31 Location Models
There are two camps that claim “location theory”. Urban economists are generally much more interested in the demand side, asking questions about why certain groups of people, or household types, or industrial sectors choose to locate in certain places in a region over others. These are critical questions for understanding the role of place in social mobility (as in input or output) and the ways that race and class intertwine to produce spatial patterns. This branch of theory comes from the von Thünen (1826), Alonso/Muth/Mills tradition, and the methods come from McFadden (1978) and discrete choice analysis. In this case, we adopt a structural approach and try to infer the demand function, recovering what people value about location. These are critical questions for understanding, e.g. housing and land policy
By contrast, scholars from Operations Research and spatial optimization tend to think about the supply side, asking questions about the most efficient way to distribute a given resource. This assumes we know the demand quantity we need to optimize the supply function to allocate resources. This branch comes from Christaller (1937), Lösch (1940), Weber (1929), Hotelling (1929) and the methods come from the Church Legacy of (Chen et al., 2021; Church & Murray, 2008; Murray & Church, 1996; Wei & Murray, 2012, 2014, 2016) including linear programming, location-allocation, and optimization modeling. These are critical questions for understanding, e.g. logistics or service delivery.
These are very different angles on understanding space, where one is behavioral and the other is algorithmic. That means the demand side requires support from a great deal of additional theory, because we’re relying on structural assumptions about how people behave (rather than testable assumptions about how to optimize a linear system of equations). But they both claim “location theory,” so the literature can be obtuse1. The way “location” is modeled as an outcome tends to depend heavily on disciplinary background, with sociologists focusing on neighborhood status as a dependent variable, economists focusing on which discrete unit (housing unit or neighborhood) is chosen, and geographers focusing on the optimal set of “location covering” firms.
31.1 Attainment Models
Locational attainment models are a hallmark of stratification research where scholars, particularly in demography, examine some measure of neighborhood or location as a continuous outcome (e.g. by measuring median incomes or neighborhood educational attainment (Freeman, 2008; Leibbrand & Crowder, 2018; Logan et al., 1996; Logan & Alba, 1993; Pais, 2017; Quillian, 2015; Rosenbaum & Friedman, 2001; Sampson & Sharkey, 2008; South et al., 2016; Woldoff, 2008). Classically, sociologists think about inequality as a result of systematic social processes, e.g. where social and economic systems reward certain personal characteristics over others. A racist economic system, for example, will stratify social mobility as a function of race, allowing those with privilege to climb the ladder faster.
As a result, the traditional “locational attainment” model in demography examines how people translate their individual capital and personal traits into spatial capital, as an expression of social class (interestingly, this hints at a Tieboutian process–and the fact that “equilibrium” is a function of existing inequality in location choices because groups differ in their ability to optimize location capital). Nearly identical in concept to the human capital model in economics where wages are expressed as a function of education, the locational attainment model expresses residential neighborhood quality as a function of individual attributes (race, class, education). In the U.S., these models are built commonly using restricted person-level data from the Panel Study of Income Dynamics (PSID), and while we will not explore them further via an empirical example, locational attainment models are nonetheless a critical piece of the “location models” literature.
31.2 Choice Models
As an alternative, some prominent scholars have argued that demographers should make more use of the discrete choice model, where neighborhood outcomes are not compressed into a single continuous outcome, but each offers a distinct bundle of attributes (Bruch & Mare, 2006; Bruch & Mare, 2012; Bruch & Swait, 2019; Hoffman & Duncan, 1988). In this approach, pioneered in economics, location is treated as a discrete outcome, and the model attempts to recover parameters of a location demand function. This is a behavorial approach recognizing that housing and transportation modeling rely on understanding discrete choices among multiple competing alternatives, like whether to buy or rent a home, which house to buy, which mode of transportation to take to work, and the route by which to travel–only one of which can be chosen. When making a location choice, we assume people optimize a utility function based on the characteristics of the unit and its surroundings, such as
\[ U = f(H,A,D,E) \]
where the utility (\(U\)) of occupying a given unit is a function of \(H\) housing stock characteristics, \(A\) access to amenities, \(D\) the demographic makeup nearby, and \(E\) is the environmental quality in the neighborhood. These map roughly to the mechanisms of neighborhood effects and the major determinants of housing value we have seen earlier. We also know from the historical structure of cities these elements are correlated: lower income and minority populations are located downtown, as is access to jobs. Greater environmental quality and newer housing stock tend to be on the periphery. Gentrification happens when \(U(A) > U(D+E)\), that is, when the gentry’s preference for urban amenities exceeds their combined preferences for segregation and access to ‘rural amenities’ like open space.
From a policy or economic development perspective, land use measures have no control over D, limited control over A or E, but a great deal of control to manage H—so housing gets redeveloped. In other words, gentrification happens when affluent preferences for accessibility outweigh their preferences for segregation and extra space. Historically, the flat bid-rent curve for high-income households means A is less important relative to D (\(A<D\)). But recently, \(A>D\), so affluent people move downtown and outbid lower income residents, leading to displacement and renovating housing stock in the process. This is a classic framework in urban economics described as “filtering” (Galster, 1996; Grigsby, 1964, 1973; Grigsby & Corl, 1983; Megbolugbe et al., 1996).
During regional planning exercises, like those done by Metropolitan Planning Organizations (MPOs) used to guide federal transportation infrastructure, sometimes \(A\) is anticipated to shift dramatically, e.g. when a new transit line is built or a new toll road is constructed. Thus, a large literature in urban planning, transportation engineering, and regional science beginning in the 1960s explores the development of complex, large-scale, “integrated” land-use and transportation demand models based heavily on choice modeling and simulation. We will scratch the surface of this research in Chapter 32.
31.3 Optimization Models
Apart from trying to understand how people and firms sort themselves into locations, the spatial optimization perspective assumes we have a set of resources to distribute and we need to choose among a set of “best” locations to do so. In this case we take the role of decision-maker with an allocation function (e.g. least cost or maximum coverage) to optimize along with a set of constraints (e.g. budget, capacity) to respect. Following we can define out intended outconme as a mathematical problem and find a solution for making the best possible choice using the help of linear and mixed-integer programming. One can also formulate the location choice process as a location allocation problem, where the objective is to maximize individual utility function subject to a budget constraint. This is where a bridge forms between the two location theory camps (Anas, 1984).
I mean that precisely as written. The literature is obtuse–not the reader–
for failing to recognize (thus confusing the reader) the common origin and relationships between these perspectives. It’s not that they don’t care, it’s that there are no structural incentives for these different perspectives, which have largely fallen into different disciplines, to any longer recognize one another.↩︎