Property Values, Water Quality, and Benefit Transfer: A Nationwide Meta-analysis

Dennis Guignet; Matthew T. Heberling; Michael Papenfus; Olivia Griot

doi:10.3368/le.98.2.050120-0062R1

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FIGURE 1
Number of Water Quality Hedonic Studies in Each U.S. State

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Table 1

Mean Elasticity Estimates of the Three Most Frequently Examined Water Quality Measures

Water Quality Measure	Unweighted Mean (1)	Cluster-Weighted Mean (2)	Variance-Adjusted Cluster-Weighted Mean (3)	RES Cluster-Adjusted Weighted Mean (4)	n	Studies	Clusters (K_d)
Chlorophyll a (mg/L)
Waterfront	0.737^* [−0.044, 1.517]	0.324^* [−0.036, 0.684]	−0.023^*** [−0.028, −0.019]	−0.026^*** [−0.031, −0.021]	18	3	3
Nonwaterfront within 500 m	0.005 [−0.201, 0.211]	0.01 [−0.085, 0.105]	0.008^*** [0.005, 0.010]	0.009^*** [0.006, 0.012]	18	3	3
Fecal Coliform (count per 100 mL)
Waterfront	−0.018^*** [−0.026, −0.011]	−0.037 [−0.088, 0.014]	−0.028 [−0.079, 0.023]	−1.3E-4^*** [−1.8E-4, −0.7E-4]	36	4	4
Nonwaterfront within 500 m	−0.020^*** [−0.034, −0.006]	−0.058^* [−0.127, 0.010]	−0.061^* [−0.129, 0.008]	−0.052^** [−0.096, −0.008]	20	3	3
Water Clarity (Secchi disk depth, m)
Waterfront	0.158 [−6.099, 6.416]	0.206 [−16.575, 16.987]	0.191 [−16.590, 16.972]	0.109^*** [0.099, 0.118]	177	18	66
Nonwaterfront within 500 m	0.028^*** [0.020, 0.036]	0.042^*** [0.025, 0.059]	0.041^*** [0.024, 0.058]	0.026^*** [0.017, 0.034]	83	6	19

Note: Confidence intervals at the 95% level are displayed in brackets. Only elasticity estimates pertaining to the three most commonly examined water quality measures in the hedonic literature are presented, but the full suite of mean elasticity estimates are presented in Appendix B.2. We present the respective units for each water quality measure in parentheses just as a reference but emphasize that the elasticity estimates are unit-less. RES, random effect size.
↵* p < 0.1;
↵** p < 0.05;
↵*** p < 0.01;

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Table 2

Descriptive Statistics of Observations Pertaining to Water Clarity

Variable	Mean	Std. Dev.	Min.	Max.
Dependent Variable
Elasticity	0.1167	0.2543	−0.6478	1.7198
Study Area/Commodity Variable
Waterfront^{^a}	0.6808	0.4671	0	1
Mean clarity (Secchi disk depth, m)	2.34	1.97	0.38	6.45
Lake or reservoir^{^a}	0.5615	0.4972	0	1
Estuary^{^a}	0.4385	0.4972	0	1
Waterbody size^{^b} (sq. km)	6.8846	5.3156	0.0002	20.8858
Median income (thousands, 2017$)	59.078	14.144	37.865	91.174
College degree (% population)	0.1366	0.0414	0.0768	0.2734
Population density (households/sq. km)	49.91	58.38	1.41	227.96
Mean house price (thousands, nominal $)	211.314	131.341	31.287	675.364
Northeast^{^a}	0.2885	0.4539	0	1
Midwest^{^a}	0.1923	0.3949	0	1
South^{^a}	0.4846	0.5007	0	1
West^{^a}	0.0346	0.1832	0	1
Methodological Variable
Elasticity variance	1,228.159	18,704.52	9.03E-06	301,448.5
Unpublished^{^a}	0.1500	0.3578	0	1
Not in situ measure^{^a}	0.6115	0.4883	0	1
Other water quality variables^{^a}	0.2192	0.4145	0	1
Assessed values^{^a}	0.0538	0.2261	0	1
Study time period (years)	10.27	3.82	3	24
Time trend (0=1994 to 20=2014)	8.59	6.17	0	20
No spatial methods^{^a}	0.3808	0.4865	0	1
Double-log^{^a}	0.4308	0.4961	0	1
Linear-log^{^a}	0.3077	0.4624	0	1
Linear^{^a}	0.0385	0.1927	0	1
Log-linear^{^a}	0.2231	0.4171	0	1

Note: Unweighted descriptive statistics are presented for n = 260 elasticity estimates in the meta-dataset per-taining to water clarity. Estimates are based on 18 primary hedonic studies, corresponding to 66 study-housing market clusters.
↵a Independent variables that are dummy variables.
↵b Size of the waterbody (or waterbodies) examined in the primary studies was only available for n = 79 of the 260 observations in the meta-dataset pertaining to water clarity. If multiple waterbodies were examined in the primary study hedonic regression models, the average waterbody size is reported.

