Spatial Flow Models – Geography – UGC NET – Notes

Introduction

Spatial interaction models seek to explain flows between locations. The two most common flows considered are those of people (e.g., migration) and goods (e.g., trade) and the most common way of modeling these is to use some form of gravity model where flows are proportional to the mass at destination and location and inversely proportional to the degree of friction between those locations. For example, trade flows between A and B are modeled as proportional to the multiple of gross domestic product (GDP) at the two locations and inversely proportional to the distance between the two locations.

As with regional impact models, gravity and other interaction models have shown themselves to be very useful for fitting data and thus provide a simple way to make predictions about the impact of certain policies. Researchers have also developed a large number of rigorous theoretical models that have an appropriately adjusted gravity model as the reduced form explaining flows as a function of mass and frictions. If one knew which of these theoretical models was appropriate, one could estimate the underlying structural parameters and then, in contrast to regional impact models, provide predictions that are not subject to the Lucas critique. Of course, the problem is that, if we only observe flows, location mass, and frictions, it is impossible to identify which theoretical model is appropriate because they all make the same prediction about the relationships between these variables. Thus, while in principle, the availability of a variety of rigorous theoretical underpinnings distinguishes spatial interaction modeling from regional impact modeling; in practice both are essentially reduced form of approaches to understanding the spatial economy.

Interestingly, the regional science versus social science split that was discussed with respect to location theory also plays out for spatial interaction modeling. The gravity model was originally based on an analogy with Newton’s law of gravitation. In providing theoretical foundations, regional science has tended to focus on drawing on the hard sciences (e.g., physics) while other researchers in quantitative geography and economics have continued to emphasize behavioral assumptions drawn from the social sciences.

Estimating flows between locations is a methodology of relevance to transportation. These flows, known as spatial interactions, enable to evaluate the demand (existing or potential) for transport services. They cover forms of mobility such as journeys to work, migrations, tourism, the usage of public facilities, the transmission of information or capital, the market areas of retailing activities, international trade, and freight distribution. Mobility can be physical (passengers or freight) or intangible (information), and each form of mobility is subject to a form of friction.

Economic activities are generating (supply) and attracting (demand) movements.

The simple fact that a movement occurs between an origin and a destination underlines that the costs incurred by a spatial interaction are lower than the benefits derived from such an interaction. As such, a commuter is willing to drive one hour because this interaction is linked to an income, while international trade concepts, such as comparative advantages, underline the benefits of specialization and the ensuing generation of trade flows between distant locations.

Three interdependent conditions are necessary for a spatial interaction to occur:

• Complementarity: There must be a supply and a demand between the interacting locations. A residential zone is complementary to an employment zone because the first is supplying workers while the second is supplying jobs. The same can be said concerning the complementarity between a store and its customers and between an industry and its suppliers (movements of freight). An economic system is based on a large array of complementary activities.
• Intervening opportunity (lack of): Refers to a location that may offer a better alternative as a point of origin or as a point of destination. For instance, in order to have an interaction of a customer to a store, there must not be a closer store that offers a similar array of goods. Otherwise, the customer will likely patronize the closer store and the initial interaction will not take place.
• Transferability: Mobility must be supported by transport infrastructures, implying that the origin and the destination must be linked. Costs to overcome distance must not be higher than the benefits of the related interaction, even if there are complementarity and no alternative opportunity.

Spatial interaction models seek to explain existing spatial flows. As such it is possible to measure flows and predict the consequences of changes in the conditions generating them. When such attributes are known, it is possible to better allocate transport resources such as conveyances, infrastructure, and terminals.

Origin/Destination Matrices

Each spatial interaction, as an analogy for a set of movements, is composed of a discrete origin/destination pair. Each pair can itself be represented as a cell in a matrix where rows are related to the locations (centroids) of origin, while columns are related to locations (centroids) of destination. Such a matrix is commonly known as an origin/destination matrix, or a spatial interaction matrix.

In the O/D matrix, the sum of a row (Ti) represents the total outputs of a location (flows originating from), while the sum of a column (Tj) represents the total inputs (flows bound to) of a location. The summation of inputs is always equaling to the summation of outputs. Otherwise, there are movements that are coming from or going to outside the considered system. The sum of inputs or outputs gives the total flows taking place within the system (T). It is also possible to have O/D matrices according to the age group, income, gender, etc. Under such circumstances, they are labeled sub-matrices since they account for only a share of the total flows. If the sample is small and disaggregated it is possible to use a simple list of interactions instead of a matrix. Still, an origin/destination matrix can be constructed out of this list.