Health effects and recreation: A model for incorporating the costs of imperfect information

HEALTH EFFECTS AND RECREATION: A MODEL FOR INCORPORATING THE COSTS OF IMPERFECT INFORMATION∗∗

Ana María Ibáñez

Department of Agricultural and Resource Economics University of Maryland at College Park

ABSTRACT

El modelo discreto de decisión es modificado para incluir explícitamente la morbilidad causada por la contaminación y calcular los costos de la información imperfecta. El modelo se aplica para valorar los beneficios de reducir la contaminación de patógenos en la Bahía de Cartagena. Los resultados confirman que ignorar la morbilidad causada por la contaminación y la información imperfecta sesga las medidas de bienestar. Las pérdidas en bienestar del modelo propuesto son 1.85 veces más altas que las pérdidas calculadas con base en los modelos tradicionales. Los beneficios de informar a los usuarios de las playas acerca de los niveles de contaminación y sus efectos sobre la salud alcanza más de la mitad de las pérdidas en bienestar ocasionadas por un incremento del 30% en la contaminación. Este resultado es de gran interés para los países en desarrollo, los cuales tienen restricciones para invertir en programas de descontaminación. En el corto plazo la información puede ser un sustituto a dichos programas.

INTRODUCTION

Recreation demand models that ignore or do not model explicitly the health

effects of pollution will underestimate the benefits from its reduction. Yet, health

costs may constitute a large portion of welfare losses from pollution. Beyond losses

from the actual contraction of the disease, consumers face additional losses

because they change behavior and forego income to reduce uncertainty. Further,

consumers not informed about the health effects of pollution do not engage in

averting behavior to reduce the probability of contracting diseases. These

individuals incur a cost of ignorance because they are more likely to contract

diseases compared withconsumers with complete information.

Given the high levels of pollution in developing countries, the effect of

contamination on human health can be substantial. Further, information about

pollution is scarce and consumers have little choice to engage in activities to avoid

or reduce the risk of contracting diseases from exposure to pollution. In this

context, health costs might be considerable and ignoring them can downplay

losses from pollution.

This paper investigates whether improved information about the health effects

of pollution can increase welfare. If the benefits of giving information outweigh the

costs, a public awareness programs about pollution and its health effects will yield

net benefits. Moreover, releases of information can be a short-term substitute for

pollution abatement policies. In developing countries where financial resources are

scarce and environmental priorities compete with the provision of basic goods,

improving informationmay yield high payoffs while pollution abatement policies are

feasible.

In this paper, I develop a discrete choice model that includes the effect of both

health and aesthetic characteristics of environmental quality. The model

distinguishes between behavioral responses of consumers who are differently

and unaware about the health effects of pollution are established, and the benefits

of releasing information are defined.

This model is applied to value the benefits of reducing pathogens in Cartagena

Bay, Colombia. Evidence from this empirical application shows welfare measures

can be biased when health effects are not modeled separately from aesthetic

effects and imperfect information is not considered.

Empirical evidence in developed countries shows that improvements in water

quality increase demand for recreational sites by increasing the number of trips

and/or increasing the probability of visiting a particular site: McConnell (1986)

estimates a demand of planned trips to New Bedford Harbor as a function of PCBs;

Bockstael et al. (1988) link trips to the beach to nutrients using a Tobit model;

Bockstael et al. (1987a) relates bacterial contamination to a system of demands

and a discrete choice model for a set of beaches in the Boston area; and Hausman

et al. (1995) use a discrete choice model to estimate welfare losses from the Exxon

Valdez spill. In developing countries, empirical evidence about the link between

variations in water quality and demand for recreational sites is scant. A study by

Niklitschhek and León (1996) determines the incidence of water pollution on the

demand for 53 beaches in Guanabara Bay, Brazil. Further investigation on the

demand for environmental quality in developing countries can help understand

preferences in different stages of economic growth. This paper also helps to fill

I. Measuring the Value of Information in a Continuous Model for Recreation Demand

I.1 Modeling the Health Effects of Pollution

Typically, the literature on benefits of pollution control in recreational sites

disregards the fact that pollution costs are comprised of aesthetic and health costs.

Yet many water pollutants affect both aesthetic and health characteristics of the

water. For example, sewage discharges increase turbidity of the water as a result

of increases in nutrients. But, sewage pollution also contains bacteria like fecal

coliforms and enterococci, which cause waterborne diseases. Health effects may

involve morbidity and mortality risks. Bacteria can increase the risk of morbidity

whereas toxic substances can increase the risk of morbidity and mortality.

In this section, a general continuous model to isolate health and aesthetic

effects is developed. Based on this model, welfare losses for consumers with

different levels of information are derived, and the value of giving information is

defined.

