groundwater games: users’ behavior in common-pool resource
TRANSCRIPT
The Pennsylvania State University
The Graduate School
Department of Agricultural Economics, Sociology and Education
GROUNDWATER GAMES:
USERS’ BEHAVIOR IN COMMON-POOL RESOURCE
ECONOMIC LABORATORY AND FIELD EXPERIMENTS
A Dissertation in
Agricultural, Environmental, and Regional Economics
by
Rodrigo Salcedo Du Bois
c© 2014 Rodrigo Salcedo Du Bois
Submitted in Partial Fulfillmentof the Requirements
for the Degree of
Doctor of Philosophy
May 2014
The dissertation of Rodrigo Salcedo Du Bois was read and approved1 by the following:
James S. ShortleDistinguished Professor of Agricultural and Environmental EconomicsDissertation Co-AdviserCo-Chair of Committee
David AblerProfessor of Agricultural, Environmental and Regional Economicsand DemographyDissertation Co-AdviserCo-Chair of Committee
Jill L. FindeisDistinguished Professor Emerita of Agricultural, Environmental andRegional Economics and Demography
Edward CoulsonProfessor of Economics
Richard ReadyProfessor of Agricultural and Environmental EconomicsCoordinator, Graduate Program in Agricultural, Environmentaland Regional Economics
1Signatures on file in the Graduate School.
iii
Abstract
Groundwater currently provides 30 percent of freshwater in the world, and it is
estimated that it potentially constitutes approximately 89 percent of the world’s fresh
water. Nevertheless, extensive extraction of groundwater in some areas is leading to
aquifer depletion.
Groundwater is considered, in some situations, a common-pool resource (CPR)
with extremely high use value. Economists and political scientists have devoted a great
amount of effort to understand how common pool resources are managed, as well as the
characteristics of institutions that emerge in order to deal with the use and distribution
of CPR. The characteristics of a CPR and how agents interact in their use are important
for the success and sustainability of CPR-dependent communities.
This dissertation will analyze the behavior and decision rules of CPR users in
an experimental context. We discuss the results from laboratory and field experiments
framed as a dynamic groundwater game in which users pump water from a shared re-
source, and the actions of users in one period affect resource availability and extraction
costs of everyone in the next period. This is an innovative design, since most of previous
studies do not consider the groundwater problem in experimental settings, and do not
conduct a groundwater experiment with actual groundwater users.
The objectives of this research are twofold. In the first part of the dissertation,
I assess the presence of strategic behavior when participants have access to an efficient
technology that yields both private and public benefits to CPR users. This situation
iv
might discourage users from adopting the new technology, which results in free-riding.
In this part of the dissertation, I am also concerned about the effectiveness of group
arrangements to improve water usage and to guarantee appropriation levels that yield
a socially-desirable economic outcome. Given the experimental design, I can partially
address both learning effects during the game and unobserved heterogeneity of partici-
pants, in order to obtain a precise estimation of the impact of the treatments. Finally, I
also analyze the factors that affect technology adoption and deviation from agreed water
usage.
In the second part of the dissertation, I address the degree of heterogeneity in
actions of participants, and aim to identify different types of behavior among participants
in the use of the shared resource . Using a methodology proposed by Geweke and Keane
(2000) and Houser et al. (2004), I can relax the rational expectations assumption in the
dynamic choice problem, and identify different behaviors in the population. Based on
the decisions that participants make during the experiment, I can identify and cluster
parameters that define the future function of the dynamic choice problem in different
“types” or groups of participants, with these groups endogenously created. I propose
a flexible mixed multinomial discrete choice model that allows parameters to be drawn
from a discrete mixture of distributions. In order to estimate the parameters and group
membership probabilities, Bayesian Markov Chain Monte Carlo techniques are used.
