Craig Meisner and Hua Wang Development Research Group The World Bank. and. Benoît Laplante Independent Consultant, Montreal, Canada

Transcription

1 Publc Dsclosure Authorzed WELFARE MEASUREMENT BIAS IN HOUSEHOLD AND ON-SITE SURVEYING OF WATER-BASED RECREATION: AN APPLICATION TO LAKE SEVAN, ARMENIA WPS3932 Publc Dsclosure Authorzed Publc Dsclosure Authorzed Crag Mesner and Hua Wang Development Research Group The World Bank and Benoît Laplante Independent Consultant, Montreal, Canada Publc Dsclosure Authorzed Keywords On and off-ste samplng, recreaton demand, zero-nflated models, truncated count data models, endogenous stratfcaton, Armena. World Bank Polcy Research Workng Paper 3932, June 2006 The Polcy Research Workng Paper Seres dssemnates the fndngs of work n progress to encourage the exchange of deas about development ssues. An objectve of the seres s to get the fndngs out quckly, even f the presentatons are less than fully polshed. The papers carry the names of the authors and should be cted accordngly. The fndngs, nterpretatons, and conclusons expressed n ths paper are entrely those of the authors. They do not necessarly represent the vew of the World Bank, ts Executve Drectors, or the countres they represent. Polcy Research Workng Papers are avalable onlne at Correspondence should be addressed to: Crag Mesner, MC2-205, World Bank, 1818 H Street, NW, Washngton, DC 20433, cmesner@worldbank.org.

2 I. Introducton Several recent travel cost studes have amed to compare recreatonal benefts derved from household and on-ste surveys (e.g. Looms, 2003; Shaw, 2003). If t can be shown that welfare estmates derved from cost-effectve on-ste surveyng technques are smlar to household survey results, ths may justfy usng on-ste surveys n leu of large and costly populaton-based surveys. However, a robust comparson of estmates obtaned from each sample requres addressng a number of mportant statstcal ssues. In partcular, household survey demand s typcally censored due to the possblty of observng a large number of zeros (or non-users of the ste). Smply treatng all zeros n the sample as users of the ste ntroduces an upward bas of the demand and welfare measures. On the other hand, on-ste sample demand s truncated at one snce t surveys only users at the ste. In ths case, estmates are prone to hgher standard errors and an upward bas from over-samplng ndvduals whose characterstcs may be correlated wth hgher trp frequences (endogenous stratfcaton - ES). In the case of household surveys, t s possble to resolve the ssue by separatng the recreaton partcpaton decson from the trp quantty decson, thus reducng the bas ntroduced by non-users of the ste. In the case of on-ste surveys, t s possble to correct for the potental bas by provdng adjustments to the dstrbuton functon (Shaw, 1988; Engln and Shonkwler, 1995). To our knowledge, none of the exstng travel cost studes have attempted to correct for both bases when conductng comparatve analyses of estmates obtaned from household and on-ste surveys. 1 In ths paper, we test the proposton of whether the household and on-ste demand estmaton yeld smlar welfare measures, after accountng for both bases dscussed above. For ths purpose, we use a household and on-ste survey conducted at Lake Sevan, Armena. Ths sngle-ste comparson has two advantages. Frst, as the ste s unque, we avod problems of havng to ncorporate substtute stes nto the decson to 1 Looms (2003) does not dscuss the prevalence of zeros n hs comparatve household sample, and does not consder ther relatve nfluence on expected trp demand or welfare. 1