Besides aesthetic effects like turbidity and bad odors, water pollution affects

expected utility by increasing the probability of contracting a waterborne disease

and intensifying the severity of the disease (e.g. restricted activity days, sick days).

Assume consumers' utility depends on a numeraire good (x), a vector (r)

representing the number of trips to n recreational sites, a vector (q) representing

(1) stay healthy (S=0) or (2) contract a waterborne disease (S=1). By assuming

only two possible outcomes, the model ignores the effects of water quality on the

severity of the disease. This assumption does not alter the generality of the results.

The major costs arising from sewage pollution are associated with the frequency of

the adverse effect, contracting a disease, rather than the severity of an individual

disease. State dependent utility is defined as

), , , , ( ) 1

( U =U x r q S

Assume that U(x,r,q,0)≥U(x,q,r,1), because ceteris paribus utility is higher when

the consumer is healthy than when he contracts an illness.

Suppose that consumers have complete information about the health effects of

pollution. That is, they know water quality levels and the probability distribution of

health effects. Consumers adjust behavior according to their beliefs about the link

between water quality and health effects. Their subjective expectations are

represented by the probability of contracting a waterborne illness, conditioned on

water quality levels and averting behavior (e.g. visiting distant recreational sites

and/or reducing the number of trips). For the sake of simplicity, suppose that only

environmental quality causes sickness. Since only two health outcomes are

possible, a discrete distribution is defined where the probability of contracting a

waterborne disease is represented by

). , ( ) 2

( π=π q r

The expenditure function when health and aesthetic effects are considered is

(

, , ( , ),

)

{

min ;

(

1 ( , )

)

( , , ,0) ( , ) ( , , ,1)

}

.

Aesthetic and health effects are distinguished in the individual's utility function.

Including environmental quality directly in the utility function captures aesthetic

effects whereas health effects are incorporated in the subjective expectations and

the state dependent utilities.

An appropriate measure for welfare losses from deterioration in water quality

should account not only for aesthetic effects and the disutility of contracting a

disease, but also for the foregone income to reduce uncertainty. Thus,

compensating variation when water quality changes from 0

q to 1

q is defined by

(

, , ( , ),

) (

, , ( , ),

)

.

) 4

( CV e pr q0 q0 r U0 e pr q1 q1 r U0

U = π − π

By accounting for welfare losses from facing uncertainty, the compensating

variation defined in equation (4) is an ex-ante welfare measure.

I.2 Dealing with Imperfect Information

Welfare losses and gains from pollution differ according to the information level.

Consumers may have different levels of information about the health effects of

pollution. Some consumers may know pollution levels in recreational sites and the

associated probabilistic distribution for health effects. Others may ignore the link

between pollution and health effects but know pollution levels at recreational sites.

At the end of the spectrum are consumers who ignore recreational sites are

To identify the effect of imperfect information in welfare changes from

pollution, two separate models are developed for consumers who know pollution

levels and its associated probabilistic distribution, called aware individuals, and

consumers who know pollution levels but do not link pollution and health effects,

called unaware individuals. While aware individuals respond to changes in

environmental quality for aesthetic reasons as well as to reduce health risks,

unaware individuals respond to changes that can only be perceived by the senses

– changes such as turbidity and odors, the aesthetic effects.

Suppose that individuals are identical except for the information that they have

about the health effects of pollution. The expenditure function of an aware

individual is defined by

(

, , ( , ),

)

{

min ;

(

1 ( , )

)

( , , ,0) ( , ) ( , , ,1)

}

.

(5) eA p_r qπ q r U0 = x+p_rr −π q r U x r q +π q r U x r q ≥U0

When water quality changes from 0

q to 1

q , the compensating variation for an

aware individual is

(

, , ( , ),

) (

, , ( , ),

)

.

) 6

( CVA =eA p_r q0 π q0 r U0 −eA p_r q1 π q1 r U0

Individuals unaware of the health effects of pollution do not respond to water

quality changes to reduce health risk. These individuals may get sick from

exposure to polluted waters without knowing the cause of the disease. They

respond to pollution only when it affects water characteristics that can be perceived

by the senses. Therefore, they choose the frequency of trips according only to

aesthetic considerations. Since unaware individuals do not adjust to changes in

(

)

(

)

(

)

{

min ;1 ( , ) ( , , ,0) ( , ) ( , , ,1) ; ( )

}

, ) ( ; , ) ( , , , ~ (7) 0 0 q r r U q r x U r q q r x U r q r p x q r U q r q q p e NA r NA NA r NA = ≥ + − + = π π π

where NA

r solves

{

min ; ( , , ) 0

}

. )

0 , ,

(p_r qU x p_rrU x r q U

NA

e = + ≥

Unaware individuals have difficulty adjusting, so that compensating surplus is

the appropriate welfare measurei. When water quality changes from q0 to q1, the

compensating surplus for the unaware individuals is defined by

(

, , , ; ( )

)

~

(

, , , ; ( )

)

.