These methods allow the estimation of highly dimensional discrete choice problems and
adds flexibility to estimation and the clustering process.
v
Table of Contents
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
Chapter 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
I 8
Chapter 2. The Economics of Groundwater Management . . . . . . . . . . . . . 9
Chapter 3. The Groundwater Management Game . . . . . . . . . . . . . . . . . 173.1 Theoretical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1.1 Basic Game (Baseline) . . . . . . . . . . . . . . . . . . . . . . 183.1.2 Investment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.1.3 Parametrization, Myopic, Rational and Optimal Behavior . . 25
3.2 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.2.1 Recruitment of Participants and Framing . . . . . . . . . . . 353.2.2 Treatments and Sessions . . . . . . . . . . . . . . . . . . . . . 363.2.3 Rewards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.2.4 Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Chapter 4. Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 454.1 Experiment Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . 454.2 Treatment Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.3 Technology Adoption . . . . . . . . . . . . . . . . . . . . . . . . . . . 684.4 Agreement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
II 81
Chapter 5. Dynamic Decision-making in the GroundwaterExperiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.1 Unbounded Rationality, Bounded Rationality and CPR . . . . . . . 825.2 Behavioral Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . 875.3 Structural Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
vi
Chapter 6. Empirical Specification and Estimation . . . . . . . . . . . . . . . . . 1006.1 Discrete Mixture Models . . . . . . . . . . . . . . . . . . . . . . . . . 1006.2 Multinomial Probit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1046.3 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.3.1 Bayesian Methods . . . . . . . . . . . . . . . . . . . . . . . . 1096.3.2 Data Likelihood and Parametrization . . . . . . . . . . . . . . 1136.3.3 Priors and Sampling Algorithm . . . . . . . . . . . . . . . . . 115
Chapter 7. Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 1187.1 Deviance Information Criteria and Group Number . . . . . . . . . . 1187.2 Parameter Statistics and Convergence . . . . . . . . . . . . . . . . . 1217.3 Classification and Characteristics of Groups . . . . . . . . . . . . . . 1277.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Chapter 8. Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140A Functional Forms of Polynomials of a Higher Degree . . . . . . . . . 140B MCMC of Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
vii
List of Tables
3.1 Parameters used in experiment . . . . . . . . . . . . . . . . . . . . . . . 273.2 Revenues with less-efficient technology . . . . . . . . . . . . . . . . . . . 283.3 Revenues with highly-efficient technology . . . . . . . . . . . . . . . . . 293.4 Pumping costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.5 Summary of sessions: Laboratory and field experiments . . . . . . . . . 373.6 Summary statistics of survey variables, laboratory experiment . . . . . . 423.7 Summary statistics of survey variables, field experiment . . . . . . . . . 43
4.1 Average outcomes by type of session, round and period: Laboratoryexperiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Average outcomes by type of session, round and period: Field experiments 484.3 Average end-of-round outcomes by type treatment and round: Labora-
tory experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.4 Average end-of-round outcomes by type treatment and round: Field ex-
periments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.5 Difference-in-Difference estimation of final outcomes in rounds 1 and 2:
Lab experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.6 Difference-in-Difference estimation of final outcomes in rounds 1 and 2:
Field experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664.7 Cox proportional hazard model of investment: Laboratory experiments . 714.8 Cox proportional hazard model of deviation from agreement: Field ex-
periments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
7.1 Deviance Information Criterion . . . . . . . . . . . . . . . . . . . . . . . 1207.2 Distribution of groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1217.3 Descriptive statistics of posterior distributions: Field experiment . . . . 1227.4 Descriptive statistics of posterior distributions: Laboratory experiment . 1237.5 Total benefits and final well depth . . . . . . . . . . . . . . . . . . . . . 132
viii
List of Figures
3.1 Equilibrium Pumping hours for Myopic, Rational/strategic and FullyCooperative behaviors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2 Benefits of pumping for Myopic, Rational/strategic and Fully Coopera-tive behaviors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3 Well depth for Myopic, Rational/strategic and Fully Cooperative behaviors 333.4 Simulated benefits for Myopic, Rational/strategic and Fully Cooperative
behaviors, and fixed arrangements . . . . . . . . . . . . . . . . . . . . . 34
4.1 Average individual hours pumped by period and treatment . . . . . . . 504.2 Average individual benefits by period and treatment . . . . . . . . . . . 514.3 Average well depth by period and treatment . . . . . . . . . . . . . . . . 524.4 Histogram of pumping hours from laboratory experiment, by Round,
