i,t-1} }, \end{aligned}$$

(17)

where i is an index for the municipality, s is an index of skill level, t is a time index, nm is absolute number of net migrants being the difference between gross in-migration and gross out-migration and pop is the population aged 15–65 for skill group s in municipality i at time t. The net migration rate used here can be interpreted as migration-induced population change for skill group s. The variable takes a value above 1 if net in-migration to a given municipality for a given skill level at time t is positive and hence increases the stock of population from the previous period $t-1$, but takes a value below one if net migration is negative.

Table 2 Description of variables used for estimation (calculated as regional differences and in logarithmic transformations)

A third data source is the OECD RegPat (version 2014) database from which the number of patent applications by Danish municipalities is extracted.¹¹ This information will be used do derive a proxy for the regional innovation activity of Danish municipalities. We have extract patent information at the ZIP code level based on the applicants’ addresses and have aggregate this information to the municipality level. Since ZIP codes are perfectly nested in the municipality level, an exact aggregation was possible. For the purpose of analysis, we then compute the municipality’s patent intensity as the number of patent applications per capita. Since patents are most commonly applied for by private companies or public institutions rather than individual persons (inventors), the use of patent applications can be seen as a workplace-related measure of agglomeration economies compared to variables such as population density and the regional concentration of human capital, which are measured by place of residence.

Fig. 1

Ten largest urban structures in Denmark

One has to note that the instruments used for IV estimations as defined in Eqs. (14)–(16) are also based on the definitions of net migration rates, income and unemployment rates in Table 2. As outlined in Sect. 3, we aim at testing for a potential regime switch among the migration response of high- and low-skilled migrants. This involves the calculation of interaction terms comprising each regressor defined in Table 2 and a skill-specific binary dummy variable ($D_{edu})$, which takes values of one if we are observing the net in-migration rate for persons with high skill levels and is zero otherwise. Based on the above classification, high skill levels are defined as persons with at least shorter and intermediate further education or university education.

To introduce the baseline urban structure in Denmark, Fig. 1 first presents the location of the ten largest urban centers in Denmark, where the national capital Copenhagen is the dominating urban agglomeration in terms of population size. Figure 2 furthermore presents the net migration rates for the year 2012 disaggregated by the four skill levels, as calculated using Eq. (17). The categories in Fig. 2 follow from a natural breaks procedure though adjusted such that one category has limit at 1. Recall that a net migration rate above 1 indicates migration-induced population growth.

Figure 2 illustrates two facts that have to be considered, when reflecting upon the urban structure in Fig. 1. A first is that the net migration rates for different skill levels render different spatial patterns. Positive net migration rates for some skill level in a municipality do not imply the same for other skill levels. Human capital therefore seems to render important spatial variation in net migration rates, which is an important aspect that will be tested through the regime-shifting variables. The other is that net migration rates do not have a clear monocentric focus in the sense that net migration is only positive in the larger Copenhagen area. Net migration has a more diverse spatial structure that has to be considered and offers a more diverse point of departure when considering policies and regional development potentials, which will be analyzed in more detail.

Fig. 2

Net migration rates among Danish municipalities by skill level, 2012. Source: Register data from Statistics Denmark and own calculations; see Table 2. Note: The municipalities of Fanø, Samsø and Læsø are not included and are in general left out of the analysis, as calculating net migration rates for these small municipalities would not be in accordance with confidentially rules of using the underlying registers. Even so, this does not imply that the analysis does not include island municipalities, as several other of such are included. Notice also that these three islands have for comparability been left out of Fig. 2

Turning to the spatial structure of income levels and unemployment rates, these can be found shown for 2012 in Fig. 3. Considering both Figs. 2 and 3, it becomes clear that there are important spatial patterns in terms of regional heterogeneity and possibly spatial dependence, which have to be considered in the course of estimation. The focus here will particularly be on possible agglomeration effects. The five variables indicating different types of agglomeration economies are for 2012 shown in Fig. 4 in the appendix. Furthermore, tests for the degree of spatial autocorrelation for the different variables using the space–time Moran’s I index (STMI) are presented in Table 7. The results show that spatial dependence is highly present and should be accounted for in the estimation approach.

