Can Density Reallocation Reshape Urban Residual Dependence?An Ex Ante TDR Design Diagnostic for Seoul

Technical Summary: Can Density Reallocation Reshape Urban Residual Dependence?

Problem Statement
Existing evaluations of density instruments—such as upzoning, Floor-Area-Ratio (FAR) relaxation, and Transfer of Development Rights (TDR)—primarily focus on first-moment outcomes: price levels, quantities, uptake, and equity. This paper addresses a gap in the literature by examining a second-moment outcome: the residual dependence structure of urban property prices. Specifically, it asks how the reallocation of permitted density via TDR reshapes the degree to which property values across a metropolitan market co-move in response to common disturbances (e.g., interest rate shifts or land-price revaluations). The central design question is whether reallocating permitted FAR alters the "saturation-neighbor network" and, consequently, the undiversifiable risk component of the metropolitan market, defined by the pairwise correlation of price residuals.

Methodology
The study employs a multi-matrix spatial-error modeling framework applied to 22,020 commercial and mixed-use property transactions across seven South Korean metropolitan cities (2018–2025), with a primary focus on Seoul where density constraints are most binding.

1. Measurement of Saturation: The author defines "nominal development saturation" ($s_i$) as the ratio of realized FAR to the base use-zone FAR benchmark. Observations with $s_i > 1$ are retained, reflecting lawful bonuses, legacy permissions, or denominator incompleteness, rather than being treated as errors.
2. Structural Model: The core estimation uses a multi-matrix spatial-error model:
   $$u = \lambda_d W_d u + \lambda_s W_s u + \varepsilon$$
   Where $W_d$ is a geographic-distance neighbor matrix and $W_s$ is a development-saturation neighbor matrix (based on $k$-nearest neighbors in saturation space). The model-implied covariance of residuals is derived from the spatial multiplier $A^{-1} = (I - \lambda_d W_d - \lambda_s W_s)^{-1}$.
3. Empirical Strategy:
   • Cross-City Validation: Reduced-form regressions test for a saturation-organized pattern of residual correlations across seven cities.
   • Structural Estimation: Maximum likelihood estimation in Seoul separates geographic dependence ($\lambda_d$) from saturation-based dependence ($\lambda_s$).
   • Temporal Validation: A rolling out-of-sample test (2023–2025) evaluates whether the saturation channel improves covariance prediction or functions merely as an in-sample descriptor.
   • Counterfactual Analysis: The paper constructs a "volume-conserving" TDR counterfactual. It holds the built stock (realized FAR) fixed while reallocating the permitted FAR denominator. This alters the saturation matrix ($W_s^0 \to W_s^1$), which is then propagated through the estimated spatial multiplier to calculate changes in the model-implied correlation matrix.
4. Design Scenarios: Six distinct designation geometries are tested (e.g., sending from the lowest saturation quartile to the highest, concentrating receivers, or administrative constraints) while holding the total transferred floor area constant.

Key Results

• Saturation Dependence in Seoul: In Seoul, a small but detectable component of residual price dependence is organized by development saturation, distinct from geographic proximity. The pooled estimate for the saturation parameter is $\lambda_s = 0.0667$ ($p=0.001$). This persists in a year-block graph (excluding cross-year links) with $\lambda_s = 0.0548$ ($p=0.012$), representing approximately 82% of the pooled magnitude.
• Out-of-Sample Limitation: The saturation channel does not improve rolling temporal out-of-sample covariance prediction. Consequently, the author treats $\lambda_s$ as an in-sample structural descriptor rather than a validated forecasting parameter.
• Metropolitan Impact: Under a volume-conserving TDR, the change in metropolitan-wide mean absolute correlation is economically negligible (ranging from -0.050% to +0.126% depending on the sample frame). The aggregate effect is statistically indistinguishable from zero.
• Local Impact and Geometry: While the metropolitan aggregate is negligible, the local effects are substantial and offsetting. Newly formed saturation-neighbor edges gain approximately 0.014 in absolute correlation, while severed edges lose approximately 0.012.
• Role of Designation Geometry: When the transferred volume is held fixed, the geometry of the designation determines the extent of the network reassignment. The share of the saturation network reassigned varies significantly across scenarios, ranging from 19.5% (saturation-proximate) to 44.2% (distance-proximate). However, the magnitude of correlation change per formed/severed edge remains nearly invariant across geometries.

Claims and Significance
The paper positions itself strictly as an ex ante policy-design diagnostic, not a causal ex post evaluation or a welfare claim. Its contributions are framed with specific claim discipline:

1. Definitional Contribution: It establishes urban residual dependence as a design-relevant outcome of density policy, moving beyond price levels to the dependence structure.
2. Empirical Location: It identifies Seoul as the market where a saturation-organized pattern is empirically visible, distinguishing it from other cities with lower saturation levels, without claiming a sharp regime break for all cities.
3. Mechanism Separation: It successfully separates geographic and saturation-based structures in a multi-matrix model, demonstrating that saturation adds a distinct, albeit small, incremental channel to residual dependence.
4. Design Diagnostic: The framework provides a protocol for monitoring. It concludes that edge-group monitoring (tracking formed and severed saturation links) is more informative than citywide averages.
5. Policy Implication: The paper claims that while TDR can alter the saturation-based network, the metropolitan consequence is negligible. The primary design lever is not the total volume transferred (which "prices" the reassignment) but the designation geometry, which determines the extent (number of pairs) of the network reassignment.

The author explicitly avoids claiming that TDR causes prices to co-move, that it raises or lowers metropolitan risk, or that it improves welfare. The significance lies in providing a falsifiable, network-based diagnostic tool for policymakers to anticipate how specific designation geometries will rewire local dependence structures before implementation.