Period and Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.5 Histogram of pumping hours from field experiment, by Round, Period
and Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.6 Average individual total benefits by round and treatment . . . . . . . . 604.7 Average individual total hours pumped by round and treatment . . . . . 614.8 Average final well depth by round and treatment . . . . . . . . . . . . . 624.9 Percentage of technology adoption by period and experiment . . . . . . 694.10 Percentage of technology adoption by period and round: Laboratory
experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.11 Histogram of agreed values of pumping hours in “AG” sessions . . . . . 744.12 Agreement deviation percentages in “AG” sessions . . . . . . . . . . . . 76
5.1 Average individual hours pumped by experiment and period . . . . . . . 895.2 Hours of pumping by period: Laboratory experiment . . . . . . . . . . . 915.3 Hours of pumping by period: Field experiment . . . . . . . . . . . . . . 925.4 Average individual hours pumped by well depth . . . . . . . . . . . . . . 94
6.1 Single vs. Mixed Distributions . . . . . . . . . . . . . . . . . . . . . . . 102
7.1 Estimated posterior distributions of parameters: Field experiment . . . 1247.2 Estimated posterior distributions of parameters: Laboratory experiment 1257.3 Trace of deviance, two chains . . . . . . . . . . . . . . . . . . . . . . . . 1267.4 Average individual hours pumped by period and type . . . . . . . . . . 1287.5 Average individual pumping costs by period and type . . . . . . . . . . 1297.6 Histogram of choices by cluster and period: Field experiment . . . . . . 1317.7 Histogram of choices by cluster and period: Laboratory experiment . . . 131
B.1 Trace of the MCMC of all the parameters of the future function of thefield experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
ix
B.2 Trace of the MCMC of all the parameters of the future function of thefield experiment - Group 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 153
B.3 Trace of the MCMC of all the parameters of the future function of thefield experiment - Group 2 . . . . . . . . . . . . . . . . . . . . . . . . . . 154
B.4 Trace of the MCMC of all the parameters of the future function in thelaboratory experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
B.5 Trace of the MCMC of all the parameters of the future function of thelaboratory experiment - Group 1 . . . . . . . . . . . . . . . . . . . . . . 156
B.6 Trace of the MCMC of all the parameters of the future function of thelaboratory experiment - Group 2 . . . . . . . . . . . . . . . . . . . . . . 157
B.7 Trace of the MCMC of all the parameters of the future function of thelaboratory experiment - Group 3 . . . . . . . . . . . . . . . . . . . . . . 158
x
Acknowledgments
This research would not have been possible to conduct without the support of
the Latin American and Caribbean Environmental Economics Program (LACEEP). I
am indebted with them for all their help. I also would like to thank my advisers James
Shortle and David Abler for their help, support and patience in all this process, especially
at the hard times. I would like to thank Jill Findeis for her encouragement and support,
especially during the first part of the process. I am also thankful to Edward Coulson
for his feedback and support. I am deeply indebted with the farmers of Aguascalientes
and the Penn State students that participated in the experiments. Without them, this
dissertation would not exist. Professors and authorities of the Universidad Autnoma de
Aguascalientes were extremely helpful in the organization of the sessions. In particular
professors Joaqun Sosa, Jess Meraz and Jos Luna. I would also like to thank Ing. Juan
Zamarripa, who was key in the recruitment of many farmers and the development of many
sessions with well owners. The work of Berenice Castillo, Viviana del Hoyo, Gabriela
Flores, AnneLiese Nachman and Charlotte Benson was crucial for the implementation
of the sessions. I also appreciate the comments received during the LACEEP workshops
and the European Summer School in Resource and Environmental Economics, especially
the comments received by Erik Ansink and Ariel Dinar. I would like to express my deep
gratitude to Miguel Angel Gutierrez and all my family in Aguascalientes, Marta, Susana,
Michel, Tey and Miguel. Their love and care made me feel as home in Aguascalientes. I
would like to thank all my friends in State College, especially David, Andrea, Roberto,
xi
Eli, Carlos, Erin, Miguel, Claudia, Hernan, GG, Luis, Juancito, Wil and Sandra. State
College would not have been the nice place that was during this time without them.
Thanks to all my extended family that was always supporting and encouraging me,
and my immediate family who always cared about my physical and mental well being.
Finally, I am deeply indebted to Veronica, who always was on my side helping and giving
me suggestions and comments, but most importantly, support and strength.
xii
Dedication
A mis padres, quienes con su trabajo sacrificado pudieron darme la salud y la edu-cacion para poder crecer profesional y humanamente; y a mi esposa, Veronica, quien consu amor incondicional y alegrıa pude obtener las fuerzas necesarias para poder terminaresta etapa, y ası poder continuar una vida juntos.
