Regional Dependencies and Local Spillovers: Insights From Commuter Flows

Krause, Melanie; Kripfganz, Sebastian Article — Published Version Regional Dependencies and Local Spillovers: Insights From Commuter Flows Journal of Regional Science Provided in Cooperation with: John Wiley & Sons Suggested Citation: Krause, Melanie; Kripfganz, Sebastian (2025) : Regional Dependencies and Local Spillovers: Insights From Commuter Flows, Journal of Regional Science, ISSN 1467-9787, Wiley, Hoboken, NJ, Vol. 65, Iss. 3, pp. 565-585, https://doi.org/10.1111/jors.12752 This Version is available at: https://hdl.handle.net/10419/323886 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/4.0/ Journal of Regional Science RESEARCH ARTICLE Regional Dependencies and Local Spillovers: Insights From Commuter Flows Melanie Krause 1 | Sebastian Kripfganz 2 1 Faculty of Economics and Management Sciences, Leipzig University, Leipzig, Germany | 2 Department of Economics, University of Exeter Business School, Exeter, UK Correspondence: Melanie Krause ([email protected]) Received: 14 August 2023 | Revised: 17 September 2024 | Accepted: 16 December 2024 Keywords: commuting | shock propagation | spatial multiplier | spatial weight matrix ABSTRACT A region's growth trajectory is influenced by the economic circumstances of other regions in its proximity. While proximity is often understood in a geographic sense, economic connectivity can take many different forms. In particular, shock transmission processes between regions are inherently asymmetric and heterogeneous, which is not captured by geographic proximity measures. As a potential channel for economic dependencies, we consider cross‐regional commuter flows. Commuters, who spend a substantial portion of their income in a different place from where they earn it, connect peripheral regions to economic centers. In an econometric framework, we estimate time‐space dynamic panel models with German county‐level data. Given those estimates, we demonstrate a considerable variation in the spatial distribution of shock responses from using alternative proxies for spatial dependency, which is hidden by the traditional focus on average marginal effects. Local spatial multipliers differ depending on the nature and origin of the shock and the assumed network structure. JEL Classification: R12, C23, J61 1 | Introduction Economic differences can persist over a long time, not just across countries, but also within countries. An important aspect of economic development is that regions are often closely interconnected in various ways, and therefore their development is not independent from one another. In the textbook Solow– Swan neoclassical growth model—and many of its extensions— these dependencies are left aside. The speed of convergence is purely determined by a region's distance from its own steady‐ state equilibrium. In recent years, a stronger focus has been placed on cross‐ sectional dependencies in the form of local and global externalities. The source of these spillovers can be in the accumulation of physical and human capital in neighboring regions (Carrington 2003), in direct contributions to each other's total factor productivity (Egger and Pfaffermayr 2006), in technological interdependence (Ertur and Koch 2007), or in factor mobility (Pfaffermayr 2012). Economic adjustment processes are then determined by the location in space and the strength of the interregional linkages. However, these spatial Solow models remain silent about the determination of the spatial network structure. In the empirical literature, the connectivity between spatial units is often modeled in an ad hoc way as a function of their geographic distance, sometimes limited to units sharing a common border (Anselin 1988; Anselin and Bera 1998). This is based on the rationale that geographic distance is an acceptable proxy for underlying economic linkages. However, geographic connectivity measures cannot account for the heterogeneity in the economic relationships. Economic activity is often geographically clustered due to comparative advantages of a certain region—such as the availability of skilled workers, a business‐friendly regulatory framework, and existing infrastructure. Some regions are gravitational centers This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2025 The Author(s). Journal of Regional Science published by Wiley Periodicals LLC. 565 of 886Journal of Regional Science, 2025; 65:565–585 https://doi.org/10.1111/jors.12752 which substantially influence the surrounding satellite regions, without much feedback in the opposite direction. Various studies have found empirical evidence that spatial spillover effects may be asymmetric; technologically advanced areas influence those with lower human capital (Benhabib and Spiegel 1994) or lower total factor productivity (Siller et al. 2021), but hardly vice versa. Such an asymmetry of regional spillover effects cannot be captured by geographic contiguity. Instead, connectivity measures should reflect the gravitational forces. While those forces are inherently latent, it is often possible to find economic or socioeconomic proxies for them. In this paper, we investigate in the context of an econometric framework how approximating the regional linkages by commuter flows as an alternative to geographic distance affects the estimation of dynamic adjustment processes. Similar to the assumptions made by Benhabib and Spiegel (1994) and Siller et al. (2021), commuter flows create asymmetric dependencies between economic “leaders”and “followers.”Rather than developing a full‐fledged structural model, we consider an empirical case study and highlight substantial differences depending on the assumptions about the spatial network. Using the bias‐corrected maximum likelihood estimator of Yu, de Jong, and Lee (2008), we estimate a time–space dynamic growth convergence model with spatial weight matrices based on either commuter flows or geographic connectivity. Subsequently, we compute spatial multipliers for counterfactual scenarios in which we assign treatment—a hypothetical shock or policy intervention—to small groups of counties. Our analysis demonstrates that the distributional effects of a shock or intervention depend considerably on which counties receive the treatment and on the assumed network structure. When spillovers are realized through commuter connections, the strongest effects are achieved by assigning treatment to counties which act as gravitational centers. In contrast, with geographic spatial weights the economic characteristics of the treated counties are irrelevant; and the strength of the multiplier effects is solely determined by the location and proximity of the treated counties. Importantly, we do not claim that commuter flows are necessarily a better proxy for regional dependencies than geographic distance. Since the true linkages are unobserved, the empirical model will be misspecified in either case. Conventional standard errors and confidence intervals only reflect sampling uncertainty, but they do not account for the model uncertainty regarding the correct spatial network structure. We therefore advocate for a comparison of results obtained with different spatial weights, to grasp the range of possible effects. In this regard, alternative network specifications can be seen as complements rather than substitutes. We construct a spatial weight matrix based on commuter data because commuter flows are a natural choice for measuring interregional connectivity at the local level. Interregional commuters earn their money in one place and spend a significant portion of it in another place, thereby contributing to important links between regions. Proost and Thisse (2019) provide an overview on the role that commuting plays in urban economics and regional science. The classical case is commuting within cities in the canonical Alonso–Mills–Muth model (Alonso 1964; Mills 1967; Muth 1969) and its extensions (Duranton and Turner 2011; Ahlfeldt et al. 2015). Yet, commuting across regions is also increasingly becoming the subject of the theoretical literature. In models of the New Economic Geography literature, regions are not only connected by trade flows and spatial knowledge spillovers, but also by commuter flows (Allen, Arkolakis, and Li 2015). Monte, Redding, and Rossi‐ Hansberg (2018) demonstrate that spatial interactions through commuting can determine local economic effects of labor market shocks. In fundamental contrast to geographic distance, a commuter flow network implies a shock transmission mechanism which is predominantly one‐way, while allowing for substantial geographic heterogeneity. In many countries, an increasing number of people work in a different place from where they live. Large numbers of interregional commuters are found particularly in countries where economic activity is relatively decentralized, the distances are not too large, and the infrastructure is solid. In the EU, on average 6% of the employed working‐age (15–64 years) population commuted to a different Nomenclature of Territorial Units for Statistics (NUTS) 2 region in 2020. Belgium topped the list with 21% countrywide, and up to 49% for some Belgian provinces. 