3 recreate. Second, snce we are not valung a change n the qualty of the lake, we also avod any qualty change mpacts on expected trp demand. The household survey conssted of 3,358 households across Armena, and the onste survey of 389 toursts recreatng at Lake Sevan. Travel cost models were constructed and estmated usng travel expendture and soco-demographc nformaton contaned n each survey. As vstaton rates n the household survey contaned a large percentage of zeros and the presence of over-dsperson n trp frequency, a zero-nflated negatve bnomal model (ZINB) was estmated. For the on-ste survey, two truncated negatve bnomal models were estmated wth and wthout an adjustment for endogenous stratfcaton (ES). Lkelhood rato tests for over-dsperson were rejected n favor of the negatve bnomal specfcaton n both the household and on-ste models. Results from the household model also reveal that the partcpaton decson s ndeed relevant to the household s recreaton decson. However, n the case of the on-ste sample, estmated coeffcents for the ES and non-es models were not sgnfcantly dfferent. Ths may suggest that characterstcs from the on-ste sample are representatve of the household sample. Other studes have found smlar results where accountng for ES dd not yeld any sgnfcant dfferences n trp demand or welfare (Ovaskanen et al., 2001; Engln et al., 2003). Per trp consumers surplus was estmated to be $8.82 for the household sample, $8.73 for the on-ste model wthout ES adjustment, and $8.21 wth ES. The remander of ths paper s structured as follows. The next secton provdes a descrpton of travel cost and count data models utlzed n ths study along wth recommendatons of how to remedy several dependent varable ssues typcally encountered wth household and on-ste recreatonal surveys. In Secton III, the two surveys are descrbed n more detal. In Secton IV, the results of estmaton are presented, along wth a comparson n expected trp demand and estmated welfare measures. Secton V provdes a bref summary and dscusson of the fndngs. 2

4 II. Travel Cost Modelng In travel cost modelng, the decson to recreate s typcally modeled as a latent demand, y *, representng the number of trps taken n one year as a functon of travel cost (P), ste qualty attrbutes (Z) and ndvdual demographc characterstcs (X): Trps = y * = f (P, X, Z ) + μ = 1, 2,, N (1) Travel cost-modelng (TCM) can be mplemented through household or on-ste surveys. However, each samplng method nvolves a number of dfferent statstcal ssues. () Household survey An mportant modelng ssue when applyng TCM pertans to the treatment of non-negatve ntegers observed n ndvdual recreatonal data, as one may encounter a large proporton of zeros n a general household survey (Shaw, 1988; Grogger and Carson, 1991; Hellersten, 1991). Observng a zero mples that the servces from the ste do not enter nto the utlty functon of the ndvdual. In the utlty maxmzaton framework, t mples that the ndvdual s currently at some choke prce where he s consumng zero trps, and that f the current market prce were to fall below the choke prce, the ndvdual would demand a postve number of trps. However, one may also observe a zero f for some reason (such as age, health-related reasons, etc.) servces from the ste would never enter an ndvduals utlty functon (Habb and McConnell, 1996). Thus, there s an mportant dstncton between observng zeros for those who are partcpants and for those who are non-partcpants ( true zeros ). Standard count data models such as the Posson or negatve bnomal assume that all ndvduals surveyed are potental users of the good n queston, and that the same varables nfluence all potental users smlarly. In the presence of a large number of zeros, and where the partcpaton queston s relevant, ths assumpton may not be vald and should be tested for ts sgnfcance. 3

5 To account for the partcpaton ssue, we consder two augmented count data models whch account for the presence of a large number of zeros - the zero-nflated Posson (ZIP) and zero-nflated negatve bnomal (ZINB) (Mullahy, 1986; Lambert, 1992; Greene, 1994; Haab and McConnell, 1996). By dstngushng between partcpants and non-partcpants, the zero observatons may contan valuable nformaton, and a gan n effcency wll be acheved by ncludng all of the observatons (Haab and McConnell, pg. 90). 2 Emprcally, zero-nflated count models change the mean structure to allow zeros to be generated by two dstnct processes, one for the partcpaton decson (logt or probt) and one for the mean number of trps (count model). 3 By expandng the standard count model to allow for ndvdual-specfc characterstcs whch may keep an ndvdual from enterng the recreaton market, one can separate factors whch nfluence the partcpaton ssue from those that nfluence the quantty of trps taken to a recreaton ste (Haab and McConnell, 1996). In estmaton, the ZIP model allows for over-dsperson n the Posson data generatng process by allowng a mass of zero observatons ndependent of the true Posson process. The dstrbuton functon for the ZIP model s: Pr(y x ) = P + ) λ ( 1 P e f y = 0, e (1 P ) λ λ y! y otherwse. (2) where E(y ) = (1 - P )λ, Var(y ) = (1 - P )(1 + P λ )λ, and P s the probablty of zero vstaton, wth mean λ = exp(x β). Note that n ths formulaton, zeros can occur n ether the bnomal process (when y = 0) or the Posson process (when y 1), snce exp(- λ )λ 0 /0! = exp(-λ ). Agan, λ can be modeled as exp(x β), and P as g(z γ), where γ s a vector of partcpaton-decson parameters and z s a vector of explanatory varables that may or may not be the same as those for the quantty decson, x. The functon g( ) can be modeled usng ether logt or probt (or cumulatve standard normal) functon as they 2 In the past, one crude opton was smply to drop the zeros from the sample. 3 The zero-nflated models dffer from the Heckman contnuous two-stage model as they allow for zero observatons n the second stage of the decson process (n the mean model). 4