Fig. 3

Income levels and unemployment rates among Danish municipalities, 2012. Source: See Table 2. Note: The island municipalities of Fanø, Samsø and Læsø have been left out when drawing Fig. 3

5 Empirical results

Turning to the estimation results, Table 3 displays the regression output for the different empirical specifications of the space–time dynamic migration equation according to Eq. (6) to Eq. (8). The reported coefficients for the non-spatial dynamic fixed effects (DFE) specifications in column one to column three in Table 3 are reduced-form marginal effects measuring the impact of an observational change in regressor (x) on the outcome variable (y). Specifically, the coefficients are given by $\partial y/\partial x=\beta /\left( {1-\alpha } \right)$, where $\beta$ is the estimated coefficient for each regressor x and $\alpha$ is the estimated coefficient for the included lagged endogenous variable (L.y) in Eq. (6) to (8). The reported coefficients for the spatial Durbin model (SDM) are the direct and spatial indirect reduced-form marginal effects as outlined in Eqs. (9) and (10) of Sect. 3.

The first column of Table 3 reports the estimation results for the basic adjustment model specification of Eq. (6) including the core set of labor market and housing market variables (Z1) and the set of measures proxying agglomeration economies (Z2). The model is estimated as a DFE specification with analytical bias correction in line with Kiviet (1995) for the estimated coefficient of the lagged endogenous regressor ($\alpha$). All regressors enter as one-period lagged variables to reduce the degree of simultaneity among the outcome variable and regressors. The estimates reported in column two extend the basic specification by industry-specific controls and time-fixed effects and the specification in column three additionally allows for the possibility of a regime change among low and high skilled migrants according to Eq. (7).

Table 3 Estimation results for space–time dynamic migration equation in sample period 2006–2012

In accordance with the theoretical expectations of the neoclassical migration theory, the results in column one show that the (one-period lagged) unemployment rate in region i relative to the Danish average appears to be negatively correlated with the outcome variable (mig), i.e., (skill specific) net migration-induced population change in municipality i. An above average unemployment rate in municipality i tends to reduce net migration-induced population change. However, contrary to the theoretical expectations of both the neoclassical migration theory and the NEG models, we observe a negative correlation between regional disparities in disposable income levels and net migration-induced regional population changes. Interpreted in the light of theoretical labor market models of migration, this theoretically unexpected empirical finding may indicate that the utility maximization approach of migrants during the time period of analysis puts a stronger weight on increasing their employment probabilities—as dominant regional labor market signal—rather than maximizing disposable income levels.

In fact, the logic of this latter result may be twofold: firstly, the estimated interregional migration response to regional unemployment differences is in accordance with a Danish labor market tightening in the period of economic downturn following the global financial and economic crisis of 2007. This period has seen a doubling of unemployment rates in Denmark, while income levels remained roughly constant caused by labor market agreements in the highly unionized economy with no or very low wage increases.¹² Second, the utilized measure of disposable regional income levels may only be partially related to regional wage signals.

In the case of Denmark being an elaborate welfare state resulting in redistribution of income among individuals and regions, this may also reflect regional differences in interregional transfers through tax-based redistribution. This may possibly hamper the effect of differences in disposable income on interregional migration (see, for instance, Schmidt 2013). Both mentioned factors may thus contribute to the explanation of the negative income coefficient found in column two of Table 3. With regard to the remainder labor and housing market variables including relative differences in house prices, crime rates and net commuting patterns, we do not find statistically significant conditional correlations with the net migration rate of Danish municipalities. Thus, from a neoclassical labor market perspective the core variables such as the regional difference in the unemployment rate appear to be the main determinants of internal population flows within Denmark for the period considered.

With regard to the importance of agglomeration economies (Z2) for the migration-induced population change, a rather clear picture emerges: with the exception of regional differences in the employment share of NACE 1.1 high-tech manufacturing industries ($\widetilde{hitec})$, all proxies for agglomeration economies exhibit a statistically significant positive correlation with the net migration rate. These positive conditional correlations are therefore in line with theoretical predictions from the NEG literature concerning the role of agglomeration economies and the regional innovation environment for attracting mobile labor. The revealed negative correlation between the net migration rate and regional differences in the employment share of high-tech manufacturing industries is likely to be driven by the recessive global business environment for the time period of analysis.