1 At the smaller county level—NUTS 3 regions— these numbers are considerably higher. As there is no EU‐wide data collection on commuting at this level of disaggregation, we restrict our attention to Germany, for which sufficiently long origin‐destination commuter flow time series can be obtained. We investigate the different shock transmission implications of commuter‐based and geography‐based spatial linkages with panel data on German counties, covering the time span from 2002 to 2017. For most of our sample period, real GDP per capita shows statistically significant negative spatial autocorrelation when regional connectivity is measured through asymmetric commuter flows, but insignificant spatial autocorrelation when symmetric geographic weights are used. Germany is a suitable case in point for the role of commuters in regional convergence and economic shock propagation. It is a territorial state with a number of economic centers and considerable regional variation in terms of prosperity. The eastern part experienced strong catch‐up growth in the 1990s and 2000s, but as a whole is still lagging behind. Meanwhile, there are both economic hubs as well as poorer regions in the south and west (Kosfeld, Eckey, and Dreger 2006; Colavecchio, Curran, and Funke 2011). In our data set, between 3% and 31% of a county's population was commuting to a different county. For the most attractive commuter destinations, the incoming commuter numbers even totaled up to 78% of their own population size. With our focus on commuter flows as proxies for spatial dependence, our paper is related to the empirical literature on regional economic convergence (see for instance Sala‐i‐Martín 1996; Badinger, Müller, and Tondl 2004; Fischer and Pfaffermayr 2018). The often rather coarse classification of regional units in the literature masks a considerable degree of heterogeneity and intra‐regional spillovers. The ties to other regions (relative to the size) tend to increase at a deeper level of disaggregation. This is also reflected in the observed commuting patterns. While there have been convergence studies at the county level—for example 566 of 886 Journal of Regional Science, 2025 Kosfeld, Eckey, and Dreger (2006) for Germany, Young, Higgins, and Levy (2008) for the US, and Cheong and Wu (2013)for China—these either did not explicitly model the dependencies across counties, or they relied on geographic proximity measures. With our work, we aim to bridge the gap between different strands of the literature: We transfer the insights on commuting from network and gravity models into spatial econometrics, where spatial weight matrices are typically purely based on geographic distances. Gravity models have a long tradition in modeling trade, migration, traffic or commuting flows (Lukermann and Porter 1960; Erlander and Stewart 1990; McArthur et al. 2011). As Niedercorn and Bechdolt (1969) motivate from a utility maximization framework, flows between two regions in gravity models increase with the size of their population and decrease with the distance between them. Hence, they vitally rely on geographic distance to rationalize flows in goods and people. Recent applications of gravity models include the prediction of commuter flows and travel times in Ireland (Ahrens and Lyons 2021) as well as Mexico (Duran‐Fernandez and Santos 2014), where the latter argue that distance should rather be measured in travel times than Euclidean distance. In fact, beyond pure distance, a number of other factors have been shown in the literature to matter for understanding commuter flows. Thorsen and Gitlesen (1998) point to specific labor market characteristics; Simini et al. (2021) use a deep learning framework to elucidate the role of the road network, transportation facilities, and land use in predicting mobility flows. Following these lines of thought, geographic distance is only one of the relevant factors which characterize gravitational forces. Commuter flows are closely linked to them as well. However, in contrast to the gravity model literature, our goal is not to predict commuter flows but to use them as a proxy for the connectivity of regions in our econometric analysis of shock propagation. Commuter networks have also been studied in network science (Barabási 2003;Amaraletal.2000). For German commuter data, Patuelli et al. (2010) find no substantial changes over the 10 years from 1995 to 2005, although they notice a slight trend towards a more distributed network structure and increased interconnectivity. Reggiani, Bucci, and Russo (2011) confirm the multi‐nodal structure as well as the stability of the German commuter flow network with data from 2003 to 2007, also pointing out that the most connected districts are large centers such as Hamburg, Berlin, Frankfurt, Munich, and Cologne in both years. The authors note a hierarchy of hubs, a phenomenon underlining the asymmetric nature of commuter flows. These are vital insights for our construction of the spatial weight matrix to capture economic shock spillovers. Networks based on commuter flows can be asymmetric, in contrast to the classical geography‐based networks. At the same time, the relative stability of commuter flows—which the data for our time periods also suggest—limits endogeneity concerns for our analysis. In our econometric setting, we analyze cross‐sectional spillover effects at the county level, which is also relevant from a policy perspective. Government interventions can have quite different local effects, depending on the economic conditions in a county and its interconnectedness with other counties. For example, consider subsidies for firms in a particular sector that are geographically clustered in certain locations. The regional general‐ equilibrium effects will be very different for subsidies to the agricultural sector compared to the financial or manufacturing sector; the provision of public goods in areas of high population density has different implications than in rural regions. Generally, the multiplier effects of an intervention in an economic center are stronger due to the spillover effects to economically dependent counties. While it may seem desirable to directly intervene in disadvantaged areas, this is unlikely to achieve the highest value for taxpayers' money. Conversely, targeting already prospering counties—with the aim to maximize the aggregate effect of an intervention—raises distributional concerns. This differential response to an initial stimulus is often overlooked in econometric studies, where it is common practice to report average effects. As we show in this paper, these distributional effects can differ substantially depending on the assumed spatial network. With geography‐based connectivity, economic centers and their periphery would be treated symmetrically. In contrast, spillovers generated by commuter flows (or other measures of economic dependence) can be very heterogeneous, which we would expect to better reflect the economic reality. 2 | Econometric Model and Methods 2.1 | Time–Space Dynamic Panel Data Model Spatial econometric methods have a long tradition in regional science and became established in mainstream empirical economics in recent decades. For the analysis of economic adjustment processes, the estimation of a time–space dynamic panel data model is becoming increasingly popular. Examples include studies of regional growth in Europe (Fischer and LeSage 2015; Fingleton 2020), Italy (Billé, Tomelleri, and Ravazzolo 2023), Korea (Evans and Kim 2014), and OECD countries linked through trade (Ho, Wang, and Yu 2013). In such a model, the growth trajectory of a region is determined by its own history and the growth path of other regions to which it is connected, reflecting persistence over time and spatial growth patterns. Due to sluggish production processes and inertia in economic environments, the impact of a shock is typically not fully absorbed immediately. This partial adjustment process can be modeled with lagged dependent variables. Besides its impact on the region where it originates, an economic shock also spreads through the network of connected regions with decreasing intensity, depending on the strength and direction of the linkages. We largely remain agnostic about the type of shock. The following econometric model can be derived from a standard growth model with Cobb–Douglas production function and spatial externalities (Ertur and Koch 2007): 2 y y Wy Wy Xπι αε θλ ρ γln = ln + ln + ln + + ++, tt NtNtttN t −1−1(1) tT=1,2,…, , where yyy y=( , ,…, ) ′ tttNt12 is a vector of real GDP per capita for counties i N=1,2,…, at time t . It is standard practice in the economic growth literature to use a logarithmic transformation for the dependent variable, which is consistent with the notion of a balanced growth path and allows to interpret the coefficients of the covariates as (semi‐) elasticities. The NN ×matrix W N is a (suitably normalized) 567 of 886 spatial weight matrix that governs the links between counties. The scalar coefficients θλ,, and ρ determine the strength of the temporal and spatial dependence. X t is an N K× matrix of covariates with coefficient vector π. ιN is an N × 1 vector of ones and the coefficients γt are common time effects to be estimated. The county‐specific effects ααα α=( , ,…, ) ′ N12 account for any unobserved time‐invariant characteristics. ε tis an N × 1 vector of idiosyncratic shocks. To facilitate the interpretation of the model's coefficients, it might be preferable to rewrite it in terms of GDP growth rates and initial GDP levels: yyWyWy Xπιαε θλλρ γ Δln = ( −1)ln + Δln + ( + ) ln ++++, tt NtNt ttNt −1− 1 (2) where Δ is the first‐differencing operator. y Δ ln t approximates the growth rate of real GDP per capita. 