Entrance opportunity vs. academic performance: unpacking the nonlinear capitalization effects of multidimensional school qualities on housing sales and rental prices

Many countries allocate access to public schools by residential proximity, which capitalizes school quality into nearby housing values and can exacerbate socio-spatial segregation. In China, point-based school enrolment since 2017 allows tenants to apply to local public schools but with lower priority than homeowners, creating gaps between sales and rental submarkets. Informal school-specific acceptance cut-off points (entrance thresholds) have emerged, guiding parental evaluations of access. This study asks whether and how entrance opportunity, alongside academic performance and other dimensions of school quality, capitalizes into both housing sales and rental prices, and whether effects differ across price segments. The authors hypothesize that academic performance will weigh more heavily for housing sales prices, while entrance opportunity will be more influential for housing rental prices, particularly for lower-priced rentals. The study aims to (1) compare the relative importance of entrance thresholds versus other school indicators, (2) identify stratified effects across sales and rental price segments, and (3) inform policies to mitigate education-capitalization-induced inequalities.

Education capitalization is grounded in the Tiebout hypothesis: households sort across neighborhoods based on preferences for local public goods, including schools, bidding up property values near higher-quality schools. This process fosters socioeconomic segregation and is well documented for sales markets but less so for rentals. In China, tenants' lower priority for school admission under point-based policies implies they may value entrance opportunity more than academic performance, unlike homeowners. Prior studies often operationalize school quality via academic outcomes (test scores, admission rates) or inputs (teacher quality, facilities) and sometimes parental impressions; few adopt multidimensional measures. The popularity and regulatory constraints shaping access (e.g., entrance thresholds) remain understudied, despite evidence that market competition and policy constraints influence capitalization. Traditional hedonic and boundary/PSM designs largely assume linearity and often use dummy measures, potentially misestimating effects and missing threshold/saturation dynamics. Machine learning, especially tree-based methods (RF, GBRT, XGBoost), has been used to model nonlinearity in hedonic contexts but not to examine multidimensional school indicators’ nonlinear capitalization into both sales and rental prices. The authors posit differential capitalization by tenure: academic performance should dominate in sales; entrance opportunity should dominate in rentals.

Study area: Shenzhen, a first-tier Chinese city in the Greater Bay Area, young and rapidly developed, with education prioritized in planning. Data: School data (435 public elementary; 216 public secondary) from Shenzhen Education Bureau, official school sites, and social media (parent discussions); housing data for 1,481 residential quarters with both second-hand sales prices (CNY/m²) and rents (CNY/month/m²) in January 2021 from CREIS; POIs and road network from Amap. School–housing matching follows school district boundaries, including universal/shared districts; when multiple schools apply, housing is matched to nearest if qualities are similar, otherwise to the highest-quality option. High schools are excluded due to boarding and score-based admissions. Multidimensional school quality: Four dimensions with 11 variables—(1) Entrance opportunity: entrance threshold measured by elementary schools’ acceptance cut-off points (points-based admission). (2) Academic performance: secondary school percentages admitted to top 4 and top 8 high schools. (3) Parental impression: unofficial rankings for elementary and secondary schools from social media lists. (4) Policy signal: official school grade (7-tier scale) and name signals (categorical scale capturing terms like “Foreign Language,” “Affiliated,” “Experimental,” “Education Group,” including combinations), plus establishment years for elementary and secondary schools. Housing hedonic controls: 18 variables across structure (building year, number of buildings/households, property fee, green ratio, plot ratio), location (district flag, SEZ status, distances to CBD, bus, subway), and neighborhood (distance to AAA hospital; number of ordinary hospitals within 15-min walk; kernel density of companies—emphasizing high-tech; distance to shopping; golf course buffer; counts of parks/squares/scenic spots and restaurants within 15-min walk). Accessibility is measured via road network distances; 15-minute walking threshold used for local amenities. Modeling: Compare linear regression (baseline) with three tree-based ML algorithms—Random Forest Regression (RFR), Gradient Boosting Regression Trees (GBRT), and Extreme Gradient Boosting (XGBoost)—to capture nonlinear effects with multicollinearity control. Implementation in R (randomForest, gbm, xgboost, caret): 80/20 train-test split; hyperparameter tuning via 10-fold cross-validation; evaluation using R², RMSE, MAE; assess residual spatial autocorrelation via Moran’s I (aiming near 0). Interpretation: Use the best-performing MLA (XGBoost) to compute permutation-based relative importance for features and to generate partial dependence plots (PDPs) for key school indicators to identify threshold and saturation effects. Spatial analysis: Bivariate local Moran’s I (GeoDa, k-nearest neighbors weights) to map spatial clusters between top school indicators (as per relative importance) and housing sales or rental prices (high-high, low-low, high-low, low-high clusters).

