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Material Information
 Title:
 Measuring the value of public goods a new approach with applications to recreational fishing and public utility pricing
 Creator:
 Carter, David William
 Publication Date:
 2002
 Language:
 English
 Physical Description:
 ix, 129 leaves : ill. ; 29 cm.
Subjects
 Subjects / Keywords:
 Commodities ( jstor )
Consumer prices ( jstor ) Cost estimation models ( jstor ) Fishing ( jstor ) Information economics ( jstor ) Market prices ( jstor ) Mathematical variables ( jstor ) Prices ( jstor ) Public goods ( jstor ) Travel costs ( jstor ) Dissertations, Academic  Food and Resource Economics  UF ( lcsh ) Food and Resource Economics thesis, Ph. D ( lcsh )
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 bibliography ( marcgt )
theses ( marcgt ) nonfiction ( marcgt )
Notes
 Thesis:
 Thesis (Ph. D.)University of Florida, 2002.
 Bibliography:
 Includes bibliographical references.
 General Note:
 Printout.
 General Note:
 Vita.
 Statement of Responsibility:
 by David William Carter.
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 University of Florida
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 University of Florida
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 Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for nonprofit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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51947322 ( OCLC )

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MEASURING THE VALUE OF PUBLIC GOODS: A NEW APPROACH WITH
APPLICATIONS TO RECREATIONAL FISHING AND PUBLIC UTILITY PRICING
By
DAVID WILLIAM CARTER
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2002
Copyright 2002
by
David W. Carter
ACKNOWLEDGMENTS
Several groups and individuals contributed to the development of the ideas in this
research. First and foremost, I would like to acknowledge the seemingly unending
support of Wally Milon and Clyde Kiker. Wally continued to help sculpt my highflying
ideas into manageable research even after moving on from the University of Florida.
Clyde ensured that didnt loose my interest in highflying ideas and provided much
needed encouragement throughout the ordeal. The other members of my Supervisory
Committee, especially Bob Emerson, are also to be commended for their timely
comments and expert guidance.
Next, I would like to implicate my fellow graduate students and the group in 1094,
especially Maxwell Mudhara, Bowei Xia, Mike Zylstra, Larry Perruso, Chris DeBodisco
and Tom Stevens. These individuals kindly filtered many of my early thoughts on this
research and provided excellent moral support. Chris DeBodisco, in particular, is to be
thanked for his insights and compassion for learning.
Last, but not least, I would like to acknowledge the support of my friends and
family for making the Ph.D. experience an enjoyable chapter in my life.
in
TABLE OF CONTENTS
page
ACKNOWLEDGMENTS iii
LIST OF TABLES vi
LIST OF FIGURES vii
ABSTRACT viii
CHAPTER
1 OVERVIEW 1
Revealed Preference Valuation Of Public Goods 2
Alternative Approach to Revealed Preference Valuation 4
Potential Applications 4
Audience 5
2 TREATMENT EFFECTS AS WELFARE MEASURES 6
Introduction 6
Structural Approaches to Public Good Valuation 8
Welfare Measures 9
Structural Demand Approaches 11
Structural Utility Approaches 15
Combined Structural Approaches and a Canonical Model 20
Critique of Structural Approaches 22
Treatment Effects Approach to Public Good Valuation 25
Treatment Effect Welfare Measures for Panel Data or Repeated CrossSections. 28
Treatment Effect Welfare Measures for CrossSection Data 31
Econometric Framework 34
Treatment Effect Welfare Measures 37
Discussion 44
3 APPLICATION TO RECREATIONAL FISHING 46
Welfare Measurement with Capital Expenditures 48
Structural Demand Approach 51
Treatment Effects Approach 55
Data 60
IV
Results 65
Travel Cost Model 65
Treatment Effects Models 68
Discussion 74
4 APPLICATION TO PUBLIC UTILITY PRICING 76
Price Perception and the Value of Price Information 77
Empirical Models 85
Water Demand Model 86
Treatment Effects Bill Model 91
Data 95
Results 99
Structural Demand Model 99
Treatment Effects Model 105
Discussion 110
5 SUMMARY 112
APPENDIX
MA THEM A TICA DERRIVATION OF THE NET UTILITY FUNCTION 115
REFERENCES 119
BIOGRAPHICAL SKETCH 129
v
r
LIST OF TABLES
Table page
1 Utility outcomes with activity choice and change combinations 16
2 Spending outcomes with public good use and change combinations 30
3 Sample means and standard deviations for rigs model variables 61
4 Replacement rules for missing variable cost data 63
5 Spending included in the variable and capital fishing expenditures 64
6 Estimates for the Poissonnormal travel cost model with selectivity 67
7 Count model welfare analysis for loss of rigs access 68
8 Annual variable expenditures treatment effects model results 69
9 Total annual expenditures treatment effects model results 71
10 Annual expenditure treatment effects and welfare estimates of rig access 73
11 Utility outcomes with price knowledge and information change 82
12 Formulas for key model parameters 91
13 Rate schedules in study area 97
14 Summary statistics for water demand data 98
15 Water demand model estimation results 100
16 Estimates for key water demand model parameters 103
17 Monthly bill treatment effects model results 106
18 Bill treatment effects and welfare estimates of price information 109
vi
LIST OF FIGURES
Figure page
1 The value of a public good change with interdependence in demand space 12
2 The value of a public good change with interdependence in utility space 17
3 Expenditure difference threshold 41
4 Value of price information: perceived price greater than actual price 84
5 Value of price information: perceived price less than actual price 84
vii
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
MEASURING lili VALI I OF PUBLIC GOODS: A NEW APPROACH WITH
APPLICATIONS TO RECREATIONAL FISHING AND PUBLIC UTILITY PRICING
By
David William Carter
December 2002
Chair: J. Walter Milon
Cochair: Clyde F. Kiker
Department: Food and Resource Economics
Program evaluation (PE) techniques are adapted to measure the value of public
good access. The premise is that interv entions in the supply of a public good can be
considered programs where use is tantamount to participation or treatment.' Three
chapters (Chapters 2 through 4) explore this premise.
Chapter 2 compares the treatment effects' approach (TEA) to conventional
revealed preference (RP) methods for valuing public good access. Program evaluation
techniques are adapted to derive access value from differences in related nonmarket
activity expenditures between actual and potential public good users. Unlike methods
such as the travel cost approach, this approach does not estimate a structural demand or
utility model to derive welfare measures. Thus, the TEA avoids many of the widely
recognized problems of endogeneity in RP models. A key insight is that alternative
counterfactual assumptions can be used to condition estimates of the demand for a public
good.
VI11
Chapter 3 applies the TEA to measure the recreational fishing value of Gulf of
Mexico petroleum platforms. Those anglers who currently fish at these platforms are the
treatment group, while those who fish elsewhere are the controls. An econometric model
developed in Chapter 2 is used to obtain a measure of the expected value of platform
access. The measure is relatively comprehensive because the TEA readily incorporates
capital expenditures. Results from the TEA model are compared to those from a travel
cost model.
Chapter 4 examines the conservation value of a program that informs public utility
customers about the price of service. An analytical model of perceived price is
developed that can be used to assess the value of price information. The corresponding
empirical models are built around a dataset of Florida water customers that assigns
households to treatment and control groups based on whether or not they know the price.
The results from demand and treatment effects models are used to derive the expected
value of price information for an uninformed household. Importantly, the notion of
counterfactuals developed in Chapter 2 allows the welfare measures to be adjusted for the
possibility that price elasticities change once a household learns the price.
IX
CHAPTER 1
OVERVIEW
The domain of consumer choice includes consumed commodities and market
goods. A commodity is valued as a source of satisfaction (utility) and/or as an input into
the production of a commodity that yields satisfaction. A market good is a commodity
whose relative social value is given by its price in a forum of exchange (i.e., a perfectly
competitive market with no externalities). These commodities are excludable and rival,
that is, they are (locally) scarce and subject to competition in use. Given nonattenuated
property rights for a commodity, the competition over use privileges will establish a price
indicative of its relative value as a market good in a Paretoefficient allocation (Randall
1987).
Commodities that are not market goods can be termed nonmarket goods. As
commodities, nonmarket goods have value, but the relative value of additional units
cannot be measured (directly) by an equilibrium market price. There are a number of
reasons why a commodity will not be traded in a perfectly competitive market, but for
present purposes the key reason relates to its public good characteristics. Briefly, a
public good is nonexclusive and/or nonrival in consumption so that a price in use or trade
cannot be established because property rights cannot be assigned. Thus, an important
difference between market and public goods for consumer choice is the absence of a
consistent indicator of relative value or price for the latter.
The lack of prices for public goods means that other measures must be used to
evaluate the relative value of changes in the supply of these commodities. Such measures
1
2
inform public policy about the potential benefits and opportunity costs of proposed
changes in public good supplies (Carter, Perruso and Lee 2001). This perspective
follows the long tradition of applied welfare economics, especially formal benefitcost
analysis (Johnansson 1993; Smith 1988a; Zerbe and Dively 1994). The tradition has seen
the development of tools designed to recover, directly or indirectly, economic values for
changes in nonmarket commodities, such as public goods. Direct inquiries require the
construction of (hypothetical) nonmarket valuation transactions, whereas indirect
investigations rely on the reconstruction of (actual) nonmarket valuation transactions and
values based on observed market behavior (Smith 1996). This dissertation adds to the kit
of socalled revealed preference tools that exemplify the latter indirect approach to
nonmarket valuation.
Revealed Preference Valuation Of Public Goods
The research on revealed preference methods forms a vast literature documenting
the attempts to recover monetary values from opportunity costs associated with observed
behavior related to nonmarket and public goods. Some methods, such as the travel cost
model of recreation demand, measure opportunity costs in terms of what consumers are
willing to give up for access to various supplies and qualities of public goods. Other
procedures, such as the averting behavior model, view opportunity costs as the amount
consumers give up to compensate for a change in the supply of a public good (or bad).
Still others, most notably hedonic models, consider the opportunity costs implicit in
tradeoffs among characteristics and prices of market goods. These approaches evolved
to derive values for public goods when some of the data necessary to estimate a demand
relationship is missing. Specifically, the first two approaches are attempts to impute
3
prices for public good experiences, whereas the third approach deals squarely with a lack
of data on the quantity of public goods purchased.
There are a host of related problems associated with revealed preference
methodologies that are common in applied demand analysis and welfare measurement. A
laundry list would surely include separability, the definition of quantity and price indices,
selection of functional form (w ith attention to choke price), recovery of compensated
measures (integrability). heterogeneity and aggregation. There are a few problems such
as the relationship among market, nonmarket and public goods, corner solutions,
incorporation of substitutes, and the identification of income effects that have been
especially troubling for revealed preference valuation of nonmarket and public good
experiences. A fairly complete summary of the issues can be gleaned from Maler (1974),
Johansson (1991), Freeman (1993), and Bockstael and McConnell (1999).
There is a more fundamental issue than aforementioned technical problems when
attempting to value changes in a public good based on revealed preferences. A thorough
welfare evaluation requires observations on consumer behavior before and after the
change in the public good supply, but such panel data is rarely available. Rather, cross
section data are the norm, and evaluations of public good changes require predictions of
behavior for hypothetical states of the world. The conventional approach in this case is to
predict (i.e., simulate) hypothetical scenarios conditional on preference information
observed either before or after the public good supply change. The difference in
observed and predicted outcomes is then used to isolate welfare measures for the change
in value caused by the change in the availability or configuration of the public good
stock.
4
Alternative Approach to Revealed Preference Valuation
The approach to valuing pubic good supply changes introduced in this dissertation
is based on a fundamentally different way of defining hypothetical scenarios or
counterfactuals. The alternative definition arises if interventions in the supply of public
goods are considered social programs. Individuals in the population who use the public
good in its program (base) state are the program participants. Others who could have
used the public good are nonparticipants. Then, following the literature on program
evaluation (Heckman 2001b), participants are the treatment group and nonparticipants are
the control group. In the tradition of the laboratory science, the net effect of the program
is given by the difference in outcomes or treatment effects between the treatment and
control groups, controlling for any inherent differences between the two groups and any
(observable or unobservable) factors that may influence the participation decision. The
main contribution of this research is a formal consideration of the cases in which such
treatment effects can be considered measures of the value of changes in the supply of
public goods. This objective is explored in three chapters. Chapter 2 develops a fairly
general model that enables the use of treatment effects as welfare measures and compares
this model with structural demand and utility equation approaches. Chapters 3 and 4 are
applications of the principals introduced in Chapter 2.
Potential Applications
The alternative approach to revealed preference valuation can be potentially applied
to evaluate public good use values in any case where the change in a public good supply
can be characterized as a social program. The only crucial requirement is that
observations on the behavior of participants (treatment) and nonparticipants (controls)
can be clearly identified in the population of possible users of the public good. This is
5
relatively straightforward using data typically available on explicit interventions like
conservation programs at public utilities (Frondel and Schmidt 2001). The challenge lies
in the identification of relevant population segments to represent participants and
nonparticipants in the implicit or unintended programs of agencies. Mother Nature, or
human error that effectively change the availability or configuration of a public good.
Two case studies presented in Chapters 3 and 4 illustrate the potential range of
applications. Chapter 3 uses the technique to evaluate a program of government
intervention in the supply of artificial habitat available for recreational fishing. In this
case, anglers who are observed using the habitat form the treatment group; and other
potential users are considered the control group. Chapter 4 evaluates the value of a
program that would fully inform public utility customers about the price of service. Here,
those customers who admit knowing the price make up the treatment group, whereas all
other customers are the controls. Note that the information about the price of service that
is supplied by the public utility is the public good of interest in this case.
Audience
The research should be of interest to applied economists and policy makers. For
applied economists, especially revealed preference researchers, the approach offers an
alternative way of characterizing and analyzing the relative value of public resource
allocation plans. The method offers a way to estimate the value of changes in the supply
of public goods using relatively flexible demand or expenditure equations such as Engel
curves. In addition, the approach can account for the possibility that preferences and/or
behaviors change because of the change in the public good supply. As with any method
that estimates the benefits and opportunity costs of policy proposals, the approach will
add to the range of estimates available to inform policy decisions.
CHAPTER 2
TREATMENT EFFECTS AS WELFARE MEASURES
New developments are more likely when one confronts a problem with general
notions of how behavioral methods work, rather than with the specific toolkit of
travel cost models, defensive expenditures, etc.
Bockstael and McConnell (1999).
Introduction
The relative value of public goods is not revealed in a competitive market. Thus,
the opportunity cost of changes in public good supplies must be inferred from
observations on what is, actually or hypothetically, given up to enjoy public good
services. The practice of observing actual market behavior to discern the value of public
goods falls under the general heading of revealed preference methods (Herriges and
Kling 1999). These methods seek to uncover the relative value of changes in individuals
consumption mix that can be attributed to changes in public good supplies and/or
qualities. This requires assumptions that separate the consumption set to isolate the
purchased commodities that are interdependent with the public good(s) of interest
(Bradford and Hildebrandt 1977; Loehman 1991).1 Depending on the nature of the
separability assumed, the ensuing analysis can focus on estimating before and after
demand equations for the related individual purchased goods or for composite
1 The ideas in this chapter are developed via partial analysis with assumptions regarding
consumption set separability. Following Hanemann and LaFranee (1992), I acknowledge
that the related welfare analysis generates partial measures of exact surpluses, but
proceed in this manner to avoid the inherent ambiguities in deriving public (nonmarket)
good values from incomplete systems without marginal valuation functions (Ebert 1998;
LaFrance and Hanemann 1989).
6
7
commodities representing groups of purchased goods. The latter notion of separability
introduces the additional complication of defining valid quantity and price indices for the
composite commodities. Still further complications arise in the absence of expenditure
information before and after the public good change.
Developing acceptable, utilitytheoretic price and quantity indices for composite
commodities related to public goods is especially difficult where such commodity groups
are delineated according to household activities. For example, recreational demand
models often seek to delineate composite commodities (e.g., trips) according to the
location or type of recreational activities. The underlying problems with this kind of
commodity group delineation is readily seen when the quantity index is defined as a
household production function (Blundell and Robin 2000). In this case, the price and
quantity indices are fundamentally endogenous to the consumer problem and cannot be
econometrically identified in a structural demand model without restrictions on
preferences and/or the household production technology (Bockstael and McConnell
1981; Poliak and Wachter 1975). Despite the inherent difficulties in defining, measuring,
and modeling valid quantity and price indices for activitybased composite commodities,
the practice continues as somewhat of a necessary evil. For example, the pooled activity
intensity, activity choice RUMs. and combined activityintensity choice models of
recreation demand all require price and quantity indices to estimate composite activity
demand equations and/or (net) utility equations.
2 The struggle with choice set definition in multiplesite recreation demand models
illustrates the problems in delineating the consumption set according to activities (Haab
and Hicks 1997; kling and Thomson 1996; Parsons and Hauber 1998; Parsons and Kealy
1992; Parsons and Needelman 1992; Parsons, Plantinga and Boyle 2000).
8
The chapter begins with a review the structural approaches to valuing public good
changes using observed expenditure data. Demand equation, utility equation, and
combined structural approaches are covered. The review highlights the importance of the
price variable in deriving public good welfare measures with each approach. Also
emphasized is the way each structural approach deals with missing data on demand or
utility outcomes with alternative states of a public good.
Next an alternative approach to measuring the value of access to this type of public
good is introduced. The approach draws on the microeconometric program evaluation
literature (Heckman 2001b) to generate uncompensated and compensated welfare
measures for public good access changes without splitting out price and quantity indices
from observed expenditures on a related nonmarket activity.3 Estimators are discussed
for panel and crosssection data, though, emphasis is on the latter since most revealed
preference (e.g., recreation expenditures) datasets are of this type. A summary
suggestions for future research concludes the chapter .
Structural Approaches to Public Good Valuation
The practical difficulties in measuring the value of public good access with
observations on interdependent market goods are wellknown (Bockstael and McConnell
1999). Therefore, after defining the welfare measures, I will provide only a brief sketch
of approaches that focus on structural demand or utility equations. The demand equation
approach characterizes a large class of methods, including the travel cost model, for
analyzing the nonmarket values at the intensive margin of activity intensity. Methods
3 Like most program evaluation techniques, this alternative approach is not necessarily
nonstructural (Blundell and Macurdy 1999). However, the approach is less structural
than the demand and utility approaches requiring the estimation of structural price and
quantity relationships.
9
following the utility equation approach are motivated by random utility theory and are
generally suited to exploring values at the extensive margin of activity choice. Models
that combine elements from the utility and demand equation approaches offer the
potential advantage of exploring valuations at both the intensive and extensive margins in
a unified discrete/continuous (D/C) choice framework. Such combined approaches can
model corner solutions in the demands for the interdependent commodities or activities,
depending on the level of analysis. Recent research in the recreational demand literature
has used combined D/C approaches to address corner solutions at the activity demand
level (Parsons, Jakus and Tomasi 1999; Phaneuf 1999; Phaneuf, Kling and Herriges
2000; Shaw and Shonkwiler 2000). The following discussion is meant to highlight the
somewhat perplexing reliance on activity based price indices in these approaches and the
way each operates in the absence of observations of behavior both before and after the
public good change.
Welfare Measures
Consider the prototypical expressions of compensating and equivalent variations
for a change in the condition of a public good from state 1 to state 0 in terms of the
minimum expenditure function
(21) CV[p\u\b\b= e(p],u\b'e(p',ul,b,s,e)
(22) EV (p\u\b\b\ste) = e[p\u\b\s,e) e(p\u\b ,s,s)
where p is a vector of prices for market goods x, u is a utility indicator referenced to the
current state of the world superscripted by /, b represents the supply (or quality) of a
public good, and s is a vector of individual control characteristics. The term e is a vector
of stochastic elements representing heterogeneity so that there is an implicit vector of
10
coefficients (not shown) on the variables in the model. Note that the presence of these
unobservables in the expenditure functions implies that CV and EVare stochastic.
Therefore, the most that can be recovered is information regarding the distribution of the
welfare measures such as the expected value or some other point of central tendency.
Following conventional terminology, CV represents the willingness to pay to prevent the
change from b1 to b and EV is the willingness to accept compensation to allow the same
change. The concepts developed in what follows are illustrated with the CV willingness
to pay measure. Discussion of EV is only offered where the notion of willingness to
accept offers additional insights.
A subset of the market goods are potentially interdependent with the supply of a
public good. Market commodities demanded x(u, p, b, s, e) that are interdependent with
the public good have generally, dx(^)/db 0 or specifically dx{^)/db > 0 for the case of
weak complementarity (WC).4 The former relationship implies that the individual is
indifferent to the condition of the public good when the market demands are at some
minimum constant quantities (Bradford and Hildebrandt 1977), while WC places this
constant minimum quantity at zero (Bockstael and Kling 1988; Maler 1974).
Consequently, WC requires the additional assumption that the interdependent market
4 The subset of the market goods that are not interdependent with the public good have
dx(p,u,b)/db = 0 such that public good changes only indirectly affect the purchases of
these goods via income effects and the budget constraint, i.e., as (dx/de^de/db) .
goods are nonessential.' With either interdependency assumption, the value of the
public good can be expressed as equivalent price changes for the interdependent
commodities
K*') ~p(h0)
(23) CV[p\u\b\b\s,e)= J x[p,u\b\s,e)dp J x(p,u ,b\s,e)dp
p' p'
where p{bJ) is the constant compensated demand price vector for market goods
related to t such that compensated demand is constant (or zero with WC) with respect to
the public good (Loehman 1991).6 The CV measure for the value of a change in a public
good is illustrated in Figure 1 for the general interdependence and WC cases. This
measure is simply the difference in the area behind two compensated demand curves.
However, since demand relations are not observable as a function of utility, it is
necessary' to use ordinary demand equations, deal directly with utility equations, or
employ some combination of demand and utility equations.
Structural Demand Approaches
Consider First strategies that rely strictly on the observed quantity demanded of the
interdependent goods. The uncompensated surplus measure in terms of observable
demand quantities is
(24)
'(*') M*0)
S(p',y,b',b'\s,e) = $ x{p,y,b\s,e\lp \ x{p,y,b",s,e)dp
5 The 'choke price' condition implied by WC is slightly different when the purchased
good is viewed as an input in the production of an nonmarket commodity that is
interdependent with the public good (Bockstael and McConnell 1983). In this case, the
purchased good must essential in the production of the interdependent nonmarket
commodity. T his condition can hold even when the purchased good is not needed to
produce the nonmarket commodities that are not interdependent with the public good.
The double overbar notion for the choke price vector follows Loehman (1991).
12
P
Figure 1. The value of a public good change with interdependence in demand space
where y is the constant income level and p' (bJ) is the constant compensated demand
price vector. The CV measure equals S in the absence of income effects and can
otherwise be recovered from (24) by analytically or numerically integrating back to
expenditure functions with an additional (Willig) condition that rectifies the difference
between p[b]) and p{bJ^ (Bockstael and McConnell 1993; Hanemann 1980). The
subset of these goods that are interdependent with the habitat in question define the
relevant commodities to use in (23) and (24). These calculations require observations
on the relevant demands before and after the change in the public good
Before After
'x, (p.y.i.el*1)'
'x, (p,y,s,eÂ¡b0)'
\ 1 J
x(p,y,s,e\b)^
(25)
13
where p references a vector of own and substitute prices and the demands for each of the
N interdependent commodities are shown as conditional on the state of the public good,
but not necessarily a direct function of the state. For example, calculation of CV or S for
a change in the supply of recreational Fishing habitat requires estimating a system of
demands for all purchased goods related to recreational Fishing before and after the
change. However, if there are observations for only one state of the public good, then
demands have to be estimated as a function of b to predict the demands in the unobserved
state
Before Simulated
> V *
' x\ (p,y,b',s,Â£)'
' i, (p,y,b\s,e)
xN(p,y,b\s,e)
V v )
x(p,y,b\s,e)
where bJ indicates the state of the public good in a manner that varies across the sample
or over time for each individual. The idea is the same if data is only available after the
change of interest. Once a functional form is specified for the commodity demands and
the related indirect utility function, the shadow price(s) of the public good(s) can be
obtained (Shapiro and Smith 1981; Shechter 1991). The value of a discrete change in the
public good can be recovered by (sequentially) integrating the estimated before and after
demand equations as shown in expression (24).
An alternative structural demand approach is to estimate a demand equation for the
interdependent activity1 using an acceptable quantity index to aggregate the relevant
purchased quantities
I will follow the convention of referring to the activity in which the interdependent
market goods are used as the interdependent activity.
14
Befare After
A A
A, (P,.y,i,e6')'
' X^P.y.s.epy
XA{P,y,s,e\b')
V v 1 )
xAp,y,s,e 6)
where Xj is a composite commodity index for the goods used in interdependent activity i
= 1, A, and P is a vector of corresponding activitybased price indices. This is
precisely what is done in the multiple site travel cost model where the trips to each site
(activity) are used as the quantity indices and site specific travel costs are the price
o
indices. As discussed earlier, when before and after data is available the two sets of
composite commodity demands can be estimated without a regressor indicating the state
of the public good. In fact, with such data it is possible to take a completely
nonparametric approach to recover bounds on the welfare measures using the price and
quantity indices (Crooker and Kling 2000). Alternatively, two systems of composite
activity demands can be estimated using the before and after data. The resulting before
and after activity demand equations can be used to evaluate and recover the welfare
measures (24) and (23) using price indices, instead of the prices of individual
commodities. If only one set of expenditure data is available, the activity demands in the
unobserved public good state have to be predicted from a demand system estimated on
the observed data
Before
Simulated
X, (P,y,S,s,e)'
' X,(p,y,b\s,eY
XA [P,y,b\s,e)
XA(P,y,b\s,e)
o
The single site pooled travel cost models is a straightforward simplification with only
one quantity index and as many price indices as there are relevant substitutes.
15
As in the individual interdependent commodity demand system, bJ indicates the state of
the public good. This indicator is defined in a manner that varies across the sample or
over time for each individual so that the expected activity demands with changes in the
public good can be simulated. If the public good indicator does not vary within each
activity, then the data across activities can be combined to estimate a single demand
equation. For example, when the activities are characterized as recreation sites, the data
in (28) can be used to estimate the socalled pooled site model.
Structural Utility Approaches
Now consider strategies based on random utility theory that use (conditional) utility
representations. This class of models focuses on discrete events and/or activity choices
involving different bundles of commodities that are interdependent with the public good.
That is, the individual has (an unknown) number of ways to discretely partition (separate)
their budget set to employ the services of the public good
(29) (yCli),(yC2i),...,(yCII),...,(yCAi)
where CJ = p x(p, y, t, s, e) is the cost of producing alternative / using an alternative
specific subset of the purchased commodities that are interdependent with the public
good. There are A such alternatives and, as before, j indicates the state of the public
good. In what follows, I will use the more common convention of representing the cost
in terms of activityspecific price and quantity indices CJ = P" that are conditional on
the state of the public good. These price and quantity indices are analogous to the indices
discussed in the structural demand approach.
Every individual implicitly has a conditional indirect utility function representing
their maximum attainable utility given the activity choice and the state of the public good
16
(210) vJ =v[i,y,J,bJ,s,e) .
where the indicator i equals one if the individual chooses alternative i with the public
good in state j and equals zero otherwise. The income variable is implicitly adjusted for
the total spending on each alternative as y'J = y Cj. Notice that the mix of
interdependent commodities enter the problem via this virtual income term in the utility
equation approach. Also note that a new dimension to the problem has been introduced.
Specifically, as shown below, the utility equation approach requires additional
information on activity choices to completely identify a change in an individuals utility
related to a change in the public good. The four possible outcomes for each alternative
are listed in Table 1.
Table 1. Utility outcomes with activity choice and change combinations
CHOOSE ACTIVITY?
YES (i=l)
NO (i=0)
PUBLIC
GOOD
CHANGE
BEFORE
(1=D
v(l ,p,y",b',s,e)
v(0,p,yol,b\s,e)
AFTER
(j=o)
v(l ,p,y\b,s,e)
v(0,p,y,b,s,Â£)
The expected unconditional utility over all alternatives is given by
(211) Â£[v(/>^,V,i,e)] = Â£[max{v1J,v2J,...,vs,...,V<'}l
which is presented in terms of expectations because of the stochastic, unobserved element
of preferences. The value of a discrete change in the public good from b' to b is the
17
difference between two expected unconditional utility functions. The money metric for
this value given by the value of CV that solves
(212) Â£[v(F,>. + C(/,.l,i,Â£)]Â£[v(/>,^.".s,Â£)] = 0
Following Hau (1985), this value and its money metric are depicted in Figure 2.
Although not shown in the graph, note that the zth activity is a WC of the public good if
dv^P_n Pt,y,b,s,e^jdb = 0.1> When these activities arent chosen, utility (and expected
utility) is unaffected by changes in the public good.
E[v]
Figure 2. The value of a public good change with interdependence in utility space
Estimates of the underlying preference parameters of the before and after indirect
utility equations are necessary to calculate the welfare measure in (212). These
preference parameters have to be recovered indirectly, however, because utility is
Implicitly, the nth purchased good is a WC of the public good if
dv^p_H,pH,y,b,s,E^/db = 0 When these commodities aren't purchased the individual
is indifferent to changes in the public good.
18
unobservable. The standard approach involves observations on alternative choice
outcomes (Hanemann 1999).10 The present case requires data on individual choice
outcomes in the before and after public good states
Before After
(213)
where RÂ¡Q is a binary index function that equals one if alternative i is selected and zero
otherwise and choices are shown as conditional on the state of the public good. The
choice over multiple alternatives when the public good is in state j is motivated by a
probability index model
/?, (p,y,s,e\b')
Ra
(214) pr(Rt = 1) = pr^v(i,P,yij,bj,s,e)~v[k,P,ykj ,bj ,s,Â£^ > oj forall& /J.
where, as typically assumed, the alternatives i and k are mutually exclusive for the given
choice occasion. This index can be specified once the form of the indirect utility
equation is selected. Then, depending on the error structure is defined, a probability
model (e.g., multinomial logit or probit) can be maximized to obtain estimates of the
indirect utility equation parameters. With before and after estimates of the indirect utility
function parameters, equation (212) can be solved to generate the value of the public
good. If only one set of choice observations is available, then the alternatives have to be
defined with different endowments of b
10 This is also the motivation behind stated preference valuation approaches where choice
outcomes are elicited for hypothetical changes in bundles of public good characteristics
and individual opportunity costs (Hanemann 1984b). However, a review of stated
preference methods is beyond the scope of this chapter.
19
Before Simulated
A A
' R^P.y.b'.s.e)'
'Rt(p,y,b,,s,e)'
Ra {P'yb >s'Â£
f {Py
where bJ is the public good endowment indicator. The random utility model is actually
designed to handle this type of simulation based on changes in alternative attributes. A
utility equation is defined with an indicator for the endowment of the public good
available from each alternative activity considered. Activities can be delineated
according to a public good characteristics. For example, fishing habitat can be defined by
location, so that the activity of fishing in an area is uniquely (and exogenously) defined
by specific public good habitat. Similarly, activities can be grouped by unique public
good features that define types of an activity. For example, fishing habitat can be
delineated according to whether it has manmade features so that the choice of fishing
alternatives is defined accordingly (i.e., fishing artificial habitat or all other habitat). Any
number of combinations is possible as well as different ways of characterizing the
sequence (i.e., nesting) in which activity choices occur (Hauber and Parsons 2000; Kling
and Thomson 1996; Morey, Breffle and Greene 2001). Once the alternatives have been
defined, a discrete choice model can be estimated to generate utility coefficients on the
public good indicator(s). These coefficients can be used to simulate the expected utility
of alternative public good configurations. The welfare measure of changes the public
good indicators is recovered by solving equation (212) using the reference and simulated
expected utility levels.
20
Combined Structural Approaches and a Canonical Model
The unconditional demands for each activity can be defined in terms of the
probability index and conditional demand functions from the two structural approaches:
(216)
The X(j functions give the amount of each activity demanded at the intensive margin,
conditional on the decision to participate and given the state of the public good.
Similarly, the pr(RÂ¡=l) functions give the probability of participating in an activity at the
extensive margin given the state of the public good. When the probability of choosing an
activity and the amount that is demanded are uncorrelated, then these decisions can be
analyzed separately as described in previous two sections. Otherwise, these decisions
should be modeled jointly in a unified comer solution model (Hanemann 1984a).11 In
this case the structural demand and utility equations come from the same consumer
problem and will, therefore, share coefficient information based on shared unobservables.
A structural maximum likelihood approach with cross equation restrictions is necessary
to obtain unbiased estimates of the coefficient information that are shared by utility and
demand equations. This approach has a long history of application to cases of nonlinear
budget constraints that arise in, for example, the analysis of labor supply and the demand
for public utility services (Hausman 1985; Herriges and King 1994; Hewitt and
Hanemann 1995; Moffitt 1986, 1990). Structural maximum likelihood has also been
used in efforts value public good changes with a combination of data on stated and
11 There are a variety of comer solution models that have been suggested and applied to
value public goods with revealed preference data (Herriges, Kling and Phaneuf 1999;
Phaneuf 1999; Phaneuf, Kling and Herriges 1998).
21
revealed preferences (Cameron 1992). In all of these applications, the statistical problem
of selfselection is given economic meaning and modeled accordingly.
In labor supply, the decision of how many hours to work is conditional on the
decision to selfselect into the workforce. When faced with a block rate pricing schedule
the amount an individual demands (and their price) is conditional on the block they self
select to consume in. The number of times someone chooses to recreate at a given site or
in a given activity is conditional on the decision to selfselect the site or activity over all
others. Note that in many of these applications, especially recreation demand modeling,
selfselection is viewed as somewhat of an afterthought or a statistical nuisance.
Consequently, the revealed preference methods that jointly model D/C behavior are
usually concerned with removing the discrete outcome bias from the continuous
outcomes and the corresponding welfare measures. This is generally true whether the
problem is addressed explicitly, as in the efforts to correct for selectivity bias in welfare
measures from recreation demand models (Bockstael et al. 1990; Dobbs 1993; Laitila
1999; Shaw 1988; Smith 1988b; Ziemer et al. 1982), or implicitly, as in the recreation
demand literature that seeks to derive welfare effects from unified (Phaneuf 1999;
Phaneuf, Kling and Herriges 2000) or linked (Parsons, Jakus and Tomasi 1999; Shaw
and Shonkwiler 2000) comer solution models of participation and quantity choice.
However, only the comer solution approaches give economic meaning to selfselection.
In the former approach to correcting selectivity bias, the choice equation has no
connection with the demand equation except for correlation in the stochastic
disturbances (Hausman 1985 p. 1262).
22
To conclude this discussion, consider the canonical D/C structural choice model
that combines the utility and demand equation approaches
(217)
otherwise
where for illustration only two mutually exclusive alternatives are considered. This
model can also be written in statistical switching regime form as
Following the discussion above, the functional forms for the utility equations in R\ and
the demand equations should embody the same representation of preferences and be
estimated simultaneously with crossequation restrictions where necessary. To recover
public good values, the canonical model requires before and after data on the
interdependent activities of the type in (27) and (213). With such data, utility equations
or the demand equations can be used to derive the welfare measures as described in the
previous sections. In the absence of before and after data, the utility or demand
simulation approaches can be used to generate the values for the public good change.
Critique of Structural Approaches
As defined, the demand and utility approaches require information on the
consumers complete choice set and an indication as to those commodities that, at any
point in time, are interdependent with the public good of interest. In absence of such
information (or a computational method of dealing with it), the consumption set must be
separated into observable/manageable components (Deaton and Muellbauer 1980).
23
Herein lies the difficulty with structural demand and utility approaches using the methods
sketched above for measuring public good values from market data.12
There are at least two things to note about the use of simulation to recover welfare
measures in the demand equation approach. First, using the structural demand
equation(s) estimated in one state of the world to predict outcomes in another state
assumes that the preference parameters will not change in response to the public good
change (Whitehead, Haab and Huang 2000). That is, the simulation approach assumes
that estimated structural parameters are policy invariant in the sense of the Lucas critique.
In this case, the public good indicator enters as a demand shifter and the portion of the
CV welfare measure from each interdependent commodity is simply a difference in
parallel lines as shown in Figure 1. Second, the D/C choice models in the recreation
demand literature allow for comer solutions in the demand for interdependent activity
based composites. This is different than modeling comers in the interdependent
purchased goods that make up the composite activitybased composites. Modeling
comer solutions at the activity level implicitly assumes that any interior solutions at the
purchased good level before the public good change will persist after the change.
However, according to Bockstael and McConnell (1993), a discrete improvement in (a
public good) can cause the individual, when maximizing utility in the new context, to
choose a positive value for (an interdependent good) when previously he consumed
none" (pp. 12481249). This means that demand system estimated on the existing data
12 Hanemann and Morey (1992) show that estimates of (21) or (22) are of no value
unless the separation is done appropriately (p. 255). I assume that separation of the
consumption set is accurate in order to focus on the issues related to the price indices for
groups of commodities in the separated sets. Proceeding in this manner means that all
calculations of (21), for instance, will be a lower bound on the desired CV measure
(Hanemann and Morey 1992).