~

) 8

( 0 0 0 1 0 1

q r U S q p e q r U S q p e CS NA r NA NA r NA

NA = −

Equation (8) measures welfare changes caused by pollution variation. Unaware

individuals do not have the opportunity to avoid possible welfare losses when water

quality deteriorates or to take advantage of additional welfare gains when water

quality improves, unless aesthetic and health characteristics are perfectly

correlated.

Consumers unaware about the health effects of pollution behave differently

than consumers with complete information. While the latter can engage in

appropriate averting behavior, the former cannot reduce the likelihood of

contracting an illness by engaging in defensive activities. These unaware

individuals may visit recreational sites an excessive number of times or may visit

polluted recreational sites, and contact polluted waters. Unaware individuals’

probability of contracting a waterborne disease may be higher compared to the

Giving objective information about the health effects of pollution induces

unaware individuals to acquire knowledge about these effects. Because full

information about the risk of environmental pollution will induce consumers to

choose the optimal consumption bundle, unaware types would be better off. The

value of information measures changes in utility in monetary units when objective

information is released. And, is defined as the amount of money necessary to

render the individuals as well off as before information about the health effects is

released, when water quality remains constant

(

( ),

)

, ; ( )) ( , , ( , ), ).

, , ( ~ ) 9

( VI =eNA p_r q0 π rNA q0 q0 U0 rNA q0 −eA p_r q0 π q0 r U0

Simply informing consumers about pollution can reduce welfare losses from

pollution regardless of whether abatement policies are implemented. The general

ideas developed in this section can be applied to discrete choices of recreational

sites.

II. Measuring the Value of Information in a Discrete Choice Model

II.1 A Discrete Choice Model for Aware and Unaware Individuals

Consider the choice of a consumer aware of the health effects of pollution.

Assume that the consumer derives utility from going to beach j. Utility from

recreation will depend on travel costs, aesthetic and health effects of pollution as

who are aware of the health effects of pollution, called aware consumers, would

choose which beach to visit based on the conditional indirect utility function

A j A j A

j v

U = +ε

) 10 (

where, superscript A indicates awareness and U_jA is the utility of an individual who

visited beach j . The term vj A

is the deterministic utility from visiting beach j. The

random term, εAj , represents characteristics unobservable to the researcher.

A rational consumer chooses recreational site j if the utility he derives from this

alternative is higher than the utility from choosing any other alternative,

[

]

.

(11) V_jA = MaxvA_j +ε A_j ∀ j

If the error terms have independent and identically distributed Extreme Type I

distributions, the probability an aware individual chooses site j is determined by

( )

( )

,

exp exp )

( (12)

1

∑

=

= _N

k

A k A j A

v v j

P

where N is the number of recreational sites.

On the other hand, an unaware individual chooses which site to visit according

to travel costs, water quality and other attributes not related to health. The

conditional indirect utility function for an unaware individual is given by

NA j NA j NA

j v

U = +ε

) 13 (

where U_jNAdenotes the utility of an individual not aware of pollution who visited site

when he decides based only on aesthetic considerations. The probability of visiting

recreational site j is equal to

( )

[ ]

.

exp exp )

( (14)

1

∑

₌

= _N

k

NA k NA j NA

v v j

P

However, even for the individual not aware of pollution, the health effects of

pollution impair utility. Thus, the conditional indirect utility from visiting recreational

site j depends on aesthetic considerations as well as on the probability of

contracting waterborne disease and the disutility of getting sick. The conditional

indirect utility from visiting site j for an unaware individual is defined by

.

) 15

( UNA_j =vNA_j +εNA_j

Decisions to visit a site are based on equation U_jNA, which captures only

aesthetic effects, while utility from visiting a site is defined by equation, UjNA which

incorporates aesthetic as well as health effects.

II.2 Welfare Measure for Aware and Unaware Individuals and the Value of

Information

Compensating variation (CV) for a single recreation trip, as showed by

Hanemann (1982), can be defined as the measure equating the expected

maximum utility before and after the change in environmental quality. Therefore,

[ ]

[ ]

. exp exp ln 1 ) 16 ( 1 0 1 1 1             =

∑

∑

= = N j A j N j A j A v v CV γ

where γ₁ represents the marginal utility of income, v1Aj is the conditional indirect

utility at the new water quality level and v0Aj is the conditional indirect utility at the

previous water quality level.

As explained before, the unaware individual chooses which site to visit based

only on aesthetic considerations, yet derives utility from both aesthetic and health

effects. Hence, the probability of visiting site j depends on the utility function U_jNA

but UNAj represents the utility from visiting this site. The expected utility can then be

defined asii

[ ]

log exp

( )

(

)

0.57721. ) 17 ( 1 1

∑

∑

= = + − +       = N j NA j NA j NA j N i NA j NA v v P v U E

where P_jNAis defined in equation (14). The first term in equation (17) is similar to

the expected utility of RUM models where health effects are not modeled

separately from aesthetic effects and imperfect information is not incorporated.