1
Chapter 1
Introduction
Groundwater currently provides 30 percent of freshwater in the world IWMI
(2010), and it is estimated that groundwater potentially constitutes approximately 89
percent of the world’s fresh water (Koundouri 2000). Groundwater has been key on the
provision of freshwater in arid areas, and subsequent poverty reduction and food secu-
rity FAO (2003). However, extensive extraction of groundwater in some areas is leading
to aquifer depletion. Many areas in the world in which groundwater is essential, such
as Western US, Mexico and India, show important declines on the water table Sekhri
(2011). Some problems related to groundwater overexploitation are increasing pumping
costs; land subsidence and further damages to surface infrastructure; changes in ecosys-
tems that rely on groundwater, such as wetlands; and availability of water for drinking
and irrigation (FAO 2003). Moreover, water quality problems are becoming frequent
in some of these areas, since high concentrations of fluor and arsenic are deposited in
deeper levels of groundwater (IWMI 2010)
Groundwater is considered, in some situations, a common-pool resource (CPR)
with extremely high use value (FAO 2003). Economists and political scientists have de-
voted a great amount of effort to understand the use of common pool resources (McGinnis
2000). CPR are, for economic and institutional reasons, nonexcludable. (Ostrom and
Gardner 1993; McGinnis 2000). Examples of CPR include fisheries, pastures, irrigation
2
systems, or even oceans and the biosphere (Ostrom and Gardner 1993). Traditional
microeconomic theory predicts that the rent-seeking behavior of individuals will result
in over-exploitation, degradation and possible extinction of such resources, the so called
“Tragedy of the Commons” (Hardin 1968).
Some scholars argue that the solution to the tragedy of the commons is privati-
zation through assignment of clear property rights. If enforceable, property rights can
ensure exclusion and provide incentives for efficient use. Others point to challenges re-
sulting from high enforcement and transaction costs, leading to market failures. Due
to these market failures, they propose that a government should be responsible for the
management of the resource and guarantee the socially optimal exploitation. Recently,
a third line argues that communities can self-regulate (Coward 1976; Ostrom 1986, 1990,
1992; Ostrom and Gardner 1993; Trawick 2003). These scholars argue that rules that
are internally created and agreed upon by the community, along with a set of tools that
ensure the enforcement of those rules, can be effective in the provision and preserva-
tion of CPR (Ostrom 1990; Ostrom and Gardner 1993; Dayton-Johnson 2000; Trawick
2003; Swallow et al. 2006). These studies have found some evidence that cooperation
among the users of a CPR can emerge, and that face-to-face communication between the
agents is important to ensure compliance of rules (Hackett et al. 1994; Cardenas 2011;
Moreno-Sanchez and Maldonado 2010).
One way to increase the availability of the resource to all its users is through
the adoption of technology that improves the efficiency of how people use the resource.
For instance, in the case of groundwater, users can adopt efficient irrigation technologies
(e.g. drip irrigation) and reduce exploitation of the resource. Nevertheless, in the case
3
of CPR, private investment in efficient technologies can yield benefits to all users. Thus,
some users might have incentives to free ride, preventing the adoption of the efficient
technology unless arrangements are made within the group.
In this regard, the characteristics of a system and how agents interact within are
important for the success of the community as an institution that ensures the sustainable
and responsible extraction of the resource. Moreover, the dynamics of the system and
how CPR users make decisions, as well the study of the behavior they manifest in a
CPR setup is important. It is necessary to understand the conditions working for and
against the sustainability of local cooperation in situations of general social and economic
interdependence (Bardhan 2000).
The analysis of institutions involved in CPR’s and the behavior of users demands
an analytical framework that goes beyond the one traditionally used by economists that
assumes non-cooperative rent seeking. We usually assume that agents choose“as if”
he/she is unboundedly rational, meaning that the potential to develop rational thinking,
given the information on hand, has no limits (Conlisk 1996). However, there is strong
evidence that agents make systematic mistakes from the perspective of economic ratio-
nality (Simon 1955; Kahneman and Tversky 1979; Conlisk 1996; Camerer 1998; Ellison
2006).