24
should address the possibility of changes in the mix of purchases that occur as the public
good changes. A demand system approach that models comer solutions (Lee and Pitt
1986; Wales and Woodland 1983) will be able to account for such changes at the
intensive and extensive margins of purchases of the interdependent goods. This raises
another issue related to the separation of the consumption set along the lines of
interdependence with the public good. A complete analysis would require that the
estimated demand system include every commodity that might be in all individuals
choice sets before and after the public good change. While this is clearly unrealistic, it
uncovers the root cause of the intimately related problems of endogenous choice sets (see
fn. 2) and endogenous prices in activity based (e.g., recreation) demand models.
The consumer chooses the relevant mix of purchased commodities (from the subset
separated by the analyst) as part of the D/C optimization problem. In this case the
marginal cost (price) of the activity will not necessarily be the same, for example, for
consumers traveling from the same distance (Bockstael and McConnell 1981). This is
especially problematic when attempting to simulate the value of public good changes
using relationships estimated with crosssection data. With a crosssection, goods prices
will not appear in goods demand equations because they do not exhibit significant
variation across the sample. Thus, any variation in composite prices used in this case will
be attributed to other factors. To the extent that these factors are related to preferences
and not household technology (e.g., distance), price indices will misrepresent the true
opportunity cost of the trip decisions.
The endogeneity problem is further exacerbated by attempts to include capital, time
and the joint production of activities (Bockstael and McConnell 1981; Poliak and
25
Wachter 1975; Randall 1994) and coherently model comer solutions (Shaw and
Shonkwiler 2000). The fact that the choice sets and activity prices are endogenously
chosen by the individual make it difficult to obtain unbiased estimates of coefficients in
activity level demand models. This is important because price and income coefficients
are crucial in the calculation of the welfare measures. Likewise, any activity based price
indices used in place of the reference and choke prices to evaluate (23) and (23) are
potentially endogenous.
There are at least three ways to deal with the problem of endogenous price indices
that have been explored in the literature. The first acknowledges that the price indices
and derived welfare measures are ordinal measures (Randall 1994) and attempts to
achieve better measures as in, for example, English and Bowker (1996). The second
approach specifically models some or all of the activity prices as latent (Englin and
Shonkwiler 1995) or endogenous (Fix, Loomis and Eichhom 2000; Ward 1984) portions
of the consumer problem. Models that incorporate labor supply constraints are examples
of this second strategy (Larson and Shaikh 2001; Shaw and Feather 1999). A third
approach attempts to choose measurement units (e.g., total distance) over which the
activity can be aggregated and price indices developed in a utility theoretic manor (Shaw
and Shonkwiler 2000). An alternative approach suggested in this chapter is to fmd ways
to recover CV from expenditures on the related activity without the use of separate price
and quantity indices.
Treatment Effects Approach to Public Good Valuation
The goal of this part of the research is to develop a welfare measure for a discrete
public good change that does not require that price and quantity indices be separated from
26
total expenditures. This welfare measure is derived from the differences in spending
/ L.0
before and after the public good change from b to b
(219)
\{p',p\y,b',b\s,E) = p'x(p\y,s,e\b')p0x(p\y,s,e\t)
= pxx[p\u\s,e\bx px[p ,u ,s,e\b j
As with the structural demand and utility approaches, a separability assumption is needed
to isolate the purchased commodities that are interdependent with the public good. In
this case, it is reasonable to assume to Hicksian separability whereby prices in the
interdependent group change by the same factor following the public good change
Before After
(220)
where the first L goods are interdependent with the public good and the remaining
commodities are independent. Differentiating the constant relative price expenditure
function with respect to the change factor gives
^(e,LplL,9iLplL,u,s,e\b) de dpÂ¡ de dp\ de dp\
(eL,eLpl>L,y,s,Â£\b)'
xl (plnPlLysÂ£\b')
\ \ i / j
XL(eL0
(221)
de
dpÂ¡ d0
+ + .
P\Xi T Pix2 T " + Plxl
dp[ de
which shows that expenditure on interdependent goods can be used as a Hicksian
composite commodity with the change factor as a price index (Deaton and Muellbauer
1980). A similar result holds for the L + 1 other commodities and the related index.
Note that following the discussion of the structural models, the price index for the
interdependent goods is fundamentally endogenous. In the household production context,
27
the index represents the marginal cost of producing an activity that is interdependent with
the public good.
The before and after expenditures composite for the interdependent commodities
can be written in terms of the change factor price indices as
before after
, , \
(222) Pxsl(dLJd>Ltyts,Â£ >') ^LPXi,(diLte>Ltytste^>0)
and the difTerence in spending after the public good change can be restated as
(223)
&(pL,y>b' ,b\s,e)
= pW (9L. y*s,e ) OslPXs, [diL,e>L, y,s,Â£ >)
Similarly, the ordinary surplus and compensating variation can be written as
S (p'^,0^L,0>L,y,b' ,b,s,e)
= /4*s/ (Ltytsfe\bx)0^/4** (eiL,9>L,y,s,Â£\b)
CV (pl,,0iL,6>L,u ,b',b\s,e)
(225)
= Pixs, (9^,9>L,u',s,Â£\b1)9^p[,x^ (0si,9>l,u ,s,e\b)
where contrary to the spending difference measure, the welfare measures hold the price
level constant across states of the world. The compensating measure also holds utility
constant at the level before the public good change. Consequently, if the relative prices
interdependent goods remain the same after the public good change, then the difTerence
in spending equals the surplus measure
A'=e(u\s,Â£6,)e(u0i,e6#)
= Px^j Px,
= Pxjy [ll1,S, Â£ fc ) PxÂ¡ (w, S, Â£ > ) = Sp
(226)
28
where P = p\, = (1)/?^ The price indices for the interdependent and independent goods
are omitted because they equals one (i.e., = 0>L = 1) if prices are the same after the
public good change.13 A similar price constant expression can be defined for the
compensating variation
CVP = e(u\s,e\bl )e(us,Â£ 1)
(227)
= Px^ (w',S,Â£ /? ) Px<Â¡ (z/,S,Â£Y)
Note also, that Loehman (1991) has shown the case of interdependent public and market
goods with constant prices implies that Y = N* C^, generally, and Y = /Â¥ = CV** if
there are no income effects. These formulations are useful in when attempting to
simulate the value of public good changes using relationships estimated with cross
section data. Before turning to the case of crosssection data, however, the following
briefly reviews ways to recover the welfare measures from longitudinal data.
Treatment Effect Welfare Measures for Panel Data or Repeated CrossSections
Expression (226) suggests that an estimate of the uncompensated surplus measure
for each individual can be recovered from panel data on expenditures before and after the
change in the public good. A simple estimator of the uncompensated surplus measure
expected value can be obtained by averaging Y = over every individual in the sample.
However, this simple approach requires observations on the expenditures of each
individual before and after the public good change.
In the absence of before and after expenditure data for each individual, an
alternative approach can be used to recover estimates of the uncompensated measure. All
If the prices of the goods that are not interdependent with the public good are not
constant before and after the change, then the remaining economic variables can be
normalized by this index to preserve homogeneity.
29
that is necessary is an expenditure observation for an individual when they use the public
good and another observation when they do not. Given this information the difference in
spending between use and nonuse observations measures CV1 in the special case of
complete loss of public good access.
To examine this claim, note that the indirect utility levels from an activity
interdependent with a public good can be divided into the four cases shown in Table 1.
In this case the activity is defined as public good use so that a ldenotes the utility
when the public good is used and a 0 denotes the utility level otherwise. The income
variable is implicitly adjusted for the total spending on each alternative as
y'J y Px4 (/,y,bJ,s,Â£). Also, the price vector in the table is implicitly defined as
p = = {1,1}. This sloppy notation is maintained in what follows to avoid
creating another table and reduce the clutter in the functions. The corresponding four
spending outcomes are listed in Table 2 where the public good use decision is explicitly
labeled.
Consider the special case where b represents the state of the world with no access
to the public good. In this case, expression in cell (2, 2) in Table 1 and Table 2 are
irrelevant because it is impossible to use the public good when access is completely
restricted. The constant price difference in spending between use and nonuse of the
public good with existing access level b1 can be written explicitly as
(228) kp = e(v (l,/?,/', 6', s,e), 61,s,f) e(v (0,/?,/, 61, s,e),A*,Â£).
Now if we assume that an individual is just as well off without access to the public good
in state b as they would be if they chose not to use the public good in state b' then
30
(229) v (O, >01, p, b', s, e) = v (O, y)0, p, b ,s,e)
and expression (228) can equivalently be represented as
(230)
'(p,y,bl,S,e) = e(p,v(l,p,y",bl,S,e),b',S,e)e(pyv(0,p,yM,b,S,e),b,,S,e)
= e(p,v",b',s,Â£)e(p,v0,b,,s,e)
= e(p,ul ,b' ,5,e) e(p,u ,b' ,5,e) = CVP
Using standard duality conditions (Loehman 1991) this expression can be also be written
as the compensating variation in (21).
Table 2. Spending outcomes with public good use and change combinations
USE PUBLIC GOOD?
YES (i=l)
NO (i=0)
PUBLIC
GOOD
CHANGE
BEFORE
(j=i)
e(p,v",b',ste)
e(Py\b\s,e)
AFTER
0=0)
e(p,vw,b\s,e)
e(p,vm,b0,s,e)
To summarize, with constant relative prices and condition (229), the CV for the
complete loss in public good access is given by the difference in spending on an
interdependent activity for an individual when they use the public good and when they do
not. A simple estimator of the compensated surplus measure expected value can be
obtained by averaging Ap = CVP over every individual in the sample. However, this
simple estimator susceptible to selection bias and contamination if any of the
conditioning variables (i.e., s ory) change between the use and nonuse events. From
31
assumption (229) an additional bias arises in this case if the conditioning variables of
nonuse outcome change between the before and after states of the world. That is, if
socioeconomic characteristics and/or their related parameters change when the public
good changes. The parametric and nonparametric estimators reviewed in Heckman and
Robb (1985) and Blundell and Costa Dias (2000) could potentially be used to correct for
these biases. The application of these socalled differenceindifferences and
matching methods to estimate the compensated measure of public good access with
panel data or repeated crosssections is a topic for future research.
Treatment Effect Welfare Measures for CrossSection Data
With crosssection data an individual is only observed at one point in time and/or
for one state of nature. That is, only one of the four possible outcomes listed in Table 1
and Table 2 is possible for any given individual in a crosssection. Consequently, each
individual will have missing counter]actual information. For users, the counterfactual is
their spending had they not used the public good. Similarly, the counterfactual for
nonusers is their spending had they chosen to use the public good. From Table 1, each of
these counterfactuals are possible before and after the change in the public good. To
simplify matters, the approaches developed here again on the special case of constant
prices and the complete loss in access to the public good from the reference access level
b'. When b represents the no public good access case, there is no missing counterfactual
for this state of the world because only nonuse is possible.
Conceptually, one individuals observed behavior can be used to infer about
anothers counterfactual and vice versa. Such inferences require information on whether
or not an individual used the public good for the interdependent activity at least once for
the reference period. Based on the work of Heckman and Vytlacil (2000; 2001a; 2001b),
32
information on public good usage and two general assumptions (defined below) can be
used to recover expectations of the counterfactual information missing from crosssection
data.
The decision to use the public good in the reference period can be modeled with an
index of net (indirect) utility
(231) D* (p,y,b\s,e) = v{\,p,yu,b\s,e)v(0,p,y',bl,s,e).
Following random utility discrete choice theory (Hanemann 1999), let there be an
indicator variable that defines an individuals use status based on the net utility index
(232)
D' = G(Z) + Â£d
D = 1 // Z)* > 0, =0 otherwise
where Z is a vector of all observable variables that influence the latent net indirect utility
variable in (231) and eD is an additive error derived from e. Note that there must be at
least one variable in Z that is not in the set (s, y, p). This exclusion restriction is required
so that we can manipulate an individuals probability of public good use without
affecting their expenditures.
The two counterfactual assumptions implicit in the index model are (Heckman and
Vytlacil 2001a):
14
C1. Given that the choice probability for individuals with observed characteristics z
is P(z'), then if you take a random sample of individuals and externally set their Z
= z \ then their choice probability is also assumed to be P(z).
C2. For any case where individuals with observed Z = z are set to Z = z' and P(z) <
P(z), then: a) some individuals who would have had D = 0 with Z = z will have
14 Heckman and Vytlacil (2001a) also specify a series of technical assumptions that are
imposed for convenience and to simplify the notation in their derivations.
33
D = I with Z = z\ and b) no individual who had D = 1 with Z = z will have D =
0 with Z = z
where = Pr(D = 1 / Z = z) is the socalled propensity score or choice probability
for the probability of choosing to use the public good conditional on Z = z. The first
statement assumes that if you take a random sample of individuals and change their
determinants of public good use, then the probability that they will choose to use the
public good is the probability of use for those users who were observed to have the
same set of determinants of participation. This corresponds to assuming eD is
independent of Z, conditional on (s, y, p), and is not essential to identify conditional
expectations of the difference in spending measures (Heckman and Vytlacil 2001a). The
second assumption is a monotonicity property which requires that a change to any set of
factors that increases the probability of participation will cause some nonusers to use the
public good, but will never cause users to stop using the public good. The monotonicity
property is implied by the additive error assumption in the index function. Both
assumptions are implicit in the standard random utility discrete choice model of rational
probabilistic choice (Gourieroux 2000).
I assume that the alternatives of public good use and nonuse are mutually exclusive
so that the sample can be perfectly segmented into two groups based on observed
behavior. To use an analogy with the program evaluation literature (Heckman 2001b),
consider access to the public good in the reference state as a program such that public
good use can be considered the program treatment. Those who actually use the public
good make up the treatment group and all other potential users compose the control
34
group. The sample will selfselect into one group or the other.15 The use of assumptions
C. 1. and C.2 allows standard selectivity methods to be used in D/C models to recover
counterfactual information necessary to evaluate the welfare measures.
The approach taken in the treatment effects model departs somewhat from the
conventional structural approach described above in suggesting that the information
inherent in selectivity biases can be used to learn about the relative value of public good
access. This alternative view is not without precedent, as Heckman (2001a) notes that
evidence from selfselection decisions can be used to evaluate private preferences for
the programme so that, in principle, the problem of self selection can be used as a
source of information about private valuations (in. 11).
Econometric Framework
The index function and the spending outcome equations can be jointly modeled as a
D/C choice switching regression system
D* = G(y,s,z\p,8,p,b') + Â£D
(233)
D = \ if D >0, =0 otherwise
(234)
(235)
where (fJ is a conformable parameter vector for s, y and a constant such that each
alternative spending outcome has its own set of parameters and an additive error term.
The notation follows the earlier model where superscripts i and j denote the public good
15 The general problem actually has two sets of selfselected samples. One set is
composed of those who choose the public good at level b' and those who do not. The
other set consists of those who choose to use the public good at level b and those who do
not. In the special case where b = 0 (i.e., no public good access), there is no self
selectivity problem because there only one class of individuals: nonusers.
35
use decision and reference condition, respectively. Note that j = 1 in both outcome
equations indicating that the model should be estimated with a crosssection from the
period where public good access is at level b'. Also, because 1 am assuming everyone in
the crosssection faces the same (relative) prices and public good access level (b'), the
estimating forms of the choice and expenditure equations are conditional on these
arguments. Since the indirect utility functions implicit in (233) and the expenditure
(demand) equations in (234) and (235) come from the same consumer problem, we
have fin = h(f?J, (?) and iP = k(eP fP). The exact form of functions h and k will depend
on the functional form selected for the expenditure (demand) equations. One form is
presented in the case studies of Chapters 3 and 4. The variable z and related parameter
are added to the index function to serve as the exclusion restriction required for the index
model specification.
The spending outcome for any individual can be written as
e = De" +(1D)
= px{y,s\pm) + D[px(y,s\P")~ px (>, 5  /301)] + [e01 +D(e" Â£0')]
where the conditioning on the existing state of the public good b1 and the constant price
level is implicit. This formulation suggests that selectivity is a problem by construction if
the decision to use the public good is correlated with the expenditure outcome decision.
The form of the error term will differ across the observations according the specific
36
public good use status.16 Consequently, the data does not have the controlled (or natural)
randomization necessary to identify the difference in expenditures measure as the
coefficient on D. Selectivity correction methods aim to purge the nonrandom features
from the data by controlling for the variation in the outcome equations due to
unobservable portions of the index (choice) equation. These methods are applied in
program evaluation analyses to identify moments on the distribution of treatment effects.
That treatment effects can be random variables is seen by rewriting expression
(236) as
(237) e = px(y,s\P') + D[px(y,s \ P")px(y,s\ p') + (e" Â£01 )] + Â£01
to reveal that the term multiplying the public good use indicator is a random parameter.
Thus, the each individual can potentially have their own difference in spending treatment
effect that depends on the idiosyncratic information in e11 and e01. In this situation there
is an underlying distribution of heterogeneous treatment effects and different
conditioning sets will give rise to different expectations of spending differences. On the
other hand, there could be only one common treatment effect parameter for all
individuals given, in this case, by px[y,s  pu) px[y,s  /301). Heckman (1997) points
to two scenarios in which treatment effects are homogeneous in this way. First, it can be
simply be assumed that there is no unobservable portion of the expenditure differences so
16 Technically, there are two ways in which the correlation between D and the
unobservables of the outcome equations can manifest. The first way is termed selection
on the unobservables because there is correlation between the unobservable portions of D
and those of the outcome equations. In the other way, called selection on the
observables, an observable element of D is correlated with the unobservables in the
outcome equations. Note that the structural D/C modeling approaches described in the
previous section generally deal with selection on the unobservables. However, a full
characterization of the structural demand and utility models in terms these two types
selectivity is left for future research.
37
that e11 e01 = 0. Second, e11 might not equal e01, but the difference between the these
elements does not determine who decides to use the public good. This could happen, for
example, if individuals do not know e11 e01 at the time they choose to use the public
good and their best guess of it is zero. The expected value of the net effect of
unobservables becomes zero if these individuals expectations ofe" e01 are typical of
the entire population. If either of these scenarios is true, then there is no distribution of
spending treatment effects and there is only one expected treatment effect measure for the
population. The following analysis assumes the more general heterogeneous treatment
effect case so that I can tailor mean spending difference parameters that correspond to the
various welfare measures discussed so far.
Treatment Effect Welfare Measures
There are two ways in which the econometric framework can be used to recover a
population level measure of The first recovers using
assumption (229) and additional assumptions based on the spending behavior of those
who use the public good and those who do not for the interdependent activity. The
second way does not require condition (229) and instead seeks to recover
E \M = E [CVP ] using an indifference set M to condition the distribution of
differences in spending with and without public good use. This second approach aims to
develop a policy relevant difference in spending measure (Heckman and Vytlacil 2001b).
Approach 1. With constant relative prices the uncompensated surplus ST for the
total loss of public good access is measured by the difference in spending by an
38
individual when they use the public good use and when they do not. For the model in
(233)(235) this difference in spending for each individual is given by
(238) Ap = px(y,s \ (3")~ px(y,s  /301 ) + (e" e()l)
where the conditioning on b' and p are again left implicit. This is the heterogeneous
treatment effect random parameter defined in expression (237). There are three
commonly used measures of the expected value of this variable using different sets of the
sample (Heckman and Vytlacil 2000). The unconditional expected value measures the
socalled average treatment effect
(239) ATE= E[kp\y,s^ = E[px(y,s\ P")px(y,s\ (3m)\y,s~^
This mean measures the expected difference in spending from public good use for a
randomly chosen individual. If corrected for selectivity, the ATE will approximate the
mean treatment effect from a randomized experiment.17 Evaluating the expected value of
the treatment effect over the support of those who chose to use the public good gives the
effect of the treatment on the treated as
(240)
7T' = ['ly..Z) = l] = E[px(jy.s  3" )px(y,s  T )]+ Â£[<="Â£01 \D = l]
A similar parameter can be defined for the segment of the sample who chose not to use
the public good
1 There are two ways in which selectivity can bias the experimental treatment average
(Winship and Morgan 1999). The mean selection bias given by E[e01 y,.s\D=T] E[e01 
y,s,D=0] indicates how spending in the reference level of the public good differs between
users and nonusers. The second source of bias occurs if the change in spending caused
by public good access/use (treatment) is different among users and nonusers. This bias is
given by e[ap y,s,D = l]Â£[p \y,s,D = o] = e\eue0i \y,s,D = l]. Neither of
these spending differences can be attributed to public good access.
39
(241)
UTk' = E[Ap\y,s,D = 0] = E[px(y,s\ p")px(y,s \ p0l)] + E[eu e0l\D = 0]
Using the counterfactual assumptions in C.l and C.2, the above treatment effects measure
the expected value of ST for the loss of public good assess for different segments of the
population. In the previous discussion, I suggested that, with panel data, condition (229)
can be assumed so that Ap = CVP for each individual. With crosssection data, however,
condition (229) alone is not sufficient for Ap to measure CK because there is additional
missing counterfactual information. Recall that this condition requires that an individual
is just as well off without access to the public good in hypothetical state b as they would
be if they chose not to use the public good in the reference state b. With a complete
panel there are observations on expenditures for each individual when they choose to use
the public good and otherwise for the interdependent activity (with the public good fixed
at b'). With a crosssection, however, there is only information from nonusers about
spending and the corresponding utility level when the public good is not used. Similarly,
only users provide information about spending and the corresponding utility level when
the public good is used. This means that a direct application of condition (229) with
crosssection data will involve an interpersonal comparison of wellbeing. The extent of
the comparison will depend on which treatment effect measure is used.
For ATE, 7TV or UTS' to measure the E [CV'] for complete loss of access,
condition (229) needs to hold for those who didnt choose to use the public good at the
reference state. In addition, for TTsr to measure E[CV1] for users we require
(242) [v(0,/1,/7,61,5,E)D = l] = [v(0,/,,jt?,61,J,e)D = 0]
40
for those who did choose to use the public good in the reference state. This assumption
requires that the indirect utility level of users (D=l), had they not used the public good, is
the same as nonusers (D=0) with the same set of characteristics {y, s, e). Similarly, to use
UTap as a measure of E[CK] for nonusers we additionally require
(243) [v(l,y1,/),,,>Â£)D = 0] = [v(l,yl,p,6',,Â£)O = l]
for those who did not choose to use the public good at the reference state. This
assumption states that the indirect utility level of nonusers (D=0), had they used the
public good, is the same as users (D=l) with the same set of characteristics {y, s, e). In
order for ATE AP = E [CF*] for the entire population, we need assumptions (242) and
(243) as well as assumption (229).
Approach 2. To motivate the task of specifying and identifying the policy relevant
treatment effects measure, consider the distribution of expenditure differences Ap shown
in Figure 3 where f0 is a function describing the relevant density of e.18 The unknown
switching threshold is shown as Ap which also corresponds to the compensation that
would make the marginal individual just indifferent between using or not using the
public good. Individuals located to the right of the threshold choose to use the public
good alternative whereas those to the left do not. Thus, there is actually a related
* *
distribution of for the marginal and nonmarginal individuals. If the public good
does not have value to the individual outside its use in the interdependent activity, then
1 8
Following Moffitt (1998) the distribution of the treatment effect in can be depicted as
A
in Figure 3 by assuming that the choice between alternatives is based entirely on Ap and
that this selection is positive: individuals with high values of Ap are relatively more
likely to choose the first alternative than those with lower values.
41
Ap* corresponds with the CVf measure. Similarly, the expected value of Ap' for the
population corresponds with the EfCf*'] measure.
Ap
Figure 3. Expenditure difference threshold
Referring again to Figure 3, the unconditional mean of Ap will not correspond to an
exact welfare measure of public good access (unless the conditions specified in Approach
1 for ATEy are met). The mean of the treatment effect has to be conditioned in order to
*
recover a value that represents the central tendency of the exact measure Ar The
expected value of Ar can be thought of as the expected value of A; conditional on
being at the point of indifference for each individual or
Â£[^] = Â£[P v(l,p,yl\b',s,e) = v(0,p, v01,^',5,f)]
= e[ap\d =o]
(244)
42
This type of treatment effect is known as the marginal treatment effect (MTE) or the limit
version of the socalled local average treatment effect.19 According to Heckman and
Vytlacil (2001a), the MTE has the interpretation as a measure of willingness to pay on
the part of people on a specified margin of participation in the program (fn. 16). The
conditioning expressions in this case can be viewed as the indifference set (Heckman
1997). Using the definition of Kp in (238) and the additiveerror index function
specifications in (233), this expectation can be written as
Â£['"]=[A'] + Â£[Â£"Â£d = C(>.,,z)]Â£[Â£0'ei>=G(>,,z)]
(245) L J l i
= Â£['] + (<711d <71D)[G(y,.?,z)]
where J is the unconditional average treatment effect from (239) and the
conditioning set for the index function G (\ ,5, p,bl) is omitted to simplify the
notation. The terms o01D and o'10 measure the covariance between the public good use
decision and the unobservable portion of each expenditure outcome. These covariances
show how, for a given set of set of (y, s, z), spending on the interdependent activity
change with a change in the net utility of public good use. Information about an
individuals preferences can be recovered by examining the signs of (o'10 o01D) and
G(j. If these terms have opposite signs, then the propensity to change spending is
greater with public good use than without. In this case, an individual prefers to use the
19 Attribution for this treatment effect parameter is given footnote 18 of Heckman and
Vytlacil (2001a).
7ft
Note that the covariances arise in the derivation from the general expression for the
expectation of a random variable conditional on another random variable, i.e., E[e1J  eD] =
01jDÂ£D.
21 The economic interpretation of the switching regression covariances is similar to the
use of these parameters in the labor literature that examines comparative and absolute
advantage (Dolton and Makepeace 1987; Emerson 1989).
43
public good, otherwise they do not. Furthermore, since the first term on the righthand
side is simply a difference in expenditure, the remainder has the interpretation as the
additional amount necessary to make the individual indifferent with and without public
good use. This becomes apparent when we recognize that o11D and a0ID give the slope of
lines that showing how the expenditures of users and nonusers, respectively, vary with
the net utility of public good use indexed by G(j. The term G(j for each individual
gives the value of the unobservables necessary to maintain the same utility level (i.e.,
D*=0) with and without the public good (use). The constant covariance term translates
this amount into the money measure of the additional compensation necessary to
maintain the same utility level when the public good (use) is not available.
The relationship among the treatment effect measures of spending differences in
(239)(241) and the exact measure in (245) can be used to formulate a model of public
good use participation. The expected value of the exact measure represents the
mean threshold of public good use for the sample. It is straightforward to show that
participation is expected on average if
(246) Â£[/*]> ATE*
because this implies that the utility of using the public good is greater than the utility
otherwise.23 The corresponding expressions for the users and nonuser groups are,
respectively,
22 The with and without public good (use) expenditure equations could be drawn on the
same graph as a function of net utility. This may provide a useful way of visualizing the
treatment effect welfare measure(s). I leave this for future research.
23 From (226) and (227), CVP > AT => e(u ,p, b,s,e) ^ e(u, p, b,s,e) which holds if u
> u (all else equal) because the expenditure function is increasing in utility. Note that u
is the utility with the public good (use) and u is utility otherwise.
(248)
E \nonuser J > UT^
These conditions provide a consistency test on the treatment effects model results.
We would expect condition (247) to be true for those who actually choose to use the
public good for the interdependent activity. However, the inequality in condition (248)
is expected to be reversed because this expression applies to the group of individuals who
choose not to use the public good.
Discussion
This chapter introduced the treatment effects approach to evaluating the welfare
effects of changes in the condition of public goods. The approach applies techniques
from the program evaluation literature to develop measures of welfare changes from
spending on market goods that are interdependent with a public good. This approach
views interventions in the supply of public goods as programs where the segment of the
population currently using these goods are viewed as the treatment group and other
potential users are considered the control group. Measures of the value of public good
access are recovered from differences in expenditures among users and nonusers. This
approach offers the advantage of using price constant specifications of demand relations
(e.g., Engel curves) because the typical choke price argument is not required to evaluate
the access restrictions.
There are several directions for future research on the treatment effects approach.
First, the model can be extended to evaluate continuous treatment effects (Heckman
1997) to deal with a continuum of possible changes in public good conditions. This
would also allow for a richer consideration of the counterfactual assumptions required for
45
cases other than with and without public good access case considered in this chapter.
Second, there is more work necessary to examine the role of substitutes in the treatment
effects approach. The importance of substitutes other revealed preference approaches
such as the travel cost model is welldocumented (Kling 1989; Rosenthal 1987; Smith
1993). Recent research on program evaluation (Heckman, Hohmann and Smith 2000)
suggests methods to account for substitute programs in estimates of treatment effects that
may be useful in generalizing the approach introduced in this chapter. A related direction
for further research is to examine models for multiple programs that could be used as a
treatment effects analog to the multisite travel cost model.
Fourth, future work on the treatment effects approach should include applications
the nonparametric estimators developed in the program evaluation literature to the public
good valuation problem. Finally, the longitudinal measures introduced here should be
explored further. This would require a panel or repeated crosssections of expenditures
on activities interdependent with a public good. Although the former is relatively rare,
repeated crosssections are regularly collected by variety of resource management
agencies.
CHAPTER 3
APPLICATION TO RECREATIONAL FISHING
There are approximately 4,000 offshore oil and gas structures in the state and
federal waters of the Gulf of Mexico. These structures account for a major proportion of
the available fish habitat in the Gulf and they are utilized by a variety of recreational
users (Quantech 2001). More than 100 structures are removed annually but the U.S.
Mineral Management Service has adopted a RigstoReefs policy to mitigate the loss of
these structures to maintain the public good benefits of fisheries habitat (Dauterive 2000).
This policy involves leaving the structures in place, toppling the structures to create
benthic habitat, or moving them to a new location. While the costs of removal are
relatively well known, the economic benefits of current usage and of retaining these
structures have not been estimated.
This chapter presents an analysis of the value of access to petroleum rigs for
recreational fishing. It is hypothesized that fishing at offshore rig sites requires additional
fishing capital compared to other types of angling. Consequently, the analysis measures
opportunity costs in terms of per trip costs and expenditures on fishing capital. This
requires that models of recreational fishing, such as the travel cost model, be adapted to
jointly model choices over durable and nondurable goods.
Randall notes that in applications of the travel cost model the allocation of the
costs of owning and maintaining vehicles and other durable equipment to any particular
trip (activity) proceeds, if at all, in an arbitrary fashion (p.90). This is largely due to the
additional complications that arise when attempting to introduce (joint) capital
46
47
expenditures into fundamentally endogenous price indices for nonmarket activities
(Bockstael and McConnell 1981; Poliak and Wachter 1975). From Chapter 2, such price
indices are necessary in the travel cost model in order to estimate a demand equation for
the nonmarket activity and derive welfare measures of access or quality changes.
However, it may not be possible to derive valid quantity and price indices when trips
are used as the aggregator for recreation commodities.1
Linear random utility models also typically ignore capital expenditures because it is
presumed that these expenditures do not vary with the number of visits to a particular site
or type of site. In this case, capital stock or expenditures are individualspecific variables
that drop out of the model because the estimation is based on utility differences and these
variables do not vary across sites or activities. This may be a valid assumption when
(perfect) substitute sites or activates are available that jointly use the durable equipment;
that is, when expenditure categories are not uniquely related to the attributes of an
activity or site. In other cases, however, ignoring such expenditures could seriously
misstate welfare estimates for policies that stand to affect the access to, or quality of
capitalintensive activities.
This chapter presents two approaches to incorporating annual capital expenditures
into estimates of the value of access to petroleum rigs for recreational fishing. The first
approach is a simple adaptation of the structural travel cost model to incorporate the stock
of fishing capital among explanatory variables. Like the conventional travel cost model,
1 Shaw and Shonkwiler (2000) demonstrate that the price indices suggested for trips in
the literature are not valid or that these indices do not enter the trip demand equations in a
valid way. A valid price index for a Hicksian composite commodity is linear
homogenous in goods prices and the specification of the trip demand equation is
homogeneous of degree zero in income and the price index.
48
this adaptation requires that price and quantity indices be separated from fishing
expenditures to estimate a structural model of fishing trip demand. The second approach
is based on the treatment effects framework for measuring public good values presented
in Chapter 2. This framework involves conditions whereby welfare changes can be
measured by differences in the observed expenditures of two segments of the population
who participate in recreational fishing: petroleum rig users and nonusers. The method
can be implemented with raw expenditures on a recreational fishing activity that is
interdependent with access to petroleum rigs. Price and quantity indices do not need to
be separated from the aggregate annual expenditures for each individual. Data used in
the analysis are drawn from intercept and phone surveys of marine recreational anglers
along the Gulf of Mexico coast (Alabama to Texas) that elicited detailed information
about sitespecific activities and expenditures for variable and capital goods directly
related to the activity. The econometric estimation procedure developed in Chapter 2
controls for (and actually takes advantage of) activity specific selectivity, in this case, the
choice whether to fish near an petroleum structure or not.
Welfare Measurement with Capital Expenditures
There are few, if any, attempts to systematically incorporate expenditures on
durables into models designed to measure the value of changes in public goods. Studies
frequently use indicators of existing capital stock as explanatory variables in demand
equations. Travel cost analyses of recreational fishing, for example, often incorporate
dummy variables for boat ownership. However, the rationale for including such variables
is usually not fully developed beyond an implicit notion that the behavioral relationships
estimated are conditional on the existing stock of capital (Poliak 1969). Capital stock
indicators are included among regressors to control for variations in holdings in demand
49
and welfare calculations. This formulation treats capital as an exogenous portion of the
consumer problem and is correct to the extent that the additions to capital are fixed over
the (decision) period of interest. In many cases, though, the stock of capital is better
characterized as quasifixed so that periodic increments are chosen along with (non
capital) commodities as part of the same optimization process (Conrad and Schroder
1991).
Consider that the choices regarding where and how frequently to fish annually are
conditional on boat ownership, but that a boat could be purchased at any point during the
year. In this example, the same observable and unobservable factors that influence the
choice of capital stock levels also determine the demand for other commodities.
Consequently, measures of current capital stock and additions will be endogenous if
included in a demand equation for another commodity in the consumption set. In the
fishing demand example, the boat ownership indicator is a dummy endogenous variable
(Heckman 1978). This suggests that capital expenditure decisions should be modeled
simultaneously with other aspects of the consumer problem.
The basic neoclassical model of consumption with durable goods has the consumer
choosing the allocation of expenditures among nondurables and capital stocks to
maximize intertemporal utility (Deaton and Muellbauer 1980). This model yields
solutions for the optimal demands for nondurables and durable stock in each period that
are functions of the existing durable stock, discounted prices and the user cost of capital
for all periods over the planning horizon. With weak intertemporal separability, future
prices are irrelevant to current decisions, so the expenditure for the nondurables x and the
50
durable stock K in any period is a function of the existing durable stock AT./, current
period prices p, and the user cost of capital k
(31) e(p,u,b,s,e,k,K_{) = px (p,u,b,s,Â£,k, AT_,) kK (p,u,b,s,Â£,k, K_{)
where u is the utility level, b indicates the supply of petroleum rigs for fishing, s is a
vector of observable control characteristics and e represents unobservables.2 The
relevant nondurables and durables are those which are weak complements to (fishing at)
the petroleum rigs.
The (compensated) demand system for this problem is found by differentiating the
full expenditure function with respect to the price of variable goods and the capital stock
(32)
de , v dK(p,u,b,s,Â£,k,K_{)
= x(p,u,b,s,Â£,k,K_l) + k
3p
dpx
de v dK(p,u,b,s,Â£,k,K_,)
= x(p,u,b,s,Â£,k,K_i) + k
dpN
dpN
(33)
de dx(p,u,b,s,Â£,k,K_l)
^7 = P ^ + K(p,u,b,s,Â£,k,K^)
ok dk
Following the discussion in Chapter 2, this simultaneous system can be used to estimate
the value of changes access to the weakly complementary petroleum rigs. The
compensating variation for a discrete change in fishing access to rigs from b' to b is
2 With intertemporal separability, the user cost of capital is simply the current cost of
capital purchases. Furthermore, assuming no depreciation, K is actually a measure of
additions to capital stock. This is seen by noting that capital stock changes in each period
according to K (p,u,b,s,Â£,k,K_Â¡ ) = d (p,u,b,s,Â£,k,K_{) + (l 8) K_x where d() is the
demand for additions to capital stock and 5 is the depreciation rate. If 8 = 0, then changes
in K are proportional to d.