The second term is a correction factor representing the expected disutility of health

effects from visiting the n sites. Equation (17) considers the difficulty in avoiding

welfare losses when water quality deteriorates, or the difficulty in taking advantage

of welfare gains when water quality improves.

( )

( )

(

)

(

)

. exp exp log 1 ) 18 ( 1 0 0 0 1 1 1 1 1 0 1 1 1             − − − +             =

∑

∑

∑

∑

= = = = N j NA j NA j NA j N j NA j NA j NA j N j NA j N j NA j NA v v P v v P v v CS γ

where v1NAj is the conditional indirect utility at the new water quality level, NA j v0

is

the conditional indirect utility at the previous water quality level and P1NAj , NA j P0

represent the probability that an unaware individual chooses site j evaluated at the

new and previous water quality level respectively.

Giving consumers more information about the health effects of pollution

increases their utility because they are choosing appropriately. Individuals are

willing to forego income to obtain information. The value of information is

( )

(

)

. ) exp( exp log 1 ) 19 ( 1 0 0 0 1 0 1 0 1             − −             =

∑

∑

∑

= = = N j NA j NA j NA j N j NA j N j A j v v P v v VI γ

When unaware individuals acquire objective information about the health

effects of pollution, they can choose optimally which recreational site to visit. This

implies that their utility from engaging in recreational activities will be higher than

when they were maximizing utility in ignorance. The value of information

III. Empirical Results

III.1 The Travel Cost Survey

The multinomial random utility model (RUM) for aware and unaware individuals

defined in section II is estimated using maximum likelihood procedures. The data

used for estimating the RUM and for obtaining the costs of imperfect information in

Cartagena Bayiii are based on a survey conducted during the first few months of

1998. Interviewers questioned 1,200 visitors at eight beaches.

From the 1,200 surveys, 27 were eliminated due to inconsistencies in the travel

cost data. Travel costs accounted for monetary transportation costs as well as the

opportunity cost of time. On site costs were not calculated because they do not

vary greatly among beaches. Time on site was assumed to be constant among

beaches. To include an accurate estimate of the opportunity cost of time, the

method proposed by Bockstael et al. (1987b) was applied.

III.2 RUM Estimates

Three variations on the basic model were estimated to identify the consequences

of modeling explicitly health effects and incorporating imperfect information. Model

1 does not distinguish between health and aesthetic effects or between aware and

unaware individuals. Health and aesthetic effects are combined in the secchi disc

pollution. The next two models differentiate between aware and unaware

individuals and health and aesthetic effects. Randomness of health effects is

considered by including different moments of the bacterial count distributioniv.

Model 2 includes the mean and standard deviation of enterococci readings to

represent health effects and the secchi disc parameter to represent aesthetic

effects. Model 3 includes the minimum value of enterococci readings. Equally to

Model 2, the secchi disc parameter represents aesthetic effects and the minimum

value of enterococci readings represents health effects. The names, definitions,

means and standard deviations of the variables are given in Table 1.

The probability of visiting beach j for Model 1 is defined by

[

]

[

( * ) (sec * )

]

.

exp ) * (sec ) * ( exp ) ( (20) ₈ 1 6 5 4 3 1 2 6 5 4 3 1 2

∑

= + + + + − + + + + − = k k k k k k k j j j j j j road music coco con mon d time road music coco con mon d time j P γ γ γ γ γ γ γ γ γ γ γ γ

Total water quality effects - health and aesthetic effects – may be captured by the

coefficient for secchi disc readings,γ3.

Since respondents who visit the beach frequently are more likely to be

surveyed, the ith contribution to the likelihood function is weighted by a function of

the predicted number of trips per year of respondent i. If xˆ_i is the predicted

number of trips, the likelihood function is defined as

∏∏

= =

=1,173

1 8 1 ). ( ˆ 1 ) 21 ( i i j i j P x

The estimated coefficients were all of the expected sign and were

statistically significant different from zero. Increases in beach j's monetary and

time costs reduce the probability of visiting beach j. Beaches with restaurants

serving native food are more attractive. When beaches have restaurants playing

tropical music the probability of visiting the beach decreases. The probability of

visiting beaches where automobile access is difficult is lower than for beaches

where access is easy. The parameter estimate for water quality, secchi disc, has

the expected sign and is significant at the 1% level. As the secchi disc can be

seen at a greater depth, the probability of visiting beach j increases. This

parameter combines health and aesthetic effects from water pollution. The

following models try the more difficult task of disentangling aesthetic and health

effects and behavioral responses of aware and unaware individuals.

