# Estimating Welfare Measures Using Travel Cost Method with Truncated and Censored Data Arcadio Cerda, Ph.D. Universidad de Talca, Chile Felipe Vásquez,

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Estimating Welfare Measures Using Travel Cost Method with Truncated and Censored Data Arcadio Cerda, Ph.D. Universidad de Talca, Chile Felipe Vásquez, MSc. Ph.D. Student UC Berkeley, USA Universidad de Concepción, Chile & Sergio Orrego, MSc. Ph.D. Student Oregon State University, USA Universidad Nacional de Medellín, Colombia Trieste; July 20, 2004 Ecological and Enviromental Economics – EEE Programme

Contents 1. Introduction Introduction 2. Objectives Objectives 3. The Travel Cost Method (TCM) The Travel Cost MethodThe Travel Cost Method -Theoretical Aspects -Truncated and Censored Models -Maximum likelihood (ML) and Ordinary Least Squares (OLS) estimators -Count Distribution functions 4. Methodology Methodology 5. Results Results 6. Conclusions Conclusions

1. Introduction  TCM is used to value recreational uses of the environment: –Value the recreational benefits associated to improvement in water quality –Value the recreational loss associated with a beach closure  Since TCM is based on observed behavior, it is used to estimate use values only.  It is useful split travel cost models in single-site and multiple-site models

 Single-site models work like conventional downward sloping demand functions  The demand function slopes downward, if trips decline with distance to the recreational-site  Single-site are useful when the goal is to estimate the total use or access value of a site (Parson, 2003)  There are some variations of the single-site model that can be used for valuing changes in site characteristics such as improvement in water quality

2. Objectives  estimate welfare measures using truncated and censored data –compare the results of different functional forms –compare the results of different estimation methods

3. The Travel Cost Method -Theoretical Aspects -Truncated and Censored Models -Maximum likelihood (ML) and Ordinary Least Squares (OLS) estimators -Count distribution functions

donde: y : number of visist y : number of visist z : composite hicksian gods z : composite hicksian gods d: non-wage income d: non-wage income w: wages rate w: wages rate m: total income m: total income t w : labour time t w : labour time t 1 : travel time t 1 : travel time t 2 : time in situ t 2 : time in situ T : total time T : total time c 1 : travel monetary cost c 1 : travel monetary cost c 2 : site monetray cost c 2 : site monetray cost Theoretical Aspects

Labour Income travel cost permanency cost

y

Graphically Travel Cost \$ Yo Y1 Number of trips TCo A+B = Willingness to pay for trips A = consumer surplus B = Total trip cost C = Benefit of improved site quality A c B

Some Implicit Assumptions  Number of trips are complement of site- environmental quality  Individual responds to the travel cost in the same way as they would do to a change in access cost  Visit only one site  Time in the recreational site is exogenous and fixed  No substitution  Rate of wage represents the opportunity cost of time

Truncated and Censored Models Tobin (1958) Modelo Tobit For a recreational-site demand : Therefore for a recreational-site demand: Censored in zero - for on site-sampling truncated in 1

Maximum likelihood (ML) and Ordinary Least Squares (OLS) estimators Pro example: Lineal Function Maximum Likelihood Function Censured sampling adfdf OLS  MLE : Reduce bias

Count Distribution Functions (1) Poisson Distribution Fn. Poisson Likelihood Fn. Tobit  Poisson: Integer & non-negative

Count Distribution Functions (2) Negative Binomial Poisson  NB: Consider the possibility of overdispersion

4. Methodology  Description  The model  Consumer surplus estimates

Description  Dichato Beach, Chile  N=161 (truncated sample)  Censured (85% zeros)  Censured (flexible Haab & McConnell, 1996) 20%

The model

Models OLSL: Y  N( X ,  2 ) OLSS: Y  N( exp( X  ),  2 ) MLEL: Y  N( X ,  2 ) Y is observed if Y>0 MLES: Y  N( exp( X  ),  2 ) Y is observed if Y>0 POIS: Y  Poisson( = exp( X  )) TPOIS: Y  Poisson( = exp( X  )) Y is observed if Y>0 BNEG: Y  BinNega( = exp( X  ),  ) TBNEG: Y  BinNega( = exp( X  ),  ) Y is observed if Y>0