51
CVK ,b) = e(p, u ,b' ,s,Â£) e(p, u ,b ,s,Â£,k, )
(34) = \^px[p,u ,b\s,e,k,K_i)+ kK [p,u ,b\s,E,k,K_x)^
~^px{p,u ,b ,s,e,k,K_]) + kK [p, u',b, s,e,k, K_x)]
Note that to the extent capital stock is actual fixed over the decision period the second
terms in (32) and the entire expression in (33) can be ignored in demand estimation. If
capital stock is fixed before and after the change rig access, then the second terms in the
last two lines of the CV in (34) can also be ignored. This is what is done in the
conventional formulation of the travel cost model that focuses on the first term in (31) or
the variable expenditure function (Conrad and Schroder 1991). The welfare measure in
this case reduces to
(35) CV (b',b) = px(p,u',b',s,Â£,K_i)px(p,u',b,s,Â£,K_l)
where since there is no longer a tradeoff between spending on nondurables and spending
on capital additions, the cost of capital is omitted. The structural demand approach
defined below follows the conventional travel cost formulation to recover the variable
cost welfare measure in (35). The alternative treatment effects approach presents a way
to recover the welfare measure of the value of rig access in (34) that includes spending
on fishing capital.
Structural Demand Approach
The structural approach to recovering the welfare measure in (34) requires
estimation of at least part of the system of interdependent commodity and capital stock
demands. Two strategies have been applied in the literature. The first strategy is to
estimate a partial demand system with the commodities that are (assumed) interdependent
with the public good (Shapiro and Smith 1981). The capital augmented model shown in
52
system (32)(33) also requires the estimation of equations for all of the interdependent
capital stocks. The second and more common strategy is to aggregate the interdependent
goods and estimate a demand equation or system for a composite commodity or system
of composites. The travel cost model is a classic example of this second strategy where
the composite commodity is trips and the price index is travel costs. This approach is
taken for the present application. However, it is acknowledged that the approach is
problematic in the travel cost model because the composite commodities are delineated
according to activities and/or locations chosen by the household. See Chapter 2 for a
discussion. Adding capital costs into activitybased price indices compound the problems
because there is no straightforward way to allocate the fixed capital costs to any one
activity type, location or specific trip (Poliak and Wachter 1975). Consequently, separate
capital stock equations should be estimated simultaneously.
For the empirical application of the structural approach, I do not estimate a demand
system with capital stock equations. I follow the conventional travel cost approach in
assuming that capital stock is fixed over the decision period and estimate the demand for
a tripbased composite commodity representing only system (32). However, the
previous period capital stock is included among the influences of the trip demand
decision. Trip demand is specified as a pooledsite model for recreational fishing at
petroleum rigs in the Gulf of Mexico.
Following the canonical discrete/continuous model in the Chapter 2, the structural
trip demand system consists of an index equation and a trip demand equation
(36) R = af + (Pr Pnr )aRp + K_^aR + saR +eR
(37)
Tr a'/ + Pra+ Poa'J + +sa'' +Â£n
53
where R is a binary indicator that equals 1 if an individual fished at a rig in the previous
year and zero otherwise3, Tr is the total annual fishing trips to petroleum rigs, Pr is the
average cost of a rig trip, PQ is the average cost of a nonrig trip, y is income, K.Â¡ is the
existing stock of fishing capital, s is a vector of socioeconomic control variables. The
unobservables of the selection decision ^ and trip demand e" are assumed to be joint
normally distributed.
The number of rig trips per year in (37) is modeled as Poisson process (Hellerstein
1999) so that estimated trip demand equation is
(38) Prob[Tr =c] = exp(~Tr )Trc/c\ c = 0,1,2,
The extra error term in the trip equation of (37) relaxes the usual Poisson assumption
that the mean and variance of the estimator are equal. This allows for unobserved
heterogeneity and addresses overdispersion common in count models. The extra error
term also allows a convenient way to model selectivity that parallels the standard
approaches with linear models. An example application of this estimator is given in
Haab and McConnell (2002) and the construction of the likelihood function is shown in
Greene (1995 pp. 580582).
Based on the discussion of demand interdependence in Chapter 2, the value of a
public good change can be measured as areas behind the demand curves estimated with
(36)(38) before and after the change. However, the data used in this case study is from
a crosssection before the public good change so the welfare effects have to be simulated.
3 1 assume that the net utility of the rig use decision can be modeled by a reduced form
index equation that is linear in variables. This simple approach is taken because of the
complexity of the indirect utility function corresponding to the semilog demand equation
of the count model. With this assumption, only the unobservable portions of the rig use
decision and the trip demand are related.
54
The simulation to recover value of fishing access to petroleum rigs involves an
integration under the demand curve for rig trips from the current cost of a trip to a
choke cost. The expected annual consumer surplus consumer surplus of rig access is
Â£[S]=J
V
(39)
r
Â¡[
Pr
\[ (eu)Tr]del
V
E[l]
a''
de'
dP_
a,!' *0
where the denominator is the coefficient on the rig trip cost variable from (37), () is
the normal probability distribution function, and 4* is the support of the unobservables in
the trip demand equation (Hellerstein 1999). Following the notation in Chapter 2, P' is
the choke price for the uncompensated demand equation. Based on Hanemanns (1980)
derivation for the semilog demand equation, the exact compensating variation for a loss
in access to petroleum rigs for recreational fishing is
E[CV} = \
(310)
= J
Â¡[
Pr
\[
de[
dp:
In
a.
a.
iE[Tr Hr
CL
a.
where Pr is the choke price for the compensated demand equation. Note that reversal of
integration implied in these measures requires that the travel price be independent of the
unobserved heterogeneity. I use this simple measure, but note the assumption is
55
questionable because as argued in Chapter 2, the travel price (index) is endogenously
determined along with the trip quantity index (Haab and McConnell 1996).
The welfare measures use expected rig trips, adjusted for selectivity (Bockstael et
al. 1990). I also correct the expected value of the dependant variable for the lognormal
transformation implicit in the PoissonNormal model of heterogeneity so expected rig
trips are calculated as
(3n) [?;]=l[exp(a;1 +pryr'+p0yj+K_
** n=1
oc11
+ s.a: +g
ii/?
/*"+<7
n/2)]
where u" = (,) is the inverse Mills ratio term with <Â£() as the cumulative
distribution function, Oi ir is the estimated covariance of the rig choice and rig trip
decisions, and On is the estimated standard deviation of unobservables in the rig trip
equation. The last term is the correction of the mean for the lognormal distribution.4
Note that 1 do not adjust the Â£[S] and E[CV\ integration results for the appearance of the
price and income variables in Rn of the expected trips equation. This adjustment is
obviated by the assumption of exogenous prices that is used to reverse the integration in
the welfare calculations. The model is estimated in LIMDEP (Greene 1995).
Treatment Effects Approach
The structural activity demand approach outlined earlier is problematic because the
price index (travel costs) and quantity index (trips) will be endogenous to the consumer
problem. Furthermore, although not included in the model specified for this chapter, the
4 The model is estimated with the log of rig trips and the heterogeneity error term e11 of
this equation is assumed to be normal. Therefore, the trips within the Poisson probability
are assumed to take a lognormal distribution. From Greene (2000) the expected value of
the lognormal rig trips variable is E[Trn] = exp(m +
56
structural demand model requires a separate estimating equation to (simultaneously)
incorporate the demand for capital additions.
An alternative strategy, introduced in Chapter 2, doesnt require separate price and
quantity indices. Rather this treatment effects approach works to specify conditions
whereby welfare changes can be measured directly by differences in observed spending
by different segments of the population. For present case, I am suggesting that there is a
hypothetical program to allow the use of petroleum rigs as artificial habitat for
recreational fishing. Removal or expansion of this program can be considered a change
in the supply of access to a public good.
Let b1 be the reference condition of the rigs program and consider the special case
analyzed in Chapter 2 where access to rigs is zero at b so that b > 0 and b = 0. In this
case, the recreational anglers who report fishing at the rigs are the program participants or
treatment group and those who do not are the control group. The idea is to use the
differences in expenditures between these two groups to evaluate the with and without
program (petroleum rigs) welfare measure. The counterfactual assumptions required to
uncover the value of access from the difference in spending with and without rig use are
detailed in Chapter 2.
With the appropriate counterfactual assumptions, the selfselection decisions of
anglers suggest three possible sources of differences in expenditures: 1) fishing at a rig
may require higher (or lower) expenditures on average, 2) those who fish rigs may have
an inherent tendency to spend more (or less) on fishing than those who do not fish rigs,
and 3) the expenditures of those who fish rigs may change more (or less) because of a
change in rig access than those who do not visit rigs, if they had. The various approaches
57
to dealing with selection bias in treatment effects models all attempt to isolate the first
effect by controlling or capturing the second two sources of variation from estimates
(Vella and Verbeek 1999; Winship and Morgan 1999). However, as described in Chapter
2, the second two sources of spending differences provide important information about
the relative value anglers place on access to fishing at rigs
As in the structural demand approach, the decision to fish rigs is modeled with a
linear index equation
(312) D1 = G/3d' +e^
where G = {1, y, K_{,s,z}, pD> = [p?, /3VD', p^, pf, pD'}, and eD> represents the
unobservables at rig access level b1. This index is motivated by the latent net utility of
choosing to fish at least one petroleum rig in the previous year. All variables are defined
as in the structural demand model and z is an exclusion restriction required so that we can
manipulate an individuals probability of rig use without affecting their expenditures.
Note that the latent net utility value can be different for individuals with the same
observed characteristics because of the unobserved heterogeneity term eD. For example,
some anglers wont fish at a rig unless they own a boat, while others will rent a boat or
hire a charter to do so. This also suggests that capital purchases should be incorporated
in expenditures and welfare measures as shown in (31) and (34).
The index equation defines an endogenous switching regime model of annual
variable and capital expenditures with and without rig use
(313)
\px + kK] =
xp"+e" if D = 1
Xp0' + Â£01
otherwise
58
where X = {\,y,K_{,s}, piJ ={/3, PÂ¡, pK_r P} and e'J represents the unobservables in
the expenditure equations at rig access levely.5 Presently, j = l because b' is used as the
reference state of rig access. The superscript i corresponds with the binary indicator D
and equals 1 if rigs were used and zero otherwise.
Following Phlips (1983), income is normalized to the own price level and the
intercept and error term for the public good users (/' = D = /) are implicitly defined as
P)' = P','p" + P'p'p0i and e1 V, respectively. These terms are defined similarly for the
nonusers (/ = D = 0). Therefore, prices appear endogenously as a portion of the
unobservable determinants of spending.6 That is, p is not formally defined in terms of a
price index separate from total expenditures. The treatment effects approach can model
prices this way because they are not required in the derivation of welfare measures. This
is useful for reasons discussed in the introduction, especially when dealing with cross
sectional data where price variation is commonly an expression of changes in some other
variable (e.g., distance or quality). The added flexibility is also particularly important
when the public good of interest is defined as a characteristic of a nonmarket activity
(Bockstael and McConnell 1993). In such cases, including the current study, it is easier
to identify the expenditures on the nonmarket activity (e.g., fishing), than to defme the
' I experimented with other functional forms for the expenditure equations such as the
quadratic in income specification consistent with the quadratic almost ideal demand
system. However, as frequently occurs with recreational expenditure data, the income
terms did not come up significant in any specification. Therefore, I opted for the simpler
linear specification with the additive error term. It is easier to derive a linear in variables
net utility function from the linear Engel equation.
6 This specification can be integrated to recover the related indirect utility function
(Hausman 1981) that can be used to specify the form of the related net utility index. In
the Appendix I show that the resulting net utility index can be reduced to a simple linear
in variables equation with an additive error.
59
price and quantity indices necessary to estimate a structural demand model for the
activity.
The full endogenous switching estimating system is
(314)
D' =Gp +eD
(315)
[px + kKT=xp"+en
(316)
[px + kKf =Xp'+e0'
Assuming en', e", and e01 are joint normally distributed, the parameters
lpu,p\pD',crn,G0l,pnD,p0]D j can be estimated simultaneously via maximum
likelihood or in a two step procedure for simultaneous equations with endogenous
switching (Maddala 1983).7 I obtain FIML estimates of the model parameters using the
endogenous switching estimator in LIMDEP (Greene 1995).
As defined in Chapter 2, the standard treatment effect and the policy relevant
treatment effect measures for this model are (Heckman, Tobias and Vytlacil 2001):
(317) ATEkP =E[Ap\y,s^ = X(pu p')
(318) TTkP = E[Ap\y,s,D = \] = X(p" j301) +(crl,Dcr01D)A
(319) TUkP =E[Ap\y,s,D = 0] = x(p" /301) + (ct11dC701D)/T
(320) E[Ap'] = X (p" p01) + (cr,1D' <7010' )[GpD' ]
7 The covariances are easily recovered from the correlation coefficient because the
variance of the index equation is normalized to unity.
60
A" =0(g/3 )/*(g/Â§*), and A01 = <Â¡>(cpr>' 1 O^G/?" )J. Heckman, Tobias,
and Vytlacil (2001) show simple unconditional estimators for each of the four treatment
effect parameters as
(321)
where K is the treatment effect measure of interest and N is the number of observations in
the relevant set, i.e., Nis the whole sample for (317) and (320), only the users for (318)
and only the nonusers for (319). Note that expectation in (320) can be conditioned on
any subset of the sample. For example, evaluating (320) over the set of rig users, gives
the expected treatment effect welfare measure for a randomly chosen individual from this
group. This calculation and a similar one for the group of nonusers is reported in the
results.
Data
The sample for the analysis is taken from the 1999 U.S. National Marine Fisheries
Service Economic Survey of Private Boat Anglers. A subset was selected from the
sample of recreational anglers along the Gulf of Mexico coast (Alabama to Texas). See
QuannTech (2001) for more information about the intercept and phone survey
instruments and the dataset. The surveys elicited detailed information about fishing
location, target species, and expenditures for variable and capital goods. In particular,
respondents were asked to report the number of days that they fished within 300 feet of
an oil or gas rig or within 300 feet of an artificial reef created from an oil or gas rig
during the prior year. This information allowed the sample to be split into a segment that
61
fished at rig sites during the previous year and all other respondents. Brief descriptions
of the coding of the relevant variables appear in Table 3.
Note that nearly half the sample did not report household income. Missing income
values were replaced with the mean reported value from the respondents county of
residence. There was also missing trip cost data. The portion of the sample who took
Table 3. Sample means and standard deviations for rigs model variables
Variables
Users (n=372)
Nonusers (n=124) All (n=496)
Cost of a Rig Trip ($)
89.978
96.932
92.375
(52.181)
(18.280)
(43.685)
Cost of a Nonrig Trip ($)
153.470
52.435
118.637
(455.607)
(64.946)
(373.736)
Cost Difference for Rig Trip ($)
63.492
44.497
26.262
(456.379)
(63.740)
(374.720)
Total Fishing Trips
29.628
25.514
28.210
(31.769)
(42.623)
(35.878)
Rig Fishing Trips
14.241
0.000
9.332
(19.572)
(0.000)
(17.226)
Total Variable Expenditures ($)
3,406.087
1,351.461
2,697.739
(7,427.224)
(3,734.135)
(6,469.534)
Total Annual Expenditure ($)
7,602.246
2,512.929
5,847.666
(14,137.100)
(4,854.344)
(12,033.485)
Current Capital Stock ($)
11,138.121
5,045.676
9,037.705
(17,584.240)
(7,352.223)
(15,145.725)
Capital Stock Lagged ($)
6,941.962
3,884.208
5,887.778
(14,078.927)
(6,859.418)
(12,166.827)
Standard deviations in parentheses. Table continued below.
62
Table 3. Sample means and standard deviations for rigs model variables (cont.)
Variables
Users (n=372)
Nonusers (n=124)
All (n=496)
Income ($/yr)
65,863.024
60,782.662
64,111.531
(34,709.303)
(23,628.382)
(31,400.900)
Experience (years)
23.994
22.077
23.333
(14.314)
(16.159)
(14.983)
Gender (l=female)
0.082
0.113
0.092
(0.274)
(0.318)
(0.290)
Memberships (l=yes)
0.184
0.113
0.160
(0.388)
(0.318)
(0.367)
Louisiana Resident (l=yes)
0.322
0.444
0.364
(0.468)
(0.499)
(0.482)
Mississippi Resident (l=yes)
0.093
0.162
0.117
(0.290)
(0.370)
(0.321)
Texas Resident (l=yes)
0.231
0.225
0.229
(0.422)
(0.419)
(0.420)
Coastal Resident (l=yes)
0.919
0.911
0.916
(0.273)
(0.287)
(0.277)
Target Rig Species (l=yes)
0.262
0.062
0.193
(0.440)
(0.241)
(0.395)
Standard deviations in parentheses.
both rig and nonrig trips had missing data because the intercept data only reflects one of
these type of trips. Similarly, those who did not take a rig trip had no expenditure data
for this type of activity. The missing trip cost values were replaced with the mean values
over only rig users in the relevant Gulf State in order to avoid mixing across the rig and
nonrig groups. The replacement procedure is summarized in Table 4.
63
Table 4, Replacement rules for missing variable cost data
At least one rig trip in the previous 12 months?
YES (1)
NO (0)
Took a rig
trip when
intercepted?
YES (1)
Cost of a rig trip = VCÂ¡ j
Cost of nonrig trip = VCoi
(218)
Not Possible
(0)
NO (0)
Cost of a rig trip = VCw
Cost of nonrig trip = VC01
(154)
. stat*
Cost of a rig trip = VCw
Cost of nonrig trip = VCoo
(124)
The summary statistics in Table 3 are split into two subsamples: those anglers
who fished at rigs (users) in the previous year and those who did not (nonusers). The
socioeconomic characteristics reported are fairly consistent across the sample. The key
differences between the two subsamples arise with respect to the economic decision
variables such as trip costs, expenditures, capital stock holdings, and rig species targeting.
Specifically, a rig trip costs relatively more than a nonrig trip for nonusers. The
converse is true for users suggesting that each group has an absolute advantage in their
O f
chosen activity. Each group also appears to have a comparative advantage in their
chosen activity. However, cost savings per trip is only part of the story. Advantages
cannot be fully studied without reference to each groups willingness to pay for rig and
nonrig fishing. This premise is explored in the results, although, the differences in
annual fishing expenditures and capital stock of the two groups in Table 3 is suggestive.
x The terms absolute and comparative advantage are commonly used in the labor
supply literature. For example, when based on earnings, either advantage can be used to
explain the type, variety, or location the of labor selected by an individual (Emerson
1989; Maddala 1983). In the case of recreational angling, the advantages are measured in
terms of (utility constant) cost savings for different types or locations of fishing.
64
The pooled site travel cost model is estimated using the number of annual fishing
trips to rigs as the dependent variable. Independent variables in this regression include
the variable cost of a rig trip, the variable cost of a nonrig trip, the stock of fishing
durables at the beginning of the year (capital stock lagged), household income and other
control variables. The cost of rig and nonrig trips is defined as any personal spending by
the respondent for the trip on which they were intercepted. A list of spending categories
included in variable trip costs is shown in Table 5. Note that the opportunity cost of time
is not included among the variable cost items. Time costs are not considered in the
present analysis.
Table 5. Spending included in the variable and capital fishing expenditures
Variable
Capital
travel
boat
lodging
motor
food
trailer
drink
electronics
boat fuel
safety gear
boat rental
rigging for fishing
dock fees
boat or equipment repairs
launch fees
rods and reels
repairs and towing on trip
fishing line
bait
lures and artificial bait
special licenses for trip
other fishing equipment
tackle and guide services
fishing books and magazines
equipment rental
fishing club memberships
special clothing
camping equipment for fishing
film, sundries, and souvenirs
fishing licenses
Two treatment effects models are estimated as defined in (314)(316). The first
uses annual variable trip rig and nonrig trip expenditures as the dependent variable in the
outcome equations in the treatment effects switching regression. These variables are
65
calculated by multiplying the respondents rig (nonrig) trip expenditures by their total
number of annual rig (nonrig) trips. The second treatment effects model uses total
annual expenditures calculated by adding the additions to capital stock during the year to
the annual variable expenditures. Spending categories included in the capital measures
are listed in Table 5.
The other control variables, as well as the variables used in the rig use selection
equation, are listed in the results. One variable of note, however, is the decision to target
rigs species. This variable is coded 1 if the respondent indicated a target preference for
species that are commonly associated with oil and gas rig habitat. The means for the
target variable indicate that a larger portion of those who fish at rigs also target rig
species. This introduces the potential modeling issues associated with multiple criteria
for selectivity (Maddala 1983 pp. 278283). In the recreational fishing demand literature
the relevant questions concern, for example, whether anglers choose a species target and
fishing location sequentially or simultaneously and, if sequentially, in what order (Kling
and Thomson 1996). I will assume that the process is sequential and the target decision
is made first by using a binary target variable as a regressor in the rigs decision equation.
The target variable also serves as the exclusion restriction necessary for the index
function setup (Heckman and Vytlacil 2001a).
Results
Travel Cost Model
The travel cost count model estimation results are shown in Table 6. Three
variables are significant in the rig use decision equation. Mississippi residents are less
likely to fish at rigs compared to anglers from other states and those who target species
associated with rigs are more likely to fish rigs. The negative coefficient on the cost
66
difference variable suggests that higher relative rig costs decrease the probability of
fishing rigs.
A number of the parameters in the trip demand equation are significant. Those
with higher capital stock at the beginning of the year tend to take relatively more rig trips.
Those living near the coast, residents of Mississippi and Texas, and members of fishing
clubs are also take relatively more rig trips.9 Females, Louisiana residents, and
individuals with more experience take less rig trips. Those with higher income also
appear to take less rig trips, suggesting a negative income effect. However, given the
measurement problems with the income variable, this result is not especially troubling.
The own price variable (cost of a rig trip) is negative, but not significant, whereas,
the substitute price term (cost of a nonrig trip) is significant and positive. The latter
result implies that rig and nonrig fishing trips are substitutes. Although not significant,
the inverse of the own price coefficient gives an expected consumer surplus per trip of
$4,442. See equation (39). Multiplying this value by the expected trips as shown in
Table 7 gives an expected annual uncompensated surplus of rigs fishing of $37,824.
Adjusting for income effects using expression (310), the corresponding expected annual
compensating variation is lower, but still very high, at $27,569. The standard deviations
shown in the table were obtained by evaluating the measures for each individual in the
sample.
The variance of the extra stochastic term in the PoissonNormal model is
significant, indicating that there is unobserved heterogeneity influencing the trip decision.
9 Residents of Alabama are the base case when all other State dummy variables are equal
to zero.
67
Table 6. Estimates for the Poissonnormal travel cost model with selectivity
Variables
Rigs Decision
Trip Demand
Constant
2.63E01
1.49E+00
(3.12E01)
(1.97E01)*
Cost of a Rig Trip ($)
2.25E04
(2.91E04)
Cost of a Nonrig Trip ($)
2.25E04
(7.53E05)*
Cost Difference for Rig Trip ($)
3.86E03
(8.9 IE04)*
Capital Stock Lagged ($)
1.10E05
1.67E05
(8.26E06)
(1.45E06)*
Income ($/yr)
3.86E07
3.42E06
(2.52E06)
(6.20E07)*
Experience (years)
4.64E03
7.84E03
(4.19E03)
(1.91E03)*
Gender (l=female)
1.69E01
2.83E01
(2.13E01)
(1.23E01)*
Memberships (l=yes)
2.93E01
5.20E01
(1.79E01)
(5.25E02)*
Louisiana Resident (l=yes)
1.08E01
2.66E01
(1.95E01)
(5.71E02)*
Mississippi Resident (l=yes)
5.07E01
2.32E01
(2.84E01)*
(6.69E02)*
Texas Resident (l=yes)
5.22E02
1.60E01
(2.15E01)
(6.24E02)*
Coastal Resident (l=yes)
8.37E02
6.19E01
(2.08E01)
(1.77E01)*
Target Rig Species (l=yes)
7.64E01
(2.73E01)*
0mps
9.55E01
(3.08E02)*
selection,trips
5.46E01
(2.59E01)*
^selection.trips
5.22E01
(2.59E01)*
Standard errors are shown in the parentheses below each estimate.
*Estimate significant at the 0.10 level.
The final value of the log likelihood function is 1603.968.
68
In addition, the correlation and covariance between the rig use and trip count decisions
are significant suggesting that selectivity is present as modeled.
Table 7. Count model welfare analysis for loss of rigs access
Mean Actual Rig Trips
Expected Rig Trips
Expected Annual Compensating Variation
Expected Annual Consumer Surplus
Standard deviations shown below the means.
Treatment Effects Models
The FIML estimated coefficients of the treatment effects model (TEM) with annual
variable expenditures and total annual expenditures are shown, respectively in Table 8
and Table 9. The signs and levels of the significant coefficients in the rigs decision
equations are roughly consistent with those estimated in the selection equation of the
travel cost model (TCM).10 Again, those who target rig species are more likely to fish at
rigs and the level of existing capital stock is not a significant influence on the probability
of fishing at rigs. Mississippi residents are less likely to fish rigs than Texas and
14.24
(19.57)
8.51
(7.38)
27,569
(12,850)
37,824
(32,784)
10 The coefficients between TCM count demand estimates and the TEM users
expenditure equation are not directly comparable because they each measure influence on
a different dependant variable.
69
Table 8. Annual variable expenditures treatment effects model results
Variables
Rigs Decision
With Rig Use
Without Rig Use
Constant
1.21E01
3.07E+03
4.57E+03
(3.83E01)
(2.52E+03)
(9.31E+03)
Capital Stock Lagged ($)
1.45E05
8.37E02
4.58E02
(9.99E06)
(2.73E02)*
(1.18E01)
Income ($/yr)
1.99E06
8.59E03
1.30E02
(2.67E06)
(1.74E02)
(3.05E02)
Experience (years)
5.52E03
5.64E+01
1.99E+01
(4.47E03)
(4.38E+01)
(5.12E+01)
Gender (l=female)
1.71E01
2.16E+03
1.71E+03
(2.18E01)
(2.35E+03)
(2.52E+03)
Memberships (l=yes)
2.63E01
2.36E+03
7.58E+02
(1.94E01)
(1.33E+03)*
(2.55E+03)
Louisiana Resident (l=yes)
3.99E01
4.18E+01
2.17E+02
(1.95E01)*
(2.33E+03)
(3.71E+03)
Mississippi Resident (l=yes)
6.35E01
1.13E+04
1.65E+02
(2.78E01)*
(1.76E+03)*
(4.83E+03)
Texas Resident (l=yes)
2.69E01
1.31E+03
1.92E+03
(2.35E01)
(2.18E+03)
(2.96E+03)
Coastal Resident (l=yes)
1.08E01
2.54E+02
2.21E+03
(3.26E01)
(1.55E+03)
(1.55E+03)
Target Rig Species (l=yes)
8.13E01
(2.78E01)*
^expend
6.50E+03
3.56E+03
(1.78E+02)*
(9.81E+02)*
pSelection.expend
4.73E02
1.59E01
(3.89E01)
(2.29E+00)
^selection, expend
5.66E+02
4.25E+06
(8.31E+03)
(6.77E+06)
Standard errors are shown in the parentheses below each estimate.
*Estimate significant at the 0.10 level.
The final value of the log likelihood function is 5244.391.
70
Alabama residents. The same is true for Louisiana residents which is somewhat
surprising given that the majority of petroleum platforms are located off the coast of
Louisiana.
Only five of the estimates in the annual variable expenditure outcome equations are
appreciably significant and most of these coefficients are for the Rig Use equation. A
similar pattern appears for the total annual expenditure outcome equations. Interestingly,
the existing level of fishing capital has a positive influence on annual variable
expenditures, but not on total annual expenditures. Based on the TCM results in Table 6,
the additional spending arises because those with larger fishing capital stocks take
relatively more rig trips. However, it appears that these individuals are not any more
likely to add to capital stock throughout the year than those with relatively smaller capital
stocks. Those with paid memberships to fishing clubs and residents of Mississippi tend
to spend more on variable and capital costs for rig trips.
The estimated variances of all the spending outcome equations in Table 8 and Table 9 are
significant, indicating the importance of unobserved heterogeneity in this sample.
However, because of relatively insignificant correlations, the covariances between the
rigs decision and spending equations are not significant. This suggests that there is a
limited degree of selfselection based on rig use in the sample. To use the analogy from
the labor literature (Emerson 1989), the lack of significant covariance between the use
and spending decisions implies that neither group has an absolute advantage in their
selected option. In the present application, an individual has an absolute advantage in
their chosen activity if that activity offers them a significantly lower cost for utility than
competing activities. For example, those with an absolute advantage for rig use can
71
Table 9. Total annual expenditures treatment effects model results
Variables
Rigs Decision
With Rig Use
Without Rig Use
Constant
1.20E01
1.09E+04
6.51E+03
(3.61E01)
(4.59E+03)*
(6.34E+03)
Capital Stock Lagged ($)
1.44E05
1.60E02
8.18E03
(8.96E06)
(6.42E02)
(8.37E02)
Income ($/yr)
2.06E06
2.00E02
1.28E02
(2.66E06)
(2.49E02)
(3.48E02)
Experience (years)
5.45E03
9.49E+01
2.31E+01
(4.59E03)
(6.98E+01)
(5.17E+01)
Gender (l=female)
1.59E01
3.81E+02
2.48E+03
(2.20E01)
(3.24E+03)
(2.21E+03)
Memberships (l=yes)
2.60E01
4.55E+03
3.21E+03
(2.16E01)
(2.25E+03)*
(2.19E+03)
Louisiana Resident (l=yes)
3.94E01
2.32E+03
1.73E+03
(1.92E01)*
(3.31E+03)
(2.35E+03)
Mississippi Resident (l=yes)
6.31E01
2.26E+04
1.51E+03
(2.69E01)*
(2.38E+03)*
(3.09E+03)
Texas Resident (l=yes)
2.68E01
1.61E+03
6.60E+02
(2.25E01)
(2.95E+03)
(2.51E+03)
Coastal Resident (l=yes)
1.02E01
3.64E+03
1.21E+03
(2.80E01)
(3.15E+03)
(1.89E+03)
Target Rig Species (l=yes)
8.24E01
(2.51E01)*
^expend
1.22E+04
4.66E+03
(4.43E+02)*
(6.15E+02)*
pSelection, expend
1.08E01
1.88E01
(3.29E01)
(9.01E01)
^selection,expend
1.32E+03
8.78E+02
(4.05E+03)
(4.30E+03)
Standard errors are shown in the parentheses below each estimate.
^Estimate significant at the 0.10 level.
The final value of the log likelihood function is 5494.606.
72
can attain the same level utility at a lower cost by using rigs than by not fishing at rigs. A
similar condition applies for those who chose not to use rigs. The weaker condition of
comparative advantage implies that the average user (nonuser) spends less for the same
utility level than the average nonusers (user) when they both (do not) use rigs. A null
hypothesis of no comparative advantage can be evaluated with a joint test of 3M = [301 and
GIID = O01D. The Wald statistics of 59.21 and 135.06 for these restrictions in the variable
and total expenditures models, respectively, rejects joint equality with greater than 99%
confidence. Thus, there is still significant information in the rig use (selfselection)
decisions of anglers in the sample that can be used to evaluate the relative valuations of
rig access. The treatment effect welfare measures introduced in Chapter 2 are designed
to exploit this information.
The unconditional treatment effects and welfare measures of rig access are shown
in Table 10. These figures are obtained by evaluating expressions (317) through (320)
for each individual in the relevant group and averaging as defined in (321). Note that
even the largest measure shown in this table is still less than a third of the values shown
in Table 7 for the travel cost model. The relatively large welfare measures in the travel
cost model are due primarily to the small coefficient estimated on the travel cost
parameter. As described in Chapter 2, the price variable is crucial in welfare analysis
with the travel cost model. The treatment effects model sidesteps this reliance by using
information from all of the model coefficients to generate welfare measures. However,
more research is need on ways to analytically and empirically compare the travel cost
and treatment effects approaches.
73
Table 10. Annual expenditure treatment effects and welfare estimates of rig access
Parameter
TEA Variable Costs
TEA Total Costs
ATE
1,737
4,950
(3,906)
(8,131)
E[CV]
2,141
5,968
(3,861)
(7,926)
TT
1,101
3,264
(3,570)
(7,276)
E[CV  users]
2,054
5,659
(3,591)
(7,268)
UT
2,945
8,156
(4,377)
(9,158)
E[CV  nonusers]
2,308
6,556
(4,339)
(9,047)
Standard deviations shown below the estimates.
The average treatment effect and the policy relevant measure of compensating
variation of lost rig access for the whole sample are shown in the first pane. A randomly
selected angler will spend an additional $1,737 in variable costs annually to fish rigs.
This amount more than doubles to $4,950 when expenditures on fishing capital is
included. The randomly chosen individual is willing to pay between $2,141 and $5,968
annually for access to rigs for fishing where the upper end measure includes forgone
capital spending. A randomly chosen angler from the group that used rigs is willing to
pay between $2,045 and $5,659 annually and has an expected annual cost for rig fishing
of between $1,101 and $3,264. Similarly, a randomly chosen angler from the group
anglers who did not use rigs is willing to pay between $2,308 and $6,556 annually and
has an expected annual cost for rig fishing of between $2,945 and $8,156.
74
The results in Table 10 are in line with model checks proposed in Chapter 2. For
users the expected compensating variation of use is considerably greater than the
spending difference measure. This is consistent with a preference for rig use, but it also
implies that users have a lot to loose if they are denied access to rigs. The nonuser results
show an expected compensating variation that is less than the extra annual costs of rig
use. This explains way this group does not fish at rigs. Interestingly, though, a randomly
selected nonuser actually has a relatively higher value for rig access than a randomly
chosen user or a randomly chosen individual in the sample. This is true of the variable
cost and total cost results. Thus, nonusers value rig access, but do not fish at rigs because
doing so requires a relatively more expenditure, especially when additions to fishing
capital are considered. These results illustrate that nonusers do not use rigs because the
benefits are less than the cost. As for the rest of the sample, the results in the first pane of
Table 10 indicate that a randomly selected individual will choose to use rigs because the
benefits do outweigh the costs. The statistical significance of these measures was not
tested directly, but the rejection of joint equality in the comparative advantage test is
suggestive. Note also that, although not shown, all of the consistency tests are met at the
minimum and maximum values of the sample.
Discussion
This chapter has explored the role of capital expenditures in revealed preference
modeling of recreation decisions. The treatment effects approach developed in Chapter 2
was used to evaluate the welfare effects of restricting access to fishing at petroleum rigs
in the Gulf of Mexico. A travel cost trip demand model was also estimated.
Based on the treatment effects model, the artificial fishing habitat offered by
petroleum rigs was found to cause a $1,737 to $4,950 increase in average annual fishing
75
expenditures among anglers in the sample. The amount that a randomly chosen angler
would be just as welloff without rigs is estimated ranges from $2,141 to $5,968. The
upper end of the range is the welfare effect including the additions to fishing capital.
These estimated values are substantially lower than the welfare measures generated with
the travel cost model. This is peculiar result could be because of the sensitivity of travel
cost welfare measures to when costbased prices are used (English and Bowker 1996;
Wilman and Pauls 1987).
The variation in the treatment effects model measures suggests that not considering
information about recreation capital acquisitions and holdings could seriously understate
the opportunity cost of restricting access to fishing at rig habitat. The results suggest a
need to consider ways to incorporate recreation capital in other revealed preference
valuation exercises.
CHAPTER 4
APPLICATION TO PUBLIC UTILITY PRICING
If a rational consumer does not know the price of a purchased commodity, then he
cannot optimally adjust budget allocations and marginal valuations to be in line with that
price.1 When prices accurately reflect social opportunity costs (as in a perfectly
competitive market), the burden of price misperception is on the consumer. That is,
following Shins (1985) hypothesis, the consumer accepts the inefficiencies from price
misperception in return for the avoided cost of determining the actual price. On the other
hand, when prices do not accurately reflect social opportunity costs, then price
misperception and the suboptimal consumption levels have welfare implications beyond
the consumers budget allocations. Classic cases of deviations from socially optimal
prices can occur, for example, in the presence of externalities and/or in the context of
administered prices for monopoly services (Carter and Milon 1998).
This chapter develops analytical and empirical models to evaluate price
misperception and the value of price information for the case of administered prices for
public utility service. In doing so, the focus is on the consumers selfreported price
awareness. This perspective is more fundamental than the studies that have used data
across utilities to examine the effect of different levels of information provision and rate
structure style on the quantity of public utility service demanded. See Cavanagh
Hanemann and Stavins (2001) for a review. The perspective is closer to the large body of
1 In the case considered here the consumer can choose not to know the price even though
this information is available with certainty. This is different than the case of choice under
irreducible price uncertainty (Johnansson 1991).