Several labels, such as “bounded rationality”, “behavioral failures” or “rules of
thumb” have been used to name those types of behavior that depart from economic
rationality. Unfortunately, there is no agreement on how these behaviors can be handled
analytically, and thus have been analyzed separately in different contexts. This is the
major limitation of non-traditional models. Their inability to replace the traditional
4
economically rational framework is due the lack of a unified formal conceptual framework,
although it has been proven that these types of behaviors are consistently supported by
data Harstad and Selten (2013).
According to Shogren et al. (2010), the economists that focus on the analysis
of deviations from unboundedly rational behavior (conventionally called “behavioral
economists”) have clearly shown two important facts of economic behavior not allowed
by the traditional economic perspective: i) preferences are context-dependent, and ii)
social preferences have an important role in economic choice. The challenge is to in-
corporate these facts in the analysis conducted by environmental and natural resource
economists, where an unbiased valuation of environmental non-market goods and the
design of institutions and mechanisms that promote cooperation in a CPR context are
needed.
Another challenge is to identify and classify these types of behaviors within a
heterogenous population. This is key in a CPR context, since the composition of the
group might have important effects on the final state of the resource and well being
of users. One way to identify the behavior of subjects is, in experimental setups, to
design the experiment in order to verify whether participants behave according to one
theory or another. To mention some studies, Lettau et al. (1999) consider different
types of agents and propose a theoretical model in which individuals choose the best
of several decisions rules, based on the state and comparison over past experiences.
Similarly, Suleimain and Rapoport (1997) consider three types: Those concerned with
equity, those who maximized utility and those that cannot be categorized. Moreover,
5
Fischbacher et al. (2001) find that a significant number of agents that participated of a
laboratory experiment can be categorized as “conditional cooperators”.
A slightly more general approach is the one followed by El-Gamal and Grether
(1995). They propose a pre-defined set of behaviors that participants might show and
then classify participants according to their actions and how close they are to the pre-
defined theoretical behaviors. A more flexible approach is one in which researchers “let
the data speak”, and behavior types are clustered according to the actions agents make.
After the clustering process, one can categorize the different behaviors existent in the
population. This approach is followed by Houser et al. (2004).
In summary, allowing behavior to depart from economic rationality implies not
only the formulation of theories that might explain the behavior of agents in a better
way, but also entails the identification of these behaviors in a heterogenous population.
Given that relaxing the rational behavior assumption opens the door to many other
behavioral theories that, in addition, allow context-dependent preferences, the identifi-
cation of agents following one or another behavior seems to be a necessary but difficult
task to pursue.
The present work contributes to this last objective. In this dissertation, I will
analyze and discuss the results from CPR laboratory experiments, in which the results
are intended to reveal the behavior of users. I propose a dynamic groundwater game
in which users pump water from a shared well, and the actions of users in one period
affect the extraction costs of everyone for the next period. This is an innovative design,
since most of previous studies do not consider the groundwater problem in experimental
settings, and do not conduct a groundwater experiment with farm groundwater users.
6
The objectives of this research are twofold. In the first part of the dissertation,
I assess the presence of strategic behavior when participants have access to an efficient
technology that yields both private and public benefits to CPR users. This situation
might discourage users from adopting the new technology, which results in free-riding.
In this part of the dissertation, I am also concerned about the effectiveness of group ar-
rangements to improve water usage and to endorse certain appropriation levels that yield
a socially-desirable economic outcome. Given the experimental design, I can partially
address both learning effects during the game and unobserved heterogeneity, in order to
obtain a precise estimation of the impact of the treatments. Finally, I also analyze the
factors that affect technology adoption and deviation from agreed water usage.
In the second part of the dissertation, I analyze the degree of heterogeneity of the
choices that participants make, and aim to identify the decision rules that participants
use during the game. Using a methodology proposed by Geweke and Keane (2000) and
Houser et al. (2004), I can relax the rational expectations assumption in the dynamic
choice problem, and identify different behaviors in the population. Based on the deci-
sions that participants make during the experiment, I can identify and cluster “types”
or groups of participants with a flexible mixed multinomial discrete choice model that
allows parameters from the structural model to be drawn from a discrete mixture of
distributions. In order to estimate the parameters and group membership probabilities,
Bayesian Markov Chain Monte Carlo techniques are used. These methods allow the esti-
mation of highly dimensional discrete choice problems and adds flexibility to estimation
and the clustering process.
