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## Urban Spatial Structure: Methods and Models

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**Urban Spatial Structure:Methods and Models**Temple University Dept. of Community and Regional Planning CRP 410 Planning Methods Professor Paulsen December 3, 2004**Today’s lecture**• Demonstrate core features of “distance-based” and “spatial-interaction” models, which can be useful in modeling spatial structures of interest to planners.**Spatial modeling, generally**• Many of the data sets planners utilize, and many of the phenomena we are interested in are inherently spatial. • Our analysis can model spatial processes and relationships explicitly. • Frequently, we essentialize “space” to mean “distance” (and drive real geographers crazy)**Spatial modeling**• A general class of models is called “spatial interaction” models, which says that the interaction between two places (cities, blocks, regions, etc) is a function of the distance between these two places.**Urban Spatial Structure**• A common model of urban spatial structure in Urban Economics is the “Monocentric” Alsonso-Mills-Muth model. • In this model, density/intensity of land uses is a function of the distance from CBD (Central Business District)**Monocentric (AMM) model**Office bid-rent curve Land Value Manufacturing bid-rent curve Residential bid-rent curve d’ d’’ Distance to CBD Density/intensity of use declines with distance Aggregate bid-rent curve is envelope of all bid-rent curves**Land Value**distance**Monocentric (AMM) model**• Utilizes a negative exponential distance function: • The population density of a metropolitan region (under certain conditions) follows the relationship: • The density at location i, which is distance di from the center (do), where gamma is the “gradient” of distance (the rate at which density falls from distance to center)**Monocentric (AMM) model**• The negative exponential density function is empirically estimable using OLS regression by taking a logarithmic transformation.**Estimation of AMM model**• For spatial units (eg. Census tracts) calculate density and distance from a central point. Estimate regression of form: Independent variable: distance Dependent Variable: ln of density Constant Estimated coefficient on distance**Estimation of AMM model**• For Philadelphia PMSA census block groups, acquire data on 2000 population and distance from City Center.**ln of Population Density**Distance from Philadelphia City Center (miles) Non-parametric Kernel density estimation of Monocentric Model for Philadelphia MSA Output created using EasyReg by Herman Bierens**Spatial interaction models**• Spatial interaction is the flow of goods, people, information, etc. between two places • Most generally, the interaction between two regions i and j is a function of the properties of regions i and j and the “distance” between them. • Relevant properties may include number of jobs, number of destinations, square feet of retail space, population, income …**Gravity models**• Gravity models are the most commonly known type of Spatial Interaction Model, based on Newtonian physics. Recall from Physics 101 that the gravitational force exerted between two bodies is a of the product of their masses over the distance between them squared, times the gravitational constant k.**Gravity models**• Likewise, we can hypothesize that the number of job-trips between point A and B is a function of the population at A and the number of jobs at B and the distance between them.**Gravity models**• Let’s specify the form more generally: • We read this as the interaction T between places i (origin) and j (destination) is a function of a constant k, a measure of the “potential” p at place i and j, over distance raised to some power lambda, where alpha and beta are parameters.**Gravity models**• Two approaches to “using” gravity models. • 1. Use theory and generally accepted practice to predict flows between i and j, based on knowledge of Pi and Pj • E.g. Based on populations and jobs data, predict commuting flows between TAZi and TAZj • 2. Use data on actual flows to estimate empirically the parameters of a gravity model.**Gravity models**• Some modeling choices: • Distance decay function. Recall the denominator was specified as: • This is called “distance decay” because the interaction of two places “decays” with increased distance between them**Distance Decay**• Choice of lambda, the distance decay parameter: • Traditionally, and in keeping with Newton’s law of gravity, researchers have used 2. But there is no clear theoretical reason why. • Next slide shows how different values of lambda lead to faster/slower rates of distance decay • Lambda represents the “friction” of distance • We should expect that lambda would be different for different types of interactions**Empirical gravity model example**• Using data on actual flows, estimate the parameters of the gravity model. • Example: County to County commuting flows in New Jersey • Data: 2000 Census for County Populations. 2000 County employment figures, BEA-REIS (Bureau of Economic Analysis-Regional Economic Information System). Commuting flows, Census Transportation data. Distance measured county centroid to centroid from TIGER files**New Jersey commuting flows**• Specify the gravity model to be used • Number of commuters between county i and county j is Tij. • Pi is population in county I (origins) • Ej is measure of employment in county j (destinations)**New Jersey commuting flows**• To make the equation estimable, we take a logarithmic transformation:**Gravity models**• We can utilize the relationships identified in the gravity model to develop “accessibility” indices for places, used in many land use allocation models. • For each location i, we want to express Ai, how “accessible” destinations of interest (j’s) are