76
77
research debating the correct price specification in models of demand in the presence of
nonlinear budget constraints (i.e., block pricing).2 The portions of this research that have
attempted to empirically test a consumers perception of the price of service is of central
interest (Chicoine and Ramamurthy 1986; Griffin and Chang 1990; Nieswiadomy 1992;
Nieswiadomy and Molina 1991; Shin 1985). This chapter extends this research by
providing a theoretical framework to analyze the comparative statics of price
misperception and identifies the value of complete price knowledge. Importantly, this
framework considers the possibility that price elasticity of demand may change when
price perception changes because of changes in exogenously supplied price information.3
The theoretical framework is used to develop a structural model of public utility
demand and a treatment effects model of expenditures on utility services. Both models
are based on the discussion of structural and treatment effects approaches to measuring
public good values in Chapter 2. Exogenously supplied information about the price of
utility service is the public good in this case. The results from the structural and
treatment effects models are used to evaluate the benefits of a hypothetical program that
would fully inform customers about the price of service.
Price Perception and the Value of Price Information
The welfare implications of price misperception with administered prices depend
on the goals of the pricing authority (e.g., public utility) and the relative abilities of the
authority and the consumer to accurately gauge the social opportunity cost of
2 Witness the lively exchanges in Land Economics among Foster and Beattie, Griffin et.
al., Opaluch, Charney and Woodard, Billings and Agthe, Ohsfeld, Polzin and Stevens et
al. in the early 1980s and subsequent literature that continued throughout decade in that
journal and Water Resources Research.
3 Shin (1985) considers the value of price information for the case where the consumer
overestimates the actual price. However, his representation implicitly assumes that the
response to price changes is the same regardless of the consumers information set.
78
consumption. If the pricing authority aims to set prices to reflect marginal opportunity
costs and/or they have explicit conservation goals, then they should also be concerned
that these prices are perceived accurately. Furthermore, when the authoritys
administered price reflects the social opportunity cost of service more accurately than the
consumers perceived price, the authority can use price information as a policy tool. This
follows because the relative costliness of a consumers price information is partly a
function of the amount of exogenously supplied information (e.g., advertising). The
exogenously supplied price information is not itself sold in the market because, like
advertising in general, it has public good characteristics that may favor other indirect
financing schemes (Freeh 1979).
Consider an consumer who perceives the price of a commodity Q as a function
p(p,b) of the actual price p and an exogenous information supply b such as advertising
or billing inserts that is available to all consumers.4 It is assumed that b is a weak
complement of Q so that the consumer is indifferent to the supply of b when Q is not
purchased (Maler 1974). This implies that b is not a direct source of utility (i.e., b has no
nonuse value) and, therefore, does not appear as a separate argument in the indirect utility
function. Note that the distinction between p and p roughly corresponds to Poliaks
(1977) conception of normal and market prices. In this case, p is a normal price signal
that affects choices, whereasp is the market price that enters the budget constraint. This
situation is exceedingly complicated to represent as a direct utility maximization problem
4 As long as the consumers are price takers (e.g., subject to administered prices) the
analysis can continue in a partial equilibrium framework. In other cases, however, a
general equilibrium treatment is required because the equilibrium price will be an
(inverse) function /?(p,6)of the existing perceived price(s).
79
so only indirect utility and expenditure function representations of preferences are
considered.
An accurate price perception is costly to the consumer so that c{b)> 0, but this cost
decreases with the level of the exogenous price information provided, dc(b)/db< 0 ,5
The conditional indirect utility function for this problem is
(41) v(p(p,b),yc(b),s,e)
where s is a vector of observed individual control characteristics and e summarizes the
unobserved individual preferences and characteristics. The price index of a numeraire
commodity is normalized to unity and is suppressed along with individual specific
subscripts to simplify notation.
The marginal value of a change in the supply price information has two effects:
dy dc (dv/dp)(dp/db)
db db dv/d(y c(b))
where the first term on the right hand side is the reduction in the cost of an accurate price
perception and the second term is the value of the change in price perception induced by
the additional information.
To carry the analysis a step further, assume that the perceived price function takes
the form p(p,b) = p b for b = (0, so]. The perceived price is assumed proportional to
the actual price by an adjustment factor b that summarizes the stock of exogenous price
information. The perceived price is bound below to be greater than zero because the
5 There have been attempts to explicitly consider the costs of price information search
(Kolodinsky 1990). The more compact representation suffices for present purposes.
80
ost
consumer will likely recognize a nonzero price if they are spending income on the
commodity.
There are three cases to consider: (a) b = 1, (b) b > 1, and (c) 0 < b < 1. In the first
case, the perceived price equals the actual price, i.e., the consumer is fully informed
about price. In terms of the expression (42) above, the first case suggests that the
additional information will not affect those who already know the price, beyond the
reduction the cost of additional price information. The second case indicates a perceived
price that is greater than the actual price and the third case indicates a perceived price that
is less than the actual price. In the latter two cases the price misperception is leading to
over or under consumption of the commodity Q relative to the composite commodity.
This is most directly shown by differentiating the expenditure function for this problem
by the actual price of Q
(43)
de(p(p,b),u,s,e)
dp
de dp
dp dp
where e() gives the minimum expenditure required to attain utility level u. Noting that
(43) is an expression of the compensated demand Qf for Q we can rearrange to get
(44)
Ip Ij = (p(p'b)usÂ£)
de Qc (p{p,b),u,s,Â£)
dp dp/dp
_ Qc [p(p,b),u,s,e)
b
for
p(p,b) = pb.
Thus, in the second (third) case where the perceived price is above (below) the actual
price, the efficient compensated demand will be deflated (inflated) by dp/dp or b so that
the consumer will be under (over) consuming O.
81
To consider the value of a discrete change in price information it will be useful to
explicitly define the conditional indirect utility function in terms of the decision to know
the price
(45) / = v(i,p(p,6'),/,i,e)
where i equals 1 if the price is known and 0 otherwise given the supply of price
information t and conditional income is defmed in terms of the cost of price information
as / = y c(i,t). The consumer will choose to know the price if
(46) D1' = vly voy > 0 .
where D* is defined as a latent variable that indexes the net utility of knowing the price
given the available price information. Table 11 shows the four possible indirect utility
outcomes for a discrete change in the supply of price information from b1 to b. The
analysis in this chapter focuses on the special case where b is the level of price
information that ensures everyone will know the price. In this case, cell (2, 2) in Table
11 is irrelevant because everyone will know the price after the change in price
information.
The compensating variation (CV) of a discrete change in the supply of price
information from b1 to the level b that generates accurate price perceptions is6
6 In general, the CV of a discrete change in the supply of price information from b1 to b
is given by
CV(b',b0) = e(p(p,b'),v,',s,e)e{p(p,b0)y',s,e).
This formulation is general because p(p,b) does not necessarily equal the actual price.
Thus, an individual may chose to know the price in either state of the world and can
switch from not knowing to knowing or vice versa following the change in the price
information.
82
lito
DOW
on
(47)
CK(A1,fc0) = c(p(p,i,),v,,,i,Â£)
= pQ(f>(Pb' pQ{p's.e)
where perceived price equals the actual price with the information level b so that
p = p (/?, b11). In this case of perfect price information the individual may or may not
know the price before the change in price information, but after the change they will
know the price. The CV measure can be recovered from observed expenditure patterns
before and after the change. When there is no data available for behavior after the
change in price information these outcomes must be simulated where needed. In this
case, observations related to cell (2, 1) in Table 11 are not available so this information
must be inferred from the data on behavior with the reference supply of price information
(row 1). Chapter 2 reviews approaches to recovering welfare measures in this case. Two
approaches are described and applied following the discussion of the value of price
information.
Table 11. Utility outcomes with price knowledge and information change
CHOOSE TO KNOW PRICE?
YES (i=l)
NO (i=0)
CHANGE IN
PRICE
INFORMATION
BEFORE
(j=D
v(l,p(p.fr1).yl,s,e)
v(0,p(p,b'),yol,s,Â£)
AFTER
0=0)
v(l ,p(p,b),y'0,s,e)
v(0 ,p(p,b),yw,s,e)
The value of price information is shown in Figure 4 and Figure 5 for the second
and third cases of price perception, respectively, for the assumed form of p(p,b) = pb
There are two compensated demands shown in each figure indicating that the slope and
83
position of a demand curve depend on the available price information. Specifically,
differentiating the compensated demand function with respect to the actual price p writes
an expression for the slope of the demand curve in actual price/quantity space
dQc dQc dp
(48)
dp
dp dp
dp
b forp{p,b) = pb
Thus, the slope of the perceived price demand curve will differ from the slope of the
actual demand curve by a factor relating the perceived price to the actual price. Those
who know the price can respond differently to the same change in actual price than those
without price information. Note that total change in uncompensated demand with respect
to a change in perceived price is manifest in the substitution effect
(49)
dQm dQc
dp dp
JQL
dp
dÂ£T
dy
'dpA
\dP J
30Iff
dy
Q"
forp(p,b)=pb
where (X is the uncompensated demand for Qj
For the first case noted above (b 7), the slopes of the perceived and actual price
a
demand curves are the same. Figure 4 illustrates the second case (b > 1), where the
consumer overestimates the actual price and the slope of the perceived price demand
curve is greater than the slope of the actual price demand curve. Area A measures the
value of price information (i.e., of a change in price perception) in (47). If more
7 The version of the Slutsky equation in expression (49) is derived as shown in Varan
(1992 p. 120), starting from compensated demand function with the perceived price
argument. Only own price effects are illustrated, but these effects represent changes in
relative value since, from above, the own price and income terms are normalized on a
numeraire good.
84
s
Figure 4. Value of price information: perceived price greater than actual price
Figure 5. Value of price information: perceived price less than actual price
85
information about the price changes price responsiveness, then perfect price knowledge
would have an additional value equal to area B. In other words, a measurement of the
value of price information that incorrectly assumes no change in behavior would
overstate the true value for the second case. Figure 5 describes the third case (0 < b < 1),
where the consumer underestimates the perceived price and the slope of the perceived
price demand curve is less than the slope of the actual price demand curve. The value of
price information in this case is shown as areas C and D. Note again that incorrectly
assuming no change in behavior provides misleading welfare measures; in this case the
value of price information would be understated.
Empirical Models
Households will chose to know the true price if the net benefit of doing so is non
negative, but the point at which an individual household will choose to do so is generally
o
unknown. Two public good valuation approaches described in Chapter 2 are applied
here to infer the net benefit of price knowledge from observations on individual behavior.
The first approach uses information from an estimated structural demand equation for
public utility services to recover the welfare areas as shown in Figure 4 and Figure 5.
The second approach adapts techniques from the program evaluation literature to
calculate treatment effect welfare measures from household expenditure patterns. Both
approaches use an index function to model the decision to know the price of service
(410)
D=nD (g)+Â£d = 
1 if D1' > 0
0 otherwise
8 The empirical section of the chapter refers to the decision unit as a household rather
than a consumer to be consistent with the case study data.
86
where //0(*) is a function of a vector G of observed random variables that affect the
decision to know the price and tJ) is an unobserved random variable that represents the
relevant portions of e. Note that D1 is the latent net utility variable in (46) so this index
function summarizes an individuals preferences over the decision to know the price or
not.
Water Demand Model
Following Hanemann (1984a) the observed quantity of public utility services
demanded before the price information change can be represented as
(411)
Q(p(p,b'),y,s,e)
5v''/,dp (p,b') if D' =\
dv0'/dp(p,b'} otherwise
Q(p(p,b'),y\s,e) if D[ = 1
Q [p (p,b' ),y" ,s,f) otherwise
With consistent specifications for the demand equation Q{ )and the observable portion of
the index equation//Â£>(), this model can be estimated as a switching regression before the
change in price information (Maddala 1983).9 The results can then be use to simulate the
welfare measures defined in Figure 4 or Figure 5. However, another wellknown
estimation issue arises with public utility services where quantity and marginal price are
determined simultaneously with block rate pricing structures.
Ideally, estimation in this context should proceed with techniques that also consider
the simultaneity of the discrete block choice and continuous quantity choice decisions
9 If the decision to know the price is not correlated with consumption decisions then OLS
can be used to estimate separate demand equations for those who know and those wrho
don't know. Otherwise, a technique to correct for endogenous sample selection must be
used to get unbiased estimates of the parameters in the two demand equations. I
hypothesize that the two decisions are, in fact, correlated and propose a general model of
endogenous switching to estimate the demand equations for the two regimes.
87
(Cavanagh, Hanemann and Stavins 2001; Hewitt and Hanemann 1995; Reiss 2001;
Rietveld, Rouwendal and Zwart 1997; Terza and Welch 1982).10 I opt for a simpler
approach, following Agthe et al. (1986) and Chicoine, Deller and Ramamurthy (1986), in
specifying price and quantity equations as a system of simultaneous linear equations.11
There is a cost associated with linearizing the budget constraint in this manner (Maddock,
Castao and Vella 1992), but I choose this approach to keep the analysis manageable and
to maintain the focus on the selfselection related to price knowledge.
Recognizing that the actual price and quantity are jointly determined with block
rate pricing, the model in (410) and (411) can be respecified as a simultaneous
equations model with endogenous selectivity (Lee, Maddala and Trost 1980):
(412)
(413)
(414)
D' =GS +eD
P" =couH + (pn?in+vn
Q"=Q(p(P'\b'),y",S) + p"V'+e
P' =comH+
Qm=Q(p(P',bl),ym,s) + pm r+e
01
if D'= 1
if D'= 0
where V1 and 1 are the jointly normal error terms in the price and demand regressions,
1 9
respectively. The model consists of five estimating equations. First, the binary
indicator variable Dl is used as the dependent variable in a probit regression on G to yield
10 Although one might question the applicability of estimation frameworks that precisely
model the choices with nonlinear budget constraints when consumers are not fully aware
of the rate schedule and their use levels. These approaches assume that consumers have
enough information to simultaneously choose or act asif they are choosing the efficient
block to consume in and the level to consume within the block.
11 The studies of water demand using instrumental variable techniques also follow this
general approach (Deller, Chicoine and Ramamurthy 1986; Jones and Morris 1984).
12 The general form of Q( ) is maintained to simplify the notation. The exact form of the
demand equations to be estimated is presented below.
88
the estimated parameter vector . Following the standard procedure for twostage sample
selection models, the predicted values of the probit equation are used to compute
)iln A" =(G)/(G) and A01 = 0(g<5)/[ 1 o(c)]
1 # # w *
for those who know (D = 1) the price and those who dont know (D = 0) the price,
lc^ respectively. The inverse Mills ratio variables A,'1 are included as regressors along with
the vector H of explanatory variables in the two price equations. The regression produces
the estimated price equation coefficients co'1 and ip'1 for each group. Note that the ip'1
parameter is a measure of covariance between the price information decision equation
and the price equation. A test of statistical significance for
information decision is endogenous with respect to the (linearized) price choice decision.
The choice of the variables H for the price equations is somewhat arbitrary since these
expressions serve as crude approximations of the true discrete relationship between price
and quantity. 1 use the specification of Terza (1986) and Nieswiadomy and Molina
(1989) that forms H with the exogenous variables in Q( ) and the prices that a given
household would face at four different levels of monthly (water) consumption (6000,
12000, 18000, and 24000 kgals). Finally, the predicted prices Pl are used along with/'7
in estimation of the two demand equations to produce the estimated coefficients and p'1
for each group. Like
information decision equation and the demand equation. A test of statistical significance
for p1' indicates whether the price knowledge decision is endogenous with respect to the
demand decision. The estimation of equations (412) through (414) will produce
consistent estimates of the parameters in the demand equations and can be executed
easily with a procedure shown in Greene (1995 pp. 64344).
89
The empirical specification of the Q( )and P functions used were developed by
Shin (1985) to measure price perception among utility service customers. The perceived
price p is defined as a function of lagged average price, AP,.], marginal price, MP, and a
price perception parameter k such that
(415)
P = MP
MP
which, implies that the stock of exogenously supplied price information is a function of
the actual price p = MP and the previous periods average price of service. As
constructed, the value of the perceived price variable depends on the parameter k: if the
consumer only responds to marginal price, then k = 0, and if they only respond to lagged
average price, then k = 1. Values for k between zero and one imply that the perceived
price is between marginal and average price, while values outside of this range suggest
that the consumer is responding to some other price level.
In doublelog form, the partial adjustment14 model estimated by Shin (1985) and
Nieswiadomy and Molina (1991) appears as:
Ln(Q)= a + Ln(Qt_x)(\0) + Ln\iMP(APl_jMP)kl^0r\
+Ln (y)0v + Ln (s)6(3
= a + Ln (Â£>,_,)(1 d) + Ln (MP)OrÂ¡ + Ln \[AP,_X/MP)]kOrÂ¡
+Ln (.y)0v + Ln (s)6[3
Note that all prices and income levels are adjusted to relative values by dividing the
monthly income and price variables by a regional CPI for the month of observation. This
adjustment is necessary to preserve the homogeneity restriction and ensure that the
estimated demand equation is consistent with utility maximization (Hanemann 1998).
14 The partial adjustment model is used because households are unable to fully adjust
their water use in the short run (billing cycle) given a fixed stock of waterusing capital. I
explicitly write out the model with the partial adjustment parameter as it appeared in
Houthakker, Verleger and Sheehan (1974). Note that all terms without ltP subscripts
indicate values at time t.
where a is the intercept, 0is the partial adjustment parameter (to be estimated), rj is the
constant perceived price elasticity, y is the constant income elasticity, and [i is a
conformable vector of parameters on s. 1 suggest an alternative formulation of the same
model that separates the Ln(MP) and Ln(AP,.Â¡) elements of the Ln(AP,.//MP) term:
LnQ =cc + Ln(Ql_i)(\e) + Ln(MP)Ori{\k) + Ln(AP^)k&ri
(417)
+Ln (,y)#v + Ln (s)9Â¡3
This form of the model reveals that Shins perceived price signal is simply a weighted
combination of the marginal price and lagged average price signals. Using the fact that
AP,.Â¡ = BILL,.i/Q,.i, the model can be simplified further to yield15
LnQ =a + Ln (Â£>,_, )\(\ 9)(\ + krÂ¡)] +Ln (MP)9n{\k)+ Ln (BILL,_X )k9rÂ¡
(418) L J
+Ln (y)9v + Ln (s)9Â¡3
This is essentially a short run specification, but the long run effects can be recovered by
manipulating the partial adjustment parameter. Full adjustment (0= 1) occurs subject to
the households price perception. If the household maintains a perceived price other than
their marginal price (k Â£ 0), then they cannot adjust Q to an efficient level relative to the
consumption of other items. The completely adjusted household (0 = 1, k = 0) will have
optimally selected its capital stock and be reacting to changes in the marginal price of
service. For reference the formulas used to recover the key parameters of interest are
shown in Table 12. The derivation of the value of price information measures from the
demand model parameters is described in the Results.
15 BILLti is a nonlinear function of Q,./ because of the block nature of the rate structures
so the there is less chance of introducing multicollinearity by including both variables as
regressors.
91
Table 12. Formulas for key model parameters
Ln(Q) = [bO] + [bl]Ln(QM) + [b2]Ln(MP) +
[b3]Ln(BILLM) + [b4]Ln(Y) + [(3]Ln(X)
Parameter
ShortRun
LongRun
Income elasticity
b4
b4(1bl)
Perceived price elasticity
b2+b3
(b2+b3)/(lbl)
Marginal price elasticity
b2
b2/( 1 b 1)
Price perception (k)
b3/(b2+b3)
b3/(b2+b3)
Partial adjustment (0)
1 (bl/(l+b3))
1
Treatment Effects Bill Model
The general treatment effects framework introduced in Chapter 2 is an alternative
way to recover the value of price information. This framework is designed to evaluate
welfare measures for public good changes with expenditure data for different segments of
population. For the present case, I am suggesting that there is a hypothetical program to
fully inform consumers about the price of Q. The additional price information can be
considered a change in the supply of a public good from b1 to b such that /?(/?, 6") = p.
Formally, the difference in an individuals monthly bill with and without the additional
price information is the treatment effect of price information program
A = e(p(p,b'),vn,S,Â£)e(p(p,b'),Vl,S,e)
(419) =e[p(p,bx),y,s,Â£)e(Kp(p,b"),y,s,Â£} .
= BILE1 BILE0
where the first line suggests that that this spending difference is an uncompensated
measure of the value of price information shown in (47). This measure can be directly
recovered with observations on the two spending outcomes for each individual. The
approach developed in Chapter 2 can recover the welfare measures in (419) and (47)

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MEASURING THE VALUE OF PUBLIC GOODS: A NEW APPROACH WITH APPLICATIONS TO RECREATIONAL FISHING AND PUBLIC UTILITY PRICING By DAVID WILLIAM CARTER A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2002
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p ri 1 ht _ \I v art r
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ACKNOWLEDGMENTS Several groups and individuals contributed to the development of the ideas in this research First and foremost I would like to acknowledge the seemingl y unending support of Wally Milon and Clyde Kiker. Wally continued to help sculpt my highflying ideas into manageable research even after moving on from the University of Florida. Clyde ensured that didn t loose my interest in highflying ideas and provided much needed encouragement throughout the ordeal. The other members of my Supervisory Committee especially Bob Emerson are also to be commended for their timely comments and expert guidance. Next I would like to implicate my fellow graduate students and the group in I 094 especially Maxwell Mudhara Bowei Xia Mike Zylstra Larry Perruso Chris DeBodisco and Tom Stevens These individuals kindly filtered many of my early thoughts on this research and provided excellent moral support Chris DeBodisco in particular is to be thanked for his insights and compassion for learning Last but not least I would like to acknowledge the support of my friends and family for making the Ph D. experience an enjoyable chapter in my life lll
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r \ I l l IL I L: \ I( \\ I I 1 1 I I ...................... . .......................... .......................................... 111 I I I I I \l l [ ... .. ................... ... ...... ....................... . .. .... \ I I I I J l R[ .... .. . . . .. . . . . . . . . . . . ... . . . .. .. . . . ........... .... .. ... .... 11 \B \ \lll II\ f : R \\ l R 1 he t Publi d Ju ti n ............. .. .... ............... .. ...... . .. . .... .. n .. . .... . .. .. .. r R p tcd r ti n In.: l n )111 tn I r,1111 \\ rk .... . ...................................................... 4 Ir ttm : nl l Ir l \\ I fan; h.:a un.: I I LI i )11 ...................................... ..... .. ... .. ... . ... ............. .. ................................. .... .. 44 ... \I I I I \ 11 RI 1 l \ II \l I I 111 .................................................. 4 \\ 11,u 1 .1 ur nH.:nt \\ith .1pit:.1l I p nditur .............................................. ... ... 4 tru llH .11 I 111,111 1 \pp n .1 h ..................................................................................... : I lr,llnH.:n 1 11 t \pp1< 1 h ....................................................................................... r ., t., ............................................................................................................................. I\
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Results ........ ..................... .... ................... .... ................................ ....................... .. .. 65 Travel Cost Model. .... .... . .................. .... ........... ... ..................... .... ..................... 65 Treatment Effects Models ................. . .... . .. ................. ............................ .... .... 68 Discussion ... .... . . ............. . .. ................... .... ..................................... ............. ...... ... 74 4 APPLICATION TO PUBLIC UTILITY PRICING .................................................... 76 Price Perception and the Value of Price Information ............. .. ................................... 77 Empirical Models ......... ............................................................................................ 85 Water Demand Model ................... ..................................................................... 86 Treatment Effects Bill Model ........ ..................... ............ .............. ........ ............. 91 Data ...................... .. .. ... ..... .... ............. ..... ............................................................... 95 Results ............. . ... .......... ... ....................................................................................... 99 Structural Demand Model .... ......... ............... ......... ... ....... ........................ .. ......... 99 Treatment Effects Model ............... ................................................................... 105 Discussion ..... . .... ... .... .. .. . ... .................................................................................... 110 5 SUMMARY .. ..... .... ................................... ............................................................. 112 APPENDIX MATHEMATICA DERRIVATION OF THE NET UTILITY FUNCTION ............ 115 REFERENCES .. .. ....... . ... . .......................... .. .................................................... .. ...... 119 BIOGRAPHICAL SK.ETCH ....................................................................................... 129 V
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' .. Ll F BU :' I. bk tilit ut mt.: \\ith, ti\ it n mbin ti n ................................. 1 \\1th publi mbin n tandard d viati n rn m d I ri bl 4 R pl t.:m nt rul fi r mi in g \ari bl t d ....................................................... in Jud d in th \ ari bl nd capital fi hing p nditur ............................ 4 tim t fi r th P i nn rmal tra t m d I \ ith I tivitv .......................... 7 7 unt m d I\\ fi r I nnu I i bl xp nditur tr atm nt f[i t m d I r ult ................................... tr tm nt nnu nt ffi and f ri access ..... .... ... ..... 7" 11 ti Ii t \\.ith pri kn "I d and infi rm ti n han I_ m1ul fi r k m d I paran1 t r ........................................................................... R tc h dulc 1n tu ar a ................... .. .............. ... .................................................. 7 14 umm ti m nd d ta ................................................................. I \: lt.:r tim ti n r ult .................................................................... 1 r kc w t r d mand m d I ram tcr .................................................. 1 1 7 1c nth!) ill tr tmcnt dfc t m de! r ............................................................. l I t I ill tr' tmcnt cffl: t rm in nn ti 11 ............................. 1 \ I
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LIST OF FIGURES Figure 1 The value of a public good change with interdependence in demand space ............... 12 2 The value of a public good change with interdependence in utility space .................. 17 3 Expenditure difference threshold .......................................................................... ..... .41 4 Value of price information: perceived price greater than actual price ......................... 84 5 Value of price information: perceived price less than actual price .............................. 84 Vll
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!LA PPL! A I d \ Ir t r I i rt ti r tht: L ni, t:r it 1 f I I qum : m nt f r the "id illiam art r m r n mt ad pt d t m ur th he pr mi i th t int rv n ti n in th up p I publi lu publi an i tantam unt t parti 1p ti n r tr tm nt. hr u h 4 x p I r th i pr mi r_ mp r th 'tr tm nt h n\' nti nal n;\ C pu Ii d Pr ram luati hniqu d \ lu rm di I. ti\ it tu I dp t nti u r nlik m th h, thi ppr hd n t tur Id mand utilit 1 m de! t d rt\ "clC rem ur m 1) f the "i I) r 1 111I pr hi m f en g cn it) in m \ k.c 1 in i u ht i th t It m ti, n r tu a l 1 umpti n nh u nditi 11 : um cm nd r u Ii g \ Ill
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Chapter 3 applies the TEA to measure the recreational fishing value of Gulf of Mexico petroleum platforms. Those anglers who currently fish at these platforms are the treatment group while those who fish elsewhere are the controls. An econometric model developed in Chapter 2 is used to obtain a measure of the expected value of platform access. The measure is relatively comprehensive because the TEA readily incorporates capital expenditures. Results from the TEA model are compared to those from a travel cost model. Chapter 4 examines the conservation value of a program that informs public utility customers about the price of service. An analytical model of perceived price is developed that can be used to assess the value of price information. The corresponding empirical models are built around a dataset of Florida water customers that assigns households to treatment and control groups based on whether or not they know the price. The results from demand and treatment effects models are used to derive the expected value of price information for an uninformed household. Importantly, the notion of counterfactuals developed in Chapter 2 allows the welfare measures to be adjusted for the possibility that price elasticities change once a household learns the price. lX
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fhc d min h 1 e in lucd th di t th t tiv m titi mark t with n th t i th JI pr mm ditie and mark t ti n utilit an r an input int l. mmodit p rfi tl and ri al n nonatt nuat d ill tabli h a pri indi ti, fit r l tiv lu mark t g d in a Par t ffi nt allocati n (Randall 7 mm iti th t n t mark t an b t rm d nonmark I g od s mm lu but th r I ti alu f dditi nal unit ann t tl b an quili rium mark t pri Th r ar a mun r of r mm dit ,, ill n t trad d in p rfi ti m titi mark t but fi r pr nt pur the kc re od ri fl a that a n mu r trade bli hcd b au hu an imp rtant di rri r n l \\ ccn m ._ rk. t and ubli d h th a fa n i t nt indi at r rr latiH: ,alufi r th I tt r. Th,l ~ ck. r pri n th l th rm ur mutb u d t C \ a lu '" l the rt: I ll\ c \ luc h n g c in the u pl fth mm diti uhm ur
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2 inform public policy about the potential benefits and opportunity costs of propo s ed changes in public good supplies (Carter Perruso and Lee 2 001 ). This p e r s p e ctiv e follows the long tradition of applied welfare economics especially formal benefitc o s t analysis (Johnansson 1993 ; Smith 1988a ; Zerbe and Dively 1994) The tradition has s e en the dev e lopment of tools designed to recover directly or indirectly economic values for changes in nonmarket commodities such as public goods Direct inquiries require the construction of (hypothetical ) nonmarket valuation transactions whereas indirect investigations rely on the reconstruction of (actual) nonmarket valuation transaction s and values based on observed market behavior (Smith 1996) This dissertation adds to the kit of socalled re v ealed preference tools that exemplify the latter indirect approach to nonmarket valuation. Revealed Preference Valuation Of Public Goods The research on revealed preference methods forms a vast literature documenting the attempts to recover monetary values from opportunity costs associated with observed behavior related to nonmarket and public goods Some methods such as the travel cost model of recreation demand measure opportunity costs in terms of what consumers are willing to gi v e up for access to various supplies and qualities of public goods Other procedures such as the averting behavior model view opportunity costs as the amount consumers gi v e up to compensate for a change in the suppl y of a public good ( or bad ) Still others most notably hedonic models consider the opportunity costs implicit in tradeoffs among characteristics and prices of market goods. These approaches evolved to derive v alues for public goods when some of the data necessary to estimate a demand relationship is missing Specifically the first two approaches are attempts to impute
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.., pn t: l r pu 11 a t nth ti t: paien ,.., hL:re thL: third ith lack f publi d rrn : lh mm n in ppli e d d m nd ma ur m nt. un r Ii l ,, th d quantit and pric indic fun ti rm ith tt nti n t pn of mp nsat d m ur int n it and ar [i pr bl m u h ti n hip t and publi d cm r luti n d th id ntifi ti n t that ha b n r r aluati n f n nmark t and public 0 d xp mp t umm fth I l an d fr m al r 1974 J han 1 r man and 11 19 m r fundam nt Ii u n d t chni al probl m alu han ma pu db d nr th I ar n r Ulr n n um r b ha i and aft r th han in th publi d uppl ut u h pan I d t i rar l a ilabl Rath r r ti n d ta r th n rm. and fpu Ii pr 1 f r I. f\ cd nd pre in , luL: t k. f th ,, rid d th nu d t inD rm ti n in ur fi r th han thL: h n g in th ilit) r nfi ur ti n fth
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4 Alternative Approach to Revealed Preference Valuation The approach to valuing pubic good supply changes introduced in this dissertation is based on a fundamentally different way of defining hypothetical scenarios or counterfactuals. The alternative definition arises if interventions in the supply of public goods are considered social programs. Individuals in the population who use the public good in its program (base) state are the program participants. Others who could have used the public good are nonparticipants. Then following the literature on program evaluation (Heckman 2001 b ), participants are the treatment group and nonparticipants are the control group. In the tradition of the laboratory science, the net effect of the program is given by the difference in outcomes or treatment effects between the treatment and control groups, controlling for any inherent differences between the two groups and any (observable or unobservable) factors that may influence the participation decision. The main contribution of this research is a formal consideration of the cases in which such treatment effects can be considered measures of the value of changes in the supply of public goods. This objective is explored in three chapters. Chapter 2 develops a fairly general model that enables the use of treatment effects as welfare measures and compares this model with structural demand and utility equation approaches. Chapters 3 and 4 are applications of the principals introduced in Chapter 2. Potential Applications The alternative approach to revealed preference valuation can be potentially applied to evaluate public good use values in any case where the change in a public good supply can be characterized as a social program. The only crucial requirement is that observations on the behavior of participants (treatment) and nonparticipants (controls) can be clearly identified in the population of possible users of the public good. This is
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r I ti\ d tr i}htf rnard u in l pi all ailable n pli it inten nti n lik ti n pr ) ram t publi I and hmidt h 11 n g Ii in th id ntili di n r I ant p pul ti n m nt p rti ip nt and n np rti ip nt in th impli it r unint nded 'pr ram f th r tur r human rr ti th a ii bilit I r nfi g ur ti n publi d. w pr and 4 illu trat th p f ppli ti n h pt r u th t hniqu t alu t pr ram f mm nt int nti n in th uppl f artifi i I h bitat a ailabl for r r ati nal fi hin In thi du ing th h bi tat fi rm th tr atm nt r up and th r p t nti l u r ar ntr 1 gr up. hapt r 4 aluat alu fa pr ram th uld full in.ti rm public utilit u t m r ab ut th pri of th u t th r u t uppli b th publi utilit h r ar h h uld ppli It mati II Th 111 f pu Ii um urvc In dditi h n u th l tim add t th r n g f c tim ng th pri mak up th tr atm nt group. t that th infi rm ti nab ut th pnc f n i that th publi d f int r t in thi udi n f int r t t al d pr n mi t an p Ii m r n h n \\ t arhr,th th r lati tim l th Ju lu mand r c:p nditur unt fi r th i Ii t "in th d u ly Ii ) pr p al th Ii y d an an r with an m th d hwill
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CHAPTER2 TREATMENT EFFECTS AS WELFARE MEASURES New developments are more likely when one confronts a problem with general notions of how behavioral methods work rather than with the specific toolkit of travel cost models defensive expenditures etc. Bockstael and McConnell ( 1999 ) Introduction The relative value of public goods is not revealed in a competitive market. Thus the opportunity cost of changes in public good supplies must be inferred from observations on what is actually or hypothetically given up to enjoy public good services. The practice of observing actual market behavior to discern the value of public goods falls under the general heading of revealed preference methods (Herriges and Kling 1999). These methods seek to uncover the relative value of changes in individuals consumption mix that can be attributed to changes in public good supplies and/or qualities. This requires assumptions that separate the consumption set to isolate the purchased commodities that are interdependent with the public good( s) of interest (Bradford and Hildebrandt 1977 ; Loehman 1991 ). 1 Depending on the nature of the separability assumed the ensuing analysis can focus on estimating before and after demand equations for the related individual purchased goods or for composite 1 The ideas in this chapter are developed via partial analysis with assumptions regarding consumption set separability Following Hanemann and Lafrance (1992) I acknowledge that the related welfare analysis generates partial measures of exact surpluses but proceed in this manner to avoid the inherent ambiguities in deriving public (nonmarket) good values from incomplete systems without marginal valuation functions (Ebert 1998 ; Lafrance and Hanemann 1989). 6