6 both gve smlar results. In the presence of over-dsperson 4 (varance>mean), the partcpaton decson can be smlarly decomposed n a zero-nflated negatve bnomal model as: Pr(y x ) = 1 α 1 P + (1 P ) f y = 0, 1+ αλ Γ( y + 1 α) 1 (1 P ) y Γ( + 1) Γ(1 α) 1+ αλ 1 α αλ 1+ αλ y otherwse. (3) where E(y ) = (1 - P )λ and Var(y ) = (1 - P )[1 + λ (α + P )]λ. The presence of the α parameter n the calculaton of the condtonal varance of y (f greater than 0), guarantees that the varance s greater than the mean. As α 0, the moments of the dstrbuton converge to a Posson dstrbuton and so testng for α=0 provdes a case for selectng the negatve bnomal over the Posson, and ndrectly for the presence of over-dsperson. The flexblty of modelng the partcpaton decson n ths manner has lead to a number of nterestng applcatons n recreatonal demand analyss, ncludng beach trps (Shonkwler and Shaw, 1996; Haab and McConnell, 1996), rock clmbng (Shaw and Jakus, 1996), lake recreaton, (Gurmu and Trved, 1996), water-based recreaton (Curts, 2003), and anglng ste choce (Scrogn et al., 2004). () On-ste samplng Intervew surveys conducted on-ste obvously avod the non-partcpaton ssue, but as the dependent varable y s strctly non-zero, the truncated demand relatonshp 4 An undesrable feature of Posson count models s the assumpton that the condtonal mean and varance are equal (Yen and Adamowcz, 1993). Ths s especally problematc n emprcal research because condtonal varances are typcally greater than condtonal means n soco-economc data (also known as over-dsperson, a form of heteroskedastcty). The presence of over-dsperson stll allows for consstently estmated means of parameter estmates (Goureroux et al. 1984), but causes the standard errors of these estmates to be based downward, resultng n erroneous tests of ther statstcal sgnfcance (Cameron and Trved, 1986). The equalty of the mean and the varance property of Posson count models led to the development of negatve bnomal models (Hausman et al., 1984). Ths model allows for over-dsperson by combnng the Posson dstrbuton wth a gamma dstrbuton and hence allowng for heterogenety to be gamma dstrbuted. 5

7 measures only those wth smaller error terms. In addton, because the sample s on-ste, there s a hgher lkelhood of nterceptng a person whose characterstcs are correlated wth hgher trp frequences, or what s known as endogenous stratfcaton n samplng. The mplcaton s that the sample s not representatve of the populaton at large, and n measurng welfare effects, consumers surplus estmates wll be based upwards as t s only capturng the effect of avd recreatonsts. Truncaton and endogenous stratfcaton was frst explored by Shaw (1988) n the case of the Posson dstrbuton and extended by Engln and Shonkwler (1995) to the negatve bnomal dstrbuton. The basc mplcaton s to weght ndvdual observatons by the nverse of the expected value of trps. Assumng that the densty functon of the th person n the populaton s f(y * x ), Shaw (1988) shows that the densty functon of the same person n the on-ste populaton s: Pr(y x ) = y f ( y t= 1 x ) t f ( t x ) (4) If the condtonal densty f(y * x ) s chosen to be Posson wth the locaton parameter λ, then the on-ste sample s densty functon s: Pr(y x ) = y 1 λ e λ ( y 1)! (5) where E(y x ) = λ + 1 and Var(y x ) = λ. Defnng w = y - 1, the standard Posson model can be estmated, substtutng w for y n (5) above. In the presence of over-dsperson, the equalty of the mean and varance s volated and thus the negatve bnomal model s preferred wth the followng densty functon (Engln and Shonkwler, 1995): Pr(y x ) = y Γ( 1 α y ( 1 ) 1 Γ y + α α y 1 λ 1) (1 ) 1 1 y + Γ α + αλ + αλ (6) 6

