1# RECORD 2f1c2029c5f2034d797bc4a5ae390cff3782ab602# TITLE: Area-Based Hedonic Pricing of Urban Green Amenities in Beijing: A Spatial Piecewise Approach3# YEAR: 2024.0 VENUE: Environmental and Resource Economics DOI: 10.1007/s10640-024-00861-24# AUTHORS: Zhaoyang Liu; Heqing Huang; J. Siikamäki; Jintao Xu5# PAGES: 26 CANDIDATE TABLE PAGES (1-based): [17, 18, 19]6# ABSTRACT: This study explores a spatial piecewise approach for the hedonic valuation of the area of urban green space at different distances from a property, using a rich census dataset collected from Beijing. We explore three novel empirical strategies that improve the identification of the spatial boundary or threshold distance within which green space is capitalised into housing prices. We first delineated a series of concentric circles surrounding each property and measured the area of green space within each doughnut-shaped ring. We next estimated the hedonic price using three methods. The first is a regression spline model combined with a machine learning type of model selection procedure which objectively selects the exact location of the threshold distance that optimises the model’s predictive performance. The second is a novel matching algorithm that minimises covariate imbalance for a continuous treatment variable (i.e., the area of green space) to provide stronger causal evidence on the hedonic prices of green space at different distances. The third is a spatial difference-in-differences approach that further accounts for endogeneity bias associated with unobserved factors. For our dataset, we found that housing prices are more likely to be affected by green space within a 1 km radius.789===== PAGE 1 (score 6, numeric-paren 0, table-words 0, var-words 6) =====1011Vol.:(0123456789)12Environmental and Resource Economics (2024) 87:1223–124813https://doi.org/10.1007/s10640-024-00861-2141 315Area‑Based Hedonic Pricing of Urban Green Amenities 16in Beijing: A Spatial Piecewise Approach17Zhaoyang Liu1 · Heqing Huang2 · Juha Siikamäki3 · Jintao Xu218Accepted: 1 March 2024 / Published online: 25 March 2024 19© The Author(s) 202420Abstract21This study explores a spatial piecewise approach for the hedonic valuation of the area of 22urban green space at different distances from a property, using a rich census dataset col-23lected from Beijing. We explore three novel empirical strategies that improve the identi-24fication of the spatial boundary or threshold distance within which green space is capital-25ised into housing prices. We first delineated a series of concentric circles surrounding each 26property and measured the area of green space within each doughnut-shaped ring. We next 27estimated the hedonic price using three methods. The first is a regression spline model 28combined with a machine learning type of model selection procedure which objectively 29selects the exact location of the threshold distance that optimises the model’s predictive 30performance. The second is a novel matching algorithm that minimises covariate imbal-31ance for a continuous treatment variable (i.e., the area of green space) to provide stronger 32causal evidence on the hedonic prices of green space at different distances. The third is a 33spatial difference-in-differences approach that further accounts for endogeneity bias associ-34ated with unobserved factors. For our dataset, we found that housing prices are more likely 35to be affected by green space within a 1 km radius.36Keywords Urban green space · Hedonic pricing · Regression splines · Model selection · 37Covariate balancing matching for continuous treatment · Spatial difference-in-differences38JEL Classification Q51 · Q57 · R3039This paper is an output of the Ecosystem Services Accounting for Development project jointly initiated 40by the Environment for Development Initiative and the Swedish Environmental Protection Agency 41(SEPA Reference Number: NV-05230-14), and funded by the Swedish International Development 42Cooperation Agency (SIDA Reference Number: 13/000230). The authors declare that they have no 43relevant or material financial interests that