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7 mm itit; n .: pr cntin ur h cd h I tter n ti n p bili cJ iti m I mpl i ti n ( definin g lid quantit nd pri indi fi r th it i till furth r mpli ti n n p nditur re md h e r th publi d h n g pn and quantit indi r mp os it r I t d t publi diffi u h mm di g r up ar d lin t d rdin g t r ampl r er ati nal d mand m d Jin mm rdin g t the ti fr r ati nal ti i ti he und rl m pr bl m th thi kind of mm di in ti n 1 r dil n h nth quantity ind d fin d as a h u h ld pr du ti n fun ti n Jund 11 and R bin 2000 In thi ca the pric and quanti indi B k ta I and c onnell pit th inh r nt diffi ulti in d finin m asunn and m d lin alid quantit and pri indi d c mp it c mmoditi th pr ti ntinu fan int n it ti it m in a ti f ti n d mand Ulf n and quanti indi timat mp it a ti it m n qu ti n an r net utilit qu ti n n l : P ar r re ti n d
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8 The chapter begins with a review the structural approache s to valuing public good changes using observed expenditure data Demand equation, utility equation, and combined structural approaches are covered. The review highlights the importance of the price variable in deriving public good welfare measures with each approach. Also emphasized is the way each structural approach deals with missing data on demand or utility outcomes with alternative states of a public good. Next an alternative approach to measuring the value of access to this type of public good is introduced The approach draws on the microeconometric program evaluation literature (Heckman 2001 b) to generate uncompensated and compensated welfare measures for public good access changes without splitting out price and quantity indices from observed expenditures on a related nonmarket activity. 3 Estimators are discussed for panel and crosssection data though emphasis is on the latter since most revealed preference ( e g. recreation expenditures) datasets are of this type. A summary suggestions for future research concludes the chapter Structural Approaches to Public Good Valuation The practical difficulties in measuring the value of public good access with observations on interdependent market goods are wellknown (Bockstael and McConnell 1999) Therefore after defining the welfare measures I will provide only a brief sketch of approaches that focus on structural demand or utility equations. The demand equation approach characterizes a large class of methods including the travel cost model for analyzing the nonmarket values at the intensive margin of activity intensity. Methods 3 Like most program evaluation techniques this alternative approach is not necessarily nonstructural (Blundell and Macurdy 1999). However the approach is less structural than the demand and utility approaches requiring the estimation of structural price and quantity relationships
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t II \\ 111 the utilit qu ti n appr h r m ti t db r nd m utilit th and r t:ner II uited t pl rin lu t th ti it h i th t m 111 and d m nd p t nti 1 d ant unifi d di t b th th int n i and t n i margin m m del rn r d p ndin nth fram n in th d mand fi r th rk. uch combined appr ach an mmoditi or acti iti R c nt r ar h in th r er ational d mand lit ratur h mbin d I appr ach to addr com r olution at th acti i d mand n Jaku and oma i 1999 Phaneuf 1999 Phaneuf Kling and H rrig s 000 ha and h nk ii r 2000). The following di cu sion i meant to highlight th om v hat p rpl ing r lianc on acti ity ba d pric indic in th s approach and th ach op rat in th ab nee of ob ervation of beha ior both b fore and after the publi g od hang We lfar e M a ur e on id r th prot picaJ e pr 10n of comp n ating and qui al nt ariations fi r a chang in th c nditi n fa public good from tate 1 to tat O int rm of th mm1mum p nditur function 21 ( 1 1 b b o ) ( 1 1 b p ll , 6 = e p U ,6 ( 1 1 b o ep,u .. ,6 r 1 1 b b o p ll , 6 6 o o b o p ,LI wh r pt a t r f pri [i r mark t ll I utilit indi d t th UTT nt th \ rid l, b r pr nt th uppl r qualit fa pu r f indi\ idual ntr hara Th t rm i a, e t r f t h ti mcnt r pr cnting h ter an 1m Ii it
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10 coefficients (not shown) on the variables in the model. Note that the presence of these unobservables in the expenditure functions implies that CV and EV are stochastic. Therefore the most that can be recovered is information regarding the distribution of the welfare measures such as the expected value or some other point of central tendency Following conventional terminology, CV represents the willingness to pay to prevent the change from b 1 to b 0 and EV is the willingness to accept compensation to allow the same change The concepts developed in what follows are illustrated with the CV willingness to pay measure. Discussion of EV is only offered where the notion of willingness to accept offers additional insights. A subset of the market goods are potentially interdependent with the supply of a public good Market commodities demanded x(u p b s, that are interdependent with the public good have generally, ox ()/ob* 0, or specifically ox ()/ob~ 0 for the case of weak complementarity (WC). 4 The former relationship implies that the individual is indifferent to the condition of the public good when the market demands are at some minimum constant quantities (Bradford and Hildebrandt 1977), while WC places this constant minimum quantity at zero (Bockstael and Kling 1988; Maler 1974). Consequently, WC requires the additional assumption that the interdependent market 4 The subset of the market goods that are not interdependent with the public good have ox (p u b) / ob = 0 such that public good changes only indirectly affect the purchases of these goods via income effects and the budget constraint i.e. as ( ox/ oe) ( oe/ ob)
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I l nti l. 5 ith ith r int rd p nd "' n ump ti n th alu f th publi an ui 1 nt pri han g fi r th int rd p nd nt mm diti ;(b o V p 1 u 1 ,b 1 ,b 0 p u b' 'P f x p u 1 b 0 / 'P = b j ) i p th ., n tant mand pn r fi r mark t g d r I t d t lJ u h that n tant ith th publi g ma ur for th in a publi g di illu tr t d in 1 gur 1 fi r th g n ral int rd p nd n and C Thi m imp! th in th ar a b hind o omp n at d d mand curv d mand r lati n ar n t b abl a a fun ti n of utilit it i n rdinar d mand quati n d al dir tl th utilit r m m ination f d mand and utili quati n tru tural D mand pproacb int rd p nd nt d m n quantiti __ 4 h h k pn that r I tri tl n th ob d quanti d mand d f th Th un mp n at d urplu m ur in t rm f b f\ abl ;(,.o) I b' h o p. ' , p f x I b o t p'
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p p(bo) A I I I I X 12 x(u 1 ,b 0 ) X Figure 1 The value of a public good change with interdependence in demand space where y is the constant income level and p' ( b j ) is the constant uncompensated demand price vector. The CV measure equals S in the absence of income effects and can otherwise be recovered from (24) by analytically or numerically integrating back to expenditure functions with an additional (Willig) condition that rectifies the difference between ; ( b j ) and p' ( b j ) (Bockstael and McConnell 1993 ; Hanemann 1980) The subset of these goods that are interdependent with the habitat in question define the relevant commodities to use in (23) and (24 ). These calculations require observations on the relevant demands before and after the change in the public good Before After (25) xN (P y,s, lb 1 ) x N (P y, s lb 0 )
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13 h r pr a t r and ub titut prt and th d mand r a h fth int rd p ndent mm diti n tat fth public g d but n ril a dir t fun ti n fth tat r amp! cal ulati n f r for han in th uppl fr r ati nal fi hing h bitat r quir timating a y t m f d mand fi r 11 pur ha d good r lat d t recr ational fi hing before and aft r the rvati n for only on tate of the public good th n d m nd h b timat d a fun ti n of b to predict th demand in the unob erved tat B ifor c) 2 X (P y b' c) x p y b ( ~o c) h re b 1 indicat the tat of th public good in a manner that ane aero the amp! r tim for ach indi idual. The id a i th ame if data i only a ailab l e aft r the nc a fun ti nal fi rm i pecifi d for the commodity demand and th r lat d indir t utility fun ti n th hado price( ) of the public good( ) can b btain d hapir and mith 1 ht r 1 91 Th alue of a di er t hang in the public g d an b r integratin th timat d b D r and aft r d mand nm pr 1 n 24 n alt rnati timat a demand quati n fi r th i111 rd p 11d nt a tivif) 1 u in an ptabl quantit ind th r 1 ant pur ha d quantiti mark t th n nt i n fr rrin t th ti it m hi h th int rd p nd nt arc u d a th int rd p nd 111 a ti, ity
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14 B ef or e Afte r (27 ) wher e X i i s a compo s ite commodity index for the goods used in interdependent activity i = 1 .. A, and Pis a vector of corresponding a c ti v i ty ba se d price indices. This is precisely what is done in the multiple site travel cost model where the trips to each site ( activity) are used as the quantity indices and site specific travel costs are the price indices. 8 As discussed earlier when before and after data is available the two sets of composite commodity demands can be estimated without a regressor indicating the state of the public good In fact with such data it is possible to take a completely nonparametric approach to recover bounds on the welfare measures using the price and quantity indices (Crooker and Kling 2000). Alternatively two systems of composite activity demands can be estimated using the before and after data The resulting before and after activity demand equations can be used to evaluate and recover the welfare measures (24) and (23) using price indices instead of the prices of individual commodities. If only one set of expenditure data is available, the activity demands in the unobserved public good state have to be predicted from a demand system estimated on the observed data Before Simulated X 1 (P ,y, b 1 s E) x i (P ,y, b 0 s E) (28) X A (P ,y, b 1 s E) XA (P ,y, b 0 s E) 8 The single site pooled travel cost models is a straightforward simplification with only one quantity index and as many price indices as there are relevant substitutes
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15 m th indi idual mt rd p nd nt mm dity d mand m, b 1 indi at th tat of th publi hi indi t r i d fin d in a mann r that arie acr the sample or r tim r h indi idual that th p cted acti ity d mand ith hange in the pub Ii g d can b imulat d If th publi go d indicat rd n t ary ithin ach a ti it th n th data a r acti iti an b combined to timat a ingl d mand quati n r ample h n the acti iti are characterized a recreation ite the data in 2an b u d t e timat the a called p ol d ite model. tru c tur a l tili ty ppr ac h o nsid r trat gi ba d on random utility th ry that u conditi nal utdity r pr entati n Th cla of model focu e on di crete e nt an or acti ity choice m l ing diffi r nt bundl of commoditie that ar interdep ndent with the public good. That i th indi idual ha (an unknown number of way t discret ly partition ( eparate) their budg t et to mploy th ervice of the public good 2!J = p' '(p, b', i th co t f producing altemati i u ing an altemati pecific ub t of th purcha d comm diti that ar int rd p ndent ith the public g d h r ar A u h It mati and a j indi at th tat f the public g d In ill u n nti n of r pr nting th 0 t int rms fa ti it pn and quantit indi ') !J that ar c nditi nal th tat fth pu d Th pn and quantit indi ar anal tru tural d mand appr a h nditi nal indir t utilit fun ti n r pr nting n th ir ma 1mum attainabl utilit nth ti it and th tat f th pub Ii g d
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16 (210) ij ( ij b j ) V V z ,y S,c where the indicator i equals one if the individual choose s alternati ve i with th e public good in state j a nd equals zero otherwise The income variable is implicitly adjusted for the total spending on each alternative as /i = y c f Notice that the mix of interdependent commodities enter the problem via this virtual income term in the utility equation approach Also note that a new dimension to the problem has been introduced Specifically as shown below the utility equation approach requires additional information on activity choices to completely identify a change in an individual's utility related to a change in the public good. The four possible outcomes for each alternative are listed in Table 1 Table 1 Utility outcomes with activity choice and change combinations CHOOSE ACTIVITY? YES (i=l) NO (i=0) BEFORE v(l p / 1 b 1 s c) v(O,p ,y 1 ,b 1 s c) (j=l) PUBLIC GOOD CHANGE AFTER v(l p ,y1, b 0 s,c) v(O p ,y 0 b 0 s,c) (j = 0) The expected unconditional utility over all alternatives is given by (211 ) [ ( j )][ { lj 2j ij Aj }] E v P y, b s c E m~x v v ... v ... v which is presented in terms of expectations because of the stochastic unobserved element of preferences The value of a discrete change in the public good from b 1 to b 0 is the
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17 b l. n tv t d unc nditi nal utility functi ns The money metric for thi alu gi n by th alu Vthat 212 [ (P + V,b 1 ,s)]E[v(P,y,b 0 ,s)]=o ing Hau (1 thi alu and it m ney metric are depicted in Figure 2 1th ugh not hown in th graph note that the ith activity i a W of the public good if a (P P, b )/ab = 0 9 Wh nth e activitie ar n't cho en utility (and expected utility) i unaffected by hange in the public good. [ ] y b1, c:)] E[ (p, y b 0 s c:)] [ O ] 1gur 2. h alu fa pub! ic good hang ith int rd p nd n in utility pace b fi r and aft r indir ct ulil it al ulat th . lfar m a ur in 21 h au utilit fth publi d if mm diti ar n 't pur ha d th indi idual i mdirfi rent t han in th publi
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18 unobservable The standard approach involves observations on alternative choice outcomes (Hanemann 1999) 10 The present case require s data on individual choice outcomes in the before and after public good states Before A ft e r (2 13) where R ; O is a binary index function that equals one if alternative i is selected and zero otherwise and choices are shown as conditional on the state of the public good The choice over multiple alternatives when the public good is in state j is motivated by a probability index model for all k :;t i} where as typically assumed the alternatives i and k are mutually exclusive for the given choi c e o c casion This index can be specified once the form of the indirect utility equation is selected. Then depending on the error structure is defined a probability model (e g ., multinomial logit or pro bit) can be maximized to obtain estimates of the indirect utility equation parameters With before and after estimates of the indirect utility function parameters equation (2 12) can be solved to generate the value of the public good If only one set of choice observations is available then the alternatives have to be defined with different endowments of b 10 This is also the motivation behind stated preference v aluation approaches where choice outcomes are elicited for hypothetical changes in bundles of public good characteristics and individual opportunity costs (Hanemann 1984b ). However a re v iew of stated preference methods is beyond the scope of this chapter.
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l b 1 th publi g d nd m nt indicator. h random utility mod I i actual! d ign d t handl thi typ f imulation ba ed on change in alt mati e attributes. A utilit qu ti n i d fin d ith an indicator for the endo ment of the public good a ail bl fr m a halt mati acti ity considered. Acti itie can be delineated according to a publi g od chara t ri tic or exampl fi hing habitat can b defined b lo at ion that th a ti ity of fi hing in an area is uniquely (and exogenou ly d fined by pecific public g d habitat. imilarly acti itie can be grouped by unique public good fi atur that d ftn typ of an acti ity. For example fishing habitat can be delineated according to hether it ha manmade feature o that the choice of fi hing altemati i defin d accordingly 1.e. fi hing artificial habitat or all other habitat Any numb r of combination i p ibl a 11 a diffi r nt ay of charact rizing the qu nc (i . n ting in hi h acti ity ch ice occur Haub rand Par ons 2000 Klin and Thom on 19 r y Br ffle and Gr ne 2001 Once th altemati ha e b n d fin d a di er t publi g d indi at r f alt mati publi g d indi at r I m d I can b Th co ffi nt d nfi urati n h oeffi nt on th an b u d to imu l t the If. r han t d utilit th publi quati n 212 u in th and imul t d
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20 Combined Structural Approaches and a Canonical Model The unconditional demands for each activity can be defined in t e rm s o f th e probability index and conditional demand functions from the two structural approaches : (2 16 ) X,.(P,y,b 1 ,s,)= pr(A ,. = l)X(i P ,/i, b i,s, ). The X() functions give the amount of each activity demanded at the int e nsi ve margin, conditional on the decision to participate and given the state of the public good Similarly the pr(R ,= 1) functions give the probability of participating in an activity at the exte nsive margin given the state of the public good When the probability of choosing an activity and the amount that is demanded are uncorrelated then these decisions can be analyzed separately as described in previous two sections. Otherwise, these decisions should be modeled jointly in a unified corner solution model (Hanemann 1984a ). 11 In this case the structura l demand and utility equations come from the same consumer problem and will therefore share coefficient information based on shared unobservables. A structural maximum likelihood approach with cross equation restrictions is necessary to obtain unbiased estimates of the coefficient information that are shared by utility and demand equations. This approach has a long history of application to cases of nonlinear budget constraints that arise in, for example the analysis of labor supply and the demand for public utility services (Hausman 1985 ; Herriges and King 1994 ; Hewitt and Hanemann 1995 Moffitt 1986 1990). Structural maximum likelihood has also been used in efforts value public good changes with a combination of data on stated and 11 There are a variety of comer solution models that have been suggested and applied to value public goods with revealed preference data (Herriges, Kling and Phaneuf 1999; Phaneuf 1999 Phaneuf Kling and Herriges 1998).
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r e 21 a m r n 1 2). In all of the application th stat' tical problem g 1 n In l b r uppl y th n mic meaning and m d I d accordingly i i n of how many hour to work is conditional on the d I f I t i nt th e orkforce When fac d with a block rate pricing chedule th m unt a n indi idu Id mand (and their pri e) i conditional on the block they elf t to con.sum in h e number of times someone choo e to recreate at a given site or m a g 1 n a ti it y i c onditional on the decision to self select the site or activity o er all th r ote that in many of these applications especially recreation demand modeling lflection i i w d a omewhat of an afterthought or a statistical nuisance n qu ntly the rev al d preference methods that jointly model D I C behavior are u ually concern d with r mo v ing the discrete outcome bias from the continuous outcome and the corre ponding welfare mea ures This is generally true whether the problem i addre d xplicitly a in the effort to correct for electi ity bia in welfare m a ur from r creati n d mand models (Bock tael et al. 1990 ; Dobbs 1993 Laitila mith 19 b Ziemer et al. 1982) or implicitly as in the recreation d mand literature th a t to deri e elfare effect from unified (Phaneuf 1999 2000) or linked (Par ons Jakus and Toma i 1999 ha a nd h nkwil r 2000 lution m d l of participation and quantity h i nl y th m r luti n mic meaning to lf1 tion I n th fi rm r a ppr a h t rr tin g ti it y bi a 'th choic quation h a no n n t i n v ilh th d mand qu a tion c pt fi r rr l a ti n in th H u ma n 1 p 1 2 2.
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22 To conclude this discussion consider the canonical D I C structural choice model that combines the utility and demand equation approaches (217) av(l,P ,y1j b j ,s, )ja?i av ( 1 P y1j, b j, s, )jay av(0, P, yj, b j, s, )jaPo av ( 0 P yj, b j, s, )jay otherwise where for illustration only two mutually exclusive alternatives are considered. This model can also be written in statistical switching regime form as (218) Following the discussion above the functional forms for the utility equations in R1 and the demand equations should embody the same representation of preferences and be estimated simultaneously with crossequation restrictions where necessary. To recover public good values, the canonical model requires before and after data on the interdependent activities of the type in (27) and (213). With such data, utility equations or the demand equations can be used to derive the welfare measures as described in the previous sections. In the absence of before and after data the utility or demand simulation approaches can be used to generate the values for the public good change. Critique of Structural Approaches As defined the demand and utility approaches require information on the consumers complete choice set and an indication as to those commodities that at any point in time are interdependent with the public good of interest. In absence of such information ( or a computational method of dealing with it), the consumption set must be separated into observable / manageable components (Deaton and Muellbauer 1980).
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23 H r in Ii th di I ult ith tru tur Id mand and utility appr a h u ing the m thods r mea uring public g d alues fr m market data. 1 2 thing to n t ab in th d mand quati n appr a h. ir t, u ing the tructural demand qua ti n ) ti mat din n tate of the orld to pr diet outcome in another tate a ume that th preferen parameter will not change in re ponse to the public good hang hit h ad Haab and Huang 2000 That i the irnulation approach a ume that timated tructural param ter are policy in ariant in the sense of the Luca critiqu ln this ca th public good indicator enter a a demand hifter and the portion of th V w !fare mea ure from each interdependent commodity is simply a difference in parallel lin a hown in Figure 1. Second the D I C choice model in the recr ation demand literature allow for comer solution in the demand for interdependent acti ity ba ed compo ite This is different than modeling comers in the interdependent purcha ed good that make up the cornpo ite activitybased cornpo ite odeling com r olution at the activity le el implicitly a ume that any interior olutions at the pur ha ed go d le el before the public good change will persist after the chang Ho er according to Bock tael and Mc onnell 1993) a discrete impro ement in a public go d can cau e th indi idual hen maximizing utilit in th n cont t to ho a p iti alue for an int rd pend nt good iou I he consum d n ne (pp 124 1249 Thi m an that d mand t m timat don th 1 2 Han rnann and 2 ho,,: that unl th f 21 or 22 ar ofn alu um that eparation f th r lat d t th ric indic ti r Proc in thi mann r mea that all r und n th d ir d m a ur
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24 should address the possibility of changes in the mix of purchases that occur as the public good changes A demand system approach that models comer solutions (Lee and Pitt 1986 ; Wales and Woodland 1983) will be able to account for such changes at the intensive and extensive margins of purchases of the interdependent goods. This raise s another issue related to the separation of the consumption set along the lines of interdependence with the public good A complete analysis would require that the estimated demand system include every commodity that might be in all individuals' choice sets before and after the public good change. While this is clearly unrealistic it uncovers the root cause of the intimately related problems of endogenous choice sets (see fn 2) and endogenous prices in activity based (e.g., recreation) demand models. The consumer chooses the relevant mix of purchased commodities (from the subset separated by the analyst) as part of the D I C optimization problem. In this case the marginal cost (price) of the activity will not necessarily be the same, for example, for consumers traveling from the same distance (Bockstael and McConnell 1981 ). This is especially problematic when attempting to simulate the value of public good changes using relationships estimated with crosssection data. With a crosssection, goods prices will not appear in goods demand equations because they do not exhibit significant variation across the sample. Thus any variation in composite prices used in this case will be attributed to other factors To the extent that these factors are related to preferences and not household technology (e.g., distance) price indices will misrepresent the true opportunity cost of the trip decisions. The endogeneity problem is further exacerbated by attempts to include capital time and the joint production of activities (Bockstael and McConnell 1981 ; Pollak and
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25 ht r I 7 ; R ndall I 4 nd c luti ns ( haw and h nk\J il r 2 t and activity price ar ndogenously n by th indi idual mak it difficult to obtain unbia ed e timate of coefficient in a ti ity I l d mand m d I Thi is important b cau e price and income coefficient ar crucial in th alculation of the elfare mea ure Likewi e any activity based price indi u din plac ofth r fer nee and choke price toe aluate 23) and 2 3) are pot ntially nd Th r ar at lea t three way to deal with the problem of endogenous price ind ice that ha e b en e plored in the literature. The fir t acknowledges that the price indice and derived welfare mea ures are ordinal measures (Randall 1994) and attempts to achie e b tt r mea ur a in, for example Engli hand Bowker (1996 The econd approach p cifically model ome or all of the activity prices as latent (Englin and honkwiler 1995) or endogenous (Fix Loomis and Eichhorn 2000 ard 1984 portions of the consumer pro bl m. ode! that incorporate labor upply constraint are example ofthi cond trat gy (Lar on and haikh 2001 haw and Feather 1999). A third approach attempt to choo e mea urement units (e.g., total di tance) o er which the acti ity can b aggregated and price indice de eloped in a utility theoretic manor ha and h nk il r 2000 An alt rnati e approach ugg t d in thi hapter is to find a r fr m penditur on the related a ti it ithout the u e of eparate pric and quantity indice T r a tm nt ff ec t ppro ac h t Publi G d a Juati o n h g al f thi part f th r ar h i t d lfar m a ur ti r a di publi d hang th t d n t r quir that pri and quantit indi b parat d fr m
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26 total expenditures. This welfare measure is d e rived from the differenc es in s pending before and after the public good change from b 1 to b 0 As with the structural demand and utility approaches a separability assumption is need e d to isolate the purchased commodities that are interdependent with the public good In this case it is rea s onable to assume to Hicksian separability whereby prices in the interdependent group change by the same factor following the public good change Before After (220) where the first L goods are interdependent with the public good and the remaining commodities are independent. Differentiating the constant relative price expenditure function with respect to the change factor gives (221) o e (e s L P !L, e sL P !L, u,s b 0 ) oe op: oe op ~ oe opl =++ +oe sL opi oe SL op ~ oe S L opl oe S L I I I I I I = P1 X 1 + P 2X2 P LXL which shows that expenditure on interdependent goods can be used as a Hicksian composite commodity with the change factor as a price index (Deaton and Muellbauer 1980 ) A similar result holds for the L + 1 other commodities and the related index Note that following the discussion of the structural models the price index for the interdependent good s is fundamentally endogenous. In the household production context
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27 th ind r pr nt th marginal t f pr ducing an a tivity that is interdep nd nt with th public d Th b for and after xp nditur compo ite for the int rdependent commoditie can b writt n in terms of the change factor pric indices a before after 222) and th differ nc in pending after the public good change can be restated as 223) Ll(p ~, ,e sL e >L y,b' b 0 ,s = P ~ 1X s 1 (e s L e >l Y S,cJb )e sL P ~ 1X s 1 (e s l,e > L>Y S,cJb 0 ) imilarly the ordinary surplu and compensating variation can be written as (224) (p ~ 0 sL ,e >L Yb b 0 c) = P : ,x s (e s l,e > l y s cJbl)e s LP ~ ,x s (e s l e > l y, ,cJbo) (225) CV (p ~ ,e sl e > l u b 1 b 0 ,s = P ~1 X s1 ( e SL e >l u Jb )e sL P ~ 1X s1 ( e SL e >l u' S Jb 0 ) here c ntrary to the p nding differ nee mea ure the welfare mea ure hold the price le el con tant aero of th orld The com pen a ting mea ur al o hold utilit th public g d change. Cons qu ntly if the r lati e price int rd pendent g od r main th ame aft r the public good change then th differen e in p nding qual th urplu m a ur P = (u clb )(u 0 cJb 0 ) 22 = Px s ( Jb ) Px s ( lb 0 ) = P x s (u lb )Px s, ( u 0 lb 0 ) = P
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28 where P = p ~ = (1) p ~. The price indices for the interdependent and independent goods are omitted becau e they equal one (i.e., 0 ~L = 0 >L = 1) if prices are the ame after th e public good change. 1 3 A similar price constant expres ion can be defined for the compen ating variation (227) CV P = e (u 1 ,s, lb 1 ) e (u 1 s clb 0 ) = Px 51 ( u 1 s lb 1 )P x 51 (u 1 s lb 0 ) ote also that Loehman ( 1991) has shown the case of interdependent public and market goods with constant prices implies that S'1 = d Cv11 generally, and S'1 = d = Cv11 if there are no income effects These formulations are useful in when attempting to simulate the value of public good changes using relationships estimated with cross section data. Before turning to the case of crosssection data however the following briefly reviews ways to recover the welfare measures from longitudinal data. Treatment Effect Welfare Measures for Panel Data or Repeated CrossSections Expression (2 26) suggests that an estimate of the uncompensated surplus measure for each individual can be recovered from panel data on expenditures before and after the change in the public good. A simple estimator of the uncompensated surplus measure expected value can be obtained by averaging S'1 =dover every individual in the sample. However this simple approach requires observations on the expenditures of each individual before and after the public good change In the absence of before and after expenditure data for each individual an alternative approach can be used to recover estimates of the uncompensated measure. All 13 If the prices of the goods that are not interdependent with the public good are not constant before and after the change then the remaining economic variables can be normalized by this index to preserve homogeneity.
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2 th t i n ry 1 n p nditur ob rvati n f; ran indi idual h n they u e th public g d nd an th r b rvati n h nth yd n t. i n thi inf; rmation the differ nc m nu e and n nu ob e ati n m a ure in the pecial ca e of of publi g d a ce To amin thi clai~ not that the indir ct utility level from an acti ity irtt rd p nd nt with a public good can be di ided irtto the four ca es hown in Table 1 In thi ca the acti ity i defmed a 'public good use' o that a 1 'denote the utility hen the public good i u ed and a 'O denotes the utility level otherwise. The income ariable i implicitly adju ted for the total pending on each altemati e as ij = y Px SJ (i, y, b s E). Al o the price v ctor in the table i implicitly def med a p = {0 sL e >L }= {l l}. This loppy notation is maintained in what follows to a oid creating another table and reduce the clutter in the functions. The corresponding four spending outcomes are li ted in Table 2 where the public good u d cision i explicitly lab led. onsid r the p cial ca where b 0 r pre ents the stat of the orld ith no acce s to the public good. In thi ca e expre ion in cell (2 2) in Table 1 and Table 2 ar irr l ant b cau e it i impo ible to u the public good h n a ce is complet 1 r trict d. h constant pric difference in p nding be and nonu e of th public g d ith xi ting a c le I b 1 can b writt n e pli it I a A ( (1 p II b C) b 1 E )( (o P 01 b' E) b 1 E). 22 p ) if that an indi idual i ju ta t th publi d ill tat b 0 a th uld b if th n tt u th publi d in tat b I th n
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30 (229) v(0 ,/ 1 p b 1 ,e )=v(O 0 p b 0 ,s,e ) and expression (228) can equivalently be represented as (230) t:. P (P y, b 1 s, e) = e (P v (1 p y 11 b 1 s e ) b 1 s ,e ) e (P v ( 0 p y 00 b 0 s, e) b 1 s, e) =e(p v 11 b 1 ,s, e)e(p ,v 00 b 1 ,s, e) = e (p u 1 b 1 ,s e)e(p,u 0 b 1 s,e)=CVP U ing standard duality conditions (Loehman 1991) this expression can be also be written a the compensating variation in (21 ). T bl 2 S d . h bl" a e ,pen mg outcomes wit pu 1c goo d use an d h c ange com mations USE PUBLIC GOOD? YES (i=l) NO (i=0) BEFORE e(p,v 11 ,b 1 ,s,e) e(p, v 01 ,b 1 ,s,) (j=l) PUBLIC GOOD CHANGE AFTER e(p,v 10 b 0 ,s,e) e(p v 00 ,b 0 ,s e) (j=0) To summarize with constant relative prices and condition (229), the CV for the complete loss in public good access is given by the difference in spending on an interdependent activity for an individual when they use the public good and when they do not. A simple estimator of the compensated surplus measure expected value can be obtained by averaging f1 P = CV P over every individual in the sample However this simple estimator susceptible to selection bias and contamination if any of the conditioning variables (i.e., s or y) change between the use and nonuse events From
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31 a ump ti n 22 an additi nal bia an e in thi ca if the conditioning variables of n nu ut m h ng b tw n the b fore and after tates of the world. That is, if haract ri tic and/or their related parameters change when the public g d hange h param tri and nonparametric estimators reviewed in Heckman and R bb 5 and Blund II and o ta Dia (2000) could potentially be used to correct for th bia e The application of the e ocalled 'differenceindifferences' and mat hing m thod to e timate the compensated measure of public good access with pan I data or rep ated cro sections is a topic for future research. Treatment Effect Welfare Measures for CrossSection Data With cro ection data an individual is only observed at one point in time and/or ti r on tate of nature. That is, only one of the four possible outcomes listed in Table 1 and Table 2 i po ible for any given individual in a crosssection. Consequently each indi idual will ha e mi ing counterfactual information. For users, the counterfactual is th ir pending had they not u ed the public good. Similarly, the counterfactual for nonu r i their pending had they chosen to use the public good. From Table 1 each of the counterfactual are po ible before and after the change in the public good. To implify matt r th approache developed here again on the special case of constant pnc and the compl te lo m acce to the public good from the reference acce s le el b 1 Wh n b 0 r pr ti rthi tat fth n public good ace ca e there i no mi ing counterfactual rid b cau only nonu po ible. idual ob r d b ha ior can b u d t inti r ab ut unt rfa tual and r n t an indi idual u d th publi p n d a d nth r quir informati n n h ther int rdep nd nt a ti it at 1 a t nc ti r rk f H man and la il 2 0 2 1 a 200 lb
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32 information on public good u age and two general as umptions (defined b low) can be u ed to recov r expectation of the counterfactual information mis ing from cro ssection data. The decision to use the public good in the reference period can be modeled with an index of net (indirect) utility (231) Following random utility discrete choice theory (Hanemann 1999), let there be an indicator variable that defines an individual's use status based on the net utility index (232) n=G(Z)+t: 0 D = 1 if n 0, = 0 otherwise where Z is a vector of all observable variables that influence the latent net indirect utility variable in (231) and 0 is an additive error derived from. Note that there must be at least one variable in Z that is not in the set (s, y, p). This exclusion restriction is required so that we can manipulate an individual's probability of public good use without affecting their expenditures. The two counterfactual assumptions implicit in the index model are (Heckman and Vytlacil 200la) : 14 Cl. Given that the choice probability for individuals with observed characteristics z' is P(z ') then if you take a random sample of individuals and externally set their Z = z then their choice probability is also assumed to be P(z'). C2 For any case where individuals with observed Z = z are set to Z = z' and P(z) < P(z') then: a) some individuals who would have had D = 0 with Z = z will have 14 Heckman and Vytlacil (2001a) also specify a series of technical assumptions that are imposed for convenience and to simplify the notation in their derivations.
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33 D = 1 ith Z = z and b n individual who had D = 1 with Z = z will have D = 0 ith Z = z' P (z) = Pr(D = 1 / Z = z) i th ocalied prop nsity core' or 'choice probability' fi r the probability f ch o ing to us the public good conditional on Z = z. The first tat m nt a um that if you tak a random ample of individual and change their det rminant of public good use, then the probability that they will choose to u e the public good i the probability of use for tho e 'u er who were observed to have the ame t of determinant of participation. Thi corresponds to assuming c: 0 is independent of Z conditional on {s, y, p) and is note sential to identify conditional xp ctations of the difference in pending measures (Heckman and Vytlacil 2001a). The econd a umption i a monotonicity property which requires that a change to any set of factors that increase the probability of participation will cause some nonuser to use the public good but will never cause users to stop using the public good. The monotonicity property is irnpli d by th additiv error a sumption in the index function Both assumptions are implicit in th tandard random utility di crete choice model of rational probabili tic choice Gouri roux 2000). I a um that th altemati e of public good u e and nonu e are mutually exclu i e o that the amp! can b p rfi ctly gm nted into two group ba d nob e ed b ha ior. To u e an anal gy ith th pr gram aluati n lit ratur (H ckman 200 lb n id r a c tat a a pro ram u h th a t public g du can b c nsid r d th pr g ram tr atm nt h g d mak up th tr atm nt g r up and a ll th r p t ntial u r mp th e public th control
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34 group. The sample will selfselect into one group or the other. 1 5 The use of assumptions C. l. and C.2 allows standard selectivity methods to be used in D I C models to recover counterfactual information necessary to evaluate the welfare measures. The approach taken in the treatment effects model departs somewhat from the conventional structural approach described above in suggesting that the information inherent in selectivity 'biases' can be used to learn about the relative value of public good access. This alternative view is not without precedent, as Heckman (2001a) notes that evidence from selfselection decisions can be used to evaluate private preferences for the programme so that, in principle, the 'problem' of self selection can be used as a source of information about private valuations" (fn. 11 ). Ec onom etric Fra m ew or k The index function and the spending outcome equations can be jointly modeled as a D I C choice switching regression system (233) ( I D 1) D D = G y,s,z /3 8,p,b +t: D = 1 if n 0, = 0 otherwise (234) 01 ( 01 bl 01 I /301 )( I /301 b l ) 01 e = px p,u ,s,t: = px y,s p, +t: (2 35) 11 ( 11 bl 11 I /311 )( I /311 bl) 11 e = px p u , s, t: = px y, s p + t: where /f 1 is a conformable parameter vector for s, y and a constant such that each alternative spending outcome has its own set of parameters and an additive error term. The notation follows the earlier model where superscripts i and} denote the public good 15 The general problem actually has two sets of selfselected samples One set is composed of those who choose the public good at level b 1 and those who do not. The other set consists of those who choose to use the public good at level b 0 and those who do not. In the special case where b 0 = 0 (i.e. no public good access), there is no self selectivity problem because there only one class of individuals : nonusers.
