Spatial Selection and the Multiscale Dynamics of Urban Change

Abstract

Growth is a multi-layered phenomenon in human societies, composed of socioeconomic and demographic change at many different scales. Yet, standard macroeconomic indicators average over most of these processes, blurring the spatial and hierarchical heterogeneity driving people's choices and experiences. To address this gap, we introduce here a framework based on the Price equation to decompose aggregate growth exactly into endogenous and selection effects across nested spatial scales. We illustrate this approach with population and income data from the Chicago metropolitan area (2014-2019) and show that both growth rates and spatial selection effects are most intense at local levels, fat-tailed and spatially correlated. We also find that selection, defined as the covariance between prevailing income and relative population change, is concentrated in few spatial units and exhibits scaling behavior when grouped by county. Despite the intensity of local sorting, selection effects largely cancel in the aggregate, implying that fast heterogeneous micro-dynamics can yield deceptively stable macro-trends. By treating local spatial units (neighborhoods) as evolving subpopulations under selection, we demonstrate how methods from complex systems provide new tools to classify residential selection processes, such as abandonment and gentrification, in an urban sociological framework. This approach is general and applies to any other nested economic systems such as networks of production, occupations, or innovation enabling a new mechanistic understanding of compositional change and growth across scales of organization.

Figures (8)

• Figure 1: Local income and population growth rates are very heterogeneous and spatially correlated. In Chicago, A) relative income growth (left) and population growth (right) in neighborhoods (census tracts) vary strongly, on the order of $\gamma_{p_\textrm{tr}}= \pm 5\%$/year and $\Delta\gamma_{p_\textrm{tr}}\pm 8\%$/year respectively. The insets show how the local heterogeneity and correlations in growth rates at the tract level wash out under averaging ($\textrm{E}_\textrm{cm}[\cdot]$) into community areas. B) Heterogeneity, measured by the standard deviation at each organizational level across the MSA, decreases under aggregation. Shifts in the mean value encode selection effects to be explored in this paper. C) Differences between income growth aggregation methods, defined in Eqs. \ref{['eq:priceaggregation']} and \ref{['eq:oleypakesaggregation']}, and a standard measure of aggregate income growth via Eq. \ref{['eq:empiricalgrowth']} encode information about growth dynamics.
• Figure 2: Schematic of 3-level decomposition in a typical community area with no population growth but positive income growth. Between tracts (mid-level) the population rebalances from the low-income A to the high-income tract B. Between block groups (lowest level), populations and incomes are growing in tract B's lower income areas, and populations are declining in tract A's low income areas. These changes are recorded as selection effects and transmitted via averaging to the community level.
• Figure 3: Population selection on income varies widely across neighborhoods and scales. A. The raw income and population growth data are divided into three regions (contour lines). B. Local income selection effects transmitted to the community area level, mapped for the city of Chicago by region are computed from block group-level effects (left) and tract-level effects (right). The aggregate selection effect for each unit is amplified or hidden, depending on whether the selection is complementary (same-sign) or competing (opposite-sign).
• Figure 4: Analyses of local selection enables a more systematic understanding of urban dynamics. A. Aggregate income and population growth data are complemented by selection, suggesting potential hypotheses of local change. B. Selection effects are spatially concentrated, with 20% of tracts (communities) accounting for 59% (64%) of overall selection. C. The average selection magnitude is larger in more populated counties. D. Selection magnitudes, $\rho_j^p$, are the highest within tracts, however selection effects transmitted via the Price equation, $\omega_j^p$, are the most consistent across communities in a county. Low transmitted selection effects indicate they largely counterbalance in the Chicago MSA.
• Figure 5: Income and population growth rate data reported between the 2014-2019 period. A) Population and income growth rates are symmetric and fat-tailed, while log incomes are fit with a Gaussian distribution. B) Community-level maps demonstrate that populations were concentrated on the north side and far-west side, however most population growth was measured along the eastern lakefron. Incomes were concentrated along the lakefront in 2014, however most income growth was observed inland in the northwest side neighborhoods, and southwest side communities.