relate to the research described in this paper. The authors 44sincerely appreciate the very helpful comments provided by Dr. Jessica Alvsilver, Dr. Christopher 45Campbell-Duruflé, Dr. Timothy Hamilton, Prof. Nick Hanley, Prof. Thies Lindenthal, Dr. Richard 46Mulwa, Dr. Matías Piaggio, Dr. Carolin Hoeltken, Dr. Per Stromberg, Dr. Byela Tibesigwa, Dr. Jane 47Turpie and Dr. Dawit Woubishet. In addition, the authors are greatly indebted to Mrs Cyndi Berck for 48editing the paper. Last but not least, the authors gratefully acknowledge two anonymous referees and 49the editor for their very helpful comments on an earlier version of the paper.50Extended author information available on the last page of the article515253===== PAGE 17 (score 21, numeric-paren 0, table-words 6, var-words 5) =====5455123956Area‑Based Hedonic Pricing of Urban Green Amenities in Beijing:…571 358We estimated four DID regressions (Models 4–7, Table 4), which have the same speci-59fication as in Eq. (5) but differ in whether Radiussi is defined as within 1, 2, 3 or 4 km. In 60Model 4 where the radius is 1 km, the positive and statistically significant coefficient on the 61interaction term ‘ After × Radius ’ suggests that a new green space tends to increase housing 62prices within a 1 km radius. In our DID dataset, the average size of green spaces is 4.14ha. 63This suggests that, approximately speaking, a new hectare of green space increases housing 64prices in a 1 km radius by CNY 147.82 or USD 22.26 per m2 of housing. This is notably 65higher than the counterpart estimates from the regression spline and matching analyses, 66although the DID estimate refers to only a subset of the green spaces in the regression 67spline and matching analyses. In Models 5–7 (where the radius is 2, 3 or 4 km), the coef-68ficient on the interaction term ‘ After × Radius ’ is statistically indistinguishable from zero 69(the lowest p value = 0.49), and the absolute value of the estimated effect is much smaller 70than that for a 1 km radius. These results provide further evidence that a new green space is 71more likely to be capitalised into housing prices within a 1 km radius.72Our DID approach has controlled for all location- and time-specific factors, in addition 73to the control variables listed in Table A1. If there are no other confounders, the mean dif-74ference in the (residualised) treated and control housing prices would not vary over time 75before the creation of the green spaces, known as the parallel trends assumption (Wool-76dridge 2020). Otherwise, the main causal strength of this DID analysis would be confined 77to accounting for location-specific time-invariants (both observed and unobserved) at a 78more detailed level (compared to the regression spline and matching analyses), at the cost 79of focusing on only a subset of the green spaces in our dataset. Figure A5 in the appen-80dix provides some visual evidence for the applicability of the parallel trends assumption 81in our analysis. A Wald test further corroborates that the mean differences between the 82treated and control housing prices are statistically equal across the two pre-treatment years 83(p value = 0.64). These assessments find no evidence that the parallel trends assumption is 84violated.85Table 4 Difference-in-differences estimates86Asterisks indicate statistical significance: * p value < 0.10, ** p value < 0.05, *** p value < 0.01. Standard 87errors are in parentheses88DV: log (housing price)89Model 490Model 591Model 692Model 793Radius = 1 km94Radius = 2 km95Radius = 3 km96Radius = 4 km97EV98After99−1.04 × 10−2*100−1.01 × 10−2*101−9.09 × 10−3102−8.83× 10−3103(5.35 × 10−3)104(5.47 × 10−3)105(5.73 × 10−3)106(6.52 × 10−3)107Radius108−4.13 × 10−3109−1.01 × 10−31101.11 × 10−2***1112.22 × 10−2***112(8.04 × 10−3)113(4.45 × 10−3)114(3.56 × 10−3)115(3.64 × 10−3)116After × Radius1172.31 × 10−2*1184.62 × 10−3119−6.58 × 10−4120−1.11 × 10−3121(1.23 × 10−2)122(6.73 × 10−3)123(5.38 × 10−3)124(5.57 × 10−3)125Green space location fixed effects126Yes127Yes128Yes129Yes130Time fixed effects131Yes132Yes133Yes134Yes135Housing controls (Table