3 In the absence of spatial spillover effects, a value of ∈θ(0, 1) reflects conditional convergence; counties with a lower initial real GDP per capita level are catching up with wealthier regions by growing at a faster pace (conditional on differences in the explanatory variables X t and time‐invariant county‐specific differences captured by α ). Lower values of θ indicate faster convergence. Regarding the spatial terms, λ >0reflects the co‐movement of connected regions; a region benefits from being linked to other fast‐growing regions, or is constrained in its economic development by being dependent on other slow‐growing regions. The coefficient ρ measures the extent to which the initial conditions in connected regions matter for the convergence process. A positive value of ρ implies a phased response to changing economic conditions in other regions; a negative value of ρ indicates that any initial spillover effects are (partially) offset in the following period. The latter characterizes a situation in which the initial response to a shock in a neighboring region overshoots, followed by a subsequent correction. If this correction is imperfect, ρ λ>−, then having strong ties to other rich regions yields an additional boost for a region's catch‐up growth. 4 For our main estimation method,weneedtoassumestrictexogeneity of the covariates X t and the spatial weight matrix W N with respect to the innovations ε t. The latter are assumed to be independent and identically distributed with mean zero. The correlation between the observed variables and the unobserved time‐ invariant effects α i can be left unrestricted. We also assume that W N and all slope coefficients are constant over time. In principle, it would be desirable to allow for more flexibility. However, especially given a relatively short time horizon, allowing for time variationintheeffectsandspatial relationships becomes econometrically challenging. The same applies to the endogeneity of X t or W N with respect to the shocks ε t. In general, there is a tradeoff between parsimony/efficiency and feasibility/accuracy. We provide some discussion of these issues in the following subsections. 2.2 | Spatial Weight Matrices In a time–space dynamic panel data model, the spatial weight matrix is crucial for capturing the links between the units. In our study, we estimate the model with different spatial weight matrices and analyze the resulting implications. Spatial weights based on geographic proximity have a long history in empirical spatial analyses (Anselin 1988; Anselin and Bera 1998; LeSage and Pace 2009). The leading examples are the binary contiguity matrix with weights (in row i and column j of matrix W N )        w ij ij =1, and share a common border 0, and do not share a common border , ij (3) and the inverse distance matrix with weights w d =1, ij ij (4) which are the inverse Euclidean distances d i j between two regions (based on geographic centroids). 5 By convention, the diagonal elements are set to zero; that is, w =0 ii . Note that both these matrices are by construction symmetric, so that a shock from region i to j has the same impact as the other way round. Yet, alternative approaches to capture the spatial spillover effects have become more and more prominent in recent years. Bavaud (1998) and Corrado and Fingleton (2012)recognize that there is no one true spatial weight matrix that is adequate in all situations, and that spatial interactions are often determined by relative economic distances rather than geographic boundaries or distances. An example of such economic weights are trade flows capturing international interdependencies, as in Ertur and Koch (2011) and Ho, Wang, and Yu (2013). Amarasinghe et al. (2018)considerweightsbased on socioeconomic distance such as ethnic links and road networks, and Incaltarau et al. (2021) use travel times. Fingleton (2001), Carrington (2003), and Zhang and Wang (2017) combine geographic distance with a measure of relative economic importance. Another idea that we do not pursue here is estimating the spatial weights rather than constructing them from observed variables. While this is a seemingly flexible approach, it also has its limitations. An unrestricted estimation is generally infeasible due to the large number of elements in the spatial weight matrix, especially when allowing for asymmetries (Beenstock and Felsenstein 2012). When the spatial weights are estimated from empirical correlations (Bhattacharjee and Jensen‐Butler 2013; Bailey, Holly, and Pesaran 2016), they are symmetric by construction. Even with a data‐driven approach, imposing some structure (Getis and Aldstadt 2004) or a sparsity assumption (Ahrens and Bhattacharjee 2015; Piribauer, Glocker, and Krisztin 2023) is unavoidable. 6 In urban and regional economics, commuter flows constitute a particularly important transmission mechanism (Allen, Arkolakis, and Li 2015). Monte, Redding, and Rossi‐Hansberg (2018) model the dependency of regions through a combination of trade and commuter flows. Calibrating their model to US regional data, they find that both flows correlate with each other, with commuter flows responding more to distance than trade flows. In particular at more disaggregate levels of analysis, they argue that commuter flows are vital for understanding the 568 of 886 Journal of Regional Science, 2025 connectivity of regions. Commuting can be an individually optimal decision when there are differences in local amenities and job opportunities across counties. By earning their income in one region and spending a significant part of it in another region, commuters constitute vital economic linkages between those regions. A county's susceptibility to income shocks originating in another county can be reasonably modeled as an increasing function of the share of residents working in that other county. We argue that geographic spatial weight matrices fail to capture these dependencies because they do not account for the heterogeneity of the counties. Economic activity is often clustered in certain regions. A thriving economy in these counties radiates to a larger area depending on the strength of the linkages. Conversely, the economic center is often largely insulated against adverse developments in surrounding counties. This means that economic spillover effects can be very heterogenous across regions, as documented, inter alia, by Destefanis, Di Serio, and Fragetta (2022) for Italy and Sotirou and Tsiapa (2015) for Greece. They can also be asymmetric, with a stronger dependence of lagging regions on technologically advanced leaders (Benhabib and Spiegel 1994; Siller et al. 2021). Such an asymmetric dependence cannot be characterized by geographic measures, but it is an inherent characteristic of commuter flows. While commuting is a significant phenomenon in small‐scale regions, we do not claim that commuter flows are a perfect proxy for economic inter‐county links. There are certainly other cross‐county interconnections along the value chain. Yet, it can be very difficult or even impossible to obtain alternative measures of economic connectivity—such as trade flow data—at a very disaggregated geographical level. Commuter flows might thus be the best available proxy for the economic network structure. In applications with a different regional scope, other measures—if available—might be more suitable. 7 The intuitive idea of why commuter flows can capture dependencies between regions and matter for shock propagation is that commuters earn their income in one region and spend a certain part of it in another region. This channel is independent of whether people physically leave their home and get into their place of work every day, or whether they (partially) work from home. Telecommuting has grown in importance in the wake of the COVID‐19 pandemic and has added to further de‐coupling employees' place of residence from their employer's work site, as documented, among others by Dingel and Neiman (2020) and Barrero, Bloom, and Davis (2021). Consequently, even long‐ distance commuter linkages can be potentially relevant for the shock transmission in the network. Since our measure of commuter flows relies on individuals' and employers' locations—rather than physical commuting—the commuter‐ based weight matrix continues to capture these linkages in a changing working world. Note that in contrast to the literature on gravity models and network science mentioned earlier, we do not aim to explain or predict commuter flows in this paper; we rather use them as a descriptive network measure in our econometric shock propagation analysis. We initially construct the commuter weights as the commuter outflow C i j from county i to county j relative to the population size P i of county i : ≠            w C Pij ij =, 0, = . ij ij i Asymmetry of W N thus follows from different absolute commuter levels ≠CC ij j i or different population sizes ≠ P P ij . Let us illustrate the implications of different weight matrices based on a minimal extract from our German county‐level data set, as shown in Figure 1. The first county in this example is the city