Particularly, manufacturing firms in Denmark over the period of the global financial and economic crisis have experienced marked reductions in employment. Given that high-tech manufacturing in some instance in Denmark is targeted towards a high-end market for B2C and B2B products, these firms may be more sensitive to increased cost awareness following the crisis. In contrast, the relative endowment of municipalities with workplaces in the field of knowledge-intensive services correlates positively with net migration rates. Finally, the results in column one of Table 3 show that temporal adjustment processes in migration rates matter as indicated by the positive and statistically significant adjustment parameter $\alpha$. This result hints at the role of persistent migration networks as indicated by earlier theoretical and empirical work.

As already indicated above, adjustments to global shocks stemming from the financial and economic crisis of 2007/2008 may interfere with the obtained regression results for our sample period. To further account for such time- and sector-specific shocks, the estimation output presented in column two of Table 3 additionally includes time-fixed year effects—controlling for common shocks to all Danish municipalities—as well as a set of industry-specific control variables based on regional differences in the employment shares of one-digit NACE industries.¹³ The estimation results in column two of Table 3 show that both time-fixed effects and industry-specific employment shares turn out to be highly statistically significant control factors in order to avoid estimation biases arising from global shocks.

Furthermore, the reported CD test according to Pesaran (2004) clearly shows that the inclusion of time-fixed year and industry effects significantly reduces the degree of cross-sectional dependence in the error term. While the augmented specification in column two of Table 3 increases the statistical validity of the model, the empirical results for the estimated coefficients of labor market and housing variables as well as agglomeration economies remain roughly stable compared to column one. One distinct difference is that we observe a statistically significant negative correlation between the net migration rate and regional differences in crime rates. This result indicates that higher crime rates reduce regional attractiveness and net in-migration flows, which is in line with migration theories focusing on the role of regional amenities (see, e.g., Greenwood et al. 1991).

As outlined by the NEG theory, agglomeration-induced migration patterns may be heterogeneous for different skill groups. In column three of Table 3 we therefore test for the statistical significance of a regime change in the migration response to changes in labor market variables and agglomeration economies according to Eq. (7). However, the joint F tests for $H_0\!:\delta _1 =0$ and $H_0\!:\delta _2 =0$ reported in column three of Table 3 do not reject the null hypothesis of coefficient homogeneity in the migratory response among low- and for high-skilled migrants. Hence, we cannot reject that migration responses to the different regressors are the same for different skill levels, which indicates that migration patterns of Danes are to a high degree correlated with the same “push” and “pull” factors irrespective of skill level or human capital. This may be interpreted in the context of Denmark being a small and relatively homogenous country, which may reflect upon the diversity of factors that are important when considering expected utility of migration choices.

Further, the columns four and five in Table 3 extend the DFE model to a space–time dynamic specification, where the spatial modelling is assumed to be of a spatial Durbin model type (SDM-DFE). In order to meaningfully interpret this space–time dynamic specification, we report the above-described summary measures for direct and spatial indirect reduced-form marginal effects together with simulated standard errors for the net migration rate specification according to Eq. (8). Note that although the spatial econometric literature commonly refers to the notion “effect,” these direct and indirect summary measures still only reflect conditional correlations. The SDM model does not account for all types of simultaneity and endogeneity potentially arising in this small-scale labor market system. IV estimates accounting for reversed causality among migration and labor market variables will be reported as robustness checks in the next section.

The spatially extended regression specification in columns four and five mainly supports the non-spatial DFE estimates in columns one to three and points to the fact that the migration determinants are mainly of a “direct” or local nature. That is, interregional differences in income levels and unemployment rate disparities, as well as the relative employment share in high-tech manufacturing industries, are found to be negatively correlated with migration-induced regional population changes. Furthermore, in line with the results in the first three columns, there is a statistically significant positive correlation for interregional differences in the population density, the patent intensity, the endowment with human capital as well as the employment share of knowledge-intensive services with migration-induced regional population changes. With regard to spatially indirect effects, we only observe a negative neighborhood effect for regional differences in house prices. This may possibly hint at the existence of macro regional clusters with a common house price dynamics given that some of the municipalities are quite small in terms of land area. This especially applies in the capital region of Copenhagen. From a theoretical perspective, the estimated negative effect is in line with most migration theories modelling house prices as a cost factor in the prospective migrant’s utility-maximizing decision-making process (see, for instance, Gabriel et al. 1992; Potepan 1994; Bitter 2008).

