Barrier to Do Recreation

8/3/2019 Barrier to Do Recreation

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JOURNAL OF ENVIRONM ENTAL ECONOMICS AND MANA GEME NT 7, 65-76 ( 1980)

Simultaneous Estimation of Jointly DependentRecreation Participation Function 1MARGRIET F. CASWELL .

Departm ent of &ricultura~ and Resource Economics,University of California, Berkeley, California 9@%0

AN DKENNETH E. MCCONNELL

Depa?W&?nt of Agricultural and Resource Economics,University of Maryland, College Park, Maryland 20742

Received July 24, 1978; revised June 4, 1979The purpose of this paper is to develop and estimate a simultaneous model of recreation

participation. The logic of the model is that participation in one activity (for examp le,boating) is influenced by and influences participation in other activities (for examp le,fishing). For the empirical part of our paper we have used the simultaneous logit modeldeveloped by P. Schm idt and R. P. Strauss (Eccmometrica 43, 745-755, 1975). For theapplication, we have applied the simultaneous logit model to participation in sum merrecreational activities in Rhode Island. Our results show that simultaneous equationmodels tend to forecast better, but that the specification bias from excluding the endog-enous variables tends to be sma ll.

1. INTRODUCTIONEconomic research on outdoor recreation has been motivated by the increasingdemand for recreation facilities. Between 1950 and 1975, participation in several

outdoor recreation activities doubled. This increase in demand induced a largeincrease in capital outlays by federal, state, and local governments for recreationalfacilities and implied a substantial opportunity cost by removing natural resourcesfrom their alternative uses in the market economy. Because of the high directcosts for building faci lities and the substantial opportunity costs of keepingnatural resources for recreational use, it is important that researchers improvetheir ability to forecast future participation in recreation activities.Beginning with Davidson et al. [6], economists have divided the forecastingprocedure for outdoor recreation activities into two steps. The first step is to

i Contribution 1857 of the Rhode Island Agricultural Experiment Station. This paper wa swritten when both authors were in the Departm ent of Resource E conom ics at the Univers ity ofRhode Island. This research received support from the Univers ity of Rhode Island Sea GrantProgram and the Rhode Island Agricultural Experiment Station. W e appreciate helpful com me ntsfrom Timoth y J. Tyrrell , two reviewers, and the Editor.65

OO95-0696/8O/O10O65-12$O%OO/Ocopyright 0 i9ad by Academic&S IhcAll r ights of rqmduction in any form r&v&


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66 CASWELL AND MCCONNELLestimate the probability function for an individual participating in a particularrecreation activity. The second step is to estimate the function analyzing thefrequency of participation in a particular activ ity among members of the popula-tion who participate, This approach was given its fullest treatment by Cicchetti[4) in his work, Forecasting Recreation in the United States.A particular problem in many of the early studies concerned the specificationof the model. Researchers were aware that many variables influence both thedecision to participate and the frequency of participation. Until the work byDeyak and Smith [7], however, there was no rigorous justification for modelspecification and estimation. Deyak and Smith advanced the art in two ways.Firs t, they adapted the household production function approach for use in estimat-ing participation functions for outdoor recreation. Second, they emphasized theimportance of model choice on final results, making the interpretation of resultsmore intuitive.Economists have been concerned with the simultaneous nature of choicesamong recreation decisions. Cicchetti, in discussing the modeling of participationdecisions, states behavioral variables that relate to the recreation sector, however, are determined jointly or simultaneously (Cicchetti [4, p. 4)). Thissimultaneity of choice among activities has not been addressed empirically.

Simultaneity in recreation decision making arises from three sources. First,the existence of a budget constraint implies that income spent on a trip to onesite cannot be spent on a trip to another site. This type of simultaneity wasdealt with in the studies by Burt and Brewer [Z] and Cicchetti et al. [S]. Second,the existence of a time constraint implies that time spent in one activ ity at onesite cannot be spent at another site. The empirical implications of the timeconstraint are perhaps not different from the budget constraint. The theoreticalimplications have been examined in part by McConnell [S]. Third, simultaneityexists because of complementarity of tastes. Thus, even without the time andbudget constraints, we would expect that participation in one activ ity wouldinfluence participation in another activity. This kind of simultaneity existsthrough interdependence in the util ity function, for example, in the sense thatincreasing participation in camping increases the marginal utility and participa-tion in hiking.

