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Abstract
When modelling interregional flows it is standard to identify the origin and destination of a flow with the point of production and consumption. However, the presence of hub-spoke structures or multimodal flows may introduce bias, such as being an additional source for cross-sectional correlation between dyadic flows. The aim of this paper is to model inter-provincial flows within a country (Spain) considering this potential bias using a novel dataset with 50 inter-provincial flows and four transport modes. We then feed this dataset into various specifications of a gravity model that incorporates cross-sectional dependence attributable to hub-spoke structures.
Tendance intra-nationale à privilégier le marché intérieur, au niveau des grossistes, de structures en étoile, et des livraisons par des moddes de transport multimodaux
RÉSUMÉ lors de la modélisation de flux interrégionaux, la méthode standard consiste à identifier l’origine et la destination d’un flux avec le point de production et la consommation. Toutefois, la présence de structures en étoile ou de flux multimodaux est susceptible de fausser les données, en constituant, par exemple, une source additionnelle de corrélation transversale entre des flux dyadiques. Le but de la présente communication est de modéliser des flux interprovinciaux au sein d’un certain pays (l’Espagne), en tenant compte de ce parti pris potentiel, et en tenant compte d’un nouvel ensemble de données avec cinquante flux interprovinciaux et quatre modes de transport. Nous intégrons ensuite cet ensemble de données dans différentes spécifications d’un modèle à gravité incorporant une dépendance transversale attribuable à une structure en étoile.
Favoritismo local intranacional en la presencia de mayoristas, estructuras de interconexión radial y repartos con transporte multimodal
Resumen al modelar flujos interregionales, es normal determinar el origen y el destino de un flujo con el punto de producción y consumo. Sin embargo, la presencia de estructuras de interconexión radial o flujos multimodales puede dar origen a favoritismos, por ejemplo ser una fuente adicional para la correlación transversal entre flujos diádicos. El objetivo de este estudio es modelar los flujos interprovinciales en un país (España) considerando este posible favoritismo usando un conjunto de datos nuevo con cincuenta flujos interprovinciales y cuatro modos de transporte. Posteriormente introdujimos este conjunto de datos en varias especificaciones de un modelo de gravedad que incorpora la dependencia transversal atribuible a las estructuras de interconexión radial.
涉及批发商、轴辐式结构及多模式运输交付能力情况下的国内本土影响
摘要 : 在建立跨区域流动模型时, 标准做法是通过生产点和消耗点确认流动的出发地和目的地。然而, 轴辐式结构或多模式流动可能造成不必要的影响, 例如它们可以作为二元流动之间跨地区联系的另一来源。本文的目标在于考虑这一潜在影响, 为国家内 (西班牙) 跨省流动建模, 并在过程中运用包含五十个跨省流动及四种运输方式的新式数据集。我们之后将该数据集输入一个引力模型的各项规格中, 该引力模型将源自轴辐式结构的跨地区依赖性纳入其中。
Notes
1. This applies strictly to the cited literature on trade and the gravity equation. Interesting and subtle strategies have been developed to model transport networks, transport-mode competition and cooperation in freight and passenger trips, but a detailed review of this alternative literature and its modelling strategies lies beyond the scope of this paper.
2. For example, with ‘production-chain fragmentation’ and ‘value-added trade’, transit flows and re-exporting may produce double counting problems and misinterpretations of the current account balance. See, for instance, Antràs & Chor (Citation2012); Antràs et al. (Citation2012); Ling feng et al. (Citation2012); Baldwin & Lopez-Gonzalez (Citation2013). In the border-effect literature, moreover, we observe that the presence of two (or more) transport flows corresponding to the same trade operation can bias estimates of the border effect (Hillberry & Hummels, Citation2003). On the other hand, re-exportation within the destination region (e.g., through capillarity distribution from outskirt warehouses to urban centres) can lead to an overestimation of intra-national trade and therefore of home bias within the country. However, if the re-exportation scheme should be a concatenated set of inter-provincial deliveries of the same item (e.g., intermodal transport delivery with load/unload operations in the hub), it is inter-provincial freight flows that will suffer from double counting and lead to an underestimation of the intra-regional home bias. For a similar insight into multi-stage production and US home bias, see Kei-Mu (Citation2010).
3. There is a broad literature on spatial-interaction models. The gravity model is doubtless the most well-known approach, having received much attention in varied fields, and has thousands of applications for trade, freight, commuting, finance or migration flows. This paper takes up two strands of the literature: the use of gravity models to model trade flows between and within countries (see Head & Mayer, Citation2014, for a recent review) and the combination of gravity models with spatial econometric terms (Fischer & Griffith, Citation2008; LeSage & Pace, Citation2008, Citation2009). Additional approaches are not covered in this paper.
4. Without loss of generality, i denotes the province of origin, and j denotes the province of destination. Thus, if i = j, we have intra-provincial flows, whereas if i ≠ j, we have inter-provincial, intra-national flows.