Finally, testing for the presence of a regime change for the quantitative importance of different determinants among low- and high-skilled migration patterns, the estimation results of column four and five for the SDM-DFE in Table 3 indicate that we can only reject the null hypothesis of coefficient homogeneity for the subset of spatially lagged regressors based on measures for agglomeration economies ($H_0\!:\delta _4 =0)$. If we take a closer look at the individual regression coefficients,¹⁴ the observed heterogeneity across skill groups is predominately driven by a statistically significant negative coefficient for the interaction term between the high-skilled education dummy and the spatial lag of the relative regional employment shares in high-tech manufacturing sub-sectors. This potentially indicates that high-skilled migrants more strongly respond to changes in the interregional employment distribution of high-tech manufacturing sectors for the time period 2006–2012. Overall, this negative labor market signal stemming from regional concentrations of high-tech manufacturing employment reflects the overall sectoral dynamics for Denmark in this period: while high-tech manufacturing sectors reduced the total number of employees by roughly 3.8 % in the time period of 2006 to 2012, the sector aggregate of knowledge-intensive services increased employment levels by roughly 3.1 %. A positive coefficient for the interaction term between the high-skilled education dummy and the regional differences in human capital endowments can furthermore be observed. Albeit statistically significant only at the 10 % confidence level, this result hints at the fact that highly skilled migrants are attracted by larger regional endowments with human capital across Danish municipalities.

Table 4 Space–time dynamic specifications for interregional income and unemployment rate differences

The estimation results of Table 4 extend the empirical analysis to an investigation of feedback effects running from the migration variable to regional labor market signals. For this reason, explicit equations for interregional differences in disposable income levels according to Eq. (12) and interregional disparities in unemployment rates according to Eq. (13) have been estimated in the spirit of the core migration equation. That is, both equations contain the same set of regressors (Z1, Z2) and are estimated by means of a SDM-DFE approach.¹⁵ The reported coefficients in Table 4 are again reduced-form direct and spatially indirect marginal effects. For the outcome variable of the relative disposable income level in municipality i relative to the Danish average reported in column one and two of Table 4, the regressions show a statistically significant correlation with the regional net migration rate, regional differences in crime rates and population density. While the latter exhibits both a direct and spatially indirect negative correlation with the region’s relative disposable income level relative to the Danish average, the net migration rate is found to have a positive direct and spatial indirect correlation with interregional income differences.

At first sight, this reported positive correlation hints at an amplification of interregional inequalities as predicted by NEG-type theoretical models given the fact that net migration inflows increase relative to income levels. One has to bear in mind, though, that the estimated relationship of regional income differences on the net migration rate was found to be negative in first place. That is, in a first step initial income differences across Danish municipalities drive migration flows to regions with lower income levels, while controlling for the other influencing variables. In a second step, a positive feedback effect of the net migration rate on the region’s relative income level can then be carefully interpreted in terms of an equilibrating effect of labor migration. However, this only holds conditional on the revealed positive effect of agglomeration economies on the net migration rate, which would favor a NEG-type of spatial adjustment processes.

Moreover, as the example of a positive correlation between relative regional income levels and regional differences in crime rates shows, one has to be very careful in terms of giving these obtained correlations a “causal” interpretation. In fact, the positive correlation of the latter crime and income variables rather hints at the fact that increasing relative crime rates are a “reflex” of high regional income levels rather than its “cause.” This holds especially in the presence of time-persistent simultaneity among the included variables, which cannot be ruled out by simply lagging the set of regressors by one period. For this reason, robustness tests based on instrumental variable (IV) estimation will be given in the next section.

