1. Meta-Analysis of Wetland Values: Modeling Spatial Dependencies Randall S. Rosenberger Oregon State University Meidan Bu Microsoft

2. Overview  Spatial relationships in metadata  Spatial econometric modeling  Application to wetland valuation studies in North America  Sensitivity analysis to intra-study dependence  Conclusions

3. Research questions  Are wetland values correlated across space?  What is the spatial relationship of wetland welfare estimates?  geographic closeness  ecological linkages  socio-economic characteristics of local people

4. Spatial Relationships  Proximity matters – location, location, location Hedonic values increase with proximity to positive amenities Hedonic values decrease with proximity to disamenities  Spatial heterogeneity matters (50km radius) Previous wetland values MRA results Marginal values increase with local GDP Marginal values increase with population density Marginal values decrease with resource density

5. Statistical Problems Locational aspects lead to:  Spatial heterogeneity Metadata augmentation – GDP, population & resource density  Omitted variable problem  Spatial dependence Spatial lag – correlation in dependent variable  Omitted variable problem – biased, inconsistent estimates Spatial error – correlation in errors  Uncorrelated error problem – inefficient estimates

6. Spatial Modeling

7. The Empirical Model

8. Spatial Weight Matrix Definition

9. Spatial Weight Matrices  W defined as Threshold (Euclidean) distances Ecological similarity Economic similarity

10. Threshold Distance W  Any two sites within a threshold are considered neighbors

11. Ecological similar neighbors  Any two sites located in the same boundary are considered neighbors  The USGS Hydrologic Unit 2 (HUC2) unit (n=21)

12. Economic similar neighbors  Any two sites sharing the same socioeconomic attributes (i.e., latent demand) are considered neighbors local education level population density within 50km radius county level average personal income local GDP  Multivariate hierarchical clustering analysis local education level Group observations into clusters (n=40) that have similar values of measured variables

13. Multivariate hierarchical clusters

14. An economic similarity cluster

15. Wetland Metadata  Wetland welfare estimates from primary studies conducted in North America through 2011 80 studies, 163 value estimates  Explanatory variables  Study attributes  Valuation methodology  Wetland ecosystem type  Ecological functions valued  Geographic and socio-economic characteristics

16. Results – Methodology, Ecosystem Spatial model OLSThreshold distance Ecological similarity Economic similarity 50km lag100km lag150km lag Estimate Intercept-3.72 -3.71 * -3.80 * -3.93 * -4.90 ** -3.98 * Wetland area (ha) - log scaled-0.12-0.08-0.13 ** -0.12 * -0.05-0.12 * Economic literature dummy1.19 ** 1 0.90 * 0.94 * 0.95 * * 0.99 * Regional study dummy0.670.610.85 ** 0.82 * 0.140.61 Valuation methodology (Travel Cost Method as the reference group) CVM1.66 ** 2.01 *** 2.08 *** 2.06 *** 1.84 *** 1.60 ** Choice Experiment3.14 ** 3.54 *** 3.49 *** 3.52 *** 3.39 *** 3.34 *** Hedonic Price7.13 *** 6.80 *** 7.24 *** 7.40 *** 6.71 *** 6.86 *** Market Price1.99 ** 2.13 ** 2.13 ** 2.28 ** 2.20 ** 1.81 ** Replacement Cost4.27 *** 4.26 *** 4.22 *** 4.45 *** 4.49 *** 3.99 *** Production Function1.201.95 ** 1.85 ** 1.89 ** 1.85 ** 1.49 * Wetland ecosystem type (Estuarine as the reference group) Riverine2.00 ** 1.001.75 ** 1.82 ** 1.81 ** 1.62 ** Palustrine0.500.390.570.600.760.55 Lacustrine0.940.881.09 * 0.950.820.91

17. Results – Ecosystem Functions Spatial model OLSThreshold distance Ecological similarity Economic similarity 50km lag100km lag150km lag Estimate Ecological function valued Preservation2.89 ** 2.77 ** 3.00 *** 3.08 *** 3.04 *** 2.82 ** Restoration1.491.741.921.841.921.42 Water quality1.852.15*2.17*1.95*1.88*1.78 Flood control & water supply1.301.161.511.531.561.30 Amenity-2.69**-2.64***-2.52**-2.46**-2.32**-2.64*** Recreational fishing & hunting2.58**2.28**2.54**2.62**2.58**2.34** Non-consumptive recreation3.26***3.05***3.34***3.42***3.11***3.01*** Biodiversity1.371.471.651.641.681.46 Commercial fishing & hunting1.471.041.481.471.531.28