The simultaneity of decisions to participate is perhaps more strongly influencedby a commonality of tastes than by the income and time constraints. The effectof tastes makes the decisions to participate in two similar activit ies complement-ary. The income and time constraints would appear to have more influence onthe frequency of participation ; for example, more freshwater fishing would implyless saltwater fishing, because of the impact of the time and income constraints,causing the activ ities to appear as substitutes. To decide whether to participatein an activ ity at all would require consideration of all costs, fixed and variable,of that participation. Further decisions concerning the frequency or duration ofparticipation would involve only marginal costs. Thus, one type of simultaneitywhich we have not considered is that involving the discrete choice of whether toparticipate and the continuous choice of the frequency of participation. Thistype of simultaneity has been dealt with by Schmidt and Strauss [15], butnot in the context of the demand for recreation.In this paper, we concentrate on the simultaneous nature of decisions toparticipate in particular recreation activities. We present an empirical model


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JOINT RECREATION PARTICIPATION 67first developed by Schmidt and Strauss L-13, 141 and Nerlove and Press [12]which permits one to estimate coefficients reflecting the degree of simultaneityin the decision to participate in several recreation activities. This model, whichuses maximum likelihood methods, is one of a class of simultaneous dichotomousvariable models now being developed. (See Annals of Social and EconomicMeasurement, Fall 1976, for state-of-the-art papers on the problem.) It is presentedin general form and applied to recreation data for the state of Rhode Island.The results of the estimation process demonstrate the importance of consideringthe simultaneity in the decision process.

II. THE SIMULTANEOUS MODELThe general form of the model describing whether an individual will participate

in a recreation activity may be derived from the household production function.The household is assumed to minimize the cost of producing a number of recrea-tion days. This minimization provides the consumer with a cost function whichbecomes part of the budget constraint. The consumer then maximizes util itysubject to the budget constraint. The resultant demand functions show thatparticipation in a particular activity depends on variables which affect the costof production of recreation (such as owning a boat or living close to a recreationsite) and variables which affect the preferences for the activity (such as educationand family size). In this paper, we expand the set of variables which influencean individuals preferences for a particular activity to include other recreationactivities. Thus we specify the participation function for a particular activityto depend upon a set of exogenous variables as well as endogenous variables.

The decision to participate in one of a set of n outdoor recreation activitiescan be written as follows: let P(y; = 11 Y$) be the conditional probability thatan individual 1 participates in activity i, git = 1, given Yit, and let f(e) be afunction of exogenous variables and endogenous decisions which determinesthe probability.

whereP&i = 1 I Yi) = .f(-vI Y,>, (1)

yit = 1 if tth individual participates in ith activity= 0 otherwise,Xit = vector of exogenous variables influencing choice of participation inith activity,Y,J = (n - 1) vector of decisions (0, 1) about participation in other activities

(where n is the number of activities in the system)= (Ylt, * * *, YL Y4+1, * - *, Yn).

In this paperwe choose the logit form of the probability function.* This form iswrittenln[P(yd = 1 j Yit)/P(yit = 01 Yt)] = /3iXi + I** Crijyj",

1x1(2)

z See Schmidt and Strauss 13]. In addit ion, Nerlove and Press [ll] dea l with systems like this.


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68 CASWELL AND MCCONNELLwhere

& = a vector of unknown parameters associated with the exogenous variables,aij = the unknown parameter relating participation in activity i with that of j.3One can interpret the coefficients more clearly when Ey. (2) is rewritten as

P(Yi" = 11 Yi) = [l + exp( -@liXit - nT, "iiP(yjt = 11 Yj'))]-'.j=; (3)

Therefore, where Xikt is the kth exogenous variable of the ith equationaP(yil = 11 Yi)

d&kaP(yjt = 1 [ Yj)

axiktP(yit = 11 Yi)

j=1

X[l - P(q2 = lIYil)]. (4)The coefficients (&s) obtained by estimation represent the full effect of Xi onP(yi = l ( Y;) if X;l appears in the ith equation only, or if all aijs = 0. Other-wise, & represents only a partial effect. For example, in a two-equation model,if income is a properly specified variable in both equations and (Y s significantlydifferent from zero, the effect of income on the probability of the first activity isthe sum of the direct effects through the pis and the indirect effects associatedwith the cr.

