Spillover effects in neighborhood housing value change: a spatial analysis

Abstract

Despite numerous studies on neighborhood change, the importance of spatial dependence has largely been overlooked. This study aims to examine spillover effects among neighborhood change factors, which means that demographic, housing, and socio-economic characteristics in nearby neighborhoods affect housing value change in a given neighborhood. In analyzing spillover effects, this study used the Neighborhood Change Data Base that includes decennial census data in the U.S. and employed a spatial Durbin model that can analyze both direct and indirect (spillover) effects of neighborhood change factors. The major findings are as follows: 1) neighborhood change factors have spillover effects; 2) the spillover effects are greater than the direct effects for demographic characteristics; 3) the spillover effects of housing and socio-economic characteristics are less dominant compared to those of demographic characteristics. Based on these findings, this study suggests that efforts to promote neighborhood revitalization and to prevent neighborhood decline should take into account spillover effects coming from surrounding neighborhoods.

Keywords:

• Spillover
• neighborhood change
• spatial analysis
• housing value

Notes

1 When the correlated effects are taken into account in running a spatial model in addition to the endogenous and exogenous interaction effect, it is not easy to interpret parameter estimates due to the difficulty of distinguishing endogenous effects from exogenous effects (Elhorst, 2010). Thus, in sacrificing efficiency of estimation, it is more common to ignore spatial dependence in the disturbance than to ignore spatial dependence in the dependent variables-endogenous interaction effects and/or independent variables-exogenous interaction effects (Elhorst, 2010).

2 The largest 100 metropolitan areas are as of the year 2000.

3 The NCDB allows analyzing prior decades other than the 1990s and 2000s in fixed boundaries of census tracts. However, before 1990, the country was not fully divided into tracts so data are only available for the urban areas (https://geolytics.com/products/census-1960-70-80-90-2000). In an effort to analyze more balanced data between time panels, this study employed census data taken after 1990 and analyzed neighborhood change in the 1990s and 2000s.

4 Different people may have different boundaries for a neighborhood as they use different criteria (e.g., physical, socio-economic, and demographic characteristics) in defining a neighborhood (Sawicki & Flynn 1996). Thus, a census track or block group is not likely to exactly match with one’s personal definition of a given neighborhood. I acknowledge the limitation of using census tract as a neighborhood unit and thus suggest a case study that examines spillover effects based on neighborhood boundaries that most residents recognize.

5 The neighborhood average housing value was computed by the neighborhood aggregated value of specified owner-occupied housing units dividing by the total number of specified owner-occupied housing units in the neighborhood. For example, if a neighborhood’s relative housing value was 50 percent of the respective metropolitan average housing value in 1990 but increased to 100 percent of the respective metropolitan average housing value in 2000, then p_t/p_t-1 is 2 and its logged value is 0.69. If a neighborhood’s relative housing value was 200 percent of the respective metropolitan average housing value in both 1990 and 2000, then p_t/p_t-1 is 1 and its logged value is 0.

6 The share of middle-aged housing units (built between the preceding 20 years and 30 years) was used as reference category. While average square footage of houses in a neighborhood is more appropriate to examine the effect of housing size, the NCDB does not include any housing size variable other than the average number of rooms.

7 LeSage and Pace (2009) to and from perspectives are useful in understanding the spillover effects. With the to-a-neighborhood perspective, the spillover effects suggest that, for example, how Black, an independent variable, in surrounding neighborhoods affects neighborhood economic gain, the dependent variable, in the particular neighborhood. By contrast, with the from-a-neighborhood perspective, how Black in a particular neighborhood affects neighborhood economic gain in surrounding neighborhoods. The spillover effects to and from a neighborhood are numerically equivalent (Elhorst 2010).

8 ∂y_i/∂X_ir ≠ β_r for all neighborhoods i, variables r; ∂y_i/∂X_jr ≠ 0 for neighborhoods j ≠ i and all variables r in the spatial Durbin model.

9 The partial derivatives of y are a function of (I_n – ρW)^-1 and this can be expanded as an infinite linear combination of powers of spatial weight matrix (W) like I_n + ρW + ρ²W² + ρ³W³ +… The infinite series of W allows partitioning both the direct and indirect effects on the dependent variables by the powers of W (LeSage and Pace 2009).

10 The difference in magnitude between the direct impact estimates and estimates with non-spatially lagged explanatory variables is due to feedback effects that are impacts passing through surrounding areas, and back to the observation itself (Lesage and Fischer 2008).

11 According to Chi and Zhu (2020), while how to optimally choose a spatial weight matrix can be further explored, there is no prior study on this matter yet. Rather, they suggest utilizing a data-driven approach such as choosing a spatial matrix based on the strength and statistical significance of spatial autocorrelation. This study aims to examine whether spillover effects exist among neighborhood change factors rather than theorizing the specification of the optimal spatial weight matrix and thus took Chi and Zhu (2020) suggestion in choosing a spatial weight matrix.

12 Upon using a distance-based spatial weight matrix, a neighborhood could have too many neighbors in urban areas while a neighborhood could have too few neighbors in rural areas. Thus, I did not consider a distance-based spatial weight matrix. The following shows Moran’s I values based on different types of spatial weight matrices: In the 1990s: queen 0.326, 4 nearest 0.330, 5 nearest 0.321, 6 nearest 0.313; In the 2000s: Queen 0.309; 4 nearest 0.316, 5 nearest 0.307, 6 nearest 0.301. One might question if the estimations change when using different weight matrices other than the rook’s case. For robustness of the empirical results, I ran the spatial Durbin analysis using each of the rest spatial matrices and found that there are no practical differences between those matrices.

13 Jun (2017) shows that spatial clustering is more likely to occur for a “status” variable than a “change” variable, thereby leading to a lower Moran’s I value for a change variable than for a status variable.

14 A smaller AIC value implies that it is more likely to minimize the information loss compared to the true model (Burnham & Anderson 2002). In general, if the difference between two models is more than 10, the model with a smaller AIC is preferred (Yang et al. 2015).

15 I additionally ran the absolute neighborhood housing value change model that was not deflated by metropolitan housing price growth but the model did not fit the data well and thus was not reported. This finding suggests that relative neighborhood housing value change is more appropriate to analyze neighborhood change.

Additional information

Funding

This article was supported by Sungkyun Research Fund, Sungkyunkwan University, 2019.