8 where E(y x ) = λ α λ and Var(y x ) = λ (1 + α + α λ + α 2 λ ). As the specfcaton n (6) cannot be transformed nto any smpler form as n the case of the truncated Posson, the lkelhood functon must be programmed drectly nto a lkelhood maxmzaton routne. The log lkelhood functon used n ths context s: 5 N ln y + ln( Γ( y + 1/ α)) ln( Γ( y + 1)) ln( Γ(1/ α)) + ln L = = 1 y ln α + ( y 1)ln λ ( y + 1/ α)ln(1 + αλ ) (7) Defnng λ as the expected number of person-day-trps 6 ndvdual takes to the ste n a year, the emprcal demand relatonshp can be defned as: λ = exp(x β + ε ) = exp(β p p + x γ + ε ) = 1,,n (8) where β s a K x 1 vector of parameters, X s a 1 x K vector of explanatory varables for ndvdual, p s the travel cost for ndvdual to the ste, x s the 1 x K 1 vector of explanatory varables after p s subtracted from X, β p s the parameter on travel cost, and γ s the remanng vector of parameters correspondng to x. () Welfare measures The beneft (consumer surplus) of access to the ste s defned as the area under the estmated Marshallan demand curve specfed n (8) and above the current prce level. By ntegratng the demand functon over travel costs (prces) faced by ndvduals, we calculate expected consumers surplus as: E (CS ) = λ dp = - λ / β p (9) where λ s as defned n (8) and β p s the estmated parameter on travel cost. Summed across all, the area measures the total per trp wllngness-to-pay by all ndvduals to recreate at the ste. In the case of the ZINB model expected consumers surplus must be weghted by the probablty of zero vstaton (1 - P ), where P s a functon of varables 5 The lkelhood functon n (7) was entered nto a modfed zero-truncated negatve bnomal maxmum lkelhood routne provded by Hlbe (1999). 6 Person-day-trps were defned as the number of trps taken by the respondent n one year. All cost nformaton was then dvded by the number of days to form per-day trp costs. 7

9 that affect the partcpaton decson. Compensatng and equvalent varaton measures can also be calculated from the expendture functon mpled by the Marshallan demand relatonshp specfed above. From a welfare perspectve, CV and EV may be of nterest as measures of potental compensaton from those who degrade the resource. Table 1 summarzes the welfare measures used n the analyss. Table 1: Welfare measures Model Household sample: Negatve bnomal Zero-nflated negatve bnomal On-ste sample: Trunc. negatve bnomal/ Trunc. negatve bnomal w/endogenous stratfcaton Consumers surplus λ β p e = β _ X β p p Compensatng varaton 1 λβ ln 1+ β β p _ X β e 1 ( 1 P) λβ ( 1 P) ln 1 β β β p λ β p e = β _ X β p 1 λβ ln 1+ β β p Equvalent varaton 1 λβ ln 1 β β p 1 λβ ( 1 P) ln 1+ β β p 1 λβ ln 1 β β p Note: λ = exp ( _ X β) from equaton (8), where _ X represents the sample means; β s the coeffcent on ncome. III. Applcaton to Lake Sevan, Armena Lake Sevan s the largest hgh alttude reservor of freshwater n the Transcaucasus, and s one of the hghest lakes n the world. However, over the course of last 50 years, the level of the lake has dropped by 18 m, ts surface area has decreased by 15%, and the volume of water n Lake Sevan fell by more than 40% (from 58.5 to 34.6 km 3 ). These changes had varous sgnfcant adverse mpacts on Lake Sevan s ecology. As t s located only 70 km away from the captal cty Yerevan, Lake Sevan s the preferred and most accessble recreatonal ste of most Armenans. The Government of Armena has been workng on a Lake Sevan protecton acton plan. The objectves under consderaton by the Government of Armena nclude preventng a further lowerng of the level of Lake Sevan, and rasng the level of the lake by at least 3 meters as quckly as possble. However to date, there has not been a 8