The degree of simultaneity among the activities is determined by aij. It isthe change in the conditional probability of participating in activity i inducedby a change in the conditional probability of participating in activity ,j, multipliedby a fraction of the probability of i :

aP(yi = 1IYi')aP(yj = 1 j Yj) = aij.p(yit = l( Y,) .[l - P(yi = 1 j Yi>]- (5)The actual change depends on the current magnitude of P(yi = 11 Yi). Thepartial derivative approaches zero if the conditional probability of i approacheszero or one. However, estimation of the simultaneous model rather than thesingle-equation model also results in different values for the pis. It can be seenthat when all of the ~2s equal zero, the model reduces to the single-equationbinomial logit. The model is designed such that a;j represents the degree ofsubstitutability (aij < 0) or complementarity (aij > 0) between two activit.ies.Such information could be of particular interest to decision makers. Investmentplans for outdoor recreation facilities could be designed to use public funds moreefficiently while sti ll providing services. For example, it may be possible to demon-strate that a single investment in boat ramps would induce increased participationin boating, which in turn would induce more saltwater fishing, if the (Yassociatedwith these activities is significantly greater than zero.

* The structure of the system implies that ~i i = i i, as demons trated by Schm idt and Strauss[137. Hence there are n(n - I)/2 distinct a~.


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JOINT RECREATION PARTIC IPATION 69III. EMPIRICAL RESULTS

The maximum likelihood method was used to estimate the coefficients. Theparameter estimates are asymptotically efficient and normally distributed undergeneral conditions.4 The likelihood function is derived from the joint probabilitiesand is of the form

L = 6 exp[f (fi;X;y; + f aijYiiYjt)]/At,t-1 i-1 J#i111

63)

whereA1 = the sum of all the possible numerators,57 = the total number of observations.

Several measures of success were calculated. The percentage of correct predic-tions was determined by computing the marginal probability that the activitywill occur and comparing the results with the actual observation (i.e., if Pi > 0.5and yi l = 1, or Pi < 0.5 and yit = 0, then the prediction is correct). The Type Ierror reports on the proportion of incorrect predictions which were caused bypredicting no participation when, in fact, the household did participate. TheType II error is the remaining proportion of the error caused by predictingparticipation when there was none.6Data Sources

The analysis was conducted on data concerning participation in six outdoorrecreation activities : boating, saltwater fishing, picnicking, sightseeing, saltwaterswimming, and freshwater swimming. The data were gathered in a 1974 mailquestionnaire survey of Rhode Island households.7

The survey used a diary format, which required households to completequestionnaires as they participated in the activities. For the months of July andAugust, there were 1095 valid responses. Information was also gathered fromthe same individuals concerning certain socioeconomic characteristics and theownership of major recreation goods. Of the six activities analyzed, saltwaterfishing had the fewest participants (99, or 9% of the sample) while saltwaterswimming had the most (471, or 43% of the participants).In the estimation of recreation participation functions, the problems of sequen-tial estimation are severe because a priori hypotheses are few. Wallace [16]provides theoretical justification for practical approaches to the sequentialestimation problem for linear models. Out model is not linear, but our problemis similar. To avoid the sequential estimation problems, we proceeded as follows.

4 McFadden [ 101.r? Bl la6 A = Z exp[ 2 (BiXirZri + Z a+ZvZ ~~)], where Z ki represents the dum my value of yi

k-l j>i(0 or 1) in the kthi~~rm utation (there being 2 different possible c omb inations) ; Z is a (2 X n)matr ix.

d A FOR TRA N program was wr i t ten to est imate coeff ic ients for up to f ive equations. A copyof this program is available on request.r For a more complete discussion of the survey, the cha racteristics of the sample, and a descrip-tion of participation according to those characte ristics, see McC onnell and C&w ell [Q].


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70 CASWELL AND MCCONNELLTABLE I

Independe nt Variables Included in the Final EquationsName Descr ipt ion UnitsIn tBoatH M 2>HS


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TBLEI

TwoEqo

Mo

oReeo

Acvy

Chc

In

Bo

HM2

>HS

HS


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JOINT RECREATION PARTIC IPATION 7 )TABLE V

Pred ictive Abilities of Simu ltaneous-Eq uation and Single-Equation LogitAct iv i ty

BoatingSaltwater fishingPicnicking

SightseeingSaltwater swimmingFreshwater swimming

SingleSimultaneousSingleSimultaneousSingleSimultaneousSingleSimultaneousSingleSimultaneousSingleSimultaneous

Root mean Meansquare absoluteproportional proportionalerror (Cl) error (C,)

0.552 0.4620.521 0.4570.367 0.3880.362 0.3631.52 0.8381.48 0.8150.650 0.3900.627 0.3860.563 6.3170..566 0.3150.712 0.4910.672 0.471

work and recreation, choice of recreational gear and activity, choice of activitiesto pursue, and many other decisions. We concentrate on the simultaneous natureof decisions to participate in several recreational activities. A simultaneous logitmodel was estimated which permitted participation in one activity to depend,among other things, on whether the individual participated in other activities.