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35 u d i i n and r fi rence condition. re p ctively. ot that) = 1 in both outcome quati n indi ating that th mod I h uld b e timated with a cro section from the peri d where public good ace is at level b 1 Al o, b cau e I am a urning everyone in th cro ecti n fac the am (relativ ) prices and public good access level (b\ the e timating forms of the choice and expenditure equations are conditional on these arguments. ince the indirect utility functions implicit in (233) and the expenditure (d mand) equation in (234) and (235) come from the same consumer problem, we have /3 = h(/!1 fJ1iJ and e 0 = k( ij). The exact form of functions h and k will depend on the functional form selected for the expenditure ( demand) equations. One form is presented in the case studies of Chapters 3 and 4. The variable z and related parameter cf are added to the index function to serve as the exclusion restriction required for the index model specification. The spending outcome for any individual can be written as e = De 11 + (lD)e 0 (236) = px(y,s I 13 01 )+D[px(y,s I /3")px(y,s I 13 01 )]+[ +D(t:11 0' )] where the conditioning on the existing state of the public good b 1 and the constant price level i implicit. This formulation suggests that electivity is a problem by construction if th d ci ion to u e the public good is correlated with th expenditure outcome decision. The form of th rr rt rm will differ aero s the observations according the pecific
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36 public good use tatu 1 6 Consequently the data does not have the controlled (or natural ) randomization necessary to identify the difference in expenditures measure as the coefficient on D Selectivity correction methods aim to purge the nonrandom features from the data by controlling for the variation in the outcome equations due to unobservable portion of the index (choice) equation These methods are applied in program evaluation analyses to identify moments on the distribution of treatment effects. That treatment effects can be random variables is seen by rewriting expression ( 236) a (237) to reveal that the term multiplying the public good use indicator is a random parameter Thu the each individual can potentially have their own difference in spending treatment effect that depends on the idiosyncratic information in 11 and 0 1 In this situation there is an underlying distribution of heterogeneous treatment effects and different conditioning sets will give rise to different expectations of spending differences. On the other hand there could be only one common treatment effect parameter for all individuals given, in this case by px ( y s I l3 11 )px ( y, s I l3 1 ) Heckman ( 1997) points to two scenarios in which treatment effects are homogeneous in this way. First it can be simply be assumed that there is no unobservable portion of the expenditure differences so 16 Technically there are two ways in which the correlation between D and the unobservables of the outcome equations can manifest. The first way is termed selection on the unobs e rvabl es because there is correlation between the unobservable portions of D and tho e of the outcome equations In the other way called sel ec tion on th e obs e rvabl es, an ob ervable element of Dis correlated with the unobservables in the outcome equations ote that the structural D I C modeling approaches described in the pre v iou ection generally deal with selection on the unobservables Howe v er a full characterization of the structural demand and utility models in terms these two types selecti v ity i left for future research
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37 that 11 01 = 0. e nd 1 1 might n t qual 01 but th difti r nc between the the e l m nt d not determine who decid to u the public g od This c uld happen for ampl if individual do not know 11 01 at the time they choose to use the public good and th ir b t gue fit i zero. The expected value of the net effect of unob rvabl b ome z ro if these individuals' expectations of 11 0 1 are typical of the entire population If either of the e scenarios is true then there i no distribution of pending treatment effect and there is only one expected treatment effect measure for the population. The following analysis assumes the more general heterogeneous treatment effect case so that I can tailor mean spending difference parameters that corre pond to the variou welfare measures discussed so far. Treatment Eff e ct Welfar e Measur es There are two ways in which the econometric framework can be used to reco er a population leve l mea ure of E [ CV P ] The fir t recovers E [ i P ] = E [ CV P ] using a umption (229) and additional assumptions based on the spending beha ior of those who u e the public good and those who do not for the interdependent activity. The econd way does not require condition (2 29) and instead eeks to reco er E [~IM]= E [ CV P ] u ing an indifference et M to condition the di tribution of difference in p nding with and without public good u e This second approach aims to d lop a polic relevant difference in pending mea ur (H kman and ytlacil 2001 b pproach 1. ith con tant r lati price th un ompen at d urplu for the tal lo f publi good ace i m a ur d by the diffi r n in p nding b an
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38 individual when they u th public good use and when they do not. or the model in (233)(235) this difference in spending for each individual is given by (238) wher the conditioning on b 1 and pare again left implicit. This is the heterogeneous treatment effect random parameter defined in expression (237). There are three commonly used mea ures of the expected value of this variable using different sets of the sample (Heckman and Vytlacil 2000). The unconditional expected value measures the socalled average treatment effect (239) This mean measures the expected difference in spending from public good use for a randomly chosen individual. If corrected for selectivity, the ATE will approximate the mean treatment effect from a randomized experiment. 17 Evaluating the expected value of the treatment effect over the support of those who chose to use the public good gives the effect of the treatment on the treated as (240) A similar parameter can be defined for the segment of the sample who chose not to use the public good 1 7 There are two ways in which selectivity can bias the experimental treatment average (Winship and Morgan 1999) The mean selection bias given by E[c 01 I y, s D=l] E[c 01 I y, s D = 0] indicates how spending in the reference level of the public good differs between users and nonusers. The second source of bias occurs if the change in spending caused by public good access / use (treatment) is different among users and nonusers. This bias is gi enby E[; P I Y s, D=1]E[; P I Y s D=0]=E[t: 11 t: 01 l y, s D=l]. Neither of these spending differences can be attributed to public good access
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39 241 in g th unt rfactual a umpti ns in 1 and C.2 the above treatment effects measure th pe t d valu f for the lo of public good asses for different segments of the p pulation In the pr viou di cu ion I sugge ted that, with panel data, condition (229) can b a um d o that P = CV P for each individual. With crosssection data, however condition (229) alone i not sufficient for tJ.P to measure Cv11 because there is additional mi ing c unt rfactual information. Recall that this condition requires that an individual i ju ta w 11 off without access to the public good in hypothetical state b 0 as they would b if they chose not to u e the public good in the reference state b 1 With a complete panel there are ob ervations on expenditures for each individual when they choose to use the public good and otherwise for the interdependent activity (with the public good fixed at b1). With a cro ssection, however, there is only information from nonusers about spending and the corre ponding utility level when the public good is not used. Similarly only u er pro ide information about spending and the corresponding utility level when the public g od i u ed. Thi m ans that a direct application of condition (229 with cro ction data will in olve an interpersonal comparison of wellbeing. Thee tent of th compari on will dep nd on which treatment effect mea ure i u ed F r ATE p TT p r UT p to m a ur th E[ 01] for compl t lo of acce c nditi n (22 h Id for th who didn t cho et u e th public good at th tat In additi n for TT p ma ur r quir 242 01 p b l )ID= l] = [ ( 0 01 p b l ID=O]
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40 for those who did choos to u e the public good in the reference state. This assumption requires that the indir ct utility level of users (D = l) had they not u se d the public good, i s the same as nonu er (D = O) with the s ame set of characteri tic s (y, s, ). Similarly, to u se UT p a a measure of E [ Cv7] for nonu ers we additionally require (243) [v(l / 1 p ,b 1 s,c)ID=O]=[v(l,y 11 ,p,b 1 ,s,)iD=l] for those who did not choose to u e the public good at the reference state. This assumption states that the indirect utility level of nonusers (D = O), had they used the public good is the ame as users (D=l) with the same set of characteristics (y, s, ). In order for ATE 6 p = E[ CJtefl] for th entire population, we need assumptions (242) and (243) as well as assumption (229). Approach 2. To motivate the task of specifying and identifying the policy relevant treatment effects measure consider the distribution of expenditure differences t!, P shown in Figure 3 where JO is a function describing the relevant density of e. 1 8 The unknown switching threshold is shown as !l p which also corresponds to the compensation that would make the marginal individual just indifferent between using or not using the public good. Individuals located to the right of the threshold choose to use the public good alternative whereas those to the left do not. Thus there is actually a related distribution of !l p for the marginal and nonmarginal individuals. If the public good does not have va lue to the individual outside its use in the interdependent activity then 18 Following Moffitt (1998) the distribution of the treatment effect in can be depicted as in Figure 3 by assuming that the choice between alternatives is based entirely on t!, P and that this 'se lection is positive : individuals with high values of t!,P are relatively more likely to choose the first alternative than those with lower values.
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41 p rr p nd with th J/l mea ure irnilarly, the expected value of tip for the p pulati n corre pond with the E[ CTI'] measure. p DON'T USE USE Figure 3 Expenditure difference threshold Referring again to Figure 3 the unconditional mean of !l P will not correspond to an exact welfare mea ure of public good access ( unless the conditions specified in Approach 1 for ATE are met The mean of the treatment effect ha to b conditioned in order to r co r a value that repre ent the central tendency of the exact mea ure ti p . The xp ct d alue of A p can b thought of a thee pected alue of AP conditional on b ing at th point of indiffi rence for each individual or 244) [ A p ] = [ A p I (1 p 11 b '' = ( 0 p 01 b )] =E [ Ap ln=o]
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42 Thi type of tr atm nt ffi ti known a th marginal tr atment effe t (M or the limit version of th all d local av rage tr atment ffect. 1 9 According to Heckman and Vytlacil (2001a) th MT ha the interpr tation a a measure of willingne ss to pay on th part ofp pl on a p cifi d margin of participation in the program (fn. 16). The conditioning expr ion in thi case can be viewed a the indifference et (Heck.man 1997) U ing th d finition of fj_ P in (238) and the additiveerror index function pecification in (233), thi expectation can be written as (245) E[; J =E[; P J+E[t: 11 lc 0 =G(y,s,z)]E[t: 01 0 =G(y,s,z)] = E [ ~p] + ( (YIID (YOID )[ G (y, s, z)] where E [ ; P ] i the unconditional average treatment effect from (239) and the conditioning set for the index function G ( I /3 8 p, b 1 ) is omitted to simplify the notation The terms cr 0 ID and cr 11O measure the covariance between the public good use decision and the unobservable portion of each expenditure outcome. 20 These covariances how how, for a given set of set of (y, s z), spending on the interdependent activity change with a change in the net utility of public good use. Information about an individual's preferences can be recovered by examining the signs of (cr 1 ID cr 010 ) and G (). 21 If these terms have opposite signs, then the propensity to change spending is greater with public good use than without. In this case an individual prefers to use the 19 Attribution for this treatment effect parameter is given footnote 18 of Heck.man and Vytlacil (200 la) 20 ote that the covariances arise in the derivation from the general expression for the expectation of a random variable conditional on another random variable i.e E[ ij I c 0 ] = (j ij0 21 The economic interpretation of the switching regre sion covariance is similar to the u e of these parameters in the labor literature that examines comparative and ab olute ad antage (Dolton and Makepeace 1987 Emerson 1989 ).
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43 public good otherwi e they do not. Furthermore, since the first term on the righthand ide i imply a difference in exp nditure, the remainder has the interpretation as the additional amount nece ary to make the individual indifferent with and without public good use This becomes apparent when we recognize that cr 11O and cr 01O give the s lope of lines that showing how the expenditures of users and nonusers, respectively, vary with the net utility of public good use indexed by G(). 22 The term G() for each individual gives the value of the unob ervables necessary to maintain the same utility level (i.e., D* = O) with and without the public good (use). The constant covariance term translates this amount into the money measure of the additional compensation necessary to maintain the same utility level when the public good (use) is not available. The relationship among the treatment effect measures of spending differences in (239)(241) and the exact measure in (2 45 ) can be used to formulate a model of public good use participation The expected value of the exact measure E [ 'ti P] represents the mean threshold of public good use for the sample. It is straightforward to show that participation is expected on average if (246) b caus thi imp lie that the utility of using the public good is greater than the utility otherwi e 23 The corr ponding expre sions for the users and nonuser group are 22 The with and with ut public good (u e peoditure equation could be dra non the ame graph a a functi n f n t utility. Thi may pro id au ful ay of isualizing the tr atm nt ffi ct elfare m a ur ( ) I lea e thi for futur r earch 23 Fr m 22 and 227 e(i/,p b 0 , (u 0 p b 0 , ) hichholds ifu 1 u 0 all el qual b cau e the e penditure function i incr a ing in utilit ot that u 1 i th utility ith th public good (u e and u 0 i utility oth rwi e
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44 (247) E [ ti p lu e r] 1T 6 p (248) E [ ti p !nonu se r] ~ UT 6 p The condition provid a consi tency test on the treatment effects model re s ult s. We would exp ct condition (247) to be true for those who actually choo s e to u s e the public good for the int rdependent activity However the inequality in condition (248) is expected to b r ver ed because this expre ion applies to the group of individual s who choose not to u e th public good. Discussion This chapter introduced the treatment effects approach to evaluating the welfare effect of changes in the condition of public goods. The approach applies techniques from the program evaluation literature to develop measures of welfare changes from spending on market goods that are interdependent with a public good This approach views interventions in the supply of public goods as programs where the segment of the population currently using these goods are viewed as the treatment group and other potential users are considered the control group Measures of the value of public good acce are recovered from differences in expenditures among users and nonusers This approach offer the advantage of using price constant specifications of demand relations e g ., Engel curves) because the typical choke price argument is not required to evaluate the access restrictions There are several directions for future research on the treatment effects approach. First the model can be extended to evaluate continuous treatment effects (Heckman 199 7) to deal with a continuum of possible changes in public good condition This would also allow for a richer consideration of the counterfactual assumptions required for
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45 ca other than with and without public good acce ca econ idered in this chapter. c nd th re i mor work n cessary to examine the role of substitutes in the treatment effect approach. Th importance of ub titute other revealed preference approache s uch as the travel co t model i welldocumented (Kling 1989 ; Rosenthal 1987 Smith 1993) Recent re earch on program evaluation (Heckman, Hohmann and Smith 2000) sugge ts methods to account for substitute programs in estimates of treatment effects that may be u eful in generalizing the approach introduced in this chapter. A related direction for further research is to examine models for multiple programs that could be used as a treatment effects analog to the multi site travel cost model. Fourth future work on the treatment effects approach should include applications the nonparametric estimators develop d in the program evaluation literature to the public good valuation problem. Finally the longitudinal measures introduced here should be explored further. This would require a panel or repeated crosssections of expenditures on activities interdependent with a public good Although the former is relatively rare repeated cross sections are regularly collected by variety of re ource management agencies.
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HAPT R 3 APPLI ATION TO RECREATIONAL FISHING Th re are approximat ly 4 000 off: hore oil and ga s tructur e in the s tat e and federal waters of the Gulf of Mexico. These structures account for a major proportion of th available fi h habitat in the Gulf and they are utilized by a variety of recreational u er (Quantech 2001) More than 100 structures are removed annually but the U S Mineral Manag ment Service has adopted a RigstoReefs policy to mitigate the lo s s of th se structures to maintain the public good benefits of fisheries habitat (Dauterive 2000). This policy involves leaving the structures in place, toppling the structures to create benthic habitat, or moving them to a new location. While the costs of removal are relatively well known, the economic benefits of current usage and of retaining these structures have not been estimated. Thi chapter presents an analysis of the value of access to petroleum rigs for recreational fishing It i hypothesized that fishing at offshore rig sites requires additional fi hing capital compared to other types of angling Consequently the analysis measures opportunity co t in terms of per trip costs and expenditures on fishing capital. This require that models of recreational fishing, such as the travel cost model be adapted to jointly model choices over durable and nondurable goods Randall notes that in applications of the travel cost model the allocation of the co t of owning and maintaining vehicles and other durable equipment to any particular trip ( activity ) proceeds if at all in an arbitrary fashion (p.90). This is largely due to the additional complications that arise when attempting to introduce (joint ) capital 46
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47 p nditur into fundam ntaUy ndog n u pnc indice s for nonrnarket activities (Boe tael and Mc onnell 1981 Pollak and Wacht r 1975 From hapter 2, such price indice ar n c ary in the travel co t model in order to estimate a demand equation for the nonmarket activity and derive welfare mea ure of access or quality changes. However it may not be possible to derive valid quantity and price indices when trips are used as the aggregator for recreation commodities 1 Lin ar random utility models also typically ignore capital expenditures because it is presumed that these expenditures do not vary with the number of visits to a particular site or type of site. In this case, capital stock or expenditures are individualspecific variables that drop out of the model because the estimation is based on utility differences and these variables do not vary across sites or activities. This may be a valid assumption when (perfect) substitute sites or activates are available that jointly use the durable equipment ; that is, when expenditure categories are not uniquely related to the attributes of an activity or site. In other cases, however ignoring such expenditures could seriously misstate welfare estimates for policies that stand to affect the access to or quality of capitalintensive activities. Thi chapter presents two approaches to incorporating annual capital expenditures into estimate of the value of access to petroleum rig for recreational fi hing The first approach i a impl adaptation of the tructural tra 1 co t model to incorporate the stock of fi hing capital among explanatory aria bl Lik th con ntional tra el co t model 1 h a and honk ii r (2000) demonstrat that th pric indic ugge ted for trip ill th lit ratur ar not alid or that th indic do not nt r th trip d mand quation ill a a lid ay. ian c mp it commodit i linear h d pric p ifica tion f th trip d mand quation is z r in inc m and the pri ind
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4 thi adaptation r quire that price and quantity indice b eparated from fishing xpenditure toe timat a tructural model of fi hing trip demand. The second approach i ba ed on the treatm nt effect framework for measuring public good values presented in hapter 2. This framework involve condition whereby welfare changes can be measur d by difference in the ob erved expenditures of two segments of the population who participat in recreational fishing: petroleum rig users and nonusers. The method can be implemented with raw expenditures on a recreational fishing activity that is interdependent with access to petroleum rigs. Price and quantity indices do not need to be separated from the aggregate annual expenditures for each individual. Data used in the analysis are drawn from intercept and phone surveys of marine recreational anglers along the Gulf of Mexico coast (Alabama to Texas) that elicited detailed information about sitespecific activities and expenditures for variable and capital goods directly related to the activity. The econometric estimation procedure developed in Chapter 2 controls for (and actually takes advantage of) activity specific selectivity, in this case, the choice whether to fish near an petroleum structure or not. Welfare Measurement with Capital Expenditures There are few if any, attempts to systematically incorporate expenditures on durables into models designed to measure the value of changes in public goods. Studies frequently use indicators of existing capital stock as explanatory variables in demand equations Travel cost analyses of recreational fishing, for example, often incorporate dummy ariables for boat ownership. However the rationale for including such variables is u ually not fully developed beyond an implicit notion that the behavioral relationships estimated are conditional on the existing tock of capital (Pollak 1969). Capital tock indicator are included among regre ors to control for variations in holdings in demand
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49 and w lfare calculations. This formulation treats capital as an exogenous portion of the consumer problem and is correct to the extent that the additions to capital are fixed over the ( deci ion) period of interest. In many cases, though, the stock of capital is better characterized as 'quasifixed' so that periodic increments are chosen along with (non capital) commodities as part of the same optimization process (Conrad and Schroder 1991). Consider that the choices regarding where and how frequently to fish annually are conditional on boat ownership, but that a boat could be purchased at any point during the year. In this example, the same observable and unobservable factors that influence the choice of capital stock levels also determine the demand for other commodities. Consequently, measures of current capital stock and additions will be endogenous if included in a demand equation for another commodity in the consumption set. In the fishing demand example, the boat ownership indicator is a dummy endogenous variable (Heckman 1978). This suggests that capital expenditure decisions should be modeled imultaneously with other aspects of the consumer problem. The basic neoclassical model of consumption with durable goods has the consumer choosing the allocation of expenditures among nondurables and capital stocks to maximize intertemporal utility (Deaton and Muellbauer 1980). This model yields elution for the optimal demands for nondurables and durable stock in each period that are function of the exi ting durable stock, discounted prices and the user cost of capital for all p riod o er the planning horizon. With weak intertemporal separability, future pnc ar irrele ant to curr nt deci ion o the expenditure for the nondurables x and the
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50 durabl tock Kin any period i a function of the exi ting durable tock K. ,, curr nt period pric p and the u er co t of capital k (31) e (p u b , E k K 1 )= p x (p u b ,s, E k K 1 ) + kK(p u b ,E, k K 1 ) wh re u i s th utility I vel b indicate the upply of p e trol e um ri g for fi hin g, i a ctor of ob ervable control characteri tic and represent unob ervable 2 The r 1 vant nondurable and durable are tho e which are weak complement to (fi s hing at ) the petroleum rigs The ( compen at d) demand system for thi problem is found by differentiating th e full expenditure function with re pect to the price of variable goods and the capital stock o e ( ) oK(p u b,s E k K I ) =x p u b s Ek K 1 +kOP1 1 (32) ~ ( ) oK(p u b s,E,k,K I ) x p u,b s E k K 1 +k op OfJ N (33) oe ox(p,u b,s E k K I) ( ) p +K p u b s E k K 1 ok ok Following the discus ion in Chapter 2 this simultaneous system can be used to estimate the value of changes access to the weakly complementary petroleum rigs. The compen ating variation for a discrete change in fishing access to rigs from b 1 to b 0 is 2 With intertemporal eparability the user cost of capital is simply the current cost of capital purcha es Furthermore assuming no depreciation K is actually a measure of additions to capital tock. This is seen by noting that capital stock changes in each period according to K(p u b s Ek K 1 )=d(p u b s Ek K 1 )+(18)K 1 whered()isthe demand for addition to capital tock and 8 i the depreciation rate. If 8 = 0 then changes in K are proportional to d
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(34) 51 V K (b b 0 ) =e (p u 1 b 1 , 8 k K )e(p u ', b 0 ,s, 8 k K ) = [px (p u b ,s, 8,k,K 1 ) + kK (p u 1 b 1 ,s, 8 k, K 1 )] [px (p u ', b 0 ,s, 8 k,K 1 ) + kK (p u b 0 ,s, 8,k K 1 )] Note that to the extent capital stock is actual fixed over the decision period the second terms in (3 2) and the entire expression in (33) can be ignored in demand estimation If capital stock is fixed before and after the change rig access, then the second terms in the last two lines of the CV in (3 4) can also be ignored. This is what is done in the conventional formulation of the travel cost model that focuses on the first term in (31) or the variable expenditure function (Conrad and Schroder 1991 ). The welfare measure in this case reduces to (35) where since there is no longer a trade off between spending on nondurables and spending on capital additions, the cost of capital is omitted. The structural demand approach defined below follows the conventional travel cost formulation to recover the variable cost we l fare measure in (35). The alternative treatment effects approach presents a way to recover the welfare measure of the value ofrig access in (34) that includes spending on fishing capital. St ru c tur a l D ema nd A ppro ac h The structural approach to recovering the welfare measure in (34) require e timation of at least part of the y tern of interd pendent commodity and capital tock demand Two strategie ha e b en applied in th literature The fir t trategy i to e timate a partial demand y tern with the commoditi that are (a um d) interd p nd nt with th public good ( hapiro and mith 19 1 ). Th capital augmented model hown in
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5 2 y t m 2 33) al r quir th tim ti n f qu a ti n for II f th int rd p e nd nt capital nd nd m mm n trat y i a gg r ega te th int e rd p e nd e nt g d and timat a d mand quati n r y t m for a mpo it commodity or y tern h t m d 1 i a la 1c ampl of thi econd trategy wher th mp mm dity i trip and th pnc ind x i travel co t This approach i tak n fi r th pr nt application How v r it i acknowledged that the approach i s pr bl mati in the travel co t mod I becau the composite commodities are delineated ac ording to activitie and/or location c hosen by the household. See Chapter 2 for a di cu 10n dding capital co t into activityba ed price indices compound the problems b au i no straightforward way to allocate the fixed capital costs to any one acti ity type location or pecific trip (Pollak and Wachter 1975). Consequently separate capital tock equations should be estimated simultaneously For the empirical application of the structural approach, I do not estimate a demand system with capital stock equations. I follow the conventional travel cost approach in a urning that capital stock is fixed over the decision period and estimate the demand for a trip ba ed composite commodity representing only system (3 2 ) However, the previou p riod capital tock is included among the influences of the trip demand deci ion Trip demand is specified as a pooledsite model for recreational fishing at p troleum rig in the Gulf of Mexico Following the canonical di crete / continuous model in the Chapter 2 the structural trip demand system consists of an index equation and a trip demand equation (36) (37) T = a 11 + Pa 11 + Pa 11 + K a 11 + s a 11 + 11 r I r r o o I K 1 s
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53 wh r R i a binary indicator that equals 1 if an individual fished at a rig in the previou y ar and zero oth rwi 3 Tri the total annual fishing trips to petroleum rig Pr is the average co t of a rig trip P 0 is the average co t of a nonrig trip, y is income K 1 is the existing tock of fi hing capital s is a vector of socioeconomic control variables The unobservable of the selection decision! and trip demand d' are assumed to be joint normally distributed. The number of rig trips per year in (3 7) is modeled as Poisson process (Hellerstein 1999) o that estimated trip demand equation is (3 8 ) C = 0 1, 2, .... The extra error term in the trip equation of (37) relaxes the usual Poisson assumption that the mean and variance of the estimator are equal. This allows for unobserved heterogeneity and addresses overdispersion common in count models. The extra error term also allow a convenient way to model selectivity that parallels the standard approaches with linear models. An example application of this estimator is given in Haab and Mc onnell (2002) and the construction of the likelihood function i hown in Greene (1995 pp. 580582) Based on the discussion of demand interdepend nee in Chapter 2 the value of a public good change can be measured a areas behind the demand cur es estimated with (36)38) before and after the change. Howe er the data u ed in thi ca e tudy i from a cro ction b for the public good chang o the lfare effect ha to b imulated. 3 I a ume that then t utility of the rig u e deci ion can b mod l db a r due d form index quation that i lin ar in ariable Thi impl approach i talc n b cau e of th c mpl ity of th indirect utility function corr p nding t th milog d mand quation of th aunt m del. ith thi a umpti n onl th un b rvabl porti n of th rig u d ci i n and th trip d mand are r lat d.
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54 The simulation to recover value of fi hing ace to petroleum rig involve an int gration under the demand curve for rig trips from the current co t of a trip to a 'c hoke' co t. Th xp cted annual con umer urplu con um r urplu of rig acce [SJ = l{I [ (e )~] dP, }de (39) = 1 {[[ (e )T ]de }dP E[~] =a ll r a ll :t:0 r wh re the denominator is the coefficient on the rig trip cost variable from (37),
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55 que ti nabl b cau ea argu d in hapt r 2 the travel price index is endogenously d termin d al ng with the trip quantity index (Haab and Mc onnell 1996 Th welfar mea ure u expect d rig trip adjusted for electivity (Bockstael et al. 1990). I al o correct the expected value of the dependant variable for the lognormal tran formation implicit in the Poi onNormal model of heterogeneity so expected rig trip are calculated as where ~ 1 = ( Rn ) / ( Rn ) i the inverse Mills ratio term with () as the cumulative distribution function, cr 11 R is the estimated covariance of the rig choice and rig trip deci ions, and cr 1 1 is the estimated standard d eviation of unobservables in the rig trip equation. The last term is the correction of the mean for the lognormal distribution. 4 Note that I do not adjust the E[S] and [CV] integration results for the appearance of the price and income variables in Rn of the expected trips equation. This adjustment is obviated by the as umption of exogenous prices that i used to rever e the integration in the welfare calculation The model i estimated in LIMDEP (Greene 1995). Treatment Effects Approach The structural activity demand approach outlined earlier i problematic becau e the price index (travel cost and quantity index trips) will be endogenou to the consumer prob! m Furthermore although not included in the model p cifi d for thi chapter the 4 Them d l i timat d with th log frig trip and the h t rog neit err r term 11 of thi quation i a urned to b normal. Ther for th trip ithin th Poi on probability are a um d t tak al gnorrnal di tribution. r m reen 000 th e p ct d alu of th 1 gn rmal rig trip ariable i E[T r n] = p(m + a211 / ') h r m n = E[Ln T r n ].
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5 tru tural d mand mod Ir quir a parat timating quation to ( imultaneou ly m rp rat th d mand for capital addition An altemativ trat gy intr due d in hapter 2 doesn t require separate price and quantity indic Rath r thi tr atment effect approach works to specify conditions wh r by welfare change can be measured dir ctly by differences in observed spending by different segment of the population. For present case I am suggesting that there is a hypothetical program to allow the u e of petroleum rig as artificial habitat for r r ational fishing R mo val or expansion of this program can be considered a change in the upply of acce to a public good. L t b 1 be the refer nee condition of the rigs program and consider the special case analy z ed in Chapter 2 where access to rigs is zero at b 0 so that b 1 > 0 and b 0 = 0. In this ca e the recreational angler who report fishing at the rigs are the program participants or tr atment group and tho e who do not are the control group. The idea is to use the difference in expenditures between these two groups to evaluate the with and without program (petroleum rig ) welfare measure. The counterfactual assumptions required to unco r the alue of acce from the difference in spending with and without rig use are d tailed in Chapter 2 With the appropriate counterfactual assumptions, the selfselection decisions of angler ugge t three po ible ources of differences in expenditures : 1) fishing at a rig may require higher (or lower) expenditures on average 2) those who fish rigs may have an inherent tendency to pend more (or less) on fishing than those who do not fish rigs, and 3) the expenditure of those who fish rigs may change more (or less because of a change in rig acce than tho e who do not visit rig if they had The various approaches
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57 to dealing with el ction bia in tr atment effect model all attempt to isolate the first effect by contr lling r capturing the econd two ource of variation from e timates (Vella and Verb ek 1999 ; Winship and Morgan 1999). However as de sc ribed in Chapter 2, the econd two ourc of spending difference provide important information about the relative value anglers place on access to fishing at rigs As in the structural demand approach, the decision to fish rigs is modeled with a linear index equation (312) { } {3 DI {!3 DI {3 DI {3 DI DI {3 DI } DI where G = 1, y, K 1> s, z = 1 Y K._ 1 f3 s z and represents the unobservables at rig access level b 1 This index is motivated by the latent net utility of choosing to fish at least one petroleum rig in the previous year. All variables are defined as in the tructural demand model and z is an exclusion restriction required so that we can manipulate an individual's probability of rig use without affecting their expenditures Note that the latent net utility value can be different for individuals with the same observed characteristics because of the unobserved heterogeneity term 0 For example, some angler won t fish at a rig unless they own a boat while others will rent a boat or hire a charter to do so. Thi also ugge ts that capital purchases should be incorporated in expenditure and welfare measure a hown in (31) and (34 The index equation define an ndogenou witching regime model of annual ariable and capital e penditure with and without rig u e (313) [p x + kK] = { {3 11 11 {3 01 + 01 if D = 1 otlzerwi
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5 = {l ,y, K 1 },,B l/ = {,B ; ,B t, ,B t ,,B ; } and 'Jr pre nt theun b ervable m th quati n at rig a lj. 5 Pre ntly ,j = 1 becau b 1 i u ed a th r fi r nc tat rr p nd with th bi.nary indicator D an d qual 1 if rig w r u d and z ro oth rwi F llowi.ng Phlip ( 19 3 income i normalized to the own price lev 1 and the int r pt and rror t rm fi r th public good u r (i = D = 1) are implicitly defined as n nu r (i = D = 0 Th r fore prices appear endogenously as a portion of the un b rvabl d t rminant of p nding 6 That is pis not formally defined in terms of a pri e i.nde eparate from total expenditures. The treatment effects approach can model pnc thi way becau th y are not required in the derivation of welfare measures. This i u eful for rea ons discu sed in the introduction especially when dealing with crossectional data where price variation is commonly an expression of changes in some other ariable (e g. di tance or quality). The added flexibility is also particularly important when the public good of interest is defined as a characteristic of a nonmarket activity (Bockstael and McConnell 1993) In such cases including the current study, it is easier to identify the expenditures on the nonmarket activity (e g ., fishing), than to define the 5 I e perirnented with other functional forms for the expenditure equations such as the quadratic in income specification consistent with the quadratic almost ideal demand y tern. Howe er a frequently occurs with recreational expenditure data the income terms did not come up ignificant in any specification. Therefore I opted for the simpler linear pecification with the additive error term It is easier to derive a linear in variables n t utility function from the linear Engel equation. 6 This pecification can be integrated to recover the related indirect utility function Hau man 19 1 that can be u ed to specify the form of the related net utility index. In th ppendix I how that the resulting net utility index can be reduced to a simple linear in ariable equation with an additi e error.
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5 pnc and quantity indice neces ary t a tivity timat a tructural d mand model for the The full endogenou witching e tim a ting y tern i (314) D 1 = G/3 1 +t: 0 1 (315) [px + kK]" = X {3 11 11 (316) [p x + kK ] 01 = X [3 1 + t: 01 A suming s O1 e 11 and e 01 are joint normally distributed, the parameters {f3 11 [J 01 [3 1 CY 11 CY 01 p 1101 p 0101 } can be estimated simultaneously via maximum likelihood or in a two step procedure for simultaneous equations with endogenous switching (Maddala 1983). 7 I obtain FIML estimates of the model parameters using the endogenous switching estimator in LIMDEP (Greene 1995). As defined in Chapter 2, the standard treatment effect and the policy relevant treatment effect measures for this model are (Heckman Tobias and Vytlacil 2001): (317) (318) (319) (320) 7 The co ananc r ariance of th ind [ p ] = X ( /3 11 /3 01 ) + ( CY 11 D 1 CY O I o 1 ) [ G /3 o 1 ] a ily reco er d fr m th corr lation o ffici nt b cau e th quati n i n rmal iz d t unit
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60 A. 11 = ( cfi 01 )/ (1) ( cfi 01 ) and A01 = ( G fi 01 )] Heckman, Tobia s, and Vytlacil (2001) how imp! unconditional e timator f; reach of the four tr atment effi ct param ter a (321) wh re Ki th tr atm nt effect measure of inter st and N is the number of observations in th rel vant et i.e ., N is the whol sample for (317) and (320) only the users for (318) and only the nonu r for (319). Note that expectation in (320) can be conditioned on any sub t of the ample. For example evaluating (3 20) over the set ofrig users, gives the expected treatment effect welfare measure for a randomly chosen individual from this group This calculation and a similar one for the group of nonusers is reported in the re ults Dat a The sample for the analysis is taken from the 1999 U.S. National Marine Fisheries Service Economic Survey of Private Boat Anglers. A subset was selected from the ample ofrecreational anglers along the Gulf of Mexico coast (Alabama to Texas). See QuannTech (2001) for more information about the intercept and phone survey in truments and the dataset. The surveys elicited detailed information about fishing location target pecies and expenditures for variable and capital goods In particular, respondents were asked to report the number of days that they fished ''within 300 feet of an oil or gas rig or within 300 feet of an artificial reef created from an oil or gas rig" during the prior year. This information allowed the sample to be split into a segment that
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fi hed at rig it during th pr v1ou y ar and all other re s pondent Brief de c riptions ofth coding fthe relevant variabl appear in Table 3 ote that nearly half the ample did not report hou ehold income Missing income value wer replaced with the mean reported value from the respondent county of re idence. There was al o mis ing trip cost data. The portion of the sample who took Table 3 Samele means and standard deviations for rigs model variables Variables Users (n=372) Nonusers (n = 124) All (n=496) Cost of a Rig Trip ($) 89.978 96.932 92 375 (52.181) ( 18.280) (43.685) Cost of a Nonrig Trip($) 153.470 52.435 118.637 ( 455.607) (64.946) (373.736) Cost Difference for Rig Trip ($) 63.492 44.497 26.262 ( 456.379) (63 740) (374.720) Total Fishing Trips 29.628 25 514 28.210 (31.769) (42 623) (35.878) Rig Fishing Trips 14.241 0.000 9 332 (19.572) (0.000) (17.226) Total Variable Expenditures($) 3 406 087 1 351.461 2 697 739 (7 427.224) (3,734 135) (6,469 534) Total Annual Expenditure($) 7 602 246 2 512.929 5 847 666 (14 137.100) 4 854.344 12 033.4 5 Current apital tock ( ) 11 138 121 5 045 676 9 037 705 (17 584.240) (7 352.223 15 145 725 apital tock Lagged ( 6 941.962 3 4.20 5 87 778 (14 078.927) (6 12 166 2 7 tandard de iation in par nth e. Table continu db lo
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2 abl 2 3 1 400 00 ar 22.077 23.333 14 14 I 15 ) (14 .983 nd r ( l = fi m l 0 0 2 0 113 0 092 0. 274 (0.318) (0.290) mb r hip (l = y 0 1 4 0 113 0 160 0 .3 ) (0.318) (0.367) L ui iana R id nt (l = y 0.322 0.444 0.364 (0.468) (0.499) (0.482) ippi R id nt (l = y 0.093 0.162 0.117 (0.290) (0.370) (0.321) T a R id nt 1 =ye 0 231 0 225 0.229 (0.422) (0.419) (0.420) oa tal R id nt (l=ye ) 0.919 0 911 0 916 (0.273) (0 287) (0.277) Target Rig pecies (l=yes) 0.262 0.062 0.193 (0.440) (0.241) (0.395) tandard de iations in parentheses both rig and nonrig trips had missing data because the intercept data only reflects one of the e type of trips. Similarly those who did not take a rig trip had no expenditure data for this type of activity. The missing trip cost values were replaced with the mean values o er only rig u ers in the relevant Gulf State in order to avoid mixing across the rig and nonrig groups. The replacement procedure is summarized in Table 4
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3 Table 4 Replacement rule for mi ing variable co t data At least one rig trip in the previous 12 months? YES (1) 0 (0) Cost of a rig trip = VC11 ot Possible YES (1) . s t ate Cost of nonng tnp = VC01 (0) Took a rig (218) trip when intercepted? s ta te s t ate Cost of a rig trip= VC11 Cost of a rig trip= VC11 NO (0) Cost of nonrig trip = VC 0 1 Cost of nonrig trip= VC 00 (154) (124) The summary statistics in Table 3 are split into two sub samples: those anglers who fished at rigs (users) in the previous year and those who did not (nonusers). The socioeconomic characteristics reported are fairly consistent across the sample. The key differences between the two subsamples arise with respect to the economic decision variables such as trip costs expenditures, capital stock holdings, and rig species targeting. Specifically, a rig trip costs relatively more than a nonrig trip for nonusers. The converse is true for users suggesting that each group has an absolute advantage in their chosen activity. 8 Each group also appears to have a comparative advantage in their chosen activity. However cost savings per trip is only part of the story. Ad antages cannot be fully studied without reference to each group willingnes to pay for rig and nonrig fishing. This premi e i e plored in the re ult although, the difference in annual fi hing expenditure and capital tock of the t o group in Table 3 i ugge ti e 8 The terms ab olut and comparati ad antag ar commonl u d in the labor upply lit ratur F r ample h n ba don arning ith rad antag can be used to plain th typ ari ty or l cati nth of lab r l ct d b an indi idual Em r on 1989 Maddala 19 3 In th ca f recr ati nal anglin 0 th ad antag are mea ured in t rms of utility c n tant t a ing for diffi r nt typ r location of fi hing
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Th p I d it tra trip 4 t m d Ii e tim t du in g th e numb r f ann u a l fi hin g nt ari bl Ind p ndent variabl in thi re g r e i n include the variabl t fa rig trip th variabl o t of a nonrig trip th e t ck of fi hin g durabl a t th b ginning f th y ar ( apital tock lagged), hou ehold income and ther ontr a riabl Th t frig and n nrig trip is defined as any per onal s pending by th r p nd nt ti r th trip on which th y w re intercepted. Ali t of pending categories in Jud d in variabl trip co t i hown in Table 5 Note that the opportunity cost of time i n t includ d among the variable co t it m Time co t are not con idered in the pr ent analy i p nding includ din the variable and capital fishing expenditures tra el I dging fi od drink boat fuel boat rental dock fees launch fe s repair and towing on trip bait p cial licen es for trip tackle and guide ervice equipment rental p cial clothing Capital boat motor trailer electronics safety gear rigging for fishing boat or equipment repairs rods and reels fishing line lures and artificial bait other fishing equipment fishing books and magazines fi bing club membership camping equipment for fishing fishing licen es Two treatment effect models are e timated a defined in (314)(316). The fir t u e annual ariable trip rig and nonrig trip e penditure a the depend nt ariable in the outcome equation in the treatment effi ct witching regre ion. The e ariable are
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65 calculat d by multiplying the re pondent' rig (nonrig) trip expenditures by their total number of annual rig (nonrig) trips The second treatment effects model uses total annual expenditure calculated by adding the additions to capital stock during the year to the annual variable expenditures. Spending categories included in the capital measures are listed in Table 5 The other control variables, as well as the variables used in the rig use selection equation, are listed in the results. One variable of note, however, is the decision to target rigs species. This variable is coded 1 if the respondent indicated a target preference for species that are commonly associated with oil and gas rig habitat. The means for the target variable indicate that a larger portion of those who fish at rigs also target rig species. This introduces the potential modeling issues associated with multiple criteria for selectivity (Maddala 1983 pp. 278 283). In the recreational fishing demand literature the relevant questions concern, for example, whether anglers choose a species target and fishing location sequentially or simultaneously and, if sequentially, in what order (Kling and Thomson 1996). I will assume that the process is sequential and the target decision is made first by using a binary target variable as a regressor in the rigs decision equation. The target variable also serves as the exclusion restriction necessary for the index function setup (Heckman and Vytlacil 2001a). Results Travel Cost Model The tra el co t count model e timation re ult are hown in Table 6. Three variabl are ignificant in the rig u e deci ion quation. Mi si ippi r idents are le likely to fi hat rig compar d to angl r from oth r tate and tho e who target pecies a ociated with rig ar mor lik ly to fi h rig The negati e co fficient on the co t
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6 differ n variabl ugg t that high r r I tiv e ri g fi hing rig th probability of numb r f th param t r in th trip d mand equati n are ignificant. Th with high r apit I t k at th b g inning f th year t nd t taker latively m re rig trip h li id nt ippi and T xa and memb r f fi hing lub ar al tak r lativ ly more rig trip 9 Femat Loui iana re ident and indi idual with more xp rience take le rig trip Tho e with high r incom al o app ar to take le rig trip ugge ting a negative income effect. H wever giv nth m a ur ment prob! m with the income variable, this re ult i note pecially troubling. The own price variable ( cost of a rig trip) is negative but not significant wherea th ub titute price term co t of a nonrig trip) is ignificant and po iti e. The latter r ult implie that rig and nonrig fishing trips are ub titutes Although not significant the inver e of the own price coefficient give an expected con umer urplu per trip of 4 442 See equation (39). Multiplying thi value by the expected trip a hown in Table 7 gives an expected annual uncompensated surplus of rigs fi hing of 37 824. Adjusting for income effect using expre sion (310) the corre ponding expected annual compen ating variation i lower but till very high at 27 569. The tandard deviations hown in th table were obtained by evaluating th mea ure for each indi idual in the ample. The ariance of the e tra tocha tic term in the Poi onormal model i ignificant indicating that there i un b erved h t rogen it influ ncing the trip deci sion. 9 R id nt of lab ma ar the ba t z ro ariable are equal
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67 Variable Rigs Decision Trip Demand onstant 2 63E0 1 l.49E + 00 (3. l 2E 0 1) ( 1.97E0 1 )* Cost of a Rig Trip ($) 2 25E04 (2.91 E04) ost of a Nonrig Trip ($) 2.25E04 Cost Difference for Rig Trip ($) 3. 86E03 (8.91 E 04 )* Capital Stock Lagged ($) l. l0E05 (8.26E 06 ) Income ($/yr) 3 86E07 (2 52E06) Experience (years) 4.64E03 ( 4.19E03) Gender ( 1 =female) l .69E0 1 (2. 13E0l ) Memberships ( 1 =yes) 2.93E01 (1.79E 0l ) Louisiana Resident ( 1 =yes) l .08E 0l (1.95E 01 ) Mississippi Re sident (l=yes) 5 .07E0l (2.84E0 1 )* Texas Resident ( 1 =yes) 5.2 2E02 (2.lSE 01 ) Coastal Resident (1 =yes) 8.37E02 (2.08E 0 1 ) Target Rig Species (1 =yes) 7.64E0l (2.73E 0l )* (J tri p s p se l e ction trip (J se l ectio n tr i p s tandard error are hown in the parenthe es belo each e timate. *E timat ignificant at the 0.10 level. The final value ofth log likelihood function i 1603 968 (7.53E05)* l.67E05 ( 1.45E06)* 3.42E06 (6.20E07)* 7 .84E03 (1.91E 0 3)* 2 83E0 1 ( l.23E0 1 )* 5.20E0l (5 25E02)* 2.66 E01 (5.7 lE02)* 2.32E01 (6 .69E0 2)* 1.60E0 1 (6 24E02)* 6.19E0l (l.77E 0l )* 9 SSE01 (3.08E 0 2)* 5.46E0l (2 59E0l)* 5.22E0l (2 59E 0 1
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6 In addition, th rr lati n and c vananc b tween the rig u and trip count deci ions are ignificant ugg ting that el ctivity i pre ent a modeled Mean ctual Rig Trip Exp ct d Rig Trip Exp ct d Annual ompen ating Variation E pected Annual onsumer Surplus T r e atm e nt E ff ec t s M od e l s 14 24 (19.57) 8.51 (7.38) 27 569 (12,850) 37,824 (32 784) The FIML e timated coefficients of the treatment effects model (TEM) with annual variable expenditures and total annual expenditures are shown, respectively in Table 8 and Table 9 The igns and levels of the significant coefficients in the rigs decision equations are roughly consistent with those estimated in the selection equation of the tra el co t model (TC ). 1 0 Again those who target rig species are more likely to fish at rigs and the le el of exi ting capital tock is not a significant influence on the probability of fishing at rig issi sippi re idents are less likely to fish rigs than Texas and 10 The coefficient between TC count demand e timate and the TE u er e penditure equation are not directly comparable because they each mea ure influence on a different dependant ariable
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69 Table 8. Annual variable exeenditure treatment effects model re s ult s Variables Rig s Decision With Rig Use Without Rig Use Constant l.21E01 3 07E + 03 4.57E + 03 (3 83E01) (2.52E + 03) (9 31E + 03) Capital Stock Lagged ($) 1.45E05 8.37E02 4.58E02 (9 99E06) (2 73E02)* (1.18E0 1 ) Income ($ / yr) l.99E06 8 59E03 l.30E02 (2.67E06) (1.74E02 ) (3.0SE02) Experience (years) 5.52E03 5.64E + 0l l.99E+0l ( 4.47E03) (4.38E + 0l) (5.12E + 01) Gender ( 1 = female) 1.7 lE0 1 2.16E + 03 1.71 E + 03 (2 18E01) (2.35E + 03) (2.52E + 03) Memberships ( 1 = yes) 2 63E01 2.36E + 03 7.58E + 02 (1.94E01) (l.33E+03)* (2 55E + 03 ) Louisiana Resident ( 1 =yes) 3.99E01 4 18E + 0l 2.17E + 02 (1.95E01)* (2.33E+03) (3.71E + 03) Mississippi Resident ( 1 =yes) 6.35E0 1 l.13E+04 l.65E + 02 (2 78E0l)* (1.76E + 03)* (4 83E+03) Texas Resident ( 1 =yes) 2.69E01 l.31E+03 1 92E + 03 (2.35E01) (2.18E+03) (2.96E+03) Coastal Resident ( 1 =yes) 1.08E0 1 2 54E + 02 2.21E+03 (3 26E01) (l 55E + 03) (1.55E + 03 ) Target Rig Species (l = yes) 8 13E01 (2.78E01)* cr ex p e nd 6.50E + 03 3.56E + 03 (1.78E + 02 ) (9.81E + 02 )* p se l ection,ex p e nd 4.73E02 l.59E0 1 (3 89E01) (2 29E + 00 ) CT e l ectio n ex p e nd 5.66E + 02 4.25E + 06 (8 31E + 03 ) (6. 77 E + 06 ) Standard errors are hown in the parentheses below each estimate. *E timate ignificant at the 0 10 level. The final value of the log likelihood function i 5244.391.