10 thorough measurement of the current recreatonal benefts to nclude n beneft-cost analyss. Welfare measurement would be useful to polcymakers tasked wth weghng the alternatve optons of restorng Lake Sevan. Our model and welfare comparson s also useful n ths context as Lake Sevan s a sngle ste, wth no substtutes, so comparng the two samples s not confounded by alternatve stes that may enter nto an ndvduals water-based recreaton decson. Also, snce we are measurng current recreatonal benefts, we avod havng to predct what the mpact mprovements would have on expected trp demand. To estmate benefts by the general populaton and users of the ste, two surveys were conducted one comprsng of 3,358 households across Armena and the other an nterceptor survey of 389 on-ste toursts recreatng at Lake Sevan. 7 Both were conducted n the year 2000, wth the tourst survey durng the summer to better capture the hgh season of annual recreatonal use at the lake. The household sample was selected and stratfed by the 1996 Populaton Census of Armena, whle the on-ste survey reled on tourst ntercepton at the lake. Annual vstaton to Lake Sevan by these two groups s reported n Table 2. Household survey responses ndcate that nearly 75% dd not vst the lake n the past year, wth a sample mean of 0.81 day-trps. The tourst survey, obvously truncated at one as ntervews took place at the lake, averaged 3.17 day-trps per year. The average person from the household survey was 44 years old, earned the equvalent of 1,383 USD per annum, had 10 years of formal educaton, and a household sze of 4. The average person from the on-ste survey was 36 years old, earned $2,933 USD per annum, had 10 years of educaton and a household sze of 5 (see Appendx I for detals). In Table 2 we also note that the standard devaton of vstaton n each sample exceeds ts mean, thus we suspect the presence of over-dsperson, and therefore formally test the 7 The detaled questonnares ncluded sx major parts: (1) envronmental atttudes and perceptons; (2) a Lake Sevan acton plan for restoraton; (3) contngent valuaton questons; (4) soco-economc characterstcs; (5) recreatonal use of Lake Sevan; and (6) ntervew debrefng questons. For the purposes of ths paper, only sectons (4) and (5) are used. 9

11 negatve bnomal counterpart of the Posson dstrbuton. In addton, gven the large number of zeros n the household survey, ths leads us to formally test the use of the zeronflated negatve bnomal model for the household survey. Table 2: Frequency of vstaton Household Tourst Person-day-trps frequency Percent frequency Percent to to to to to to Total Mean Standard devaton IV. Estmaton Results () Determnants of vstaton The household sample was ntally modeled usng the Posson, negatve bnomal (NB), zero-nflated Posson (ZIP) and zero-nflated negatve bnomal (ZINB). The onste sample was modeled usng the truncated Posson, truncated negatve bnomal (TRNB) and the truncated negatve bnomal wth endogenous stratfcaton (TRNBES). Comparatve tests between each model were performed and are reported below. For brevty, only the estmaton results for the household (NB and ZINB) and on-ste models 10

12 (TRNB and TRNBES) are reported n Table 3 wth margnal effects for the ZINB and TRNBES models lsted n Table 4. From the emprcal demand relatonshp n equaton (8), we model the partcpaton and trp quantty decsons usng travel cost and several ndvdual-specfc varables that may co-vary wth each decson - ncome, age, household sze, educaton, and a Yerevan cty dummy. 8 Travel costs ncluded: (1) transport costs; (2) on-ste costs (per day); and (3) the value of tme travelng to and at Lake Sevan. The value of tme was elcted from the respondent by askng them how much they would have earned had they not traveled to Lake Sevan. Ths amount was then dvded by the number of days they were at the lake to arrve at a trp-per-day cost. Note that for the household model, each equaton (logt and mean) contan the same explanatory varables as they may contrbute to ether of the partcpaton or quantty decsons. Begnnng wth the household survey results n the second and thrd columns of Table 3, we note that the lkelhood rato (LR) test of α = 0 s rejected ndcatng the sgnfcance of over-dsperson and thus the selecton of the negatve bnomal specfcaton over the Posson. A further formal specfcaton test between the NB and ZINB s possble (Vuong, 1989). The test statstc s drectonal and dstrbuted standard normal and for values V > 1.96, the zero-nflated verson s supported. Wth a value of 4.86, the ZINB specfcaton s favored over the NB. Parameter estmates of the household ZINB model reveal that ncome, age and educaton, along wth respondents who resde n Yerevan sgnfcantly determne the household partcpaton decson to recreate at Lake Sevan (see logt nflaton model). The coeffcents are nterpreted relatve to observng a zero count, thus the postve coeffcent on age mples that older respondents are more lkely to record zero partcpaton, whereas ndvduals wth hgher ncome or educaton are less lkely to report zero trps to Lake Sevan. Those who resde n Yerevan cty are also more lkely to 8 A dummy varable to capture prevous vstaton to the lake was also ntally consdered for each model, however, over 94% of respondents n the household survey and over 95% n the tourst survey vsted Lake Sevan at least once n the past three years (and thus nsuffcent statstcal varaton). 11