of Frankfurt am Main, a large financial center in a densely populated area. It shares its northwestern and western borders with the rural districts Hochtaunuskreis and Main‐Taunus‐ Kreis (ordered second and third in the following matrices). Further west, the city of Wiesbaden connects to the Main‐ Taunus‐Kreis, but without a direct border to either of the first two counties. We ignore all other counties for this illustration. The binary‐contiguity and the inverse‐distance spatial weight matrices (before any standardization) look as follows:                                                     W W= 0110 1010 1101 0010 ,= 0 0.05 0.07 0.04 0.05 0 0.05 0.04 0.07 0.05 0 0.08 0.04 0.04 0.08 0 NN,cont. ,inv.dist. The first row/column in the contiguity matrix indicates that Frankfurt shares a border with the two rural counties, but no border with the fourth county (Wiesbaden). The rural districts are neighbors themselves, but only one of them (Main‐Taunus‐ Kreis) is also connected to Wiesbaden. The latter still experiences spatial spillovers from the first two counties (and vice versa), but only indirectly through the intermediary Main‐ Taunus‐Kreis. In contrast, the inverse‐distance weights allow for immediate spillovers among all counties, with different intensities according to the inverse distance of their geographic FIGURE 1 | Shape, location, and geographic centroids of four selected German counties. 569 of 886 centroids. We see that more distant county pairs have smaller entries. But due to the irregular shapes of the county areas, the connection between Frankfurt and Wiesbaden is of similar strength as the connection between Frankfurt and the Hochtaunuskreis, despite only the second pair sharing a border. Importantly, both matrices imply symmetric shock transmissions, ignoring the fact that the counties' economic structure is fundamentally different. From the two rural commuter belt districts, a significant share of the population works in the economic center Frankfurt, while there is very limited commuting in the opposite direction. Even though it is located furthest away, Wiesbaden is still an attractive place to live for commuters to Frankfurt—thanks to its urban character and amenities. This is reflected in the commuter‐based spatial weight matrix (rounded to 2 decimals):                           W = 0 0.01 0.02 0 0.11 0 0.02 0 0.15 0.02 0 0.02 0.03 0 0.01 0 N, comm. The entries in the first column highlight that Frankfurt attracts a relatively high share of the other counties' population, while commuting in the reverse direction is limited (first row). This asymmetry is characteristic for networks with a strong center‐ periphery structure. When constructing these matrices for our econometric estimation, we apply a spectral standardization; that is a division of all weights by the absolute value of the largest eigenvalue of W N . This is a standard procedure to ensure that the spatial lag coefficient λ in our econometric model (Equation 2)isona similar scale irrespective of the spatial weights. It implies a convenient upper bound on the parameter space, λ <1 , for IWλ− NN to be invertible. The latter is a stability requirement for the dynamic system defined by Equation (1). 8 We apply the same spectral standardization also to the traditional geography‐ based spatial weight matrices. It is important to note in this context that the spatial weights capture relative differences in the strength of the network connections. The absolute magnitude is irrelevant. For example, if commuter flows were twice as large everywhere, this would be exactly offset by the employed standardization. It is for this reason that the results from different types of weights—measured at different scales—are comparable. It is worth keeping in mind that all spatial weight matrices have their advantages and disadvantages. The simple geography‐ based matrices do not require any economic data, relying on the assumption that geographic closeness is a suitable proxy for economic connections. The inverse‐distance matrix incorporates this logic in its pure form, whereas the binary‐contiguity matrix uses the idea that neighboring regions are closely interlinked. Yet, these matrices underestimate the links between regions if a sizeable number of the workforce commutes to a larger economic center that is no direct neighbor and a significant distance away. The proposed commuter matrix comes with the drawback of requiring detailed data of commuting flow data. Yet, once this data has been obtained, it arguably captures actual economic behavior more accurately. In the context of our econometric framework, it could be argued that commuter flows might react endogenously to economic shocks. As a mitigation—and because our main estimation method requires constant spatial weights—we construct the commuter flow matrix with data from the initial year in our sample. In Section 3.2,wedemonstratethat the commuter flows remain reasonably stable over time. In this context, it is important to recognize that—in the absence of strong prior information about the true spatial dependence structure—model misspecification is unavoidable. If the true linkages are closer to those implied by a commuter network, then the potential endogeneity of slowly changing commuter flows is expected to be a lesser problem than the misspecification bias resulting from geographic weights. Because of this inherent uncertainty about the correct specification of W N , we advocate for the estimation of model (Equation 1)with alternative weight matrices, to get an idea about the range of plausible effects. 2.3 | Partial Effects and Spatial Multipliers The spatial lag W yln Ntinduces contemporaneous spillover effects among counties. Thus, the partial effect of a change in the exogenous regressors X t on the vector y l n t (conditional on the initial state y l nt− 1 ) is not just given by πbut Sπ λ() N, where S IWλλ()=( −) NNN − 1 is the short‐run spatial multiplier matrix. The resulting effects will be heterogeneous across counties. As summary measures, it is common practice to report average partial effects, differentiated between direct, indirect, and total effects (LeSage and Pace 2009). The direct effects are governed by the main‐diagonal elements of the spatial multiplier matrix. They capture the response to a shock originating in the same county, taking into account the feedback effects while the shock propagates through the network. The average short‐run direct spatial multiplier is               sS s S s λNλNλ ¯()=1′() =1tr ( ) , d i N iNi N =1 where siis a selection vector with 1 as the i ‐th element and 0 elsewhere. The off‐diagonal elements of the spatial multiplier matrix capture the indirect effects; these are the responses to shocks originating in another county j . The average short‐run indirect spatial multiplier is defined as  sS s s S ssλNλNλ ¯()=1′() =1′() , i N iN−i i N iNi ind =1 =1 − where sιs=− −iN i is a vector with 0 as the i ‐th element and 1 elsewhere. Thus, the average indirect effect can either be seen as the average response to a shock of equal size in all other counties, or as the average of the cumulative effects on all other counties, depending on whether we first sum across rows or columns of the spatial multiplier matrix. The average short‐run total spatial multiplier is then the sum of the direct and indirect multipliers: 570 of 886 Journal of Regional Science, 2025   sS ι ιSιSι sλsλsλNλ NλNλs ¯()=¯()+¯()=1′() =1′() =1′() . d i N iN N i N NNi NNN tot ind =1 =1 When the partial effects are very heterogeneous across counties, averaging them provides only little insight. For our counterfactual analyses, we are interested in the impact of a shock that originates in a selected subset of N tr counties that share some common characteristics. These are the treated counties. Let ζ be the treatment vector which contains elements 1 for all treated and 0 for all untreated counties, and ζι ζ =− N −the selection vector for the untreated counties. We define the average short‐ run multiplier for the treated counties as ζSζsλNλ ¯()= 1′(), N tr tr and the average short‐run multiplier for the untreated counties as ζSζsλNN λ ¯()= 1 −′(). N untr tr − Instead of averages, we can also compute specific quantiles and other quantities of interest from the distribution of multipliers collected in the N × 1 vector Sζ λ() N. These short‐run effects generally do not provide a complete picture if there are significant adjustment effects over time. If θ or ρ are nonzero, then there is only a partial contemporaneous adjustment of the dependent variable. There can be a short‐run overshooting that is corrected in the following periods, or a gradual build‐up of the effects over time. It is thus often more interesting to analyze the effects on the long‐run equilibrium. The long‐run spatial multiplier matrix is given by LIWθλρ θ λ ρ(, , )=((1−)−(+) ) NNN − 1 . The average long‐ run multipliers l θλρ lθλρ lθλρ lθλρ ¯(, , ), ¯(, , ), ¯(, , ), ¯(, , ) dind tot tr , and l θλρ ¯(, , ) untr are defined analogously to their short‐run counterparts above. 