To distinguish between aesthetic and health effects, the model should include

water quality variables representing consumers’ perceptions of aesthetic

characteristics, such as visiblity, as well as the probability of contracting a

waterborne disease indicating subjective expectations. A prospective

epidemiological study is necessary to estimate the probability of contracting a

waterborne diseasev. This study was not conducted in Cartagena. As an

alternative, readings of bacterial counts will be utilized as a proxy of the probability

of contracting waterborne diseases.

The following model will discriminate between aesthetic and health effects as well

as behavioral responses of aware and unaware individuals. Aware respondents

beach jvi. This amounts to 16.8% of the sample, or 197 respondents. The mean

and the standard deviation, two moments of the enterococci distribution, capture

uncertainty about health effects. The probability of visiting beach j for Model 2 is

defined by

(

)

(

)

. * * ~ and , * * ~ , * sec sec , * where , ~ ~ sec exp ~ ~ sec exp ) ( ) 22 ( ₈ 1 = k 8 7 6 5 4 3 1 2 8 7 6 5 4 3 1 2 con aw con aw con d time time road mus coc mon time road mus coc mon time j P ent j ent j ent j ent j j con j j d j ent k ent k k k k con k k d k ent j ent j k j j con j j d j σ σ µ µ σ γ µ γ γ γ γ γ γ γ σ γ µ γ γ γ γ γ γ γ = = = = + + + + + + − + + + + + + − =

∑

The minimum value of enterococci counts is a function of moments of its

distribution; thus this parameter captures uncertainty about health effects. The

probability of visiting beach j for Model 3 is

(

)

(

)

. * * ~ where . ~ sec exp ~ sec exp ) ( ) 23 ( min min 8 1 = k min 8 6 5 4 3 1 2 min 8 6 5 4 3 1 2 con aw e e e road mus coc mon time e road mus coc mon time j P j j k k k k con k k d k j k j j con j j d j = + + + + + − + + + + + − =

∑

γ γ γ γ γ γ γ γ γ γ γ γ γ γ

Equally to Model 1, models (22) and (23) were weighted by the predicted number

Parameter estimates for monetary and time costs, coco, road and music for

equations (22) and (23) are similar in magnitude and statistical significance to

those estimates of equation (20). Also, the results show no difference between the

slope of secchi disc readings from equations (22) and (23) and the slope for secchi

disc readings from equation (20). Since the coefficient on secchi disc readings

does not change when different moments of the enterococci distribution are

included, health effects from bacterial contamination might not be captured by the

secchi disc parameter. As expected, the parameter estimates on the mean of

enterococci counts from equation (22) negatively affects the probability of choosing

a beach. The estimated coefficient on the variance of enterococci counts is positive

and significant. Although a negative sign was expected, when water quality is low

on average, a high variance implies many days water quality may be acceptable

and even high. In this case, the sign of the enterococcus counts’ variance may be

positive. In equation (23), the expected sign for the minimum value for enterococci

sign occurs and the parameter is significantly different from zero.

III.3 Welfare Measures and the Value of Information about Pollution for Cartagena Bay

The models estimated in the previous section are now used to estimate the

welfare measures derived in Section II. Standard compensating variation,

compensating variation for aware individuals, compensating surplus for unaware

Consider a change in water quality for the j beaches from sec0_j to sec1_j, compensating variation for Model 1 is

[

]

[

(sec * )

]

.

exp ) * (sec exp ln 1 ) 24 ( ₈ 1 0 3 8 1 1 3 1 1             + + =

∑

∑

= = j j j j j j M con Z con Z CV γ γ γ where . ) *

( 1 4 5 6

2 j j j j j

j time d mon coco music road

Z =γ −γ +γ +γ +γ

Compensating variation calculated from this model is the traditional measure of

an improvement in water quality derived by Hanemann (1982). If γ₃captures

health and aesthetic effects, the compensating variation defined by equation (24)

includes total welfare losses when the consumer chooses with complete

information. Conversely, if γ3 does not change when moments of the bacterial

counts distributions is included, equation (24) accounts only for aesthetic losses.

Since this model does not account for losses from imperfect information, it yields

incorrect welfare measures.

Compensating variation for a change in water quality from con

k

0

sec and e_j0min to

con k

1

sec and e1jminfor aware individuals for Model 3 is

Health effects are represented in parameter γ₈ while aesthetic effects are captured by parameter γ3.

Compensating surplus for unaware individuals for Model 3 is represented by

(

)

(

)

(sec )

(

~

)

(sec )

(

~

)

. sec exp sec exp ln 1 ) 26

( 8 0min

0 8 1 min 1 8 1 8 1 8 1 0 3 8 1 1 3 1 3             − +             + + =

∑

∑

∑

∑

= = = = j con j NA j j con j NA j j con j j j con j j NA

M P e P e

Z Z

CS γ γ

γ γ γ where

(

)

(

)

. sec exp sec exp ) (sec ₈ 1 3 3

∑

= + + = k con k q k con j q j con j q NA j Z Z P γ γ and q=0,1.