13 report zero vstaton n the past year. Among those who do choose to partcpate (see mean model), ncreases n ncome and household sze ncrease trp demand, whle ncreases n travel costs and educaton decrease trp demand. For the on-ste survey, frst an LR test between a truncated Posson and truncated negatve bnomal (TRNB) was rejected ndcatng that over-dsperson n vstaton s sgnfcant, leadng to us to favor the TRNB specfcaton. Second, the TRNBES model was estmated to see whether hgher trp frequences have any systematc assocaton wth an ndvdual s characterstcs. Estmaton results for both TRNB and TRNBES show that ncreases n travel costs, age and educaton decrease vstaton, whereas ncreases household sze ncrease trp demand. In the TRNB model, estmated coeffcents and standard errors are hgher leadng to a lower sgnfcance across each explanatory varable. By correctng for ES, the magntude of estmated coeffcents falls, and standard errors fall by a greater extent such that sgnfcance rses among the major determnants of vstaton. In the next secton, we explore the consequences of these dfferences on expected trp demand as well as the mplcatons on welfare estmates. 12

14 Table 3: Household and on-ste model estmates of vstaton to Lake Sevan Varable HH: NB HH: ZINB On-ste: TRNB On-ste: TRNBES Mean model Travel costs *** *** *** *** (-5.41) (-3.46) (-3.37) (-4.79) Income *** *** (7.54) (3.63) (0.60) (0.32) Age *** *** *** (-6.36) (0.78) (-3.45) (-4.58) Household sze *** *** *** *** (4.02) (2.64) (3.57) (5.26) Educaton *** * *** (-0.43) (-2.66) (-1.66) (-2.79) Constant (-0.11) (0.56) (-0.33) (-0.12) Logt nflaton model Travel costs (0.91) Income *** (-4.77) Age *** (8.47) Household sze (0.43) Educaton *** (-4.80) Yerevan cty *** (2.68) Constant * (-1.83) α Log-lkelhood -3, , LR test (α=0) ~ χ 2 (d.f.) 6, (1) 3, (1) (1) (1) Vuong test ~ N (0,1) Number of observatons 3,358 3, Non-zero observatons Zero observatons 2,516 2,516 t-statstcs n parentheses; * sgnfcant at the 10% level; ** sgnfcant at the 5% level; *** sgnfcant at the 1% level. () Vstaton senstvty The senstvty of trp demand for the household ZINB and tourst TRNBES models to changes n the parameter values s summarzed n Table 4. Begnnng wth the household survey and under the bnary partcpaton equaton, estmated coeffcents 13

15 from the regresson are nterpreted as ncreasng or decreasng the odds of nonpartcpaton (or observng a zero). As ths may be counter-ntutve, we reverse the sgns on the estmated coeffcents and re-nterpret the results n terms of the odds of partcpaton n Table 4. A untary ncrease n age or household sze of the respondent leads to a decrease n lkelhood of partcpaton by 9.5% and 3.2%, respectvely, whereas an ncrease n one year of educaton ncreases the odds of partcpaton by 75%. Income only margnally mpacts trp demand wth ncreases by $1 USD leadng to an ncrease n partcpaton of 0.12%. Ths relatve nsenstvty to ncome changes s a common fndng among recreatonal demand studes. If the respondent lves n Yerevan, the lkelhood of partcpaton s decreased by an overwhelmng 137%. Ths may be owng to the fact that n the household sample, over 80% of the sampled househols are from Yerevan, the captal cty. For the trp count equaton, a one unt ncrease n travel costs or educaton decreases the number of trps by 1.5% and 6.6%, respectvely. Thus, although travel costs are not a sgnfcant determnant n the decson to recreate, they do mpact the number of trps a person decdes to take. Also, a person s educaton appears be mportant both decsons, but n opposte drectons. Those wth hgher educaton tend to partcpate more often, but as one frequents the ste more often ths effect dmnshes. Greater household sze also works n opposte drectons for the partcpaton and quantty decsons. A one unt change n household sze decreases partcpaton by 3.2% but for those who do go, t ncreases the number of trps by 10.2%. Upon closer nspecton of the data, t was found that households wth more chldren were assocated wth hgher trp frequences. The mpact of ncome on trp frequency was found to be neglgble. 14