2.4 | Estimation Methods Treating α in the econometric model (Equation 1) as a vector of fixed effects causes an incidental‐parameters problem since the time dimension in our data set is relatively short ( T=15 ). After applying a suitable transformation to remove these time‐ invariant effects from the model, such as deviations from within‐group means, the transformed lagged dependent variable will be correlated with the idiosyncratic error term (Nickell 1981). To adjust the estimates for the resulting bias, we apply the Yu, de Jong, and Lee (2008) bias‐corrected QML estimator, which also accounts for the endogeneity of the spatial lag in the formulation of the likelihood function. Yu, de Jong, and Lee (2008) first apply a within‐group transformation to model (Equation 1) to remove the incidental parameters α , then estimate the transformed model by QML conditional on the initial observations y l n 0 , and finally apply an analytical bias correction to the coefficient estimates. 9 A shortcoming of the QML estimator is the requirement of a constant spatial weight matrix over time. Otherwise, the bias correction would become unfeasible. In principle, allowing for time‐varying spatial weights and explicitly modeling feedback from economic growth to commuter flows would be desirable. In the current context, however, the limitations of the data prevent a more sophisticated approach. Importantly, as we emphasize in Section 3.2, the observed variation in the commuter flows over time is much less relevant than the fundamental choice of the type of spatial weights. As an alternative to QML estimation, the coefficients in model (Equation 1) could be estimated by the generalized method of moments (GMM), as discussed by Lee and Yu (2014), among others. The advantage of the GMM approach is its flexibility to accommodate different assumptions regarding the exogeneity of X t . It also allows for time‐varying spatial weights. On the other hand, GMM estimation is relatively inefficient and the potential weakness of the instruments poses identification challenges, in particular for highly persistent processes as in our application. Because of a lack of internal robustness, we decided not to use GMM as our main estimation technique, and relegate it to the Supporting Information. 3 | Data For our analysis, we combine data from several sources. Most macroeconomic data are available in GENESIS‐Online and the Regionaldatenbank Deutschland, two data bases hosted by Germany's federal and regional statistical offices. Data on employees and commuters has been obtained from the federal employment agency. The geodata used for visualization purposes and the construction of the geography‐based spatial weights is provided by the geodata center of the federal agency for cartography and geodesy. For a full description of the data sources and necessary data adjustments, as well as summary statistics, see the Supporting Information. 3.1 | Data Assembly Our unit of observation is German counties (rural and urban districts), equivalent to the NUTS 3 level of the Nomenclature of Territorial Units for Statistics. In the past decades, German states have undergone several local government reorganizations that lead to a consolidation of counties or redrawn district borders. These reforms reduced the total number of German counties from 439 to 401, of which there are 107 urban and 294 rural districts. We undertook substantial data assembly work to recreate the time series of all variables for the district structure as present at the end of our sample period. Details on the data set construction can be found in the Supporting Information. 3.2 | Commuter Flows For our purpose, commuters are defined as all employees whose official place of work is located in a different county than their 571 of 886 main residence. 10 This includes individuals with a secondary residence at or near their place of work, who may not commute from their main residence on a daily basis. Weekend commuters might still spend a substantial part of their income at their main residence, in particular if they are a family's main breadwinner. This definition also includes telecommuters, who do not physically travel to their employer's work site, a phenomenon which has increased in the wake of the COVID‐19 pandemic. In 2002, on average 12.1% of the residents in a county were commuting to a different county. 69.2% of the these commuters lived in an adjacent county to their place of work, and another 16.9% had to cross two county borders. Until 2017, the commuter share of the average county rose to 15.9%, with 66.1% of commuters working in a neighboring county and another 17.4% having to cross one additional border. There is thus a slight tendency towards increasing commuter distances over our sample period despite the overall stability. Commuter flows are quite heterogeneous across Germany. Moreover, they are highly asymmetric. In the two panels of Figure 2, it is apparent that urban areas—identifiable by their comparatively small area—attract a large number of commuters relative to their population size from the surrounding rural areas, but less so in the opposite direction. Yet, the picture is not uniform across the country. As firms in suburban areas often face a cost advantage but can still access the large pool of workers who prefer living in an urban environment, these suburban counties both send a lot of commuters out to the urban center and also welcome relatively high commuter numbers. The larger the distance to the next urban center, the smaller the commuter flows in both directions. Because the QML estimation of short‐ T time–space dynamic panel models requires a constant spatial weight matrix over time, we populate it with the initial commuter flows in the year 2002, which also helps to address potential endogeneity concerns. The variability of commuter flows over time is relatively low such that the potential adverse consequences of using constant spatial weights are expected to be small. As a measure of variability, we consider the Frobenius norm of the matrix difference between 2 years, relative to the Frobenius norm of the initial‐period weight matrix:       WW W ww w −=− , NNtF NF i N j Nij ij t i N j Nij ,2002 , ,2002 =1 =1 ,2002 , 2 =1 =1 ,2002 2 where all weights have been spectrally standardized. The relative Frobenius difference from 2002 to 2003 is only 2.4%. This figure remains relatively stable for subsequent 1‐year differences. For the whole time span, from 2002 to 2017, the difference becomes 15.3%. By itself, this number is hard to interpret but it becomes more meaningful when we compare the commuter flow matrix to alternative spatial weight matrices. The relative Frobenius difference of the spectrally normalized contiguity matrix to the initial commuter flow matrix is 90.1%. For the inverse‐distance matrix it is even higher with 128.7%. FIGURE 2 | Spatial distribution of the per capita flow of commuters from and to the 401 German counties in 2002, grouped into quartiles. 572 of 886 Journal of Regional Science, 2025 fast speed of convergence would counteract the stimulus. With minimum and maximum total long‐run multipliers equal to 6.02 and 9.77, respectively, we obtain county‐specific speeds of adjustment in the range from 10.8% to 18.2%. Because the between‐county differences are primarily driven by the indirect spill‐in multipliers, the spatial distribution of the speed of adjustment looks very similar to Figure 6, where darker shades correspond to slower adjustment speeds. 4.3 | Counterfactual Scenarios To further uncover the heterogeneity of the spatial multipliers, we consider some illustrative counterfactual scenarios. We do this by assuming that a certain group of counties is treated with a unit shock, while all other counties are only indirectly affected through the cumulative spillover effects. This approach could be easily adjusted to accommodate alternative scenarios. For example, the treatment intensity could be varied by using a continuous treatment indicator ζ instead of a binary one. In each of our scenarios, 20 counties—the top or bottom 5% of the distribution according to some treatment indicator—are directly affected by the hypothetical treatment. In Table 3, we report the average long‐run spatial multipliers for treated and untreated counties for each of the seven treatment scenarios. The former is conceptually comparable to the conventional average total multiplier. The two would be identical if the treatment was applied to all 401 counties. The average multiplier for the untreated has a similar interpretation as the average indirect multiplier, although it applies only to a subsample. Both multipliers are necessarily smaller than those in Table 2because the spillover effects originate in fewer counties. In our first counterfactual exercise, we consider the 20 counties with the highest GVA share of the financial sector (in the year 2002) as the treated counties. 