A1)136Yes137Yes138Yes139Yes140Model significance (p value)141< 0.01142< 0.01143< 0.01144< 0.01145R2 (within)1460.401470.401480.401490.40150Obs151124,137152124,137153124,137154124,137155156157===== PAGE 18 (score 18, numeric-paren 0, table-words 6, var-words 4) =====1581591240160 161Z. Liu et al.1621 31633.4 Further Robustness Tests164The DID analysis, despite focusing on a subset of the green spaces in our dataset, lends 165further support to our finding that housing prices are less likely to be affected by green 166spaces outside a 2 km radius. On the other hand, the spatial distribution of green space 167in neighbouring locations in Beijing tends to be positively correlated (Wang et al. 2023; 168Zhang et al. 2021). A location is likely to have more green space if its neighbouring loca-169tions have more green space. In fact, for the residential blocks in our dataset, the area of 170green space within 1 km has a correlation coefficient above 0.60 with the area of green 171space at 1–2 km, 2–3 km, and 3–4 km. In other words, green space outside a 2 km radius of 172a property is less likely to directly influence housing price, but tends to be highly correlated 173with green space within a 1 km radius. This suggests the possibility of instrumenting green 174space within a 1 km radius using green space outside a 2 km radius, as a means to further 175explore the implications of potential endogeneity issues. Bayer et al. (2009) adopted a sim-176ilar ‘spatial lag’ type of instrument for air quality.177To facilitate the instrumental variable (IV) estimation, we first estimated an OLS 178hedonic pricing regression (Model 8, Table 5). The right-hand side has only one green 179Table 5 Instrumental variable and placebo estimates180Standard errors are in parentheses181Asterisks indicate statistical significance: * p value < 0.10, ** p value < 0.05, *** p value < 0.01182DV: log (housing price)183Model 8184Model 9185Model 10186Model 11187OLS188IV-2SLS189OLS190OLS191Hedonic price192 Green area 0–1 km1935.90 × 10−4**1941.40 × 10−3**1951.05 × 10−3***196(2.57 × 10−4)197(6.42 × 10−4)198(3.73 × 10−4)199Future green area 0–1 km200−3.92 × 10−4201(1.01 × 10−3)202Housing controls (Table A1)203Yes204Yes205Yes206Yes207Excluded instruments208Green area 2–3 km209No210Yes211No212No213Green area 3–4 km214No215Yes216No217No218Weak IV test219Cragg–Donald Wald F stat220110.83221(H0: Weak IV)222R2 (1st stage)2230.50224Over-identification test225Sargan statistic: p value (H0: Valid IV)2260.19227IV redundancy test228LM test: p value (H0: Redundant IV)229< 0.01230Endogeneity test231Diff-in-Sargan–Hansen Statistic: p value2320.17233(H0: Exogenous ‘Green area 0–1 km’)234Hedonic price model sig.: p value235< 0.01236< 0.01237< 0.01238< 0.01239Hedonic price model R22400.682410.682420.652430.66244Obs24512702461270247889248889249250251===== PAGE 19 (score 21, numeric-paren 4, table-words 5, var-words 7) =====2522531241254Area‑Based Hedonic Pricing of Urban Green Amenities in Beijing:…2551 3256space variable, which represents the total area of all green space within a 1 km radius, 257controlling for other housing and location-specific variables listed in Table A1. The OLS 258estimate of the hedonic price (the estimate for ‘Green area 0–1 km’ in Model 8 in Table 5) 259is smaller than that derived from the regression spline approach (Model 1 in Table 2), but 260remains statistically significant at the 5% level. In Model 9, ‘Green area 0–1 km’ is instru-261mented using the area of green space at 2–3 km and 3–4 km. The F statistic from the weak 262IV test (110.83) is markedly greater than the conventional rule of thumb (10) and exceeds 263a more recently recommended threshold (104.7) (Lee et al. 2022), which provides evidence 264against the null hypothesis of weak identification. The p value from the over-identification 265test is well above the critical value (0.10), which further justifies the validity of the instru-266ments. Although the p value from the endogeneity test does not reject the null hypothesis 267of no endogeneity bias at the conventional critical level (0.10), the IV estimate for ‘Green 