16 Table 4: Margnal effects on trp demand HOUSEHOLD: ZINB ON-SITE: TRNBES Vsts Coeffcent % trps Coeffcent % trps Count partcpaton equaton Travel costs ($USD) *** *** Income ($USD) *** Age (years) *** Household sze (number) *** *** Educaton (years) *** *** Partcpaton % Pr(partcpaton) Bnary partcpaton equaton Travel costs ($USD) Income ($USD) *** 0.12 Age (years) *** Household sze (number) Educaton (years) *** Yerevan (1=lves n Yerevan) *** * sgnfcant at the 10% level; ** sgnfcant at the 5% level; *** sgnfcant at the 1% level For on-ste trp demand, untary ncreases n travel costs, age and educaton decrease the number of trps by 5.1%, 2.6% and 8.9%, respectvely, and an ncrease n household sze sgnfcantly ncreases trp frequency by 31%. Wth the excepton of age, each mpact has a smlar nterpretaton as n the household model, but the effects are much larger. In the case of age, older ndvduals are sgnfcantly and negatvely correlated wth hgher vstaton. () Estmated trp demand and welfare measures Usng the parameter estmates from the four models n Table 3, the expected _ number of trps, E( y X ), and consumers surplus (CS) measures were calculated (Table 5). 9 The expected number of trps was estmated for each model usng sample means of the ndependent varables. Comparng the NB wth the ZINB, note that the expected number of trps falls once we account for the nflaton of zeros (partcpaton). Indeed, snce the NB model s treatng every zero as beng a part of the quantty decson, ths 9 Although the CV and EV measures are not formally reported above, as the estmated coeffcent on ncome, β, n both the ZINB and TRNBES models s small, CS s tghtly bounded by CV and EV; for the ZINB model CV= $8.7984, EV=$ and for TRNBES model CV=$8.2137, EV=$

17 bases the estmates upwards, whereas the ZINB recognzes that the zeros may come from dfferent stochastc processes (partcpaton or quantty). For the on-ste model, TRNB, the expected number of trps far exceeds the demand estmated by the household survey. Ths seems reasonable snce we are comparng casual versus avd users of the ste. However, the expected number of trps s even hgher after accountng for ES (TRNBES). At frst glance ths may seem counterntutve, but recall that expected trp demand s calculated as E(y x ) = λ α λ ), and note that the only substantal dfference between the estmated parameters of TRNB and TRNBES s the value of the over-dsperson parameter, α (see Table 3). Thus t s the overdsperson that s drvng ths result. Ths fndng s smlar to that found by Engln and Shonkwler (1995), where expected trp demand s 1% hgher for ther sample-based restrcted negatve bnomal model (analogous to our TRNBES model) and 63% hgher for ther populaton-based trp demand. Martnez-Espnera and Amoako-Tuffour (2005) also fnd an 18% hgher expected trp demand n ther ES model. Estmated household consumers surplus was $8.82 per trp whereas for the on-ste sample CS was calculated as $8.73 wthout compensatng for ES and $8.21 per trp wth ES. Although all three results are close, t s rather surprsng to fnd the closest estmate to be between the TRNB and ZINB models. One would ntally expect the TRNBES to be the closest f ES were present n the on-ste sample. The most plausble explanaton s rooted n the very reason why one argues for ES adjustment; f adjustments for ES yeld only small dfferences n expected demand or consumer surplus, ths suggests that those surveyed at Lake Sevan possess characterstcs smlar to those n the household sample. Ths mples that ether the TRNB or TRNBES model s suffcent for estmaton. Ths can be more clearly seen f one vews the mean functon λ, and the smlarty of estmated characterstcs between the TRNB and TRNBES models (especally the smlarty between the estmated coeffcent on travel cost, β p ; whch s the denomnator n the CS calculaton, - λ / β p. Ovaskanen et al. (2001) and Engln et al. (2003) also fnd smlar results where the ES adjustment had lttle effect on coeffcent and beneft estmates. 16