5. Moreover, inflows to and outflows from a warehouse could be different in nature: (a) the warehouse could be owned by a logistics company offering services to the producer or to retailers. In this case, although there is no transformation of the load when it is delivered to/from the warehouse, the outflows and inflows truly correspond to trade flows; (b) however, if the warehouse is owned by the producer or the retailer, product entry into or departure from that infrastructure does not necessarily imply a trade flow between i and j but, perhaps, an intra-firm displacement of products (inventory management), with the aim of getting said products closer to the final market. An additional problem is that the products could be produced abroad and merely moved within the country.
6. There exist several explanations for these effects in most socioeconomic spatial interactions (migration, trade, commuting, etc.). For example, neighbouring origins (exporting provinces) and destinations (importing provinces) can occasion estimation errors of similar magnitude if underlying latent or unobserved forces are at work, so that missing covariates exert a similar impact on neighbouring observations. Such missing covariates can be associated with various factors, such as common agglomeration economies, common transport infrastructures, factor endowments, un-observed linkages between sectors or firms, etc.
7. Note that the same assumption can be made for any origin (i) in the system and lead to the same conclusion.
8. Note that, by means of WHa, flow i→j is associated with (subsequent) flow j→nj. This ‘network autocorrelation scheme’, which is explained by ‘re-exportation’ activity within a ‘hub-spoke’ structure, differs from the typical ‘destination-base’ SAR scheme (LeSage & Pace, Citation2008, Citation2009), where matrix Wj associates flow i→j with the flow from the same origin i to the neighbour of destination j (here labelled nj).
9. Several sources of ‘endogeneity problems’ are potentially present in our empirical exercise: (i) the specification of the gravity equation, if the ‘endogenous’ variable appears on both sides of the equation (i.e., Tij versus Yi and Yj); (ii) W, if it is defined in terms of the flows or other variables correlated with the endogenous variable; (iii) a potential contemporaneous round-causation effect between the endogenous and exogenous variables. In this section, we focus specifically on the second potential source of endogeneity problems. Regarding the other two: Our specification of the gravity model (Equation 2) shifts the YiYj terms to the denominator of the left-hand side of the equation in an attempt, suggested by Head & Mayer (Citation2000) and Poncet (Citation2003), to overcome possible endogeneity problems; with regard to the round causation effect (iii), we acknowledge that the number of warehouses and wholesalers can increase in the provinces characterized by large intensities of inflows/outflows (rather than explain the intensity of the flows). Thus, one may argue that the appearance of logistic infrastructures and intermediaries is endogenous to the flows (Xi and Xj are explained by Fij and not the other way around). Thus, by lagging (i.e., t − 5) the Xi Xj variables, such round causation can be avoided. Although we have considered that option, it was impracticable due to data limitations. Moreover, as logistic infrastructures are very complex (it takes years to build them), we believe that such circular causation is more theoretical than practical. The use of IV lies beyond the scope of this paper and, moreover, is unsuited to the available information at this fine spatial level.
10. As in LeSage & Pace (Citation2008), our WH are built using ‘zeros’, ‘ones’ or fractions of ‘ones’ (inverse of distance to the Hub). The only difference is that, instead of specifying a ‘one’ to pinpoint the node that corresponds to the flow Fnji (i.e., flows from i to the spatial neighbour of j), we specify a ‘one’ to indicate the node that corresponds to the flows FdH, that is, the flows delivered from the destination of a prior delivery (potential hub H) to another province d, which might be the final destination of a re-exportation scheme.
11. Note that in all cases, this will correspond to a zero flow in the regression. However, our SAR specification disallows the removal of observations from the sample (a square DO matrix is needed). We also considered (and rejected) the alternative of using zero (or infinity) for the distance variable for the island-inner region pairs.
12. Anecdotally, it is worth highlighting that certain inner provinces show slight (but not null) intensity of inflows/outflows by ship. This is because trade-flow statistics with Islas Canarias are, as explained in the Appendix, official statistics from the AEAT, which collects the data that establish the main transport mode used in the freight flow. That is, a freight flow originating in an inner province and proceeding by road to a port before taking a ship is nevertheless recorded as a delivery by ship from the inner province.
13. Rather than unduly lengthen this paper, we will reserve the necessarily painstaking analysis of sector-specific flows for future research. Modelling sector-specific flows by transport mode at the NUTS-3 level generates an extremely high number of zero flows. This creates a need for alternative procedures, such as pseudo-Poisson estimators, that have not yet been developed for SAR models in the context of the gravity equation (dyadic observations).
14. The main differences with alternative estimates are as follows: Garmendia et al. (Citation2012), although using inter-provincial flows within Spain, focus on deliveries by road within the Iberian Peninsula, to the exclusion of the islands. Moreover, most previous specifications use multilateral resistance terms (fixed effects for origins and destinations), which can be redundant in the posterior estimates we base on a gravity SAR model.
15. This factor of 26 (exp(3.268)) is obtained when running model M1, using road flows.