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Table 3

Variance-Adjusted Cluster-Weighted Least Squares Meta-regression Results

Variable	(1)	(2)	(3)	(4)	(5)	(6)
Waterfront^{^a}	0.1457^*** (0.046)	0.0170 (0.023)	−0.0677 (0.052)	0.1010^** (0.039)	−0.1126 (0.086)	0.1251^*** (0.042)
Midwest^{^a}		−0.1056 (0.087)	−0.1488^* (0.082)	−0.2059 (0.132)	−0.2561^*** (0.096)	−0.3156^*** (0.116)
South^{^a}		−0.2248^*** (0.076)	−0.2797^*** (0.084)	−0.3209^* (0.171)	−0.2889^*** (0.108)	−0.3945^*** (0.131)
West^{^a}		−0.1803 (0.120)	−0.1803 (0.121)	−0.1747 (0.147)	−0.3745^** (0.180)	−0.3772^** (0.174)
Estuary^{^a}			−0.0401^** (0.016)		−0.1223^*** (0.039)
Waterfront × estuary			0.1274^** (0.055)		0.1721^* (0.088)
Mean clarity				0.0375 (0.030)		0.0799^** (0.035)
Waterfront × mean clarity				−0.0684^** (0.029)		−0.1061^** (0.050)
Elasticity variance	8.97E-07^*** (1.52E-07)	6.26E-07^** (2.56E-07)	6.26E-07^** (2.57E-07)	5.10E-07 (3.30E-07)	6.02E-07^** (2.56E-07)	5.02E-07 (3.65E-07)
Time trend					0.0183^*** (0.006)	0.0223^*** (0.006)
Linear-log^{^a}					0.1973 (0.161)	0.1987 (0.159)
Linear^{^a}					0.2198^** (0.086)	0.1159 (0.083)
Log-linear^{^a}					−0.0020 (0.008)	−0.0059 (0.008)
Constant	0.0414^* (0.021)	0.2474^*** (0.077)	0.3320^*** (0.090)	0.3092^* (0.182)	0.1681 (0.122)	0.0493 (0.180)
Observations	260	260	260	260	260	260
Adjusted R-squared	0.080	0.148	0.148	0.156	0.170	0.176

Note: The dependent variable is the home price elasticity with respect to water clarity (Secchi disk depth). Clustered-robust standard errors are in parentheses and are clustered according to the K = 66 study-housing market combinations. Weighted least squares regressions are estimated using the “regress” routine in Stata 16 and defining analytical weights equal to the variance-adjusted cluster weights (see equation [3]).
↵a Independent variables that are dummy variables.
↵* p < 0.1;
↵** p < 0.05;
↵*** p < 0.01;

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Table 4

RES Cluster-Adjusted Weighted Least Squares Meta-regression Results

Variable	(1)	(2)	(3)	(4)	(5)	(6)
Waterfront^{^a}	0.0828^*** (0.018)	0.0374^* (0.022)	−0.0356 (0.050)	0.0715^* (0.036)	0.0080 (0.044)	0.0829^** (0.031)
Midwest^{^a}		−0.0204 (0.040)	−0.0462 (0.036)	−0.0475 (0.048)	−0.1565^*** (0.032)	−0.1476^*** (0.039)
South^{^a}		−0.0833^*** (0.031)	−0.1451^*** (0.043)	−0.1096 (0.081)	−0.2600^*** (0.037)	−0.2495^*** (0.044)
West^{^a}		−0.0607 (0.097)	−0.0607 (0.098)	−0.0595 (0.107)	−0.3200^*** (0.111)	−0.4216^*** (0.077)
Estuary^{^a}			−0.0181 (0.020)		−0.0534^*** (0.020)
Waterfront × estuary			0.1019^* (0.055)		0.0582 (0.050)
Mean clarity				0.0247 (0.037)		0.0601^*** (0.022)
Waterfront × mean clarity				−0.0332 (0.032)		−0.0317 (0.024)
Elasticity variance	2.22E-05 (2.18E-05)	2.05E-05 (2.04E-05)	2.01E-05 (2.01E-05)	2.01E-05 (2.01E-05)	1.91E-05 (1.93E-05)	1.86E-05 (1.89E-05)
Time trend					0.0121^*** (0.002)	0.0158^*** (0.002)
Linear-log^{^a}					−0.0371 (0.040)	−0.0953^* (0.049)
Linear^{^a}					0.0807 (0.091)	0.0493 (0.052)
Log-linear^{^a}					−0.0023 (0.005)	−0.0001 (0.005)
Constant	0.0257 (0.016)	0.1025^*** (0.031)	0.1755^*** (0.055)	0.1086 (0.098)	0.1577^*** (0.034)	0.0034 (0.063)
Observations	260	260	260	260	260	260
Adjusted R-squared	0.101	0.146	0.159	0.148	0.201	0.222

Note: The dependent variable is the home price elasticity with respect to water clarity (Secchi disk depth). Clustered-robust standard errors are in parentheses and are clustered according to the K = 66 study-housing market combinations. Weighted least squares regressions are estimated using the “regress” routine in Stata 16 and defining the analytical weights equal to the random effect size (RES) cluster-adjusted weights (see Section 2).
↵a Independent variables that are dummy variables.
↵* p < 0.1;
↵** p < 0.05;
↵*** p < 0.01;

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Table 5

Out-of-Sample Transfer Error: Median Absolute Value of the Percent Difference in Predicted Elasticities

Weighing Scheme	Weighted Mean	WLS 1	WLS 2	WLS 3	WLS 4	WLS 5	WLS 6
Comparison with Synthetic Observations for Excluded Cluster (n=85)
Variance-adjusted cluster (%)	92.5	90.5	87.0	108.1	93.9	119.0	104.2
RES cluster-adjusted (%)	76.0	76.3	82.7	89.4	89.4	90.7	78.9
Comparison with Excluded Cluster Observations (n=260)
Variance-adjusted cluster (%)	130.5	127.5	89.8	100.5	99.9	120.3	121.4
RES cluster-adjusted (%)	82.7	83.4	83.1	89.5	90.4	93.7	87.2

Note: The out-of-sample transfer error is calculated by iteratively leaving out sets of observations pertaining to each of the K = 66 clusters, estimating the model with the remaining clusters ’ observations, and calculating the predicted elasticities and resulting transfer error for the synthetic observation or the actual observations corresponding to the excluded cluster. RES, random effect size; WLS, weighted least squares.