7
In this dissertation, I repeatedly compare the results obtained in the laboratory
experiment with those obtained by Salcedo and Gutierrez (2014) and Salcedo (2014),
henceforth LACEEP 1 (2014) and LACEEP 2 (2014), respectively. In these studies,
the authors recruited 256 farmers from the State of Aguascalientes, Mexico in order to
conduct the same experimental design presented in this dissertation but on the field.
Details about the implementation of these experiments can be found in LACEEP 1
(2014).
Part I
8
9
Chapter 2
The Economics of Groundwater Management
Groundwater characterizes for being replenishable but depletable. Aquifers recharge
over time due to filtration of surface water. However, this process could be very slow,
and when the total use of groundwater exceeds recharge, the resource will be depleted.
Depletion of groundwater continues until the marginal cost of extraction is prohibitive
or the stock of water in the aquifer is exhausted. This leads to the consideration of the
use value of groundwater, since water used today reduces the opportunity of obtaining
future benefits from water. Then, an efficient allocation of water entails the considera-
tion of both the marginal cost of pumping (increasing with the water table) and the use
value. The initial economic studies that analyzed the groundwater problem focused on
the analysis of the efficient allocation of the resource. In the seminal works of Burt and
Brown and Deacon (Burt 1964, 1967, 1970; Brown and Deacon 1972), the authors used
dynamic optimization models to analyze the optimal allocation of water over time.
Later, economists started to address groundwater allocation in a competitive econ-
omy, exploiting the characteristic of open access of common-property resources. Conven-
tionally, groundwater users’ behavior is assumed to be myopic, with no consideration of
the “use value” of water. In this setup, the current marginal value of water is equalized
to the current marginal cost of water extraction (Gisser and Sanchez 1980; Nieswiadomy
1985; Worthington et al. 1985, see).
10
Most of these studies conclude that the optimal path in the controlled and the
competitive situations is the same, implying that there are no welfare gains from a
controlled optimal allocation of groundwater. This result is usually referred as the Gisser-
Sanchez effect, and it relies on the non-excludable property of groundwater. However, as
pointed out by Koundouri (2004a,b), there are reasons to believe that the conclusions of
Gisser and Sanchez should be taken with caution, since several restrictive assumptions
are made. When these assumptions are relaxed, the features of the Gisser-Sanchez
effect do not necessarily hold. First, some of the assumptions that Gisser and Sanchez
make for their model might drive the results (e.g. linear negatively sloped demand, linear
pumping cost). Second, there is no interaction among users, and therefore the possibility
of strategic behavior is absent. Third, the model does not consider heterogeneity among
users and/or locations. Fourth, it is assumed that the aquifer will never be depleted.
Finally, the model is deterministic, there is no uncertainty on recharge or maximum
capacity.
For instance, Worthington et al. (1985) solve a dynamic water allocation model
for a confined aquifer system in Southwest Montana. Due to the topological structure
of the confined system, the cost function of water pumping is nonlinear. They find
significant welfare loses under the perfect competition compared to the dynamically
efficient allocation, especially when land productivity heterogeneity exists. In a similar
way, Brill and Burness (1994) find that the differences between optimal and competitive
setups increase with a growing (non-stationary) demand, declining well yields (non-linear
cost), and low social discount rates.
11
Later, economists began using game theory to develop groundwater analytical
models. The major focus of this group of studies was to analyze the behavior and
interactions among water users given the strategic behavior that might arise in different
situations, as well as the welfare losses due to strategic behavior. Negri (1989) argues
that little attention has been paid to the “more realistic” situation in which access to the
resource could be restricted to some users. In such situations, rents do not fully dissipate
(in opposition to unrestricted setups), and welfare loses vary inversely with the number
of resource users (Negri 1989). In this situation, game-theoretic tools are appropriate.
Studies that rely on game theory for the analysis of CPR usually focus on the
sources of inefficiency based on three types of externalities generated by the appropriation
of the resource: i) Stock (Cost) Externalities, that arise when changes in the stock of the
resource affect the cost of extraction of the resource to all users; ii) Strategic Externalities,
related to the common-property feature of the resource and the difficulty of property
rights allocation, which might encourage users to extract more than optimal level of the
resource because of fear of appropriation of the scarce resource from other users in the
future (Negri 1989); and iii) Congestion Externalities, related to the spatial distribution
of the points of extraction of the resource. Provencher and Burt (1993) also identifies, iv)
Risk Externalities, that arise when the uncertainty in the availability of surface water
is considered, which increases the optimal use value of groundwater for all firms, but
firms fail to internalize this value. Gardner et al. (1990) also considers “technological
12
externalities”, that arise when the presence of a new technology adopted by one group
of users affects the extraction costs of those that did not adopt the technology. 1.