Consumer Surplus Estimates y

5. Results

Tabla 2. Truncated models (opportunity cost of time =30%) Param. OLSLOLSSMLELMLESPOISTPOISBNEGTBNEG Constante 3,1053** (3,118) 1,2289** (7,464) -13,7210 (-1,390) 1,1837** (6,474) 1,1370** (7,793) 1,0809** (6,778) 1,0742** (4,126) 0,54941 (1,250) TCP-30-0,00056864** (-3,363) -0,000087179** (-3,119) -0,0031267* (-2,345) -0,000099454** (-3,099) -0,00015241** (-5,969) -0,00017222** (-6,131) -0,00012506** (-5,206) -0,00015011** (-3,696) TCS-300,00013063* (2,053) 0,000017790 (1,691) 0,00070383 (1,679) 0,000019674 (1,699) 0,000033229** (3,612) 0,000036997** (3,683) 0,000033650* (2,026) 0,000049151 (1,844) ACCESO1,1539 (1,409) 0,15948 (1,178) 4,1299 (1,233) 0,17221 (1,198) 0,22929* (2,428) 0,23865* (2,468) 0,20358 (1,128) 0,25715 (0,694) AGUA0,70745 (1,118) 0,13645 (1,304) 3,1381 (1,096) 0,15005 (1,331) 0,16230* (2,050) 0,17480* (2,126) 0,14636 (1,111) 0,19679 (0,807) INGRESO0,000001673 (1,903) 0,000000355* (2,442) 0,000008592 (1,869) 0,000000395* (2,513) 0,000000428** (3,863) 0,000000477** (4,118) 0,000000413* (2,140) 0,000000579 (1,519)  --7,7313** (4,619) 0,64609** (15,439) ----  ------0,37565** (4,197) 1,17410** (2,728) R 2 ajustado 0,086410,07504------ log-L ---387,9332-148,1669-452,1419-446,8533-393,4177-370,9551 Valores de t entre paréntesis. ** indica que es estadísticamente significativo a un nivel del 99%. * indica que es estadísticamente significativo a un nivel del 95%. n = 161 observaciones

Regular Poisson Truncated Poisson

Table 11. Censored models (20%) (opportunity cost of time 30%) ParámetroOLSLOLSSMLELMLESPOISBNEG Constante 1,5510 (1,927) 0,6034** (3,625) -0,1348 (-0,134) 0,6034** (3,680) 0,4900** (3,362) 0,4190 (1,681) TCP-30-0,00041980** (-2,744) -0,000049976 (-1,580) -0,00038365* (-2,103) -0,000049976 (-1,604) -0,00012477** (-5,213) -0,000091874** (-2,933) TCS-300,00015230** (2,936) 0,000033078** (3,084) 0,00021298** (3,312) 0,000033078** (3,131) 0,000054470** (5,875) 0,000055173** (3,428) ACCESO2,0745** (2,648) 0,47410** (2,927) 2,7149** (2,943) 0,47410** (2,971) 0,48443** (5,153) 0,49674 (1,890) AGUA1,7711** (3,063) 0,52329** (4,377) 2,6516** (3,839) 0,52329** (4,443) 0,48387** (6,116) 0,49992** (2,658) INGRESO0,000000950 (1,302) 0,000000147 (0,977) 0,000000716 (0,806) 0,000000147 (0,992) 0,000000292** (2,785) 0,000000228 (1,079)  --4,3465** (17,329) 0,75601** (20,199) --  -----0,79914** (5,928) R 2 ajustado 0,124750,15376---- log-L ---500,3408-232,4033-588,3837-469,7138 Valores de t entre paréntesis. ** indica que es estadísticamente significativo a un nivel del 99%. * indica que es estadísticamente significativo a un nivel del 95%. n = 204 observaciones

Average Consumer Surplus per family & trip ( \$ ) (truncated sample) OLSLOLSSMLELMLESPOISTPOISBNEGTBNEG TCP-303.886,47 (US\$ 9.72) 11.470,65 (US\$ 28.7) 706,82 (US\$ 1.8) 10.054,90 (US\$ 25) 6.561,25 (US\$ 16.4) 5.806,53 (US\$ 14.5) 7.996,16 (US\$ 20) 6.661,78 (US\$ 16.7 TCP-404.623,9113.777,52 836,4212.087,517.830,856.941,07 9.570,297.982,12 TCP-505.380,1416.155,35 968,9614.186,019.138,268.110,3011.180,939.330,97 Exchange rate 1US\$ = 400\$

Average Consumer Surplus per Family & per year ( \$ ) (truncated sample) OLSLOLSSMLELMLESPOISTPOISBNEGTBNEG TCP-3017.178,2050.700,27 (US\$ 127) 3.124,14 (US\$ 7.8) 44.442,6629.000,7325.664,8635.343,0329.445,07 TCP-4020.437,6860.896,643.696,9853.426,7934.612,3630.679,5342.300,6835.280,97 TCP-5023.780,2271.406,654.282,8062.702,1640.391,1135.847,5349.419,7141.242,89

