Spatial Non-Stationarity and Wealth Accumulation: Multiscale Regression of Locational Endowments in a Heterogeneous Metropolitan County

Technical Summary: Spatial Non-Stationarity and Wealth Accumulation in a Heterogeneous Metropolitan County

Problem Statement
The study addresses the limitations of global regression models in capturing the spatial structure of household wealth within mid-sized, heterogeneous metropolitan counties. Traditional models assume spatial stationarity, positing that the relationship between locational attributes (e.g., amenities, environmental quality, infrastructure) and economic outcomes is uniform across a region. However, spatial econometric literature suggests these relationships are frequently non-stationary, varying significantly across local contexts. While Geographically Weighted Regression (GWR) has been applied to housing prices and income, there is a scarcity of fine-scale research examining composite household wealth—encompassing housing equity, income flows, and financial assets—in non-coastal, mid-sized settings where urban, suburban, and rural gradients intersect. This research aims to quantify how locational suitability conditions shape household wealth at high spatial resolution and to determine whether these relationships operate at distinct spatial scales.

Methodology
The research employs a robust spatial econometric framework centered on Multiscale Geographically Weighted Regression (MGWR), applied to a mid-sized metropolitan county in the southwestern United States.

• Data and Spatial Framework: The analysis utilizes 4,067 regular hexagonal units (each covering approximately 0.3 square miles) to tessellate the study area. This hexagonal grid minimizes the Modifiable Areal Unit Problem (MAUP) and shape distortion associated with administrative boundaries, whereas census tracts and block groups reflect administrative rather than ecological or social processes and introduce aggregation bias. Data sources include the 2016–2020 American Community Survey (ACS), NASA GES DISC, EPA, USGS, and local GIS records. Variables cover socio-demographics, environmental quality (PM2.5, CO2, elevation), and accessibility (distances to schools, hospitals, parks, highways, etc.).
• Dependent Variable: A composite household wealth index was constructed via Principal Component Analysis (PCA) combining median home value, household income, and asset income (interest, dividends, rent). This index accounts for approximately 72% of the variance in household net worth compared to Survey of Consumer Finances benchmarks.
• Exploratory Spatial Data Analysis (ESDA): Prior to modeling, the study conducted diagnostics including correlation heatmaps, Variance Inflation Factor (VIF) checks, and global/local spatial autocorrelation tests (Moran's I and LISA). Global Moran's I confirmed strong positive spatial dependence (I = 0.510, p < 0.001), validating the need for spatially explicit modeling.
• Modeling Approach: The study compares three frameworks: Global Ordinary Least Squares (OLS), Global Spatial Econometric models (Spatial Lag and Spatial Error), and MGWR.
  • MGWR Specification: Unlike standard GWR, which imposes a single bandwidth for all predictors, MGWR allows each predictor to operate at its own optimal spatial scale. The model is formulated as: $y_i = \beta_0(u_i) + \sum \beta_k(u_i, b_k)x_{ik} + \varepsilon_i$, where $b_k$ represents variable-specific bandwidths.
  • Estimation: Bandwidths were selected via data-driven optimization minimizing the corrected Akaike Information Criterion (AICc). An adaptive bi-square kernel defined spatial weights, and an iterative backfitting algorithm (via the mgwr Python library) was used for estimation.

Key Results

1. Model Performance: MGWR significantly outperformed global alternatives. It achieved an $R^2$ of 0.989 compared to 0.873 for OLS and roughly 0.90 for spatial lag/error models. Crucially, MGWR effectively eliminated residual spatial autocorrelation (Residual Moran's I $\approx$ 0.02, p = 0.214), whereas global models left significant residual clustering (Moran's I > 0.18, p < 0.05).
2. Spatial Heterogeneity and Non-Stationarity: The analysis confirmed that wealth determinants exhibit substantial spatial non-stationarity.
   • Scale Differentiation: Predictors operate at distinct spatial scales. Income-related variables function at broad regional scales (bandwidths > 100 neighbors), reflecting labor and housing market dynamics. Environmental and transit variables operate at finer, hyperlocal scales (bandwidths < 30 neighbors), governed by neighborhood-specific conditions.
   • Coefficient Variation: Several predictors exhibited sign reversals across the study area. For instance, distance to parks and hospitals was negatively associated with wealth in dense urban cores (where proximity is an amenity) but positively associated in peri-urban areas (where distance proxies for lower density and reduced congestion). Similarly, air pollution effects varied from negative near high-traffic corridors to neutral or positive in low-traffic zones.
3. Wealth Clustering: Local Indicators of Spatial Association (LISA) identified persistent "high-high" clusters in affluent foothill suburbs and "low-low" clusters in the urban core and southwestern regions, reinforcing theories of durable spatial stratification.

Significance and Contributions
The paper claims three primary contributions:

• Empirical: It provides a fine-grained assessment of wealth heterogeneity in a mid-sized, non-coastal metropolitan county, a setting underrepresented in existing spatial economics literature. It demonstrates that wealth is not merely a function of individual characteristics but is deeply structured by place-based mechanisms that vary across urban-to-rural gradients.
• Methodological: The study illustrates the capacity of MGWR to disentangle processes operating at regional, neighborhood, and hyperlocal scales within a single analytical framework. It validates that assuming a single spatial scale (as in GWR) or spatial stationarity (as in OLS) obscures critical local variations in the returns to locational attributes.
• Policy: The results offer a spatially explicit evidence base for differentiated policy interventions. The findings suggest that uniform infrastructure or environmental policies may be ineffective or counterproductive. Instead, interventions regarding amenity investment, environmental remediation, and service provision must be spatially targeted to account for regime-specific returns to locational suitability.

Limitations
The authors note that the cross-sectional design supports spatial association analysis but cannot establish causal direction. Additionally, while the hexagonal grid framework reduces MAUP, residual clustering in transition zones suggests the presence of unmodeled hyperlocal processes. Future work is suggested to address endogeneity through spatial identification strategies and to incorporate longitudinal data to capture evolving dynamics.