Finally, similar results are obtained for the unemployment rate equation in column three and four of Table 4. Here, there is a statistically significant negative direct and spatially indirect correlation between interregional differences in the unemployment rate and relative regional employment shares in knowledge-intensive services. A statistically significant negative direct correlation is also found for the region’s endowment with human capital. These results are in line with the estimated migration equation underlining the negative nexus between the net migration rate and regional unemployment rate disparities and its common determinants. That is, while net migration flows are positively affected by regional differences in human capital endowments and employment shares in knowledge-intensive services, the opposite holds true for a region’s relative unemployment rate vis-à-vis the Danish averages.

Moreover, as shown in column four of Table 4, we get evidence for statistically significant negative spatially indirect correlation between the region’s relative population density and the unemployment rate. This indicates that region’s in the vicinity of densely populated municipalities may benefit in terms of lower unemployment rates due to a common labor market. Interestingly, from the point of view of innovation, interregional differences in patent intensities do not enter significantly in the columns one and two of Table 4. Rather, innovation measured by interregional differences in patent intensities influences interregional differences in income levels indirectly, as interregional differences in patent intensities correlate positively with differences in net migration rates and differences in net migration rates correlate positively with differences in income levels. The estimation results also show that both the income and unemployment rate equation are driven by strong spatial autocorrelation effects, hinting at the existence of spatial clusters of regions with similar income levels and unemployment rates, as well as underlining the role of adjustment processes and persistence over time.

6 Robustness checks

In this section, we report two types of sensitivity checks in order to test the robustness of the benchmark estimation results for the migration–income–unemployment nexus reported in Tables 3 and 4. As a first sensitivity test, Table 5 shows the response of the net in-migration rate to labor market signals and agglomeration economies for age-specific subsamples of migrants (aged 15–34 and 35–65). A disaggregated look at the determinants of young and old age groups is motivated by previous research showing that especially young cohorts of the population are very mobile and may respond stronger to labor market variables compared to older age cohorts (see, for instance, Mitze and Reinkowski 2011).

Table 5 Estimation results for space–time dynamic migration equation based on age-group subsamples

The SDM-DFE estimation results in Table 5 underline basically two facts: firstly, for both age-specific subgroups the migration response shows a quantitatively similar negative conditional correlation with regional income disparities and the regional distribution of high-tech manufacturing employment, while migration-induced population changes for both age groups are positively related to regional differences in the patent intensity. Secondly, while we observe a positive correlation between the net migration rate and the region’s relative endowment with human capital for the young age cohort, the group of older migrants shows a statistically significant positive correlation with the region’s overall population density and a negative correlation with the region’s crime rate.

This result relates to the issue that different agglomeration economies may attract mobile labor to a different degree over the migrants’ lifetime. Young migrants may have a particular focus on innovative and dynamic workplaces as indicated by the strong direct correlation with the region’s patent intensity. Older migrants with established work-related networks may on the other hand particularly seek to exploit more general urbanization advantages as indicated by the positive correlation of the net migration rate of the older age group with the population density. Additionally, a negative spatial indirect effect of regional differences in house prices on the net migration rate of young migrants may reflect income restrictions of young migrants in early stages of their career. However, as argued before, causal interpretations of these differences across age groups should be carried out only to a limited extent given the above-mentioned issues of the estimation approach.

As for the overall migration specification and Tables 3 and 4, there is only very limited support for a regime change between the determinants of age-specific migratory flows among low- and high-skilled migrant. Only for the age group 35–65, can it be observed that high-skilled migrants are positively affected by regional employment shares of high-tech manufacturing industries. Recall that this was found to be negatively correlated with overall interregional net migration flows in Denmark. Thus, while there are some minor “quantitative” differences in the migration response, taken together, at the aggregate regional level we do not observe a specific heterogeneity with regard to both the skill level of migrants and their underlying age structure.

The second type of sensitivity analysis tackles the issue of a potential simultaneity bias in the estimation of the small-scale labor market system according to Eqs. (8), (12) and (13). Although the estimation approach in Tables 3 and 4 has attempted to reduce the problem of reversed causality and omitted variables by including one-period lagged regressors as well as spatial lags, we still cannot interpret the obtained direct and indirect effects as “causal impacts.” This limitation can be directly related to the argumentation of Fratesi and Percoco (2014) pointing out that—in a simultaneous labor market system—the decision of where to move is often made on the basis of expectations concerning regional income prospects, which, in the case of selective migration, may then turn out to be self-fulfilling.

