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. This branch of theory comes from the von Thünen (1826), Alonso/Muth/Mills tradition, and the methods come from McFadden and discrete choice. 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) inluding 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.
Steven Deller has a nice set of slides on Location Theory
31.1 Attainment Models
A linear model with a continuous outcome.
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).
31.2 Choice Models
a discrete outcome, trying to recover demand parameters
housing and transportation modeling rely on understanding discrete choices among multiple 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.
When making a location choice, people optimize a utility function based on the characteristics of the unit and its surroundings
\[ U = f(H,A,D,E) \]
\(H\) is housing stock, \(A\) is access to amenities, \(D\) is the demographic makeup, \(E\) is the environmental quality. 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 their preference for urban amenities exceeds their combined preferences for segregation and access to ‘rural amenities’ like open space. You have no control over A,D, or E, but you do over H, so housing gets redeveloped. In other words, gentrification happens when affluent preferences for accessibility outweigh their preferences for segregation. 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.
- residential discrete choice models
- ABMs and LU/TR microsimulation models
31.3 Optimization Models
a linear programming problem where demand is presumed to be known
you 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).
31.4 References
I actually mean that precisely as written. The literature is obtuse–not the reader–
for failing to recognize (thus confusing the reader) about 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 ended up in different disciplines, to recognize one another any longer.↩︎