Based on models (20) and (23), estimated losses, in dollars, from a

hypothetical 30% decrease in water quality in Cartagena Bay are measured. To

identify the costs of imperfect of information, welfare measures for Model 3 are

calculated for the same sample of respondents. Welfare losses for aware

individuals are calculated for the total sample assuming all individuals are aware.

Similarly, welfare losses for unaware individuals are calculated for the total sample

assuming all individuals are unaware. Results are reported in Table 4.

Welfare losses for Model 1 amount to 1.39 per trip. This measure does not

account for the costs imperfect information. When health effects are modeled

separately and imperfect information is incorporated, welfare losses change

considerably. Welfare losses based on Model 3 for aware individuals are 2.11 per

water quality deterioration is ignored. Welfare losses for aware consumers from

Model 3 are around 1.5 times higher than the welfare measure estimated from

Model 1. The additional benefits are a result of increases in health costs.

Comparing welfare measures for aware and unaware individuals can shed

some light about the value of information, or its opposite, the costs of imperfect

information. Welfare losses for aware individuals are 1.25 times lower than for

unaware individuals. Since unaware individuals do not adjust behavior to reduce

health risks, the probability of contracting an illness compared to the probability for

aware individuals may be higher. Because unaware individuals’ decisions may

differ from the decision they would make if they were informed about the health

effects, the costs of imperfect information may be high. As a result, an increase in

pollution causes larger welfare losses for unaware individuals.

What are the consequences when gains or losses are aggregated across

households? To aggregate households, the sample was divided between aware

and unaware and welfare measures were calculated for each group separately.

Results are shown in Appendix II. Aggregation was done by household, in effect

taking each interview in the field to represent a householdvii. When aggregating

welfare measures over consumers, the downward bias of compensating variation

based on Model 1can downplay the economic costs of pollution if the proportion of

uninformed individuals is substantial. Table 5 shows aggregate losses for the two

models.

Model 1. The underestimation of welfare losses from contamination may be

substantial in the developing world where pollution levels are high and information

about pollution is scarce. By downplaying the costs of pollution, investments on

pollution abatement may be lower than optimal.

As derived in section II, the value of information for Model 3 is

(

)

(

)

(sec )

(

~

)

.

sec exp ~ sec exp ln 1 ) 27 ( 8 1 min 0 8 0 8 1 0 3 8 1 min 0 8 0 3 1 3             −             + + + =

∑

∑

∑

= = = j j con j NA j j con j j j j con j j

M P e

Z e Z VI γ γ γ γ γ

The value of information is $1.45 per tripviii, which supports the hypothesis

formulated previously. New information about the risks from exposure to polluted

waters induces changes in the decisions of unaware beach users. Expected utility

under complete and imperfect information differs and, consequently, the value of

information is high. Merely informing consumers about pollution levels and its

associated health effects can reduce welfare losses stemming from water pollution

in Cartagena.

IV. Conclusions

This paper demonstrates welfare losses are biased when uncertainty and

imperfect information are considered. Traditional recreation demand models do

not capture health effects unless aesthetics and health effects are highly correlated

Disseminating objective information about pollution levels may reduce the

economic costs of environmental quality deterioration in spite of whether actual

contamination is reduced. In the case of Cartagena, simply informing beach users

about pollution levels and its associated health effects can reduce welfare losses

from pollution by $1.45 per trip. These results show that policies designed to

inform beach users might yield high payoffs - regardless of whether actual pollution

levels are reduced. In developing countries where investment for pollution

abatement is not readily available, informing consumers can be a short-term

substitute for pollution abatement policies.

The results of this paper demonstrate the importance of incorporating health

effects and imperfect information in recreational demand models. Further

investigation of these issues is essential to refine models estimating welfare losses

from deterioration in environmental quality. One drawback of the models estimated

is that the distribution for the likelihood of contracting an illness is not observed

and, as a result, proxies must be utilized. Prospective epidemiological models

estimate the probability of contracting waterborne disease as a function of

environmental quality indicators. Models estimating welfare losses from water

pollution can combine elements of a traditional economic study in which the costs

of pollution are measured as the foregone value of recreation and an

epidemiological study which measures the health effects of exposure to pollutants.

The advantage of such a study is that it will combine economists’ measures of the

paper can be applied to other pollutants like PCBs or stock pollutants that cannot

be perceived by the senses; and the costs of imperfect information might be higher

in these cases.

References

Bockstael, N.E., McConnell, K.E. and Strand, I.E. Benefits from Improvements in

Chesapeake Water Quality. Report to the Office of Policy and Resource

Management, USEPA (1988).