268area 0–1 km’ is notably higher than the OLS and regression spline estimates. This suggests 269that the OLS and regression spline estimates are likely to be conservative estimates of the 270true hedonic price of green space.271Lastly, we undertook placebo tests to further assess whether the foregoing analyses have 272picked up some distance-dependent patterns other than the effects of green space on hous-273ing prices. For each residential block, we measured the total area of green space at differ-274ent distances that was created after the residential block was sold. In theory, such ‘future’ 275green space is less likely to affect housing prices, compared to preexisting green space. We 276next re-estimated Model 8 after replacing the variable ‘Green area 0–1 km’ (green space 277inside 1 km that existed before housing transactions) with ‘Future green area 0–1 km’ 278(green space inside 1 km that was created after housing transactions), to test whether the 279model would falsely attribute any unexpected effect to future green space. As in Model 28010 in Table 5, the estimate on ‘Future green area 0–1 km’ is statistically insignificant (p 281value = 0.70), which is in line with intuition. Note that this placebo analysis is confined to 282housing transactions that happened before 2014, because our green space data were col-283lected in 2014, and thus do not include any future green space for housing transactions 284from 2014 onward. We thus re-estimated Model 8 using housing transactions before 2014 285to test whether the estimates could be affected by dropping subsequent housing transac-286tions. This gave rise to Model 11, where the estimate on ‘Green area 0–1 km’ remains 287positive and statistically significant, although larger in size compared to the estimate for the 288full sample. Moreover, we performed another placebo test by adding to Model 10 the area 289of future green space at 1–2 km, 2–3 km, 3–4 km and 4–5 km. As can be seen in Figure A6 290in the appendix, all these placebo estimates are statistically insignificant; the lowest p value 291is above 0.35. In comparison, the non-placebo estimates in Figure A6 were derived from 292an expanded version of Model 11, which contains preexisting green space at different dis-293tances; here, the estimate on ‘Green area 0–1 km’ is almost identical to that in Model 11.2944 Aggregate Hedonic Prices of Green Space in Central Beijing295This section derives the aggregate hedonic prices of green space using the unit hedonic 296price estimates from Sect. III. To reduce computational workloads, we confined the analy-297sis to green spaces that are larger than 0.5ha and located in Beijing’s six central districts. 298For each of these green spaces, we first searched in our dataset for all residential blocks 299located in the green space’s 1 km radius. The aggregate hedonic price was then calculated 300by multiplying the unit hedonic price (the coefficient on the variable ‘Green area 0–1 km’ 301302303===== PAGE 20 (score 4, numeric-paren 0, table-words 0, var-words 4) =====3043051242306 307Z. Liu et al.3081 3309after being converted from a semi-elasticity estimate to a monetary marginal effect esti-310mate) by the total area of the green space and the total floor area of the residential blocks 311within the green space’s 1 km radius. As an example, Fig. 6 maps the aggregate hedonic 312prices of these green spaces individually (based on the regression spline estimate in Model 313(1). Admittedly, owing to the nature of the hedonic approach, the spatial distribution of the 314Fig. 6 Hedonic prices (billion CNY in 2016 prices) of green spaces in Central Beijing315Fig. 7 Aggregate hedonic prices 316(in 2016 prices) of green spaces 317in Central Beijing. Note: M1: 318Model 1, regression spline; M2: 319Model 2, parametric covariate 320balancing generalised propen-321sity score (CBGPS) matching; 322M3: Model 3, non-parametric 323CBGPS matching; M4: Model 3244, difference-in-differences (sub-325sample); M8: Model 8, ordinary 326least squares (OLS); M9: Model 3279, instrumental variable; M11: 328Model 11, OLS (sub-sample)329