Negri distinguishes between open-loop and feedback solutions for the dynamic
program. Open-loop solutions are based on information that users hold at the begin-
ning of the game, which obligate users to commit to an efficient extraction path for the
whole time span. For the case of groundwater extraction, these solutions only consider
inefficiencies based on stock or cost externalities. On the other hand, feedback strate-
gies depend on current-period information. This type of behavior incorporates dynamic
strategic behavior, and therefore include both stock and strategic externalities. Negri
argues that commitment to an extraction path in open-loop solutions is not credible
with a lack of a property rights structure, and therefore these type of solutions are less
robust than feedback solutions. He concludes that resource extraction in feedback solu-
tions tend to increase the likelihood of overexploitation of the resource in comparison to
open-loop solutions.
The analysis developed by Negri (1989) yields to the conclusion that strategic
behavior affects the rates of water pumping, and therefore, steady-state stock levels are
lower than the open-loop equilibrium. Provencher and Burt (1993) take Negri’s argu-
ment, but relates his conclusion about strategic externalities to the fact that a finite stock
of water in the aquifer aggravates the inefficiencies that already exist (cost externality).
In their study, Provencher and Burt analyze the strategic behavior of groundwater users
where there is a limited stock of water (the name they assigned to this type of externality
1For this study, I will not consider risk and congestion externalites, given that none ofthe parameters considered in the experiments are stochastic, nor spatial or network effects areintroduced.
13
was stock externality). They analytically calculate both the cost externality and strate-
gic (stock) externality and show that the aquifer steady-state water stock level in an
open-loop equilibrium is higher than is obtained in the feedback equilibrium. Moreover,
the two equilibria are bounded from above and below by the controlled and the free (un-
controlled) solutions, respectively. Rubio and Casino (2003) also prove that a feedback
solution increases the overexploitation of the aquifer. Moreover, using nonlinear policy
functions, they also prove that, if the storage capacity is large, the difference between
the controlled and uncontrolled setup is negligible.
An instructive numerical exercise is developed in Madani and Dinar (2012). The
authors define six different management institutions for groundwater extraction and cal-
culate the differences in extraction and welfare. In the six models, three different (in
parameters) water users interact through the physical conditions of the aquifer, and only
cost externalities are considered. The six setups developed in the study are: ignorant
myopic management, smart myopic management with drawdown penalty, smart myopic
management with profit penalty, fixed ignorant non-myopic management, variable igno-
rant non-myopic management, and smart non-myopic management. They define agents
as “smart” when they notice that there are interactions with other users that affect their
profits; and “myopic” as agents that do not care about the use value of the resource. They
find that agents from a “smart non-myopic” management institution yield the highest
welfare and resource conservation, whereas the ignorant myopic management institution
(free or uncontrolled access) yields the worst. It is worth noting that, although they
do not consider feedback equilibrium, agents in the “smart non-myopic” management
institution recalculate their long-term plans extraction in each period based on the new
14
information they obtained from the water table. This situation is not exactly a feedback
strategy, given that conjectures about the actions of others are not computed, but it
considers adaptation to additional information.
Finally, in a recent paper, Suter et al. (2012) develop a groundwater game in
a laboratory setup and explore the effects of different spatially explicit hydrological
groundwater models on pumping rates and the behavior of water users. They find that
spatially explicit models (in which the depth to water is specific to each location but at
the same time depends on the decisions of the other users) show a less myopic behavior
in comparison to the “bathtub” model.