21 Six out of the 20 treated counties are in the Rhein‐Main area, with Frankfurt am Main as a center of gravity. These counties are strongly interlinked, both from a commuter perspective and in a purely geographic network. They benefit from their own treatment and the treatment of their neighboring counties. It is therefore not surprising to find a comparatively large average multiplier on the treated. Given that not all of the treated counties are located in treatment clusters, there is also considerable heterogeneity within the treated group. The strongest long‐run effect on the log of real GDP per capita is close to eightfold the size of the initial treatment, while it is less than sixfold for more isolated treated counties. There are pronounced differences between the multipliers from the three spatial weight matrices. While the lower bound for the multiplier is quite stable across network structures and counterfactual scenarios, the upper bound varies substantially. Under the first counterfactual treatment scenario, the effects are strongest based on the commuter links, which one may not have expected from the estimated spatial lag coefficients. For the untreated counties, those closely linked to clusters of treated counties reach a multiplier of up to 2.3, which is considerable given that these are entirely indirect effects. This maximum multiplier for the untreated is roughly halved under the contiguity network, and it is almost negligible when inverse‐distance weights are used, even for those counties in close proximity to the treated ones. In Figure 7, it is evident that also under the more favorable network schemes any noticeable indirect effects remain local. For the majority of untreated counties, there is hardly any measurable response. In our second counterfactual scenario, we apply the treatment to the 20 counties with the highest share of the industrial sector in their GVA. While most of those counties are located in the south of Germany, they are not strongly clustered and hardly any of them shares a common border with another treated county. Consequently, the feedback effects are smaller than in FIGURE 6 | Indirect long‐run spill‐in multipliers. 579 of 886 TABLE 3 | Average counterfactual long‐run spatial multipliers. Commuter W N Contiguity W N Inverse‐distance W N Treated Untreated Treated Untreated Treated Untreated Financial centers 6.540*** 0.228** 6.134*** 0.081** 6.024*** 0.050 (0.478) (0.102) (0.366) (0.036) (0.343) (0.094) [5.86, 7.94] [0.02, 2.31] [5.76, 6.94] [0.00, 1.22] [5.98, 6.10] [0.02, 0.15] Industrial centers 5.867*** 0.092*** 5.838*** 0.070** 6.004*** 0.051 (0.311) (0.037) (0.308) (0.031) (0.333) (0.097) [5.81, 6.03] [0.00, 1.79] [5.75, 6.09] [0.00, 0.62] [5.98, 6.02] [0.02, 0.28] Agricultural centers 5.908*** 0.022*** 6.274*** 0.076** 6.001*** 0.042 (0.315) (0.009) (0.401) (0.034) (0.330) (0.079) [5.80, 6.13] [0.00, 0.61] [5.77, 7.05] [0.00, 1.24] [5.98, 6.02] [0.02, 0.20] High GDP per capita 6.171*** 0.311** 5.824*** 0.058** 6.020*** 0.055 (0.376) (0.134) (0.306) (0.026) (0.343) (0.104) [5.85, 7.76] [0.02, 2.29] [5.73, 6.13] [0.00, 0.62] [5.98, 6.08] [0.02, 0.39] Low GDP per capita 5.877*** 0.024*** 6.008*** 0.094** 6.010*** 0.047 (0.312) (0.009) (0.342) (0.041) (0.335) (0.088) [5.80, 6.14] [0.00, 0.44] [5.76, 6.43] [0.00, 0.93] [5.98, 6.03] [0.02, 0.15] High population density 6.340*** 0.317** 6.139*** 0.071** 6.077*** 0.054 (0.416) (0.137) (0.369) (0.032) (0.389) (0.102) [5.89, 7.15] [0.02, 1.92] [5.76, 6.98] [0.00, 1.54] [5.97, 6.18] [0.02, 0.26] Low population density 5.993*** 0.014*** 6.575*** 0.054** 6.012*** 0.036 (0.325) (0.005) (0.493) (0.025) (0.334) (0.067) [5.81, 6.23] [0.00, 0.55] [6.02, 7.36] [0.00, 1.23] [5.98, 6.03] [0.02, 0.12] Note: The multipliers are computed for the regressions in columns (3), (6), and (9) of Table 1. Standard errors (in parentheses) are computed with the Delta method. The p ‐values correspond to a one‐sided test of equality to unity for the average multiplier on the treated, and a one‐sided test of equality to zero for the average multiplier on the untreated. The minimum and maximum multipliers are shown within the square brackets. In each counterfactual, there are 20 treated and 381 untreated counties. *p< 0.1 0 ;** p< 0.05; ***p< 0.0 1 . FIGURE 7 | Counterfactual long‐run spatial multipliers for treatment of financial centers. 580 of 886 Journal of Regional Science, 2025 the first scenario and there is not much variation of the long‐ run multiplier effect on the treated, with the highest multiplier barely exceeding six. In the third scenario, we use the GVA share of the agricultural sector as an indicator to select 20 counties that are predominantly rural. These are largely clustered in the northeast of Germany. The geographic proximity yields comparatively large multiplier effects from a contiguity network. In contrast, when we use commuter weights, the multipliers on the treated and untreated are both relatively low as there are no substantial commuter flows between these counties. The long‐run multipliers from the inverse‐distance spatial weights remain small due to the offsetting effects of the contemporaneous and one‐period‐lagged spatial spillovers. In the next two scenarios, we consider a treatment of the 20 richest and 20 poorest counties (in 2002), respectively. The former can be mainly found in the south and southwest of Germany, while many of the latter are clustered in the east and along the former intra‐German border. The different implications of commuter‐based or contiguity‐based spatial weights become quite apparent when comparing these two treatment scenarios. Under the former regime, the long‐run spatial multipliers are higher when the richest counties are treated because the surrounding counties tend to have strong commuter linkages with them. With contiguity weights, the reinforcement of the spillover effects is stronger from a treatment of the poorest counties, simply because of the geographic clustering. The resulting differential spatial multipliers on the untreated are apparent in Figures 8and 9. 22 Finally, the conclusions from treating counties with the highest or lowest population density are very similar to those from targeting financial centers or agricultural centers, respectively. There are important policy consequences of these findings. If it was the objective of a policy maker to maximize the total benefit for the whole country from an intervention in a limited number of counties, a commuter‐based propagation mechanism would suggest to target wealthy and densely populated areas. Yet, this would aggravate existing inequalities, as remote and poorly‐ connected regions would be left behind even further. Conversely, directly targeting the poorest regions would require a stronger stimulus to achieve the same aggregate effect due to the small local multipliers. 23 On the other hand, assuming a purely geographic shock propagation would lead to very different conclusions. 5 | Conclusion and Discussion This paper demonstrates that alternative assumptions on the spatial network structure in the analysis of regional economic growth with local spillover effects can result in significantly different local adjustment dynamics. Importantly, the regression coefficients in a time–space dynamic panel data model can be highly misleading about the magnitude of the effects. Local spatial multiplier can be large even with relatively small spatial‐ lag coefficients. Moreover, the heterogeneity of the spatial multiplier effects is masked by traditionally reported average effects. We highlight that the propagation of an initial stimulus not only depends on the assumed network structure, but also the place in which it originates. The local multiplier effects can substantially vary across counties, depending on their position in the spatial network and the nature of the considered treatment or shock. Unless there is strong prior information on the network structure, we propose to compare the results from alternative specifications to obtain an idea about the range of plausible effects. We advocate for considering a broader range of measures of spatial dependence in empirical work—depending on the research context, and data availability permitting—that are not just based on geographic distance but better reflect the underlying economic transmission mechanisms. Commuter flows can FIGURE 8 | Counterfactual long‐run spatial multipliers for treatment of rich counties. 581 of 886 be such a measure in the analysis of regional economic interdependence when the geographic units are sufficiently disaggregated. Commuter flows link regions in which employees earn their income—often comparatively rich urban areas—to those where they spend a substantial part of it—often comparatively poor rural areas—and they do so in an asymmetric way. While commuter flows are correlated with geographic proximity, they are based on workers' observed behavior and thus reflect the economic reality. In contrast, asymmetric shock propagation mechanisms cannot be adequately captured when dependencies are proxied merely by the relative geographic location of the regions. From a policy perspective, our results emphasize that the differential regional impacts of an intervention should be carefully considered. In our counterfactual scenarios, directly treating the poorest regions hardly creates any spillover effects under a commuter flow network structure, while large gains can be realized by treating the well‐connected richer counties. This creates a potential trade‐off between maximizing the aggregate welfare gains from an intervention and reducing inequality across regions. Acknowledgments We thank Michael Berlemann, Richard Bluhm, Jörg Breitung, Jan Ditzen, Paul Elhorst, Michael Pfaffermayr, Alexandra Schaffar, and the anonymous referees for very helpful comments and suggestions. Further useful comments were received from participants at the SEW in Paris, the UEA European Meeting in Amsterdam, the IAAE Annual Conference in Nicosia, the IPDC in Vilnius, the ERSA Congress in Lyon, and the virtual ES World Congress, as well as in various university seminars. We dedicate this paper to the late Horst Entorf who encouraged us to work on this topic. His support in the early stage of our careers was invaluable. Open Access funding enabled and organized by Projekt DEAL. Data Availability Statement The data that support the findings of this study are available from the authors upon request and will be made publicly available upon acceptance of this article. Endnotes 1 Source for EU commuting data: Eurostat, online data code LFST_R_LFE2ECOMM (employment and commuting by sex, age and NUTS 2 regions). 