Model performance: ML models outperform linear regression. For sales: R² ≈ 0.71–0.75 (RFR 0.747, GBRT 0.706, XGBoost 0.750); for rentals: R² ≈ 0.69–0.78 (RFR 0.779, GBRT 0.688, XGBoost 0.781). Moran’s I for ML residuals near 0, indicating little spatial autocorrelation. XGBoost selected as optimal. Relative importance: Overall, school indicators rank ahead of most other amenities. Sales submarket: academic performance dominates, followed by entrance threshold, subjective ranking, name signal, school year, official grade. Rental submarket: entrance threshold ranks ahead of academic performance; other indicators follow a similar order. Primary school indicators generally exert stronger effects than middle school analogs for subjective/name/grade/year. Price segments: In sales, the importance of academic performance_2 (share admitted to top 8 high schools) normalizes near 1 across high-, middle-, and low-price segments—homebuyers consistently value this metric. In rentals, entrance threshold importance is low-to-moderate for high/middle segments but peaks (~1 normalized) for low-price rentals, indicating tenants in the lower-priced segment are most sensitive to entrance opportunity. Nonlinear effects: Academic performance_2 shows threshold and saturation in sales and rentals. Sales PDP: negligible effect until ≈0.09 share admitted to top 8 high schools; from ≈0.09 to ≈0.18, sales prices rise steeply by about 15,000 CNY/m²; above ≈0.18, effects plateau. Rental PDP shows similar but smaller marginal effects. Entrance threshold: Sales increase from about 74,210 to 79,022 CNY/m² across the observed range (smaller than academic performance effect); Rentals rise steadily from roughly 72 to 77 CNY/month/m² across the threshold range, larger than the rental effect from academic performance. Name signals: Schools with “education group” in their names associate with higher premiums in both sales and rentals relative to other name categories. Spatial clustering: High-high clusters of academic performance_2 with sales prices in Bao’an, Nanshan, and Futian; low-low clusters in Longgang, Yantian, and Pingshan. Entrance threshold with rental prices shows a similar but less pronounced clustering pattern.

The results substantiate the hypothesized tenure-based differentiation in education capitalization. Homebuyers prioritize academic performance—especially the share of middle school graduates admitted to elite (top 8) high schools—across all price segments. Tenants, particularly in the lower-price rental market, place greater value on entrance opportunity (elementary school cut-off points), reflecting their heightened risk of exclusion under point-based admissions. These patterns reveal hierarchical school-based housing choice: advantaged households chase superior academic outcomes, while disadvantaged renters prioritize access. The nonlinear PDPs demonstrate threshold and saturation: willingness to pay intensifies from moderate to relatively high school quality, but improvements from low to moderate quality yield limited premiums. This clarifies why policies that modestly improve lower-performing schools may not immediately translate into substantial local price changes, whereas targeted enhancements pushing schools past key quality thresholds can have pronounced capitalization effects. Spatial clustering shows co-location of high academic performance with high sales prices in core districts, aligning with known urban economic gradients, while rental-entrance opportunity clustering is more diffuse, consistent with renters’ access constraints. Together, the findings refine the understanding of multidimensional school quality’s capitalization and highlight how policy-induced admission rules magnify inequalities across tenure and price segments.

This study introduces a multidimensional school quality framework—incorporating entrance opportunity, academic performance, parental impressions, and policy signals—and applies tree-based machine learning to uncover nonlinear capitalization effects on both housing sales and rental prices in Shenzhen. Contributions include: (1) identifying entrance opportunity (cut-off points) as a key, previously overlooked school quality dimension shaping rental prices, especially in low-price segments; (2) confirming academic performance as the dominant driver of sales price premiums across segments; and (3) revealing threshold and saturation effects that pinpoint the quality ranges where capitalization is strongest. Policy implications: (i) design and prioritize education groups that pair high- and low-performing schools for resource sharing to raise schools past key quality thresholds and temper housing differentiation; (ii) delink housing ownership and school access to reduce rental discrimination and associated socioeconomic pressures (including child-rearing costs); and (iii) expand high-quality vocational pathways to alleviate exam-driven anxiety that feeds school- and housing-market competition. Future research should deploy quasi-natural experiments to causally estimate policy impacts (e.g., admission rule changes, education group formation) and examine interactions among school qualities and housing attributes via structural equation modeling or related causal frameworks to disentangle synergistic and antagonistic effects.

The analysis is observational and context-specific (Shenzhen), limiting causal inference and generalizability. Entrance thresholds are sourced from publicly shared cut-off lists (social media), which may introduce measurement noise. Although ML captures nonlinearity and importance, it does not identify causal mechanisms. The study does not fully explore interactions among school quality dimensions and between school and housing attributes; alternative modeling approaches (e.g., structural equation modeling) could clarify these relationships. Finally, the post-2021 policy and market changes (e.g., reference prices for second-hand homes) may affect temporal stability beyond the January 2021 period analyzed.