Tabla 6. Total annual Consumer Surplus (Truncated sample) OLSLOLSSMLELMLESPOISTPOISBNEGTBNEG TCP-304.988.217 8.155.633 (US\$ 20389) 907.186 (US\$ 9.72) 7.149.0334.665.0484.128.4405.685.2714.736.526 TCP-405.934.721 9.795.8171.073.537, 8.594.2225.567.7364.935.100,96.804.4785.675.287 TCP-506.905.32411.486.4531.243.64210.086.2506.497.3045.766.4237.949.6416.634.319

Tabla 14. Average Consumer Surplus per Family (censored sample) Average Consumer Surplus per Family per trip ( \$ ) OLSLMLELPOISBNEG TCP-30 4.156,74 4.548,428.014,75 10.884,47 TCP-40 5.098,31 5.638,679.845,43 13.341,69 TCP-50 6.074,64 6.773,81 11.747,15 15.871,76

Tabla 14b. Average Consumer Surplus per Family (censored sample) Average Consumer Surplus per Family & per year ( \$ ) OLSLMLELPOISBNEG TCP-30 14.507,02 15.873,9927.971,48 37.986,80 TCP-40 17.793,10 19.678,9634.360,55 46.562,50 TCP-50 21.200,49 23.640,60 40.997,5555.392,44

Tabla 15. Total Annual Consumer Surplus (Censored sample) OLSLMLELPOISBNEG TCP-306.756.7887.393.4575.698.4857.738.859 TCP-408.287.3179.165.6707.000.0989.485.944 TCP-509.874.329 11.010.8308.352.226 11.284.818

Tabla 16. Comparison of Benefits Average Consumer Surplus per family & per trip ( \$ ) OLSL Trun. OLSL cens20 MLEL Trun. MLEL cens20 TPOIS Trun. POIS cens20 TBNEG Trun. BNEG cens20 TCP-303.8864.1567064.5485.8068.0146.66110.884 TCP-404.6235.0988365.6386.9419.8457.98213.341 TCP-505.3806.0749686.7738.110 11.7479.33015.871

OLSL Trun. OLSL cens20 MLEL Trun. MLEL cens20 TPOIS Trun. POIS Cens20 TBNEG Trun. BNEG cens20 TCP-3017.17814.5073.12415.87325.66427.97129.44537.986 TCP-4020.43717.7933.69619.67830.67934.36035.28046.562 TCP-5023.78021.2004.28223.64035.847 40.99741.24255.392 Average Consumer Surplus per family & per year ( \$ )

6. Conclusions

 There are differences among models: –Sampling –Statistical distributions –Value of the opportunity cost of time

Truncated Models  Advantage: –Truncated method are easy & cheaper to apply  Disadvantage: –Estimation bias  inadequate participation and lack of randomness  Exclusion of information of non-participants  Use of distribution functions that allow negative trips.

Censored Models  Advantages: –Reduce bias of truncated models –More Robust  Disadvantage: –Survey cost

Tabla 7. Variables - censored VARIABLEMEDIADESV. ESTANDARMINIMOMAXIMO VIAJES 0,708 2,3351 0,0 15,0 TCP-30 2.217,8 1.163,8 288,0 7.844,0 TCP-40 2.541,6 1.431,9 304,0 9.964,0 TCP-50 2.865,3 1.708,9 320,0 12.080,0 TCS-30 8.094,1 5.474,3 1.067,0 13.530,0 TCS-40 9.743,9 6.779,8 1.166,0 16.520,0 TCS-50 11.394,0 8.089,5 1.265,0 19.500,0 ACCESO 0,01200 0,10910 0,000 1,000 AGUA 0,06000 0,23796 0,000 1,000 INGRESO 462.400,0 371.970,0 100.000,02.000.000,0

Variable - Truncated VARIABLEMEDIADESV. ESTANDAR MINIMOMAXIMO VIAJES 4,42* 3,9789 1,0 19,0 TCP-30 3.001,6 1.978,3 330,0 11.490,0 TCP-40 3.486,6 2.366,3 370,0 13.720,0 TCP-50 3.971,7 2.764,9 400,0 16.200,0 TCS-30 12.371,0 4.853,5 1.188,0 14.910,0 TCS-40 15.233,0 6.140,7 1.353,0 18.460,0 TCS-50 18.095,0 7.431,1 1.518,0 22.010,0 ACCESO 0,16149 0,36913 0,000 1,000 AGUA 0,39130 0,48957 0,000 1,000 INGRESO 560.870,0 396.180,0100.000,02.000.000,0

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