2 Alternative model specifications include the spatial error model, where the spatial spillover effects (and the time dynamics) are modeled in the error term ε t instead of the dependent variable. This would allow for spatially correlated shocks, but excludes cross‐ sectional feedback in response to changes in the regressors X t. Yet another alternative would be to consider spatial lags in X t, leading to aso‐called spatial Durbin model. However, it is less straightforward to motivate and interpret the effects from such specifications in our context. 3 ≡≈ () yyy gg Δ ln ln −ln = ln = ln(1 + ) it it i t y y ,−1it it,−1for small values of the growth rate g. 4 In line with these arguments, researchers often find support for the coefficient relationship ρ θ λ =−in empirical convergence studies (Parent and LeSage 2012; Ho, Wang, and Yu 2013; Fischer and LeSage 2015). 5 Common variations are to also give nonzero weights to second‐order neighbors in the contiguity matrix, or to define a cut‐off distance in the inverse‐distance matrix after which all weights are set to zero. Here, we restrict ourselves to the basic versions of the geographic spatial weight matrices to keep the analysis parsimonious. 6 Notably, Piribauer, Glocker, and Krisztin (2023) find markedly different spill‐in and spill‐out multipliers, reflecting asymmetric connectivity. 7 One might consider supplementing geography‐based weight matrices using information about the road network or travel times between counties. Yet, in a country such as Germany with well‐ developed road and public transportation networks, such travel FIGURE 9 | Counterfactual long‐run spatial multipliers for treatment of poor counties. 582 of 886 Journal of Regional Science, 2025 times are closely related to the great‐circle distance. Most importantly, a network based on travel times would still be symmetric. Where travel times matter, this will be reflected in differences in the commuter flows that we observe. 8 The same upper bound could be achieved with a row standardization; that is a division of all weights by the respective row sum  w j Nij =1 . However, the latter would not preserve the underlying network structure. As Kelejian and Prucha (2010) and Neumayer and Plümper (2016) point out, this would generally result in a misspecified model. In our case, the weights would no longer be relative to the population size P i because the latter is constant within each row. As a consequence, comparatively isolated counties with few commuter links and counties that are strongly connected to others would appear to have similarly strong commuter links after applying a row standardization. 9 While this bias correction was developed under asymptotics where both T and N go to infinity, simulation evidence reveals that it works remarkably well even for short T . If our time dimension was considerably longer, we should also treat the time effects γ t as incidental parameters. Lee and Yu (2010) extend the estimator of Yu, de Jong, and Lee (2008) in that direction. 10 Note that we only have commuter flow data for employees who are subject to social security contributions. This excludes civil servants and self‐employed people. It also excludes German residents who commute to a workplace abroad. 11 Detailed summary statistics are provided in the Supporting Information. 12 The growth rate of real GDP per capita is approximated by the first difference in the natural logarithm. 13 We tabulate Moran's I and the respective standardized z‐score for all years and all three spatial weight matrices in the Supporting Information. Our empirical results are robust to the choice of the commuting base year. 14 An extreme example is the East German manufacturing lighthouse Eisenach, where the share of the industrial sector remained fairly stable between 51% and 47% before the crisis onset, but then plummeted to 27% in 2008. Since then, the industrial sector recovered and reached again 43% by 2014. 15 While the standardization of the spatial weight matrices should ensure that the upper bound for the spatial lag coefficient is unity, estimates above 1 can occur as an artifact of the bias correction procedure, as happened here in column (7) of Table 1. 16 In the Supporting Information, we present GMM estimation results treating investment as endogenous. Its coefficient turns statistically insignificant. Removing investment from the model hardly alters the results presented in this section, both qualitatively and quantitatively. 17 In a model without spatial spillover effects, the speed of adjustment can be computed as θ − ln( ) (Islam 1995). 18 LeSage and Fischer (2008) and Crespo Cuaresma and Feldkirchner (2013) address this uncertainty about the spatial weight matrix in a Bayesian model averaging framework. 19 For larger effect sizes, the log approximation becomes inaccurate. The spillover effect in percent is calculated using the exponential transformation, for example, ≈e−1 50.2 % 0.407 . 20 The magnitude of the multiplier gets smaller in the border regions of Germany. Especially for districts bordering another country, we cannot capture the full dependencies as we do not observe the full network. This is the classical boundary problem (Griffith 1983), to which no simple practical solution exists. In our application, a relatively large number of counties lies inland with only limited cross‐ country commuter links, so that the average multipliers would hardly be affected. Nevertheless, for those few counties with strong cross‐border ties, the predictions from our counterfactual analysis should be taken with caution. The boundary problem is related to the modifiable areal unit problem (MAUP), which describes the phenomenon that a result in geo‐spatial research may vary with the size or shape of the unit of analysis (Fotheringham and Wong 1991; Bailey and Gatrell 1995). Importantly, both issues arise irrespective of the spatial weight matrix used. 21 This exercise should not be interpreted as an analysis of how a shock is transmitted through the financial system. If such a shock leads to an output reduction in the financial centers, the expected macroeconomic consequences for the real economy can be studied within our framework. 22 For the remaining counterfactual scenarios, the graphical illustration of the long‐run spatial multipliers on the untreated can be found in the Supporting Information. 23 Our analysis assumed local shocks to the log of real GDP per capita of equal size. Due to the log transformation, these shocks will be larger in absolute terms for richer counties. In the Supporting Information, we consider scenarios with equally sized absolute shocks. The qualitative conclusions remain unaffected. References Ahlfeldt, G. M., S. J. Redding, D. M. Sturm, and N. Wolf. 2015. “The Economics of Density: Evidence From the Berlin Wall.”Econometrica 83, no. 6: 2127–2189. Ahrens, A., and A. Bhattacharjee. 2015. “Two‐Step Lasso Estimation of the Spatial Weights Matrix.”Econometrics 3, no. 1: 128–155. Ahrens, A., and S. Lyons. 2021. “Do Rising Rents Lead to Longer Commutes? A Gravity Model of Commuting Flows in Ireland.”Urban Studies 58, no. 2: 264–279. Allen, T., C. Arkolakis, and X. Li. 2015. Optimal City Structure. Manuscript, Yale University. Alonso, W. 1964. Location and Land Use: Toward a General Theory of Land Rent. Cambridge: Harvard University Press. Amaral, L., A. Scala, M. Barthélémy, and H. Stanley. 2000. “Classes of Small‐World Networks.”Proceedings of the National Academy of Sciences 97: 11149–11152. Amarasinghe, A., R. Hodler, P. A. Raschky, and Y. Zenou. 2018. Spatial Diffusion of Economic Shocks in Networks. Working Paper 7001, CESifo. Anselin, L. 1988. Spatial Econometrics: Methods and Models. Dordrecht: Kluwer Academic Publishers. Anselin, L. 1995. “Local Indicators of Spatial Association—LISA.” Geographical Analysis 27, no. 2: 93–115. Anselin, L., and A. K. Bera. 1998. “Spatial Dependence in Linear Regression Models With an Introduction to Spatial Econometrics.”In Handbook of Applied Economic Statistics, Chapter 7, edited by A. Ullah and D. E. A. Giles, 237–289. New York: Marcel Dekker. Badinger, H., W. Müller, and G. Tondl. 2004. “Regional Convergence in the European Union, 1985–1999: A Spatial Dynamic Panel Analysis.” Regional Studies 38, no. 3: 241–253. Bailey, N., S. Holly, and M. H. Pesaran. 2016. “A Two‐Stage Approach to Spatio‐Temporal Analysis With Strong and Weak Cross‐Sectional Dependence.”Journal of Applied Econometrics 31, no. 1: 249–280. Bailey, T., and A. Gatrell. 1995. Interactive Spatial Data Analysis. Harlow: Longman Scientific and Technical. Barabási, A.‐L. 2003. Linked: The New Science of Networks. Cambridge: Perseus Publishing. Barrero, J. M., N. Bloom, and S. J. Davis. 