18 Measure _ Table 5: Expected vstaton and beneft estmates Household: NB Household: ZINB On-ste: TRNB On-ste: TRNBES E( y X ) CS ($USD per day-trp) Total WTP 1 ($USD) 6,362,295 6,875,160 6,802,126 6,399,840 Note: X s evaluated at the sample mean. 1 Calculated for households as: CS * 779,230 households n V. Concluson In ths paper, a populaton-based household sample and an on-ste sample are modeled n a travel cost framework to compare estmated consumers surplus for the value of ste access. If each model s corrected for several dependent varable ssues, we expect the models to produce smlar welfare estmates. In the household model, we account for the potental for over-dsperson (varance>mean) by the use of a negatve bnomal dstrbuton functon, and for the possblty of observng a large number of zero vsts (a recreaton partcpaton decson) by splttng the partcpaton and quantty decsons drectly n one censored model, the zero-nflated negatve bnomal (ZINB). For the onste survey, there s a possblty of over-samplng those who recreate qute often, thus the truncated dstrbuton functon s augmented for endogenous stratfcaton (e.g. the lkelhood of surveyng respondents whose characterstcs are assocated wth hgher trp frequences). To compare the effect of ES, we model the on-ste sample as a truncated negatve bnomal wth and wthout endogenous stratfcaton (TRNB and TRNBES, respectvely). Each of these models are then appled to a unque water-based recreatonal ste n Armena, Lake Sevan. The ste has few, f any, alternatves facltatng a comparatve welfare exercse. In addton, as the surveys measured only current revealed preference behavor, no qualty changes are present to confound the measurement of expected trps outsde the current experence. 17

19 Results from the zero-nflated negatve bnomal model (ZINB) for households suggest that separatng the partcpaton and quantty decsons s sgnfcant n modelng household behavor. In ths applcaton, explanatory varables such as age, educaton and ncome were found to be sgnfcant factors n the bnary decson to recreate at Lake Sevan. The quantty of trps was determned by travel costs, ncome, household sze and educaton. Expected trp demand was found to be 0.58 trps per ndvdual per annum, and the welfare measure calculated from the underlyng demand functon reveal a per trp consumers surplus of $8.82. From the on-ste sample the TRNB and TRNBES models yelded expected trp demands of 5.9 and 7 trps per person per year wth consumers surplus values of $8.79 and $8.21 per person per year, respectvely. Expected trp demand from the on-ste models s hgher than the household sample due to the dfference n samplng casual versus more avd users of the ste. However, an even hgher trp demand s found n the TRNBES model due to a hgher estmated overdsperson parameter, α used n the calculaton of expected trp demand. All three models appear to yeld smlar welfare measures, but t appears that accountng for endogenous stratfcaton n the TRNES model dd not yeld a sgnfcantly dfferent estmate from the TRNB model. In fact, consumers surplus from the TRNB model s slghtly closer to the household result than the TRNBES model. One possble explanaton s that ndvdual characterstcs of the on-ste sample are not correlated wth hgher trp frequences (argung aganst the precse reason we factor n ES). Ths does not mply that ES s not an mportant consderaton n modelng on-ste behavor, rather the results found here suggest that the on-ste sample was merely representatve of the populaton-based household survey. Ths fndng s qute contrary to other studes where the ES bas n welfare measurement has been found to be qute sgnfcant (Shaw, 1988; Engln and Shonkwler, 1995; Looms, 2003; Martnez- Espnera and Amoako-Tuffour, 2005). Although we dd not fnd any sgnfcant dfference n accountng for ES, ths does not negate the man result that when comparng household and on-ste samples, ether can be used to derve a consstent welfare measure of access to the ste after 18

20 accountng for each dependent varable problem. As was prevously mentoned, qute often the method of surveyng s a constraned choce, usually by cost or tme. It s therefore reassurng that f one s truly constraned n some sense, that by mplementng the proper technque, the qualty of the measure need not be n queston. 19

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23 Appendx 1: Descrptve statstcs for the Household (HH) and Tourst survey (Tourst) Varable Mean Standard devaton Mnmum Maxmum HH w/ Trps > 0 HH w/ Trps 0 Tourst Trps 1 HH w/ Trps > 0 HH w/ Trps 0 Tourst Trps 1 HH w/ Trps > 0 HH w/ Trps 0 Tourst Trps 1 HH w/ Trps > 0 HH w/ Trps 0 Tourst Trps 1 Vsts (person-day-trps) Travel costs ($USD) Income ($USD) 1,861 1,383 2,933 1,623 1,246 2, ,976 14,976 15,120 Age (years) Household sze Educaton (years) Past vstaton (1=yes) Yerevan cty (1=yes) Lake Sevan (1=yes) Observatons