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7 labama r id nt h m i tru ti r L u1 1an r id nt whi h i m what urpri ing gi nth t th maJ rity f p tr I um plat ti rm ar I at d ff the coa t f L ui in. nly fi f th tim t in th annual ariable p nditur utc me equati n are a ppr i bly ignificant and m t of th c ffici nt ar ti r the Rig U e equati n. A imil r patt m pp r ti r th t tal annual p nditur utc m equations Inter tingly th a po itive influ nee on annual variable p nditur but n t n t tal annual p nditure Ba ed n the T M re ult in able 6 th additional p nding ari b cau tho with larger fi hing capital stocks take r lati ly m r rig trip How er it appear that the e individual are not any more lik ly t add to capital tock throughout the year than those with relatively smaller capital tock Tho with paid m mb r hips to fi hing club and residents of Mi i sippi tend p nd more on variable and capital costs for rig trips. The timat d variances of all the spending outcome equations in Table 8 and Table 9 are ignificant indicating the importance of unobserved heterogeneity in this ample Howe er becau e of relati ely insignificant correlations the covariances between the rig deci ion and pending equations are not significant. This suggests that there is a limited degree of selfelection based on rig u e in the sample. To u e the analogy from the labor literature (Emerson 1989 the lack of significant covariance between the use and pending deci ion implies that neither group ha an 'ab olute ad antage in their elected option. In the present application an individual ha an ab olute advantage in th ir cho en acti ity if that acti ity offers them a ignificantly lower co t for utility than competing acti itie Fore ample tho e ith an ab olute ad antag for rig u e can
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71 Ta ble 9 Total annual exeenditure tr ea tment effects model results Variables Rigs Decision With Rig Use Without Rig Use Constant l .2 0E0 1 l.09E + 04 6 51E + 03 (3.6 lE0 1) ( 4 59E + 03 )* (6 34E + 03) Capital tock Lagged ( ) l .44E05 l.60 E02 8 l 8E03 (8.96E06) (6.42E02) (8.37E02) Income ($/yr) 2.06E06 2.00E02 1 .28E 02 (2.66E06) (2.49E02) (3.48E02) Experience (years) 5.45E03 9.49E + 0l 2 3 lE + 0l (4.59E 03 ) (6.98E + 0l) (5.17E+0l) Gender ( 1 = female) l.59 E 0l 3.81E + 02 2.48E + 03 (2.20E0l) (3.24E+03) (2.21E+03) Memberships ( 1 =yes) 2 60E0l 4 55E + 03 3.21E + 03 (2. l 6E0 1) (2.25E+03)* (2.19E+03) Louisiana Resident ( 1 = yes) 3 .94E 0l 2 32E + 03 l.73E + 03 ( 1. 92E0 1 )* (3 31E+03) (2.35E+03) Mississippi Resident (1 =yes) 6 .31E0l 2 26E + 04 l.51E + 03 (2.69E0l)* (2.38E+03)* (3.09E+03) Texas Resident ( 1 =yes) 2.68E0 1 l.61E +03 6 60E + 02 (2.25E 01 ) (2 95E + 03) (2.51E+03) Coastal Resident ( 1 =yes) l.02E0l 3 .64E+03 l.21E + 03 (2.80E0l) (3.15E+03) (l .89E+03) Target Rig Species (l=yes) 8.24E0l (2.51E 01 )* (J expend 1 22E + 04 4.66E + 03 ( 4.43E + 02 )* (6.15E+02 p se l ection ex pend l .08E0 1 1 .88E 0l (3.29E01) (9.0lE 01 ) (J selection expend l. 32E+03 8.78E + 02 (4.05E+03 (4.30E+03 Standard errors are shown in the parentheses below each estimate. *Estimate s ignificant at the 0 10 level. The final value of the log likelihood function is 5494.606.
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72 an attain th I utility ta I w r t by u in g ri g th a n b y n t fi h i n g a t r ig imilar nditi n a ppli fl r th wh n t t u n g nd i t i n f utility I hyp th (JI I D = (J O I dv a nt g impli th t th a v r ag u r n nu m do n t u e ri g null mp r tiv ad a nt g an b a lu a t d with a j int t e t o f ~ 11 = ~ 01 a nd aid of 5 .21 and l 5 0 fi r th e r tri c ti n in th e va r ia bl nd t ta! p nditur int qu a lity with gr a t e r th a n % till ignific a nt inforrnati n in th rig u e ( e lfel ction d f an g l r in th amp! that can be u ed to valuate the relative valu a tion of ng a Th tr atm nt effi t welfar m a ures introduced in hapter 2 are de i g ned to plait thi infi rmati n Th un onditional treatment effect and welfare mea ures of rig acce are s hown in Table 10 Th e figure are obtained by evaluating expre sions (317 through (320 for each indi idual in the relevant group and averaging as defined in (321 ). ote that n th larg t mea ure hown in this table is still les than a third of the value s shown in Table 7 for the tra l co t model. The r latively large welfare measures in the travel co t mod I are due primarily to the mall coefficient e tirnated on the travel co t param t r d cribed in Chapter 2 the price variable is crucial in welfare analy is ith the tra I co t mod 1. The treatment effects model side tep thi reliance by u ing inforrnati n from all of the model coefficient to generate welfare mea ure Ho e er arch i n don ay to analytically and empirically compare th e tra el co t and tr a tm nt e ffi t approache
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73 Tabl 10 Annual expenditure treatment effects and welfare estimates of rig access Parameter TEA Variable Costs TEA Total Costs ATE 1 737 4 950 (3,906) (8 131) E[CV] 2 141 5 968 (3 861) (7 926) TT 1,101 3 264 (3,570) (7 276) E[CV I users] 2,054 5,659 (3,591) (7,268) UT 2,945 8,156 (4,377) (9 158) E[CV I nonusers] 2,308 6 556 (4,339) (9 047) Standard deviations shown below the estimates. The average treatment effect and the policy relevant measure of compensating variation of lost rig access for the whole sample are shown in the first pane A randomly selected angler will spend an additional $1,737 in variable costs annually to fish rigs. This amount more than doubles to $4,950 when expenditures on fishing capital is included. The randomly chosen individual is willing to pay between $2,141 and $5 968 annually for access to rigs for fishing where the upper end measure includes forgone capital spending. A randomly chosen angler from the group that used rigs is willing to pay between $2 045 and $5,659 annually and has an expected annual cost for rig fishing of between $1,101 and $3,264. Similarly a randomly chosen angler from the group anglers who did not use rigs i willing to pay between $2 308 and 6 556 annually and has an expected annual cost for rig fi hing of between 2 945 and$ 156
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74 h r ult in bl 10 ar in lin with m u r th mp n ting aria ti n of u d in hapter 2 r n id rably gr at r than the p Thi nt with a prefi r nc for rig us but it also imp Ii that u r ha a I t to loo if th y ar d ru d ac to rig Then nu er re ult h wan pect d comp n ating variation that i le than the extra annual co t of rig u Thi e plain way thi group do not fi hat rig Interestingly though, a randomly l ct d nonu r actually ha a r latively high r value for rig acce s than a randomly ho nu er or a randomly cho n individual in th amp! Thi i true of the variable co t and total co t re ult Thus, nonuser value rig access but do not fish at rigs because doing or quir a r lative l y more expenditure, especia l ly when addition to fishing apit l ar considered The e results illustrate that nonusers do not use rigs because the than the co t. As for the rest of the sample, the results in the first pane of Tab I 10 indi at that a randomly selected individual will choose to use rigs because the b n fit do outweigh the cost The tatistical significance of these measure was not te ted dir ctly but the rejection of joint equality in the comparative advantage test is ugg sti ote al o that although not shown, all of the consistency tests are met at the minimum and maximum values of the sample. D is cu ss i o n Thi chapt r has explored the role of capital expenditures in re ealed preference mod ling of recr ation decisions. The treatment effects approach de eloped in Chapter 2 wa used to evaluate the welfare effects of restricting access to fi hing at petroleum rigs in the Gulf of exico A travel co t trip demand model a al o estimated Ba ed on the treatment effect model the artificial fi hing habitat offered by petroleum rigs was found to cau e' a 1 737 to $4 950 increa e in a erage annual fi hing
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75 expenditur among anglers in the sample. The amount that a randomly chosen angler would be just as welloff without rigs is estimated ranges from $2 141 to $5 968 The upper end of the range i the welfare effect including the additions to fishing capital. These estimated values are substantially lower than the welfare measures generated with the travel cost model. This is peculiar result could be because of the sensitivity of travel cost welfare measures to when costbased prices are used (English and Bowker 1996; Wilman and Pauls 1987). The variation in the treatment effects model measures suggests that not considering information about recreation capital acquisitions and holdings could seriously understate the opportunity cost of restricting access to fishing at rig habitat. The results suggest a need to consider ways to incorporate recreation capital in other revealed preference valuation exercises.
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HAPT R4 APPL! IO TO PUBLI UTILITY PR! If a rational con umer d e n t kn w th pri of a purcha d commodity th n h cannot optimally adju t budg t allocation and marginal valuation to be in line with that I pnce h n pric a curately refl t ocial opportunity co t (a in a perfi ctly comp titi mark t) th burd n of pric mi p re pt ion i on the consumer. That i following hin' (19 5) hypo th i the consumer accepts the inefficiencies from price mi p r eption in r turn for th avoided co t of determining the actual price. On the other hand v hen pric do not accurately reflect social opportunity costs, then price mi p re ption and the uboptimal consumption levels have welfare implications beyond the consum r budg t allocation Cla ic cases of deviations from socially optimal pnc can occur for xample, in the pre ence of externalities and/or in the context of admini tered price for monopoly services (Carter and Milon 1998) Thi chapter de elops analytical and empirical models to evaluate price mi p rception and the alue of price information for the ca e of administered price for publi utility ser ice. In doing so the focus is on the consumer's elfreported price awarenes Thi per p cti e is more fundamental than the studie that ha e used data acros utilitie to examine the effect of different levels of information pro ision and rate tructur tyle on the quantity of public utility er ice demanded. ee Ca anagh Hanemann and ta in (2001) for a re iew. The per pecti e is closer to th larg bod of 1 In the ca considered here the consumer can choo e not to kno the price en though thi information i a ailable ith certainty. Thi is different than the ca e of choic under irreducible price uncertaint Johnans on 1991 76
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77 re earch debating the 'correct' price specification in models of demand in the presence of nonlinear budget constraints (i.e. block pricing). 2 The portions of this research that have attempted to empirically test a consumer s perception of the price of service is of central interest (Chicoine and Ramamurthy 1986; Griffin and Chang 1990 ; Nieswiadomy 1992 ; Nieswiadomy and Molina 1991; Shin 1985). This chapter extends this research by providing a theoretical framework to analyze the comparative statics of price misperception and identifies the value of complete price knowledge. Importantly this framework considers the possibility that price elasticity of demand may change when price perception changes because of changes in exogenously supplied price information. 3 The theoretical framework is used to develop a structural model of public utility demand and a treatment effects model of expenditures on utility services. Both models are based on the discussion of structural and treatment effects approaches to measuring public good values in Chapter 2. Exogenously supplied information about the price of utility service is the public good in this case. The results from the structural and treatment effects models are used to evaluate the benefits of a hypothetical program that would fully inform customers about the price of service. Price Perception and the Value of Price Information The welfare implications of price misperception with administered prices depend on the goals of the pricing authority (e.g. public utility) and the relative abilities of the authority and the consumer to accurately gauge the social opportunity cost of 2 Witness the lively exchanges in Land Economics among Foster and Beattie Griffin et. al. Opaluch Charney and Woodard Billings and Agthe Ohsfeld, Polzin and Stevens et al. in the early 1980's and sub equent literature that continued throughout decade in that journal and Water Resources R ese ar c h 3 hin ( 1985) consider the value of price information for the case where the consumer overe tirnate the actual price. However his representation implicitly assumes that the re pon e to price changes i the same regardless of the con umer s information et.
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7 n umpti n If the pri ing auth rity aim t t pri t r fl t marginal pp rtunity r th y ha pli it n ervati n g that th pnc urat ly. urth rm r wh n th auth rity' dmini t ial f rv1c mor accurat ly than th c n um r' p r iv d pri auth rity an u pn infi rmati n a a policy to l. Thi foll w b cau the r lati fa consum r' pnc infi rmation i partly a fun tion f th amount of xogen u ly uppli d infi rmation ( e.g. adv rti ing). The e g nou ly upplied pric information not it elf ld in the market becau e like adv rti ing in g neral it ha public good characteri tic that may favor other indir ct financing ch me (Frech 1979). onsid r an con umer who perceive the price of a commodity Q as a function p(p,b) ofth actual price p and an exogenou information upply b such as adverti ing or billing in rt that i available to all consumer 4 It is as urned that b is a weak complement of Q o that the con umer is indifferent to the upply of b when Q i not purcha d ( al r 1974 Thi imp lie that bis not a direct source of utility (i.e., b has no nonu e value) and, therefore doe not appear a a separate argument in the indirect utility fun tion ot that the di tinction between p and p roughly correspond to Pollak's ( 1977) conception of normal and market prices. In this ca e p is a normal price signal that affect choice herea p i the market price that enter the budget con traint. This ituation i e c dingly complicat d to repre ent a a direct utility maximization problem 4 long a th on um r are pric tak rs ( e g. subject to admirii tered price ) the analy i an c ntinue in a partial quilibrium frame ork. In other ca e ho e er a g n ral quilibrium tr atm nt i r quir d becau e th equilibrium price ill b an in r ) fun ti n p (f> b) of th xi ting p re i ed pric
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79 o only indirect utility and expenditure function representations of preferences are considered An accurate price perception is costly to the consumer so that c(b) 0 but this cost decreases with the level of the exogenous price information provided oc(b )/ob< 0 5 The conditional indirect utility function for this problem is (41) V (p (p b) ) y C ( b) ) s) C) where s is a vector of observed individual control characteristics and summarizes the unobserved individual preferences and characteristics The price index of a numeraire commodity is normalized to unity and is suppressed along with individual specific subscripts to simplify notation. (42) The marginal value of a change in the supply price information has two effects: dy = oc (ov/op )(op/ob) db ob ov/o(yc(b)) where the first term on the right hand side is the reduction in the cost of an accurate price perception and the second term is the value of the change in price perception induced by the additional information To carry the analysis a step further, assume that the perceived price function takes the form p(p b) = p b for b = (0, oo ]. The perceived price is assumed proportional to the actual price by an adjustment factor b that summarizes the stock of exogenous price information. The perceived price is bound below to be greater than zero because the 5 There have been attempts to explicitly consider the co ts of price information search (Kolodinsky 1990) The more compact repre entation uffice for present purposes
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: ost 0 con umer will lik ly r cognize a nonzero price if they ar pending income on the commodity. Th r ar thr ca to nsid r : (a b = l, (b b > I, and c O < b < I In th fir t a th p re iv d pri qua! th actual pri e i . th nsumer is fully infi rm d ab ut pri In t rms f th xpr i n ( 42 ab ve, the fir t ca e ugg t that th additi nal inti rmati n will n t affi t tho wh alr ady know the price b y nd the r du ti nth t f additi nal pric Lnfi rmati n. Th ond ca e indicat a perc ived pn that i gr at r than th actual price and th third ca e indicate a p rceiv d price that than th a tual pric In th latt r two ca e the price mi perception i leading to r und r consumption of th commodity Q relative to the composite commodity. Thi i mo t dir ctly hown by differentiating the expenditure function for this problem by th actual price of Q (43 oe (p (p b) u E) op = oe op ofJ op wh r e() gi e th rrummum penditure required to attain utility level u. oting that (43 i an pr ion ofth comp nsated demand Q c for Q we can rearrange tog t Op Oe c (" ( ) ) op op = Q P P, b u, E (44) oe Q C (p (p b) u s E) =op op/op Q C (p (p b) u 'E) = ,.. b for p (p b) = p b. Thu in th cond third ca e here the percei ed price i abo e (b lo ) the actual pric th ffici nt comp n at d demand will be deflated inflated by op/op or b so that th onsumer ill b und r ( o r consuming Q.
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81 To consider the value of a discrete change in price information it will be useful to explicitly define the conditional indirect utility function in terms of the decision to know the price (45) ij ( ( b j ) ij ) V V l p p ,y ,S, E where i equals 1 if the price is known and O otherwise given the supply of price information lJ and conditional income is defined in terms of the cost of price information as / 1 = yc(i /J). The consumer will choose to know the price if (46) where D* is defined as a latent variable that indexes the net utility of knowing the price given the available price information. Table 11 shows the four possible indirect utility outcomes for a discrete change in the supply of price information from b 1 to b 0 The analysis in this chapter focuses on the special case where b 0 is the level of price information that ensures everyone will know the price. In this case cell (2, 2) in Table 11 is irrelevant because everyone will know the price after the change in price information. The compensating variation (CV) of a discrete change in the supply of price information from b 1 to the level b 0 that generates accurate price perceptions is 6 6 In general, the CV of a discrete change in the supply of price information from b 1 to b 0 is given by CV(b 1 ,b 0 )=e(,v(p,b 1 ),/ 1 ,s c:)e(,v(p b 0 ) / 1 s,c:). This formulation is general because p (p b 0 ) does not necessarily equal the actual price. Thus an individual may chose to know the price in either state of the world and can switch from not knowing to knowing or vice versa following the change in the price information
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1lt o now o n 47 V ( b 1 b 0 = ( p p b 1 ,1 ( ,I p p=p (p b o ) kn\; th pn kn v th pn = p p p b l In thi r th . ithth in rm t i nl cl b 0 th l rmati n th indi idu I m y r ma y n han g e they will r d fr m b e rv d expenditure patt e rns d ta a ailabl for b havior after the ut m mu t b imulated where needed In thi 2 1) in Tabl 11 are not available so this information mu t b infi rr d fr m th data n b ha ior with the reference supply of price information ar d rib d and applied following the di cus ion of the value of price infi rmati n outcome with rice knowled e and information chan e BEFORE U = l) AFTER U = 0) CHOO E TO YE (i = l) OW PRICE? 0 (i=0) v ( 0 p (p b 0 ) /xi s E) The alue of price information is shown in Figure 4 and Figure 5 for the second and third cases of price perception re pecti ely for the assumed form of p (P b = p b There are two compensated demands shown in each figure indicating that the lope and
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83 position of a demand curve dep e nd on the available price information Specifically differentiating the compensated demand function with respect to the actual price p write s an expression for the slope of the demand curve in actual price / quantity space (48) for p (p b) = p b Thus the slope of the perceived price demand curve will differ from the slope of the actual demand curve by a factor relating the perceived price to the actual price Those who know the price can respond differently to the same change in actual price than those without price information Note that total change in uncompensated demand with respect to a change in perceived price is manifest in the substitution effect (49) for p (p b) = p b where <;t1 is the uncompensated demand for Q 7 For the first case noted above (b = 1) the slopes of the perceived and actual price demand curves are the same. Figure 4 illustrates the second case ( b > l ) where the consumer overestimates the actual price and the slope of the perceived price demand curve is greater than the slope of the actual price demand curve. Area A measures the value of price information (i.e. of a change in price perception) in ( 47). If more 7 The version of the Slutsky equation in expression ( 49) is derived as shown in Varian (1992 p 120) starting from compensated demand function with the perceived price argument. Only own price effects are illustrated but these effects represent changes in relative value since from above the own price and income terms are normalized on a numeraire good.
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p(p,b l ) p 4 (p(p,b') Q (P, vo' ,s,) .______ __ _.__ ______ Q ob erved 01 V Figure 4 alu of price information: perceived price greater than actual price p C Q (P V Oi Q(p(p b l ) V Oi c) ...._ ____ _....__ _____ Q Q(observed) Figure 5 alu of pric informati n: percei ed pric than actual price
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85 information about the price change s price re s ponsivene ss, then perfect price knowledge would have an additional value equal to area B In oth e r word s, a mea s urement of the value of price information that incorrectly assumes no change in beha v ior would overstate the true value for the second case. Figure 5 de s cribes the third ca s e (0 < b < 1 ), where the consumer und e restimates the perceived price and the slope of the perceived price demand curve is l e ss than the slope of the actual price demand curve The value of price information in this case is shown as areas C and D Note again that incorrectly assuming no change in behavior provides misleading welfare measures ; in this case the value of price information would be understated Empirical Models Households will chose to know the true price if the net benefit of doing so is non negative, but the point at which an individual household will choose to do so is generally unknown. 8 Two public good valuation approaches described in Chapter 2 are applied here to infer the net benefit of price knowledge from observations on individual behavior. The first approach uses information from an estimated structural demand equation for public utility services to recover the welfare areas as shown in Figure 4 and Figure 5. The second approach adapts techniques from the program evaluation literature to calculate treatment e ff ec t welfare measures from household expenditure patterns Both approaches use an index function to model the decision to know the price of service ( 410) 1 (G) 0 {1 if n 1 o D D + 0 oth erw i se 8 The empirical s ection of the chapter refers to the decision unit as a household rather th a n a con s um e r to b e con s i s tent with th e c a se s tudy data.
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wh r o ) i a fun ti n fa v ct r rv d rand m ari bl th t a t th kn w th prt and r d rand m vari a bl th that . th lat nt n t utility v riabl in 4thi ind t I fun ti n umm n z n indi r th d n t kn w th pn r n t. Wa t r D m a nd M d 11 wing H n m nn l 4a) the b rved quantity f public utility rvt d mand d b fi r th pri infl rmation hange can be r pr cnt d a otherwi s e 411 if D 1 = 1 otherwise ith con i t nt p cification for the demand equation Q{ ) and the observable portion of the ind equation o this model can be estimated as a switching regression before the change in price information (Maddala 1983). 9 The results can then be use to simulate the welfare mea ures defined in Figure 4 or Figure 5. However, another wellknown e timation i ue ari es with public utility ervices where quantity and marginal price are determined simultaneously with block rate pricing structures Ideally estimation in this context should proceed with technique that al o consider the imultan ity of the di er te block choice and continuou quantity choice deci ions 9 If the deci ion to kno the price i not correlated with consumption decisions then OL can be u d to e timate eparate demand equation for tho e who kno1, and those ho don t know therwise a technique to correct for endogenou ample election mu t be u ed to get unbia ed e timate of the parameters in the two demand equation I hypoth ize that the t o deci ion are in fact correlated and propo ea general model of endogenou itching to e timate the demand equations for the tv o re g ime
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87 (Cavanagh Hanemann and Stavins 2001 ; Hewitt and Hanemann 1995; Reiss 2001 ; Rietveld, Rouwendal and Zwart 1997 ; Terza and Welch 1982) 10 I opt for a simpler approach, following Agthe et al. (1986) and Chicoine Deller and Ramamurthy (1986) in specifying price and quantity equations as a system of simultaneous linear equations. 11 There is a cost associated with linearizing the budget constraint in this manner (Maddock Castano and Vella 1992) but I choose this approach to keep the analysis manageable and to maintain the focus on the selfselection related to price knowledge. Recognizing that the actual price and quantity are jointly determined with block rate pricing, the model in ( 410) and ( 411) can be respecified as a simultaneous equations model with endogenous selectivity (Lee, Maddala and Trost 1980) : ( 412) (413) p11 = m11H +
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1ck th tim I d p r m t r r 6. m th t nd rd pr dur r t mpl r th th th d pri p ar m t r i am nd th pri infi rrnat i h c h i pr a nd quantit I u th pr di t d lu th pr bit c qu a ti n r u d t mput 1 = I th pri nd th d n t kn 1 = 0 th e pri ill rati ariabl A. 11 r ith in th tw pn ti h r g r i n pr du ffi i nt w 1 and t1 are u ed along ith J .' 1 m timati n f th tw d mand quation to produce th e timat d coefficient nd p 1 for a h gr up Like
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89 The empirical specification of the Q{ ) and P functions used were developed by Shin (1985) to measure price perception among utility service customers The perceived price p is defined as a function of lagged average price, APrJ, marginal price, MP, and a price perception parameter k such that (415) which implies that the stock of exogenously supplied price information is a function of the actual price p = MP and the previous period's average price of service. 13 As constructed the value of the perceived price variable depends on the parameter k: if the consumer only responds to marginal price, then k = 0, and if they only respond to lagged average price then k = 1. Values fork between zero and one imply that the perceived price is between marginal and average price, while values outside of this range suggest that the consumer is responding to some other price level. In doublelog form the partial adjustment 14 model estimated by Shin (1985) and Nieswiadomy and Molina (1991) appears as: ( 416) Ln(Q) = a+Ln(Q 1 1 )(18)+Ln[ MP(AP, JMP/]ery +Ln ( y )8v + Ln (s )8/3 = a+ Ln (Q 1 1 )(18) + Ln (MP)8ry + Ln [ (AP, 1 / MP)]k81J +Ln (y )8v + Ln (s )8/3 1 3 Note that all prices and income levels are adjusted to relative values by dividing the monthly income and price variables by a regional CPI for the month of observation. This adjustment is necessary to preserve the homogeneity restriction and ensure that the estimated demand equation is consistent with utility maximization (Hanemann 1998) 14 The partial adjustment model is used because households are unable to fully adjust their water use in the short run (billing cycle) given a fixed stock of waterusing capital. I explicitly write out the model with the partial adjustment parameter as it appeared in Houthakker Verleger and Sheehan ( 197 4). Note that all terms without 't 1 subscripts indicate values a t time t.