Table 6 IV estimation results for small-scale labor market system of Danish municipalities in 2006–2012

For this reason, we estimate the three-equation labor market system constituted by Eqs. (8), (12) and (13) by means of instrumental variables as outlined in Sect. 3. The instruments arrive from fixing the initial differences in regional disparities in net migration rates, income and unemployment differences at values for the initial sample period in 2006 while accounting for the aggregate dynamics in the Danish labor market for the sample period until 2012. As the estimation results in Table 6 show, the use of natural instruments according to Eqs. (14)–(16) results in only small qualitative and quantitative differences compared to the basic estimation results for the SDM-DFE approach in Tables 3 and 4. With regard to the migration equation, this basically holds with the exception of the estimated coefficient of regional income differences, which now turns out to be statistically insignificant. That is, initial regional differences in income levels in combination with the overall income dynamics in Denmark are not a significant determinant of the net migration rate in the period until 2012.

Moreover, the estimation results show a positive indirect effect stemming from regional differences in the unemployment rate on migration-induced population changes. This indicates that initial regional differences for this labor market signal affect the interregional migration decision of Danish residents. This positive indirect effect may reflect a “poaching-effect” among neighboring municipalities. That is, if the migration decision can be seen as a hierarchical two-stage selection process (see, for instance, Fotheringham 1983; Hu and Pooler 2002), where the prospective migrant first selects the broader macro region as preferred in-migration destination and then, in a second step, finally selects the specific destination municipality within this macro region, an increase in the relative unemployment rate in municipality j may increase the inflow of migrants to municipality i, if the latter has become more attractive relative to its neighbor in the second stage of the selection process. Thus, a positive spatially indirect effect for the migration response to changes in the relative regional unemployment rate in neighboring regions would be consistent with utility-maximizing migration decisions.

In line with the benchmark regression results for the income equation in Table 4, we still observe a positive feedback effect from the net migration rate on regional differences in disposable income levels. The negative effect of income differences in the migration equation has been cancelled out in the IV estimation approach, while the strong effect of agglomeration economies on the net migration rate is still present. The estimated positive effect of the net migration rate on regional differences in income levels may thus support the predictions of NEG-type theories of a circular process of cumulative causation. However, obviously a longer time period for estimation would be an advantage in order to fully assess the above-sketched mechanism.

Taken together, the reported estimation results and robustness checks underline the basic hypothesis of the “new” migration literature pointing to the importance of different types of agglomeration economies as influencing factors of labor mobility. We find significant effects on net migration from general measures of agglomeration economies as the region’s relative population density, indicating an ongoing process of urbanization in Denmark, and specific measures related to the region’s innovation performance measured by the patent intensity, the regional endowment with human capital and the employment share of creative, knowledge-intensive business. Interestingly, we do not find evidence for particular migration regimes at the regional level, when controlling for the skill level of migrants or the age structure. Here, future research should attend this result in more detail through other approaches of analysis.

7 Policy discussion and conclusion

Migration theories have traditionally focused on the role of regional labor market signals, amenities and housing markets to explain internal migration flows and therefore result in migration-induced population changes. In the context of changing demographic structures with an ongoing aging process of population and lower fertility rates in most European countries, theoretical and empirically driven studies of the causes of migration and its role for balancing demographic and labor market disequilibria among regions have thus become increasingly important. Furthermore, migration flows associated with specific competences and human capital levels can be seen as vital in ensuring regional competitiveness in terms of income levels, job creation and low unemployment. Accordingly, the focus of this empirical investigation has been on the (inter-) regional migration–income–unemployment nexus.

Based on modern theories on agglomeration economies, the paper focuses on the role played by different types of agglomeration economies for this nexus among Danish municipalities in the period 2006–2012. Conceptualizing the role of agglomeration rate economies in the process of knowledge-driven regional development, both input factors in terms of human capital endowments and output factors in terms of patent applications may be important in that respect, as different types of spillovers may arrive at different stages rendering externalities and localization effects in the course of regional development. Furthermore, the role of market size and general urbanization advantages has to be taken into account, which mainly arises from functional specialization, labor market pooling and forward-backward linkages across industries in densely populated urban areas.