Bockstael, N.E., Hanemann, W.M. and Kling, C. L. “Estimating the Value of Water

Quality Improvements in a Recreational Demand Framework.” Water

Resources Research 23(5):951-960 (1987a).

Bockstael, N.E., Strand, I.E. and Hanemann, W.M. “Time and the Recreational

Demand Model.” American Journal of Agricultural Economics 69

(5):951-960 (1987b).

Foster, W and Just, R. “Measuring Welfare Effects of Product Contamination with

Consumer Uncertainty.” Journal of Environmental Economics and

Management 17:266-283 (1989).

Hanemann, M.W. Applied Welfare Analysis with Qualitative Response Models. California Agricultural Experiment Station Working Paper No. 241. Berkeley, CA: University of California (1982).

Hausman, J.A., Leonard, G.K. and McFadden, D. “A Utility-Consistent, Combined Discrete Choice and Count Data Model. Assessing Recreational Use

Losses Due to Natural Resource Damage.” Journal of Public Economics

56:1-30 (1995).

Leggett, C. “Evironmental Valuation with Imperfect Information: The Case of the Random Utility Model.” Working Paper WP 99-15. Department of Agricultural and Resource Economics. University of Maryland, College Park, MD (1999).

McConnell, K.E. The Damages to Recreational Activities from PCBs in the New

Bedford Harbor. Cambrige, Mass. Industrial Economics (1986).

Morey, E.R. “Two RUMs unCLOAKED: Nested-Logit Models of Site Choice and

Nested-Logit Models of Participation and Site Choice” in Valuing

Recreation and the Environment (eds. Herriges, J.A. and Kling, C.L.)

Niklitschek, M. and León, J. "Combining Intended Demand and Yes/No Responses

in the Estimation of Contingent Valuation Models." Journal of

Table 1. Names, Definition, Mean and Standard Deviation

Names Definitions Mean Standard

monj monetary travel costs to beach j in

dollars

16.2 18.1

timej travel time in minutes to beach j in

minutes

93 126

D = 1 when individuals do not answer the

secondary job question

0.87

-Aw = 1 when the beach user is informed

about the health effects of pollution

0.16

-con = 0 when the individual presents

inconsistencies between answers to the survey and actual behaviorix

0.96

-cocoj = 1 when beach j has restaurants

serving native food

0.5

-musicj = 1 when beach j has restaurants with

tropical music

0.25

-roadj = 1 when the road to beach j is in a bad

condition

0.25

-j

sec Mean of secchi disc readings for beach

j, in centimeters

335 360.7

ent j

µ Mean of enterococci readings for beach

j

92.04 66.91

ent j

σ Standard Deviation of enterococci

readings for beach j

73.41 62.67

min

j

e Minimum Value of enterococci readings

for beach j

Table 2. Parameter Estimates and t-statistics for Model 1 Equation (20)

Monetary costs -0.000067

(-18.155*)

Time costs -0.0167

(-18.800*)

Secchi disc 0.0013

(6.609*)

Coco 2.2419

(19.360*)

Music -1.2541

(-9.907*)

Road -0.656

(-5.171*)

Number of Observations 1,173

Log-Likelihood -1864.855

Log-Likelihood Ratio Test

a

1021.707*

a

Table 3. Parameter Estimates and t-statistics for Model 2 and Model 3 Equation (22) Equation (23)

Monetary Costs -0.000067

(-18.146***)

-0.000067 (-18.119***)

Time Costs -0.0167

(-18.822***)

-0.0167 (-18.696***)

Secchi Disc 0.00131

(6.682***)

0.00138 (7.034***)

Coco 2.214

(18.946***)

2.327 (19.637***)

Music -1.257

(-9.922***)

-1.343 (-10.399***)

Car -0.614

(-4.753***)

-0.74312 (-5.748***)

Mean Enterococci -0.004156 (-1.864*)

S.D. Enterococci 0.00891

(4.112***)

Enterococci Min. -0.0124

(-2.972***)

Number of Observations 1,173 1,173

Log-Likelihood -1,863.65 -1,859.77

Log-Likelihood Ratio Test a

1024.12*** 1,037.87***

a _{Null hypothesis: all the slopes coefficients are zero}

Table 4. Welfare Losses per Trip to the Beach (In dollars) a Mean and Standard Deviation

Losses

Total Aware Unaware

Model 1 1.39

(0.73)

Model 3 2.11

(0.93)

2.65 (1.17)

a

The exchange rate used is 1 US$=1345.65 pesos

Table 5. Aggregate Welfare Losses (in dollars) a Losses

Model 1 124,361

Model 3 230,561

a

APPENDIX I

Derivation of Equation (2.8)x

The expected utility can be defined asxi

[ ]

_{∑ ∫}

(

)

(

)