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erceived a of le wh r a. i th int r pt, v'i th p rti I dju tm nt p ram t r t b tirnated 77 1 th e la ticit y i th c n tant inc m cla ticity and f3 i nfi rm bl m d I th t par t th Ln ( MP) and Ln (. P 1_, 1 m nt f th Ln (A P ,_/ MP t rm : 17 Ln = a+ Ln ( 11 ( I 0) + Ln (MP) 017 ( l k + Ln (A~  k0T] + Ln ( ) 0 + Ln ( ) 0 f3 hi fi rm f th m d Ir al th t hin p r i d pric ignal i imply a w ight d mbin ti n f th marginal pri and l agg d av rag pric ignal ing the fa t that P1 = Bf LL ,_ 1 /i ,_, th m d I an b irnplifi d Furth rt yi Id 15 41 LnQ = a+Ln( 1 )[(1 0)(l+krJ)]+Ln(MP)071(I k)+Ln(BILL 11 )k071 + Ln (y )0 + Ln ( )0/3 ntially a h rt run pe ificati n but th long run effect can b recovered by manipulating th partial adju tment param ter. Full adju tm nt fJ = I occur ubject to the hou ehold' price perc ption. If the hou ehold maintain a percei ed price other than th ir marginal pric k :j:. 0) th n they cannot adju t Q to an efficient le el relative to the con umption of oth r items The completely adju ted household (fJ = 1 k = 0) will have optimally l ted it apital tock and be reacting to change in the marginal price of ervice For r ference the formula used to reco er the key parameter of interest are h n in Tab! 12. The deri ation of the alue of price information measure from the d mand mod 1 param ter is described in the Re ults. 15 BILL 11 i a nonlinear functi n of Q ,. 1 becau e ofth block natur of th rate tructur th th r le chanc f introducing multicollin arit b including both ariabl a r gr or
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91 Table 12 Formulas for key model parameters Ln(Q) = [bO] + [bl]Ln(Q t1 ) + [b2]Ln(MP) + [b3]Ln(BILL tl) + [b4]Ln(Y) + [~]Ln(X ) Parameter ShortRun LongRun Income ela s ticity b4 b4(1bl ) Perceived price elasticity b2 + b3 (b2 + b3 )/( 1b 1 ) Marginal price elasticity b2 b2 / (lbl ) Price perception (k) b3 / (b2 + b3 ) b3 /( b2 + b3 ) Partial adjustment (8) 1 (bl/(1 + b3 )) 1 Treatment Effects Bill Model The general treatment effects framework introduced in Chapter 2 is an alternative way to recover the value of price information. This framework is designed to evaluate welfare measures for public good changes with expenditure data for different segments of population. For the present case I am suggesting that there is a hypothetical program to full y inform consumers about the price of Q The additional price information can be considered a change in the supply of a public good from b 1 to b 0 such that j; (P b 0 ) = p Formally the difference in an individual's monthly bill with and without the additional price information is the treatment effect of price information program ( 419) Li= e(p (p b 1 ) v ; 1 s )e (P (p b 0 ) /, s = e(p (p b 1 ) y, s )e(p (p b 0 ) y, s = BIL 1 BIL 0 where the first line suggests that that this spending difference is an uncompensated measure of the value of price information shown in (47 ) This measure can be directly recovered with observations on the two spending outcomes for each individual. The approach developed in Chapter 2 can recover the welfare measures in ( 419 ) and ( 47 )
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)f 2 h n n p nding ut m nl ii bl r p n d re th in pn in rm ti n h ppli t th 1du kn th pn n b 0 r thi th n b r p nding ith nd 1th ut pn = (P p b l V Oi ) j;(p b 1 II 2 = (P(P b 1 ), 1 (p = BILL 01 Blll 11 h Ir aim nl th in th ampl h th pn I int r up imp th rt nt. roup nd th up r th p ibl ur v h d n t th nlrol r up in indi idual m p nditur pattern am ng p nditur b tween th pnce ntr I gr up : 1 pri kn wl dg may I ad t higher or mm dity 2 th ho know the pric may pend nth mm dit in th fir t place and 3 the xpenditure of tho e who becau e of the price knowledge than pn if th y did d crib d in hapter 2, the information f ariation can be u ed to infer the relati e value of the d i i n t I am th pric H ck.man 2001 a pecifically the deci ion to know the price In th tr atm nt effi ct approach TE expenditur ar modeled a an ndog nou it bing r gre 10n
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( 421) { BILL 11 if D 1 = 1 BILL= BILL 01 oth e rwi se 93 where j = I because b 1 is used as the reference s tate of price information and D 1 is the price know ledge index equation defined in ( 410 ). Ex penditure for the monthl y public utility services bill is modeled with a linear Engel relationship : (422 ) BILE 1 = 13 ;1 + BILL 13 11 + 13 ;1 + s l3 ;1 + ;1 / 1I BILL,_ 1 y y s where following Phlips (1983 ), income is normalized to the own price level and the intercept and error term for the public good users (i = I ) are implicitly defined as 13 ) 1 = jj ) 1 p1 1 + P 1 p 01 and 11 p 11 respectively These terms are defined similarly for the nonusers (i = 0) Thus prices appear endogenously as a portion of the unobservable determinants of spending. The lagged dependent variable appears as a regressor because as was assumed in the structural demand model a household s water use and spending can only partially adjust towards their optimal consumption level in the short run. Following the procedure in Chapter 3 ( 422 ) is integrated to reco v er the related indirect utility function necessary to specify the form of the related net utility index D 1 In the Appendix I show that the resulting net utility index can be reduced to a simple linear in variables equation with an additive error. The full endogenous switching estimating system is ( 423 ) ( 424 ) ( 425 )
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4 wh r th variabl ar c llect d in = ( I BILL 1> and = (1, y, ,z ) andth nfi rmabl param t r v t r ar /3 = (f3 ;t f3 ~~u .,_, /3 ;', /3 ; 1 ) fi r th p nding qu tin and /3 1 = (/3 :' ,/3 : 1 /3 1 ,/3 1 ) f; rth indexcquati n t that nt th lu i n re tri ti n r quir d fi r th g n ral ind quati n p ific ti n H kman nd ytla ii 200 I a urning e 0 c 11 and c 0 1 are j int n nnally di tributed th H L timt th fth paramter {/3" /3 1 f3 1 a 11 a 01 ,p 11 0 p 0101 }ar bt in d u ing th nd witching e ti.mat r in LIMD P re ne l 95 16 The par m t rd finiti n are d rib d in th r ult d fined in hapter 2 and imp mented in hapter 3 the standard tr atm nt ffi t and th policy r I vant tr atm nt effect mea ure for thi model are (Heckman, bia and Yytlacil 2001): (426) 427) 42 42 A 11 = ( G fi O ) / ( G fi O ) and A 01 =  ( G fi O ) /[ 1 ( G 0 ) ] are th rn r pr i n (429 is the p licy r l ant tr atm nt f[l t w lfar m a ur for Thi 16 Th co anan e a ily reco er d fr m th c rr lati n quati n i n rmaliz d to unit ffic i nt cau e th
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95 calculation evaluates the difference in spending at the point where, based on the index equation, the individual is just indifferent to knowing the price or not. See Chapter 2 for a full discussion of this welfare measure. Heck.man Tobias and Vytlacil (2001) show simple unconditional estimators for each of the four treatment effect parameters as (430) where K is the treatment effect measure of interest and N is the number of observations in the relevant set, i.e., N is the whole sample for ( 4 26) and ( 429), only the users for ( 427) and only the nonusers for ( 428). Note that expectation in ( 429) can be conditioned on any subset of the sample. For example, evaluating (429) over those who know the price, gives the expected treatment effect welfare measure for a randomly chosen individual from this group. This calculation and a similar one for those who don't know the price is reported in the results. D ata The data set is composed ofresponses from a 1997 survey ofNorthCentral Florida households (BEBR 1997) and the corresponding 199799 monthly billing records from the water/sewer utilities in Gainesville, Ormand Beach, and Cocoa Beach. Monthly precipitation and temperature records from the nearest regional airport for each utility were also added to each observation Missing data for all variables, except water use, were set to the mean values observed in the relevant utility service area. All monthly observations with no reported water use for two consecutive months in Gainesville and
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a B a h r dr pp d fr m th mpl 17 hi d n primanly t ace mm dat n b rati n liz d t th e t nt th t th rmand B h ha f H witt (2 nd t th m rgm I pri indi r u d d m nthly II t any b rv d at r u th unifi rm harg Th fmal id d b ut nly am ng the thr utility ar a . g ., cati n ) II wing th th all w n d f742 Tabl 13 pr nt th rat ti r the thrc utilitie in th ample. t that nly n ab lut that th pri er the amp! p riod occurr d (in rrnand each ampl i mainly cro ectional in nature Th marginal imp! uniform harge but the rate chedule at ain ille and a B a h ar m hat p cu liar b cau of ap on the amount of monthly water u that an b billed at th ew r rat 1 Oddly the ewer cap in ocoa Beach cau e th mbin d wat r and er marginal price to incr a e up to the cap decline immediately mpli ati n du to a onal charg and a w r cap that varie per hou eh ld ba ed on th ir ma imum 11 int r u age Th differ nc in rate chedul ugge t that it may co t 1 7 to d t rmin th marginal pric at Ormand Beach than for th oth rt o utilitie om hou bold ill pri r to fi r both at r and ev r rv1ce becau e refl ct th j int co t of the e rv1ce introduc d th p t ntial e timation i u v ith combin d at r but th re ha been littl if an publi h d d cu ion ince.
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97 Table 13 Rate schedules in study area Blocks $ / 1000 gallons 3 Water Sewer Total 6 $ / month Water Sewer Total 6 Ormand B e a c h Before 10 / 97 02 0 00 0 00 0.00 > 2 1.93 2 70 4.63 7 68 10 02 17 70 After 10 / 97 02 0 00 0 00 0.00 > 2 2.03 2 84 4.87 8 06 10 52 18.58 Cocoa B e a c h 08 1.36 2 80 4.16 9 12 1.58 2.80 4.38 13 16 1.58 0 00 1.58 7.99 6 00 13 99 17 24 1.90 0.00 1.90 > 24 2 56 0 00 2.56 Gaines v ille c November All Usage 0.98 2.43 3.41 March April 09 0 98 2.43 3.41 3.00 2 11 5.11 October >9 1.29 2.43 3.72 3 All charges are for water and sewer service and are shown as nominal values They were adjusted to relative monthly values before estimation with the monthly all item CPI for Southern cities of size class B / C. bSome households in the sample are not connected to the sewer system. The total marginal and monthly charges for these observations only reflect the cost of water service. crhe complete rate structure for Gainesville is not shown in the table because sewer charges are conditional on a household's maximum winter usage. This household specific quantity is determined in the months of January and February and forms a cap on billable sewage for the rest of the year Table 14 lists the summary statistics over all households and months for the other relevant study data according to a household s reported price knowledge Only 6 % of the households in the sample reported that they knew the marginal price for water service Interestingly these households used about a thousand gallons less water on a v erage each month than those who did not know the marginal price The former also faced a lower marginal price on average than the latter which may be due to increasing block features
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ri bl i II nth .i, nth! In m b,c \ n IL b II Id iz b mp p B rink ttl d a t r. b ut Fl b L Hard b ut aping. b rmand B a h R id nt me p !PIT Tl RI TL D T R FLO DB H B BR l 7. fth 4 3 0 3 22 0.450 0 500 0 .77 0 0.420 0 30 rt t a tions a a II 7 3. l 1.1 7 ) .5 0 .5 .3 0 3 36 3 .2 1 0.4 0 .62 0 0 630 0.4 0 0. 0 0 .36 0 = B
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99 in two of the sample rate structures. 19 I assume that all variables, except water use price bill, temperature and precipitation are fixed for the study period That is the household values for these variables are assumed to be the same in 1998 and 1999 as they were reported in the 1997 survey. This assumption is plausible for the basic socioeconomic variables, such as household size and lawn size but is somewhat tenuous for the variables relating to bottled water consumption and knowledge of conservation practices For example, a household that did not consume bottled water in 1997 may have started to consume this product in 1998 or 1999. More critically for present purposes though, is the possibility that a household who did not know the marginal price of water service in 1997 may have actually learned the price in the subsequent years. In this case the results will be conservative approximations of the actual statistical differences in water use behavior between the know and don't know groups. Results Structural Demand Model The estimation results for the price information decision equation (Info Decision) and the price/demand equations for each knowledge regime are shown in Table 15. In the prob it estimation (far left column) of the price information decision equation all variables, except income are significant at the 5 percent level. Income is probably not a statistically important factor in the probability of knowing the marginal price because water bills constitute a small share of household income. The probability of knowing the marginal price increases with lawn size, but decreases with household size. It may be that people with larger lawns have a greater interest in the cost of irrigating and thus the 1 9 Simple ttests indicate that mean water use and price as well as the means of several socioeconomic variables are significantly different between the two the know and don t know samples
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, , abl B TL TER L WFL ER.! PE R BE H BILL ,_, TE PERAT RE PRE IPITATJ ,_, 1PT 6 000 gal. PT 1 000 gal PT 1 000 gal. PT 5 000 gal MPT ,t 01 5 79 01 1.42 01 01 1 2E02 2.04 02)* 01 3 24 02 l.0 0 I l 22E0 l )* 2 36 02) (2.03 02)* 4.70E02 l.65E02 3 99E02 (1.77E02 (3.0 E03)* 2. 95E03)* 5 99 01 4 77E0l 6.81E0l ( 74 02 l.5 lE02 4 02E02 7.74E02 (4. 4 02 2.42E0l 1.0 0 I ( 1. 5 02 2. 9E0l 2.45E0l (7.44 02 (1.4 02 b lo\ a h timate L
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101 price of water. For large households knowledge of the marginal price may be less likely if water takes on public good characteristics such that one household member is unable to influence the water use of others Knowledge of low flow fixtures and xeriscaping increases the probability of !mowing the marginal price, as does the regular consumption of bottled water. These variables represent water awareness factors and the positive correlation with the price awareness variable establishes the consistency of household responses. A dummy variable is included for the utility (Ormand Beach) with the simplest rate structure. The parameter on this variable is positive indicating that ( all else equal among utilities) households facing a simple rate structure are more likely to say they know the marginal price. The results of the price instrument estimations are reported in the second and fourth columns of Table 15. These estimates are not the primary focus here, but note that the parameters cp 11 and cp 01 on the A. 11 and A. 01 terms, respectively, are not statistically significant in the price equations. This indicates that separate OLS estimation of the price equations with this dataset would not be subject to sample selection bias. Of central interest in this chapter are the results from the demand equation estimations (columns 3 and 5 in Table 15) The parameter cr 11 on the A. 11 term in the know' price equation is significant at the 10 percent level and the cr 01 parameter on the A. 01 term in the 'don t know' price equation is not significant. Thus, the covariance between the decision equation and the demand equation is (weakly) significant for those who know the price, but not for those who do not. So the decision to learn the marginal price may be related to the water use decision if a household actually chooses to learn the pnce.
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:ely e to lD 1 2 h p r m t r tnnat r th kn w th pnc r r ughly mp r bl t th re t imp rt ntly th nth mar in I pri p r gc pri BIL I I diffirntbt n gr nt nth m rgin I pri C ffi nl fi r lh d 11 t kn w r up. urth rm re, the nth pn t rm i n t tali ti lly ignifi ant fi r th kn w r up but i nifi ant nd p iti fi r th d n 't kn gr up th data fi r th e wh ay th th marginal pri r u but n t n ay that th r ult I nd upp rt t thi hibi t a tati ti al r l ti n hip b tw n marginal price e n a erage pn and at r u e cann t up actu lly r pondin to marginal price but the e ibility. Th r ult al ugg t that th /..,710} gr up 1 m r pnce ensitiv than the don't /...71or gr up and that th latt r may actually r p nd to om combination of marginal and information Th hort run and long run la ticitie are hown in Table 16 fi r mpan n T plor th cond premi e I u ed th formula in Table 12 to alculat th pn p re ption parameter and the p rcei ed price at the mean value for th don t h10r gr up. Th pnc p rception parameter for the don't know group i k = 4 10 gi mg a p r i d price of 0.33. 2 0 Thi p re i ed price i not tati tically different fr m z r at at nfidence le el ugge ting that tho e ho do not know th pn of ater could b beha ing a if ater ere free. gain thou~ e cannot attribut cau alit to th tati tical r lationship This interpretation hould al b i \l d cautiou I a th e timated price perception param ter for the don't know group i 0 Th a ymptotic tandard rror of the pric p re ption param t r and p re ti r th don t lmo1rv group ar r p cti ly 1.49 and 0 26 d price
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103 roughly four times larger than any value reported in previous studies (Shin 1985; Nieswiadomy 1992 ; Nieswiadomy and Cobb 1993; Nieswiadomy and Molina 1991) Table 16. Estimates for key water demand model parameters Parametera ShortRun LongRun Know Don't Know Know Don't Know Income elasticity 0.076 0.077 0.190 0.243 (0.032)* (0.005)* (0.091)* (0 018)* Perceived price elasticity 0.085 0.035 0.213 0.108 (0.056) (0.009)* (0.167) (0.031)* Marginal price elasticity 0.283 0 176 0.705 0 553 (0.102)* (0.017)* (0.135)* (0.031)* Price perception 2.312 4.103 2.312 4.103 (2.654) (1.499)* (2.654) (1.499)* Partial adjustment 0.165 0.173 1.000 1.000 (0.054)* (0.008)* Standard errors are shown in the parentheses below each estimate. asee Table 12 for corresponding formulas *Parameter estimate significant at the 5 percent level. The econometric results indicate that those in the sample who do not know the marginal price for water are responding to a price lower than the actual price. This corresponds to the situation in Figure 5 where the value of price information is shown as areas C and D. The information from the demand estimations is used to calculate these areas as follows The rectangle of total monthly (variable) expenditures on water / sewer service is calculated as VE= (Pactual Ppercieved)*Qobserved Then the estimated parameters are used to calculate the change in consumer surplus between the perceived and actual price for two demand situations using Hausman's (1980) exact measure. The first demand situation uses the information from the don't know estimation and assumes that the marginal price behavior (i e. elasticity) would remain unchanged if they really knew the price For the second situation I speculate that the price behavior of the don t know
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gr up ul b m r lik th know r up i th did a tually kn the pnc It ti ity r m th know g r up I u cd ti w r up. t that the nstant quati n i n d mand lin mt r l at ob rvc:d, u tra tin th fir t m nd n umcr urplu ur fr m th t im t d ri bl nditur ar a nd ubtr tin th nd n um r urplu tr t gi h ar p rfi rm d fi r h rt and l ng run effi t ln th h rt run th t lack f price kn wl dge ar a 0 4 per m nth fi r th a ra h u h Id that did n t kn w the marginal price If th price infi rm ti n tually au d th a rag h u eh Id t chang th ir price b ha ior, then th additi tu f th prtc kn wt dg (ar a D would b 1.2 p rm nth Hr.u ,P"Pf th ar a D calculati n ha a r Jati ely large tandard rr r ( 0 42) and a aid t t indicat that it i not tati tically ignificant from zero at the l Op rcent le el. The alu i only 0.02 p r nt of monthly incom for the average hou eho ld and the urn of area and D c n titute ab ut 0.05 percent indicating that the alue of price ry mall r lati t income Th I ng run ere p nditur du lack f price kn ledge wa lightly high r at 0. 7 p rm nth fi r the a erag hou h ld, again about 0 02 percent of month) ill r, th alu of pri informati n a urning a change in price beha 1 r id rabl I in th l og run at 0 90 Thi r ult app ar b cau th partial adju tm nt param t r fi r th pnc is mall r than th for tho \ ho d n't kn \ th lntuiti I th h u hold \J ithout price inforrnat i n a r furth r
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105 off their optimal expenditures on water and can adju s t relatively more in the long run Compared to the short run value the long run value of areas C and Dis a slightly smaller portion 0 04 percent of monthly income for the average household. Treatment Effects Model The estimation results for the treatment effects model are shown in Table 17. The significant parameters in the price information decision equation are similar in sign and magnitude to those estimated in the water demand model. This is expected as the probit estimates shown in the water demand model (Table 15) are used as (part of) the starting values for the FIML estimation of the treatment effects model. Interpretation of these results follows the discussion presented for the water demand model. The main interest in the treatment effects model is the estimates for the expenditure equations shown in the second two columns of Table 17. Although the magnitude of the estimates for these equations model are not directly comparable with the water demand model in Table 15, the signs are remarkably similar. The only anomaly among significant parameters is the coefficient on lawn size for the don t know price results. This parameter is positive in the water demand model (Table 15) and negative in the treatment effect bill model (Table 17). Thus while those with larger lawns use more water their bills tend to be less than those with relatively smaller lawns. This discrepancy likely occurs because the treatment effects model does not control for the variation in charges faced by households in the crosssection. The water demand model does control for differences in charges across service areas with prices among the independent variables Since these variables are not explicitly included as regressors in the treatment effects model the lower expenditures attributed to larger lawn sizes may actually occur because most of the households with larger lawns just happen to live in an
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I H U, H L B TTL i T R l. ERi p Rlvf DBE H BILL ,. 1 TE fP ERAT RE PRE IPIT TIO p elecuon.e~end CJ elett1on e"
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107 area with relatively low charges for water service. 2 1 This result points to a need for more work on the role of prices in the treatment effect framework. The significant coefficients in the expenditure equations with and without price knowledge are also similar in magnitude and sign. The only substantial difference is between the parameters on the household size variable. Both coefficients are positive but the influence of larger households on water expenditures is greater when the price is not known. The water demand model results in Table 15 suggest that this result occurs because household size has a relatively greater effect on water demand without price knowledge Therefore, unlike the result for lawn size, the variation in the influence of household size can be attributed to differences in behavior rather than differences in (exogenous) control characteristics. The estimated variances of the spending outcome equations are significant, indicating the importance of unobserved heterogeneity in the sample. However, because ofrelatively insignificant correlations, the covariances between the price knowledge and spending equations are not significant. This implies that there is a limited amount of self selection in this sample based on water price knowledge. Following the characterization in Chapter 2 and 3, the lack of significant covariance between price knowledge and spending decisions suggests that neither group has an 'absolute advantage' in their selected option. That is price knowledge does not offer those who chose to know the price a significantly lower cost for utility than not knowing the price. A similar observation can be made for those who chose not to know the price. 2 1 A casual comparison of mean lawn size and price variables by utility service area confirms that the two areas with the largest average lawn size also have the lowest mean charges
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he, t; k.cr ntl1t1 n r mp r t1 gc' ppltc hcnlh avrng r Lhc me ul1lil le; cl th n Lh h u 1.:h Id \\ 1th ut \J 1th pn. kn th d n't kn \ th pri :. A null h n mp r ti n be C lu led 1th j int LC l f~ll ~ O I nd I l O 0 1 L> I fi r the r ln LI ns rCJ Cl j int qu lil hu Lh r nific nt in fi rm ti n in th prt kn I dg n d ample th t an b u d alu, l th r lati f pri infi rmati n he treatment ffi lfar m a ur intr due d in h pt r 2 ar d ign d Lo expl it thi in rmati n h un nditi nal tr atm nt ffi ct and el far mea ure fi r the alue f price infi rmati n ar Ii t d in T bl 1 Th figur ar btained bye aluating xpre i 42 fi r ach indi idual in the rele ant group and a eraging defined mp n nt f th policy rele ant mea ure of compen ating ariation of pn hown in the fir t pane. randomly elected pend 2. mor p r month if they know the price. Ho e er thi rand ml ch n indi idual i n t illing t pay a po iti e amount for the price kno inti rmati n th tra p nding for the price kno I dge i not ju tified. Thi e plain r p r nt f h u eh ld reported not k.no ing th marginal price of ervice Th d rrunanc f th Tabl 1 ithout price knowledge i e ident in th la t pan of p r month r pecti el th e timat d pending difference and willingn t pa fi r perfi ct pric information for a randomJ cho en hou hold
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109 from this group are very close to the estimates for the sample shown in the first pane of Table 18. Table 18 Bill treatment effects and welfare estimates of price information Parameter Bill Difference TEA ATE E[CV] TT E[CV I know] UT E[CV I don't know] Standard deviations shown below the estimates. 2.38 (2 82) 1.42 (2.85) 1.78 (1.96) 0.69 (1.97) 2.67 (2.87) 1.47 (2.89) The story is somewhat different for those who reported knowing the price. From the second pane in Table 18, this group actually spends less by $1.78 per month with price information although they have a negative $0.69 willingness to pay for this information However, households in this group still choose to know the price because it saves them money. All results satisfy the treatment effects model consistency checks proposed in Chapter 2 The expected compensating variation is greater (less negative) than the spending difference (TT) for a randomly chosen household from the group that knows the price This is not true for a randomly chosen household from those who do not know the price (UT) and from the sample in general (ATE). While the statistical significance of
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11 d ntn uggc lt c t al ,, n II the nsi lcn m t t the minimum nc.i ma 1mum luc I the ample h1 h tptcr in tig tc th dt rcn in n urnpt1 n Id \ ith, nd \ ith ut in rmnt1 n b ut th m r g m I prt h ught, in part, t d tennin \ h th r r n t m ur d a i di r igni 1 anti fr m infi nncd re p ns th p d t fi rmally re iew the c mparat1 e th tr prt lu pn infi nnati n. The implication of the tructural ater d rnand model and a m d I ba d on th framework intr due d in hapter 2 ult fr m th imultan ou quations d mand model ith ugg t that there are differ nee m a erage co umption d pric pecifically tho e ho \ ing th marginal pric con um d le than a erage and ere r lati el ariation Tho e without pric informati n beha d a if the w r r p ndmg to a ignal much lo r than the actual marginal pric qu ntl, thi gr up wa er on urning publi utility rv1 r lat i oth r good and could p 1bl readju ting their budget to p nd le rv1c Th pp rtunit co t of th o r e p nditur on utilit c nstitut th value f pri inti rmation for tho ho d not kno\ th pnc This opportunit co t w timat d u ing the r ult from d mand and e p nditur mod 1 Th w lfar m a ur
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111 of the value of price information in the demand model improve on existing approaches in considering the possibility that price know ledge changes the response to price changes. The estimated average value of price information with the demand model i s small relative to the average household s monthly income. This supports Shin s (1985 ) hypothesis that households do not know the price because the relative value of this information is relatively low. The results from treatment effects model suggest that the value of the information may be negative but that some households would still learn the price because it saves them money The upshot is that if public utilities (in the study area) make an effort to reduce the cost of obtaining accurate price information then average consumption will decline as households who learn the marginal price adjust their budget allocations accordingly. This could be a point of interest for public utility managers interested in encouraging water conservation because it suggests that a relatively simple effort such as clearly posting charges and usage information on water bills could help achieve more efficient 2 2 levels of conservation from their residential customers 22 If water consumers know the actual marginal price for water service then they can use this information to make efficient water conservation decisions with regard to utility maximization. However the aggregate level of conservation achieved by the public utility will only be socially efficient to the degree that the marginal price for service reflects the full opportunity costs of providing that service (Carter and Milon 1999).
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ht di crtnl1 n lu1.: r publ1 g d by b!:>cr ing th tuunl 'mg n tr t hapter, lu nd intr duce th rn ti tr atm ~ nt fl t appr a h T th th n nti nal and A appr rk b nditur ms hange with chang in the publi f int r t. 11 di r in the way they p rate h n d t 1 un tat fthe orld b fore rafter the public n nti nnl m th timat tructural d mand and/or utility equation for mm iti ut m nr n nti n I nal ppr r indi iti that ar r 1 t d t a public go d f int re t. With a umpti n hip b t\ n publi and mark t good mi ing demand or utility qui al nt price change Thu price are param unt in th t m a uring public good value Troubling a p ct of relian on activityba ed price indice are a o re ie d in an att mpt to a oid om of th problems r lated to acti it ba d price e penditure for acti itie related to a public g od. H we er, ;p nditur ar n t pljt int acti ity price and quantity indic to ti.mat a tru tural d mand or utilit model. Thi i b cau th T d not imulat rru mg nditure ut m r lated to a public good cbang u mg nc han Rather, m th d fr m the 11
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113 program evaluation literature are used to reco v er missing information using the observed expenditures of different groups of individuals Those in a sample who use a public good for a specific activity are considered to be the treatment group and those who do not are considered to be the control group Two ways are suggested for using such a natural e x periment to derive values for public good access. Chapter 3 applies a travel cost model and the TEA to measure the value of access to petroleum rigs in the Gulf of Mexico for recreational fishing. Both approaches are adapted to incorporate expenditures on fishing capital into welfare measures. The adaptation of the travel cost model turns out to be difficult because capital is not easily allocated at the trip level. However the TEA readily incorporates outlays on capital equipment into the annual expenditure differences used to develop welfare measures The welfare measures calculationed for the travel cost model are unusually high because of a particularly low estimated coefficient on the trip cost variable. This suggests that other variations of the model should be estimated to examine the sensitivity of welfare measure estimates. Future work with this dataset should also include estimation of a conventional random utility model to generate alternative welfare measures of rig access The results for the TEA model estimation are promising Annual measures of the value of rig access are reasonable and the consistency tests proposed in Chapter 2 are satisfied. Specifically the results indicated that rigs are not used by some individuals because they are not willing to pay the extra cost of rig use. This is true even though nonusers are willing to pay more on average than those who actually fish rigs. The inclusion of capital expenditures more than doubles the value of the TEA measures
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11 utla ar an imp rtanl part lh pp rtunit c ~t re ln t111 rig fi hin h plcr u tru lur 1: m el l c mine pm; pcrc ptl n in th m n If r publt utiltt er 1cc and the aluc pn c in rmat1 n n anal I al m d Ii nL d pn infi rm ti n. mpnr ti fun ti n V ill h Th and ntral f pri kn a diffi r impli th rid Th ampl L pn mi pcrccpt1 n and id nt1fy th e luc f pcrlc tnti uggc t th l th pn a ll I b ing pn C ti it fd mand than th wh d n t kn w the pn annlyti al m d I ar analy d with a at r demand m de! p nditur plit int n a mpl f h u eh ld from n rthd knowing th price and th h d th rwi he d mand m d l r ult ugg t that th aid they kn \ pri had a larg r pri la ticity of demand than th e ho did not kn th price. Furth rm r th v ho aid th y did not kno the price ere b ha ing a if v ater re fr Th timat d alue of price information for this group is lo,. The alue i nly lightly high r if pric ene i allo ed to hange v ith price kno 1 dg Tho e v ho k:ne the price compo the tr atm nt group and other form the control gr up fi r th T m d l. h diffi r nc in at r bill o the e t o group ar u d t id ntify th ct d a1u of pric information, For mo t hou ehold in the ampl tbi alue i lo r Jati e to th e p ct d diffi r nc in p nding a ociated ith pnc kno\ I dg Ho\ r, th r ult indicate that the gr up that report d kno ing the pn actuali a ed m n b d ing o
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APPENDIX MATHEMATICA DERRIVATION OF THE NET UTILITY FUNCTION Following Hausman ( 1981 ) expenditure is characterized as a minimum value function that traces the minimum expenditure necessary to achieve a constant utility level given changes an exogenous variable. Hausman considers changes in a price variable but I consider changes in the level or quality of an exogenously supplied public good z Note that the public good indicator does not appear directly in the functional form chosen for the Engel equation: px = a + g m. [ z ] + c s + e a+e+cs+gm[z] where a is a constant m is expenditure with parameter g s is a vector of control variables with a conformable vector of parameters c, and e is an error term. Following Phlips (1983 p 104) the underlying demand equation for this model can be defined as X i = aj + bi p/pi +gm/pi+ ei. In this case the constant and error terms of the Engel equation are implicitly defined as a= ai Pi+ bi+ pj and e = ei Pi ,, respectively. This formulation treats prices as endogenous. Following the approach in Hausman (1981) write the (uncompensated) Engel equation as a differential equation and solve for the expenditure as a function of the quantity or quality level of the public good: mz = D Solve [ m [ z ] == px m. [ z ] z ] ((m[z] a~c 3 +~ 9 1lC[l1}} 115
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1 I tc thnt th den l1 \ 1th re pe e l l the publl g d uppl rather th n pn c ' tncc th pn nabl arc a umed end g en u un b en blc 1cr ampl I c fi r the n tant r int gr l1 n th le cl f md1rc l ut i l i t 1 u CI l I /. Solve I (m I z I / mz I [ l I I) C [ 1 I I I I 1 I I I!!( + e +gm +cs) g lhL: In rt the mdir l utillt un ti nm l rms f m me l g l thL: xpcnd1turc fun ti n : expd m / Solve [1du .. u, m) [ [11 I ecs+I!!,. u g R y' Id ntit and th indir t utility fun ti n t FullSupllfy [ D [ 1du, z I / D [ 1du, I I a+e+gm+cs L mm and th r th publi g d : CZ = D(expd, Z] l!!g gu ti r th compen ated demand T d ri th be u ed in the public g od u e I tion quati n fir t param t riz indir t utilit functi n for alt mati e i and j: didu = Full S i.J"t>l it y [ idu /. JI\ ( m ( px /. n[ z ] + JT\ ) ] + C S) ldUl. = did /. { + C Cl, e e1, 1duJ = did /. { + J + J, e .... eJ, g+ J}
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1?9i 11 (1 + gi) (ai + ei + gim.+ ci 3) gi 1?9j 11 (1 + gj) (aj + ej + gj m.+ cj 3) gj 117 Next Calculate the difference in indirect utility from choosing alternative i over j: ud = idui iduj I? gi ( l + gi) ( ai + e i + gi m. + c i 3) + gi 1?9j 11 (1 + gj) (aj + ej + gj m.+ cj 3) gj Collect variable terms: udc = Collect [ud, { s, m.}] ai l?gi (1 + gi) l?gis ei (1 + gi) + gi gi aj
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I I (~i(+ l)+ l(1+ )) G, 1) C' A, Ftn ll c pre the net tndtr l uliltt funcl1 n in terms flh rcdu d fi rm param l r : r dformud = udc / /. rep A+ ed Gm+ C t" th t lhc int rati n r ull in an argum nl fi r th public g d c ndili n ppc nng m multipl nth param t r of th r due d fi rm n l utility funcl1 n quentl th inde and pending qual1 n amp! in th di that c mbmc h th ti al and ta am r n 1 2 It may b po ible luc fth pu li g d indi ator u ing th tunat d reduc d fi rm param t r Th i n t tt mpt d in th pr nt r ar b.
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I_ Par J 8 It.: 1rr \ h I c el R rt.:ut I n Demand "Lund E unom,c 7 n I ham.:ul, J 11 Ou I ppr a ht rnt.:r Juum ,Io v1runm nt It: v11om1 md \,/ uw Phaneuf', l J lut i ns in Rccrcat1 m n I 7, n I I c. I cmcnt I encr 11,cd mt.:r t:n and 11 R ,v, W o E 1101111 dd w i th Phlip pp!t J 011 ump/1011 l11al 1 SI\' rk : m tcrdam rth1 I II nd Pub . I P II k, I n The II LI r/ ,fl ,n . 11 Pn cp ndcnt Pr Ill ~ n an onom, R IW 7 n 2 I 77 : 7 p II k, R ht r II C th II u ch Id Pr duct1 n run ll 1m 11 Journal o P l111 c al E c onom_l LI nt nn ppr a I 7 ,, ith th Tra th it ati f Ri t, R nth I, H "Th ub titut Pn m n c II J umal of A ricultural Eco11on11 c h ir II A.d\.'Gll C In ., l I. r nmark f h I atural R mic 7 n rking Pap r ar h 2 I. C I "R p rt our c and 7 al e uh 1ar t l L. n 3,
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127 Shaw, D. "OnSite Samples' Regression: Problems ofNonNegative Integers, Truncation, and Endogenous Stratification." Journal of Econometrics 37, no. 2(1988): 211223 Shaw, W. D., and P. Feather. "Possibilities for Including the Opportunity Cost of Time in Recreation Demand Systems." Land Economics 75, no. 4(1999): 592602. Shaw, W. D., and J. S. Shonkwiler. "Brand Choice and Purchase Frequency Revisited: An Application to Recreation Behavior." American Journal of Agricultural Economics 82, no. 3(2000): 515526. Shechter, M. "A Comparative Study of Environmental Amenity Valuations." Environmental and Resource Economics 1, no. 2(1991): 12955. Shin, J.S. "Perception of Price When Price Information Is Costly: Evidence from Residential Electricity Demand." Review of Economics and Statistics 67, no. 4(1985): 59198. Smith, V. K. "The Influence of Resource and Environmental Problems on Applied Welfare Economics: An Introductory Essay." Environmental Resources and Applied Welfare Economics. ed. V. K. Smith, pp. 343 Washington D.C.: Resources for the Future 1988a. . "Selection and Recreation Demand." American Journal of Agricultural Economics 70, no. 1(1988b): 2936. . "Welfare Effects, Omitted Variables, and the Extent of the Market." Land Economics 69, no. 2(1993) : 12131. . Estimating Economic Values for Nature: Methods for NonMarket Valuation. Brookfield: Edward Elgar, 1996. Terza, J. V "Determinants of Household Electricity Demand: A TwoStage Probit Approach." Southern Economic Journal 52, no. 4(1986): 113139. Terza, J. V., and W. P. Welch. "Estimating Demand under Block Rates : Electricity and Water." Land Economics 58, no. 2(1982): 18188 Varian, H. R. Microeconomic Analysis 3rd Edition. New York: W.W. Norton & Co., 1992. Vella, F., and M. Verbeek "Estimating and Interpreting Models with Endogenous Treatment Effects." Journal of Business and Economic Statistics 17, no. 4(1999): 473478. Wales, T. J., and A. D. Woodland. "Estimation of Consumer Demand Systems with Binding NonNegativity Constraints." Journal of Econometrics 21, no. 3(1983): 26385
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htl . I l aab, and J .pr tlnYin, E crb R m 12 ri bit.: in 1 ra d l cm nd n umt.:rs' urplu E tinr lt.: to afr tion tkl l/1 ulwn Journal o ,t nc 11l1u al b er ati nal and f ra uc
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BIOGRAPHICAL SKETCH David Carter was born in Columbus Ohio USA and promptly moved to Florida to grow up ; A task he is still working on. David attended schools in the Tampa Bay area before enrolling in Stetson University in Deland Florida After receiving a degree in economics he began his nearly eight year career as a Gator at the University of Florida. This career as a professional student culminated in a M S and now a Ph D. from the Food and Resource Economics Department. David plans to continue studying choices related to the natural environment in Florida and beyond. 129
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l l n1 I I .,t I I., H. a I ti 1. u I\ ind tllat ir n o 1rnon ll <., r l ,rm to ., ,. 1.,1 It .111, 11d .. 1 h, larl; J ll ll ,,1101 ,md i u7 ad~qu7. '" ope and 4u 111 ., Ir 11.,11,11 l111 ti, le 'll' if I m 1111 ol l'hdo o h ~ : a/ alter ilon < h ,u >Ur C.: OTnl( tud) and that in rn i i ,n it u nlurm I <. L n, h ti Jt I ha\l: read thi al e ta k ta, dard > th larl rL,uJWtion and i full) adL4t1, tL. 111 o t.: an 4ualit_ owir ol l::_p / fl a di. Lrtaw n I >r the de 1 r c I) d I 1 Lr 11d .m ] Lrtif) t} at J ha\ r ad thi tu h ptabl tandar >f. h larl) 1 c l nt 1 it n an i di. crtati( n for the dcgre D tm J P > I l Pnd a 1 l f e 1 u r c >nt lllll ur l l'rtlly that I ha\ c rLnd th1. tudy ,md that in m mi11n It u n rm qualit_. h I rl) rl' L n 1 inn and i ull) 3dLqu.1IL. in p and uali .. c..'rt,1111111 f nr the..: de 1 r c..: f Dl t< r 1 Phil h). I u. rti1) ti t 1 h \ rt th1. tlld\ nd h. tin m) ini1 n Jl ,1 t'pt.1hlL .tnt ,1rJ o d1 Lrt,1 1, n lnr he.. I) rrc.. c.. 111 i1 n ,md i. 1ull) <: p an qu .11 j I () I I ( Phil h) Gu,v,A.;,,.~ lJ I ~l\\ L 11 t.: \\ l'llll\ Pr 1. ( r 1 J n m,
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Thi di e rtati on v.. a ubmitted to the radu a te 1a cuity of the Coll f'e of An ultural an d Life i n t .and to the Graduat c ool an d was ace pt d as partial fulfillm n1 of the requir m nt. for th d gr e of Do tor f Philo ophy. (_ D mber 2002 D ean. II g of Agricul 1 n e D an. radua te School
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