The empirical strategy taken here has been to estimate a small-scale labor market system with functional equations for the region’s net migration rate, relative income levels and unemployment rate with the potential of feedbacks among these three outcome variables of the system. This system has been estimated allowing for space–time dynamics dependence and as such may reveal cumulative causation among initial regional endowments with agglomeration factors, labor mobility and mobility-driven income evolution. The use of a space–time dynamic approach also allows for an identification of the extent to which agglomeration economies and other factors arrive from spatial dependence among the geographical entities or whether these are predominantly local with regard to the individual sample regions. Finally, as there are possible issues of endogeneity and simultaneity, these specifications have been combined with an instrumental variable approach.

Pertaining to the fact that spillovers are often at the core of agglomeration economies, the results show that a set of different variables associated with agglomeration economies indeed appears to be crucial for regional migration-induced population growth. If we first consider the role of local linkages excluding spatial indirect neighborhood effects, here the relative regional endowment with human capital, share of knowledge-intensive services and patent intensities are all important for migration-induced population growth. Furthermore, population density—associated with general urbanization effects—is also found to be positively correlated with a region’s net migration rate. Interestingly, these factors associated with more modern theories of migration seem to render more robust results compared to neoclassical theories, as factors such as difference in unemployment rates and income levels do not seem to be robust across different specifications. Given these results are all purely local, this points to the importance of local spillovers and externalities as measured by these variables.

Turning to indirect effects through spatial neighborhood linkages, the results in terms of significant estimates are scarce. Exceptions are regional differences in housing prices and unemployment rates, which can be potentially interpreted in terms of a hierarchical two-stage information process, where the prospective migrant first selects the broader macro region as preferred in-migration destination and then, in a second step, finally selects the specific destination municipality within this macro region based on regional attractiveness (e.g., low unemployment rates). Finally, modelling a system of equations allows for the assessment of cumulative causation. Agglomeration forces driving migration-induced population growth sets off a process, where mutual feedbacks between migration-induced population growth and income levels thereupon result in a circular process of cumulative causation. The importance of this is stressed by the interesting result for a small labor market system that innovation outputs in the form of patent intensities have a first-order effect on net migration rates and only appear to have a positive effect on income in a second-order effect through the net migration rate. These results underline the hypothesis that agglomeration economies are an important attractor for mobile labor and that this does seem to render a cumulative process in a local labor market system.

From a regional policy perspective, which aims to attract/canalize mobile labor flows, these results point to the importance of strengthening local agglomeration economies. An important aspect in that respect is the support to regional innovation processes in order to increase patent intensities and build a base for a stronger presence of human capital. In the Danish context, numerous efforts have been undertaken policy wise to underline this innovation-driven development process. Particularly on agglomeration economies associated with human capital and innovation, policies supporting a wider imputation of knowledge into firms through different employment patterns have been established. Specifically, programs such as wage subsidies for “knowledge pilots” for SMEs and for industrial Ph.D. programmes have been implemented. Such initiatives have recently SMEs strategically been placed in a concerted effort under an Innovation Fund, which have similar initiatives under an “InnoBooster”-program. The results found here point to some important issues, when designing such programs and subsidies. While such initiatives may be beneficial in general, designing them in a manner that builds on establishing effects through agglomeration economies may render these even more effective allowing for cumulative processes in local labor market systems. Furthermore, the results point to some important aspects of regional policies with respect to making different locations attractive from the viewpoint of migration-induced population change and associated economic development. Innovation appears to be a crucial driver of such dynamic processes. At the same time, in the a Danish context of increasing monocentricity focusing on the capital region, it finally also points to some of the factors that should be observed in an attempt of ensuring a more diverse development pattern in a wider geography.

Appendix

See Fig. 4 and Table 7.

Fig. 4

Measures of agglomeration economies among Danish municipalities, 2012. Source: Register data from Statistics Denmark and own calculations; see Table 2

Table 7 STMI test statistic for univariate spatial autocorrelation in sample variables