The simultaneous logit model is estimated for three pairs of recreation activitiesin which Rhode Island households participated. Our empirical results confirmour a priori expectations about the influence of participation in one activity on thedecision to participate in another activity. We show that participating in boatingincreases the probability of participating in fishing : that picnicking increases thelikelihood of sightseeing ; and that freshwater swimming increases the probabilityof saltwater swimming. The model, which is estimated using maximum likelihoodmethods, estimates a coefficient which can be interpreted as a measure of comple-mentarity or substitutability between the activities. Significance tests on thesecoefficients showed them different from zero at a high level of confidence.Estimation of recreation participation functions simultaneously is valuablebecause of the insight it gives to the making of the participation decision, andbecause it permits simultaneous forecasts of consistent recreation participation.Consistency of forecasts cannot be achieved using single-equation models.

Although the findings are promising for Rhode Island, the approach needs tobe tested on other data. For example, a set of national data on hunting andfishing, or hunting and wildlife watching might lend itself to analysis usingsimultaneous participation functions.REFERENCES

1. J. Benus, J. Km enta, and H. Shapiro, The dynam ics of household budget al location tofood expenditures, Re v. Ew n. Statis t. 58, 129-138 (1976).2. 0. R. Burt and D. Brewer, Estimation of net social benefits from outdoor recreation, Eco-nometrica 39, 813-827 (1971).


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76 CASWELL AND MCCONNELL3. M . &sw ell, Estimating Jointly Dependent Rrecreation Participation Functions , un-

published Mas ters thesis, Unive rsity of Rhode Island, Kingston, 1978.4. C. J. Cicch etti , Forecasting Recreation in the United States, Lexington Book s, Lexington,Mass, (1973).5. C. J. Cicch etti , A. C. Fisher, and V. K. Sm ith, Econom ic models and planning outdoor

recreation, Operations R es. 21, 1104-1113 (l973).6. P. Davidso n, F. G. Adam s, and J. J. Seneca, The social value of water recreational facil i t iesresulting from an improvem ent in water quality, in Water Research (A. V. Kneese andS. C. Sm ith, E ds.), Johns Hopkins Press , Baltimore (1966).7. T. A. Dey ak and V. K. Smith, Congestion and participation in outdoor recreation : A householdproduction function approach, J. Environ. Econ. Manag. 5, 63-80 (1978).8. K. E. McC onnell, Some problems in estimating the demand for outdoor recreation, Am er.J. Agric. Ecw n. 57, 330-334 (1975).9. K. E. McC onnell and M . F. C& well, Report on a Survey of Rhode Island Householdsconcerning Their Outdoor Recreational Activities, Univers ity of Rhode Island MarineMem orandum No. 50 (1978).10. D. McF adden, Conditional logit analysis of qualitative choice behavior, in Frontiers inEconometr ics (P. Zarembka, Ed.) , Academic Press, New York (1974).

1 I. M . Nerlove and S. J. Press , Univariate and Multivariate Log-Linear and Logistic Models,Rand Corp., R-1306 (1973).12. P. Schm idt and R. P. Strauss , Estimation of models with jointly dependent qualitativevariables : A simultaneous logit approach, Paper presented at Econom etric Society meeting

(1974).13. P. Schm idt and R. P. Strauss , Estimation of models with jointly dependent qualitativevariables : A simultaneous logit approach, Ecunpm ettia 43, 745-755 (1975).14. P. Schm idt and R. P. Strauss , The effect of unions on earnings and earnings on unions: A

mixed logit approach, Znt. Ew n. Re v. 17, 204-212 (1976).15. T. Toyoda and T. D. Wa llace, Pre-testing on part of the data, J . Eco twm et. 10, 119-123(1979).16. T. D. Wallace, Pre-test estimation in regression: A survey , A mer. J. Agric. Econ. 59, 431-443(1977).

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Barrier to Do Recreation