2021. Why Working From Home Will Stick. Working Paper 28731, NBER. 583 of 886 Bavaud, F. 1998. “Models for Spatial Weights: A Systematic Look.” Geographical Analysis 30, no. 2: 153–171. Beenstock, M., and D. Felsenstein. 2012. “Nonparametric Estimation of the Spatial Connectivity Matrix Using Spatial Panel Data.”Geographical Analysis 44, no. 4: 386–397. Benhabib, J., and M. Spiegel. 1994. “The Role of Human Capital in Economic Development: Evidence From Aggregate Cross‐Country Data.”Journal of Monetary Economics 34, no. 2: 143–173. Bhattacharjee, A., and C. Jensen‐Butler. 2013. “Estimation of the Spatial Weights Matrix Under Structural Constraints.”Regional Science and Urban Economics 43, no. 4: 617–634. Billé, A., A. Tomelleri, and F. Ravazzolo. 2023. “Forecasting Regional GDPS: A Comparison With Spatial Dynamic Panel Data Models.” Spatial Economic Analysis 18, no. 4: 530–551. Carrington, A. 2003. “A Divided Europe? Regional Convergence and Neighbourhoud Spillover Effects.”Kyklos 56, no. 3: 381–393. Cheong, T. S., and Y. Wu. 2013. “Regional Disparity, Transitional Dynamics and Convergence in China.”Journal of Asian Economics 29: 1–14. Cliff, A. D., and J. K. Ord. 1981. Spatial Processes: Models & Applications. London: Pion. Colavecchio, R., D. Curran, and M. Funke. 2011. “Drifting Together or Falling Apart? The Empirics of Regional Economic Growth in Post‐ Unification Germany.”Applied Economics 43, no. 9: 1087–1098. Corrado, L., and B. Fingleton. 2012. “Where Is the Economics in Spatial Econometrics?”Journal of Regional Science 52, no. 2: 210–239. Crespo Cuaresma, J., and M. Feldkirchner. 2013. “Spatial Filtering, Model Uncertainty and the Speed of Income Convergence in Europe.” Journal of Applied Econometrics 28, no. 4: 720–741. Destefanis, S., M. Di Serio, and M. Fragetta. 2022. “Regional Multipliers Across the Italian Regions.”Journal of Regional Science 62, no. 4: 1179–1205. Dingel, J. I., and B. Neiman. 2020. “How Many Jobs Can Be Done at Home?”Journal of Public Economics 189: 104235. Duran‐Fernandez, R., and G. Santos. 2014. “Gravity, Distance, and Traffic Flows in Mexico.”Research in Transportation Economics 46: 30–35. Duranton, G., and M. A. Turner. 2011. “The Fundamental Law of Road Congestion: Evidence From US Cities.”American Economic Review 101, no. 6: 2616–2652. Egger, P., and M. Pfaffermayr. 2006. “Spatial Convergence.”Papers in Regional Science 85, no. 2: 199–215. Erlander, S., and N. Stewart. 1990. The Gravity Model in Transportation Analysis—Theory and Extensions. Utrecht: VSP. Ertur, C., and W. Koch. 2007. “Growth, Technological Interdependence and Spatial Externalities: Theory and Evidence.”Journal of Applied Econometrics 22, no. 6: 1033–1062. Ertur, C., and W. Koch. 2011. “A Contribution to the Theory and Empirics of Schumpeterian Growth With Worldwide Interactions.”Journal of Economic Growth 16, no. 3: 215–255. Evans, P., and J. U. Kim. 2014. “The Spatial Dynamics of Growth and Convergence in Korean Regional Incomes.”Applied Economics Letters 21, no. 16: 1139–1143. Fingleton, B. 2001. “Equilibrium and Economic Growth: Spatial Econometric Models and Aimulations.”Journal of Regional Science 41, no. 1: 117–147. Fingleton, B. 2020. “Exploring Brexit With Dynamic Spatial Panel Models: Some Possible Outcomes for Employment Across the EU Regions.”The Annals of Regional Science 64: 455–491. Fischer, L. B., and M. Pfaffermayr. 2018. “The More the Merrier? Migration and Convergence Among European Regions.”Regional Science and Urban Economics 72: 103–114. Fischer, M. M., and J. P. LeSage. 2015. “A Bayesian Space‐Time Approach to Identifying and Interpreting Regional Convergence Clubs in Europe.”Papers in Regional Science 94, no. 4: 677–702. Fotheringham, A., and D. Wong. 1991. “The Modifiable Areal Unit Problem in Multivariate Analysis.”Environment and Planning 23, no. 7: 1025–1044. Getis, A., and J. Aldstadt. 2004. “Constructing the Spatial Weights Matrix Using a Local Statistic.”Geographical Analysis 36, no. 2: 90–104. Goldin, C., and L. F. Katz. 2008. The Race Between Education and Technology. Cambridge: Harvard University Press. Griffith, D. 1983. “The Boundary Value Problem in Spatial Statistical Analysis.”Journal of Regional Science 23, no. 3: 377–387. Ho, C.‐Y., W. Wang, and J. Yu. 2013. “Growth Spillover Through Trade: A Spatial Dynamic Panel Data Approach.”Economics Letters 120, no. 3: 450–453. Incaltarau, C., G. C. Pascariu, A. Duarte, and P. Nijkamp. 2021. “Migration, Regional Growth and Convergence: A Spatial Econometric Study on Romania.”Annals of Regional Science 66, no. 3: 497–532. Islam, N. 1995. “Growth Empirics: A Panel Data Approach.”The Quarterly Journal of Economics 110, no. 4: 1127–1170. Kelejian, H. H., and I. R. Prucha. 2010. “Specification and Estimation of Spatial Autoregressive Models With Autoregressive and Heteroskedastic Disturbances.”Journal of Econometrics 157, no. 1: 53–67. Kosfeld, R., H.‐F. Eckey, and C. Dreger. 2006. “Regional Productivity and Income Convergence in the Unified Germany.”Regional Studies 40, no. 7: 755–767. Lee, L.‐F., and J. Yu. 2010. “A Spatial Dynamic Panel Data Model With Both Time and Individual Fixed Effects.”Econometric Theory 26, no. 2: 564–597. Lee, L.‐F., and J. Yu. 2014. “Efficient GMM Estimation of Spatial Dynamic Panel Data Models With Fixed Effects.”Journal of Econometrics 180, no. 2: 174–197. LeSage, J. P., and M. M. Fischer. 2008. “Spatial Growth Regressions: Model Specification, Estimation and Interpretation.”Spatial Economic Analysis 3, no. 3: 275–304. LeSage, J. P., and R. K. Pace. 2009. Introduction to Spatial Econometrics. London: Chapman. Lukermann, F., and P. Porter. 1960. “Gravity and Potential Models in Ecoomic Geography.”Annals of the Association of American Geographers 50, no. 4: 493–504. McArthur, D., G. Kleppe, I. Thorsen, and J. Ubøe. 2011. “The Spatial Transferability of Parameters in a Gravity Model of Commuting Flows.” Journal of Transportation Geography 19, no. 4: 596–605. Mills, E. S. 1967. “An Aggregative Model of Resource Allocation in a Metropolitan Area.”American Economic Review 57, no. 2: 197–210. Monte, F., S. Redding, and E. Rossi‐Hansberg. 2018. “Commuting, Migration and Local Employment Elasticities.”American Economic Review 108, no. 12: 3855–3890. Moran, P. A. P. 1950. “Notes on Continuous Stochastic Phenomena.” Biometrika 37, no. 1/2: 17–23. Muth, R. 1969. Cities and Housing: The Spatial Patterns of Urban Residential Land Use. Chicago: University of Chicago Press. Neumayer, E., and T. Plümper. 2016. “W.”Political Science Research and Methods 4, no. 1: 175–193. Nickell, S. 1981. “Biases in Dynamic Models With Fixed Effects.” Econometrica 49, no. 6: 1417–1426. 584 of 886 Journal of Regional Science, 2025 Niedercorn, J., and B. Bechdolt. 1969. “An Economic Derivation of the ‘Gravity Law’on Spatial Interactions.”Journal of Regional Science 273–282, no. 9: 273–282. Parent, O., and J. P. LeSage. 2012. “Spatial Dynamic Panel Data Models With Random Effects.”Regional Science and Urban Economics 42, no. 4: 727–738. Patuelli, R., A. Reggiani, P. Nijkamp, and F.‐J. Bade. 2010. “The Dynamics of the Commuting Network in Germany: Spatial and Connectivity Patterns.”Journal of Transport and Land Use 2, no. 3/4: 5–37. Pfaffermayr, M. 2012. “Spatial Convergence of Regions Revisited: A Spatial Maximum Likelihood Panel Approach.”Journal of Regional Science 52, no. 5: 857–873. Piribauer, P., C. Glocker, and T. Krisztin. 2023. “Beyond Distance: The Spatial Relationships of European Regional Economic Growth.”Journal of Economic Dynamics and Control 155: 104735. Proost, S., and J.‐F. Thisse. 2019. “What Can Be Learned From Spatial Economics?”Journal of Economic Literature 57, no. 3: 575–643. Reggiani, A., P. Bucci, and G. Russo. 2011. “Accessibility and Impedance Forms: Empirical Applications to the German Commuting Network.”International Regional Science Review 34, no. 2: 230–252. Sala‐i‐Martín, X. X. 1996. “Regional Cohesion: Evidence and Theories of Regional Growth and Convergence.”European Economic Review 40, no. 6: 1325–1352. Siller, M., T. Schatzer, J. Walde, and G. Tappeiner. 2021. “What Drives Total Factor Productivity Growth? An Examination of Spillover Effects.”Regional Studies 55, no. 6: 1129–1139. Simini, F., G. Barlacchi, M. Luca, and L. Pappalardo. 2021. “A Deep Gravity Model for Mobility Flows Generation.”Nature Communications 12: 6576. Sotirou, A., and M. Tsiapa. 2015. “The Asymmetric Influence of Structural Funds on Regional Growth in Greece.”Environment and Planning C: Politics and Space 33, no. 4: 863–881. Thorsen, I., and J. P. Gitlesen. 1998. “Empirical Evaluation of Alternative Model Specifications to Predict Commuting Flows.”Journal of Regional Science 38, no. 2: 273–292. Young, A. T., M. J. Higgins, and D. Levy. 2008. “Sigma Convergence Versus Beta Convergence: Evidence From U.S. County‐Level Data.” Journal of Money, Credit and Banking 40, no. 5: 1083–1093. Yu, J., R. de Jong, and L.‐F. Lee. 2008. “Quasi‐Maximum Likelihood Estimators for Spatial Dynamic Panel Data With Fixed Effects When Both nand T Are Large.”Journal of Econometrics 146, no. 1: 118–134. Zhang, H., and X. Wang. 2017. “Combined Asymmetric Spatial Weights Matrix With Application to Housing Prices.”Journal of Applied Statistics 44, no. 13: 2337–2353. Supporting Information Additional supporting information can be found online in the Supporting Information section. 585 of 886