= ∞ −∞ = + − + = N j NA j NA j NA i NA j i NA j NA j NA j d v v F v U E 1 , ε ε ε ε

where F_i denotes the derivative of the cumulative distribution function with respect

to the ith argument and

{

_{1 1} , _{2 2} ,..., NA

}

.

j NA i NA j NA NA i NA NA NA i NA NA j NA i NA

j v v v v v v v

v − +ε = − +ε − +ε − +ε

Assuming an Extreme Type I Distribution, equation the Expected Utility becomes

[ ]

_{∑ ∫}

(

)

_∑

(

)

= ∞ −∞ = = −      _{− − − +} + = N j NA j NA j N i NA j NA i NA j NA j NA j NA j d v v v U E 1 1 . exp )) ( exp exp ε ε ε ε ε

To simplify, make the change of variables w=v_jNA+εNA_j ,

[ ]

=

_{∑ ∫}

N ∞

(

− +

)

_− − 

_∑

_

( )

−

( )

NA

N NA NA NA NA dw v w v w w v v U

Assume

∑

=

= N

i

NA i v D

1

)

exp( , substituting and rearranging terms

[ ]

_∑

(

) ( )

_∫

[

]

( )

_∫

∞

[

]

( )

−∞ = =

∞ −∞ =

− −

− +

− −

− −

=

w N

j w

NA j NA

j NA j NA

dw w w

D Dw

dw w w

D D

D v v

v U

E exp exp exp( )exp exp exp( )exp .

1

Since the density function for a Type I Extreme Distribution with mode LnD

amounts to

(

exp( )

)

, exp

) exp( )

(w D w D w

f = − − −

the expected utility can be rewritten as

[ ]

exp( )

(

)

0.57721.

1

+ − +

=

∑

=

NA j NA j N

j

NA j NA

v v D

v LnD

Appendix II

Welfare Measures for Aware and Unaware Individuals

Table 1. Welfare Losses per Trip to the Beach (in dollars) a Mean and Standard Deviation

Losses

Total Aware Unawar e

Model 1 1.39

(0.73)

Model 3 1.95

(0.79)

2.70 (1.20)

a

The exchange rate used is 1 US$=1345.65 pesos

i

Compensating surplus is the amount of money required to keep the consumer as

well off after the change as in the initial state when he is not free to adjust

consumption quantities other than the numeraire.

ii

See derivation in Appendix I.

iii _{Cartagena Bay lies on Colombia’s Caribbean Sea, in the extreme northwestern}

corner of South America.

iv

Cartagena’s water company obtained three water samples from the eight

Enterococcus are pathogens that transmit waterborne diseases such as hepatitis,

typhoid fever, gastroenteritis and ear, eye and skin ailments. The author obtained

Secchi disc’s readings.

v

In a prospective study, a cohort of individuals who differ in their exposure to

beach polluted waters is compared in terms of illness incidence. Incidence of

waterborne diseases is determined by exposure to polluted waters, denoted by

swimming duration, and a measure of bacterial count in the water.

vi

The response to this question depends on whether the individual knows about

the health effects of pollution and, if so, on pollution levels of beach j. Since water

quality levels of each beach determine the response, the definition of awareness is

endogenous to the model. To avoid the bias introduced by endogeneity, the

predicted probability of awareness can be included. Several definitions of

predicted probability of being aware were estimated. The predictive accuracy of the

regressions was low. When the predicted probability of being aware was included

in regressions (22) and (23) the wrong signs for the water quality variables

appeared.

vii

From a randomly drawn telephone survey to 200 residents, 83% visited the

beach at least once in a year. This result was extrapolated for the total population,

which means 107,794 households of Cartagena perceive recreational gains from

improvements in water quality. To account for the proportion of households aware

proportion of 16.8% who are aware of the influence of pollution holds at the

population level. Then the aggregate benefit from the estimation is given by:

[

Proportion Aware*CVAware Proportion Unaware*CVUnaware

]

* Households gains

or losses

Total = +

viii

The exchange rate used is 1 US$=1345.65 pesos.

ix

Even though some aware individuals perceived the risk of getting sick from

swimming in Cartagena’ beaches extremely high, they swam. Hence, they were

classified as respondents behaving inconsistently with respect to water quality

variables. In the model, these individuals will respond to other beach characteristic

different than water quality.

x

This derivation draws on the derivation developed by E.R. Morey, “Two RUMs

unCLOAKED: Nested-Logit Models of Site Choice and Nested-Logit Models of

Participation and Site Choice” in Valuing Recreation and the Environment (eds.

Herriges, J.A. and Kling, C.L.)

xi

This equation was developed by Chris Legget in Leggett, C. “Evironmental

Valuation with Imperfect Information: The Case of the Random Utility Model.”

Working Paper WP 99-15. Department of Agricultural and Resource Economics.