18. Results – Geographic/Socioeconomic Spatial model OLSThreshold distance Ecological similarity Economic similarity 50km lag100km lag150km lag Estimate Geographic and socio-economic information Ramsar Site dummy0.190.460.370.350.080.00 Wetland area in 50km radius (ha)/1000 - log scaled-0.26 * -0.30 ** -0.29 ** -0.30 ** -0.27 ** -0.27 ** Population in 50km radius -log scaled0.40 ** 0.26 * 0.27 * * 0.25 * 0.38 ** Education (county level)0.06 ** 0.07 *** 0.06 *** 0.06 ** 0.08 *** 0.06 ** Distance to city (km)0.07 ** 0.10 *** 0.08 *** 0.08 *** 0.08 *** 0.08 *** -0.002 ** -0.003 *** -0.003 *** -0.003 *** -0.003 *** -0.003 ***

19. Results – Test Statistics Spatial model OLSThreshold distance Ecological similarity Economic similarity 50km lag100km lag150km lag Estimate N163 R2R2 0.50 0.1760.1430.1380.1790.095 Likelihood ratio test statistic1710994 P-value for the likelihood ratio test <0.000*** 0.001 *** 0.003 *** 0.003 *** 0.036 ** AIC726 710 717 718 719 723

20. Recap – Spatial MRAs  Positive spatial correlation for all three neighborhood criteria  Threshold distance neighbors are strongest correlation Spatial correlation exists as far as 150km  Economic similarity defined neighbors has the weakest correlation  Covariate estimates are robust to spatial dependence, although magnitude varies some

21. Intra-study Correlation  What about confounding intra-study correlation?  An unbalanced panel meta-dataset with  163 observations from 80 wetland sites  39 wetland sites report multiple measures (max = 16 obs.)

22. Bootstrap Sensitivity Analysis  Bootstrap draw one observation per wetland site  Form 1000 sub-datasets  Repeat spatial MRAs  Test the significance of spatial correlation for every combination  Count the number of significant LLR results  Test the robustness of the spatial correlation

23. Sensitivity Analysis Results Weight Matrix Significant LLR tests @ p ≤ 0.05 Binomial test Significant LLR tests @ p ≤ 0.10 Binomial test 50 km threshold933p < 0.00984p < 0.00 100 km threshold908p < 0.00957p < 0.00 150 km threshold747p < 0.00874p < 0.00 Ecological similarity49p = 0.58107p = 0.24 Economic similarity12p = 1.0045p = 1.00

24. Recap – Sensitivity Analysis  Significant evidence of spatial correlation exists in threshold distance defined neighbors  Inconclusive evidence of spatial correlation in ecological and economic defined neighbors Ecological similarity – HUC2 may be too large Economic similarity – intra-study correlation

25. Conclusions  Spatial correlation exists, although partial effects are robust to specifications  Threshold distance is robust to intra-study correlation   Future issues: Other spatial models (e.g., spatial error specification)? What are the implications for international benefit transfers? Are results consistent for other spatially dependent metadata?

26. Q&A We hope you enjoyed this tour of spatial econometric modeling in an MRA framework THANK YOU!

27. The Parking Lot - Descriptives MeanMeanSt. Dev.MinMax Wetland welfare estimate/ha/year in 2010 USD – log scaled 5.85 5.85 2.65 2.65 -1.50 -1.50 11.81 Wetland area (ha) - log scaled8.468.464.024.020.050.0516.73 Economic literature dummy0.630.630.480.4801 Regional study dummy0.420.420.500.5001

28. The Parking Lot - Descriptives MeanMeanSt. Dev.MinMax Valuation methodology (binary variables) CVM0.240.240.430.4301 Choice Experiment0.040.040.190.1901 Travel Cost0.190.190.390.3901 Hedonic Price0.050.050.220.2201 Market Price0.280.280.450.4501 Replacement Cost0.090.090.280.2801 Production Function0.120.120.330.3301

29. The Parking Lot - Descriptives MeanMeanSt. Dev.MinMax Wetland ecosystem type (binary variables) EstuarineEstuarine0.400.400.490.4901 RiverineRiverine0.100.100.310.3101 Palustrine0.390.390.490.4901 Lacustrine0.110.110.310.3101

30. The Parking Lot - Descriptives MeanMeanSt. Dev.MinMax Ecological function valued (binary variables) Preservation0.140.140.350.3501 Restoration0.050.050.220.2201 Water quality0.070.070.260.2601 Flood control & water supply0.100.100.310.3101 AmenityAmenity0.090.090.280.2801 Recreational fishing & hunting0.230.230.420.4201 Non-consumptive recreation0.120.120.330.3301 Biodiversity0.070.070.260.2601 Commercial fishing & hunting0.150.150.360.3601

31. The Parking Lot - Descriptives MeanMeanSt. Dev.MinMax Geographic and socio-economic characteristics Ramsar Site dummy0.290.290.460.4601 Wetland area in 50km radius (ha)23683224403385783930 Population in 50km radius61695797088556613700000 Education (county level)23.669.269.261145.4 Distance to city (km)14.8056.020496

32. The Parking Lot – Best Fit Model  We also isolated the best fit (i.e. largest LLR) single observation model from among the 1000 bootstrapped samples  These results follow: Inferences remain consistent across models Magnitudes of effects are not robust to model specification  Likely due to small observations – n = 80

33. Best Fit Single Observation Models Spatial lag model OLSThreshold distance weight Ecological similarity weight Economic similarity weight 50km lag100km lag150km lag Estimate Intercept0.62 -3.76 3.21 3.28 -1.56 3.72 Wetland area (ha) - log scaled-0.30***-0.21-0.27***-0.25***-0.22-0.30*** Economic literature dummy-0.36-0.58-0.54-0.720.380.37 Regional study dummy1.39*0.930.99*0.90*-0.361.05* Valuation methodology (Travel Cost Method as the reference group) CVM0.071.231.39*1.36*1.290.54 Choice Experiment4.85**5.31***3.84***4.56***1.284.06** Hedonic Price11.68***10.51***12.29***13.49***10.21***10.75*** Market Price-0.011.89*2.65**3.17**1.622.73** Replacement Cost3.80**3.49***2.57**3.32***2.41*3.38** Production Function-0.071.72*2.08**2.35**0.481.21

34. Best Fit Single Observation Models Spatial lag model OLSThreshold distance weight Ecological similarity weight Economic similarity weight 50km lag100km lag150km lag Estimate Ecological function valued Preservation6.64**6.74***2.59**2.91**5.41**1.67 Restoration4.035.41**2.46*2.128.72***-1.34 Water quality3.865.61**1.870.826.23**-0.24 Flood control & water supply4.054.61**2.022.206.83**1.83 Amenity-1.65-1.23-7.26***-7.68***-1.61-7.17*** Recreational fishing & hunting7.15**7.38***2.78**3.18**6.96**1.70 Non-consumptive recreation7.41**7.65***3.41***3.76***7.13***2.71** Biodiversity8.06**9.34***5.66***6.27***7.85***4.06*** Commercial fishing & hunting6.06**4.79**0.540.456.68**-0.09

35. Best Fit Single Observation Models Spatial lag model OLSThreshold distance weight Ecological similarity weight Economic similarity weight 50km lag100km lag150km lag Estimate Geographic and socio-economic information Ramsar Site dummy-0.70-0.11-0.53-0.48-0.65-0.86 Wetland area in 50km radius (ha)/1000 - log scaled-0.12-0.16-0.21*-0.22**-0.23*-0.14 Population in 50km radius -log scaled0.110.17-0.07-0.100.010.13 Education (county level)0.010.05*0.06**0.04*0.020.01 Distance to city (km)0.050.09***0.07**0.07**0.000056*0.04 Education * City-0.002-0.003***-0.002**-0.002** -0.000002 **-0.001

36. Best Fit Single Observation Models Spatial lag model OLSThreshold distance weight Ecological similarity weight Economic similarity weight 50km lag100km lag150km lag Estimate N80 R-square64.47% Rho0.220.270.290.230.16 LLR test statistic13.8225.8327.808.1610.39 P-value for the LLR test<0.000***<0.000***<0.000***<0.000 ** *<0.000*** AIC371.33 339.09 334.81 332.84 365.16 360.82