Another strand of research has focused on the analysis of investment decisions in
common-pool resources. In the context of groundwater, investment in efficient irrigation
technology might alleviate the depletion of the resource. However, there is no agreement
among researchers on the impacts of irrigation efficiency on water saving (Peterson and
Ding 2005; Ward and Pulido-Velazquez 1989; Pfeiffer 2009), since individual gains in
efficiency might yield public benefits in this context. Moreover, increases in efficiency
often lower the cost of consumption, which might increase water consumption through
substitution or income effect (Pfeiffer 2009). This is known as the Jevon’s Paradox
or “rebound effect” (Jevons 1865). Now, farmers might have the incentive to shift
towards improving parcels that were not irrigated, or switch to more water-demanding
crops. Lichtemberg (1989) develops a model in which the introduction of land quality-
augmenting technologies generates a substitution between the acreage of good and bad
quality land. In an empirical test of the model, Lichtemberg uses the adoption of center
pivot technology as a land quality-augmenting technology, and finds that the capital cost
15
of the technology significantly affects the cropping patterns. Ward and Pulido-Velazquez
(1989) develops a basin scale hydrologic model of the Upper Rio Grande Basin of North
America and show that subsidies directed to partially support the adoption of more
efficient irrigation technologies encourage a shift to more water-efficient technologies,
but do not reduce water depletion under any of the scenarios. They find that irrigated
acreage increases with the adoption of the new technology. Moreover, the study shows
that important return flows are lost because of the increase in efficiency. The same
results are found in Peterson and Ding (2005) and Scheierling et al. (2006). This research
suggests that irrigation efficiency improving investments give farmers incentives to shift
to more water-demanding crops.
When there is interaction between users (as there is in the aquifer problem),
strategic investment behavior might arise due to technological externalities (Gardner et
al. 1990). For instance, Agaarwal and Narayan (2004) develop a dynamic two-stage game
in which agents choose the level of initial investment for the capacity of a well and subse-
quent extraction. They show that agents strategically invest in excess capacity, leading
to further depletion of the aquifer. Barham et al. (1998) also analyze the relationship
between sunk costs and strategic behavior but in a context of a non-renewable resource.
The groundwater model studied in this dissertation considers the possibility of
ameliorating the depletion of the resource through adopting efficient irrigation tech-
nologies. However, due to strategic behavior, some groundwater users could have the
incentive to delay adoption, given that they are already being benefited by those farmers
who already adopted. The problem presented in this study is similar to the one presented
16
in Moretto (2000) and Dosi and Moretto (2010) without considering uncertainty in re-
turns. Moretto (2000) develops a theory where irreversibility effects and war-of-attrition
effects are compounded in the decision of producers to adopt a new technology. They
find trigger values at which producers will switch from one technology to another.
17
Chapter 3
The Groundwater Management Game
The theoretical model that serves as the basis for the framed experiments follows
the model proposed by Provencher and Burt (1993). In order to facilitate the exposition,
the model of groundwater management with no investment is presented first, with the
solutions for three different types of behavior: myopic, rational and fully coordinated.
Then, the individual model for both groundwater consumption and optimal investment
is presented, followed by the description of the parameters used and the experimental
design. It is important to mention that all the theoretical models were solved numerically,
and water use paths were calculated for each type of behavior. Therefore, it is possible
to compare the theoretical behaviors obtained from the model with the results obtained
in the experiments.
3.1 Theoretical Model
The model considered in the study is a simple dynamic groundwater model with
a finite number of users that interact through the aquifer. All users are assumed to have
dug the wells beforehand. Also, it is assumed that pumping costs change with the water
table. Nevertheless, open access is not considered, so it is possible to perform a game
theoretical perspective, since rents do not fully dissipate.
18
The functional forms that I have chosen for the experimental design follow Wang
and Segarra (2011). These authors consider a profit function that is linear in respect to
the demand of water. They argue that crop water-related yields tend to increase linearly
with the amount of water applied until they reach a plateau, due to the natural capacity
of plants to absorb the water. Provencher and Burt (1993) is modified to consider depth-
to-water instead of the stock of water that remains in the aquifer. This is because depth
is more meaningful to user as it determines pumping costs directly. The model considered
by Provencher and Burt (1993) is presented, and then the modifications are shown for
clarification.
3.1.1 Basic Game (Baseline)
There are N groundwater users. They pump water from a “bathtub-type” aquifer
tapped through wells and they do not have access to surface water. In the model, I
assume wells have been dug, and costs are only those related to pumping from existing
wells. 1.
Farmer profits conditioned on water is are denoted by:
Bit = αwith− witβ
St− k = wit
(αh− β
St
)− k
Where wit is the amount of water pumped by farmer i in period t, α is the marginal
value of production of irrigated land, h, 0 < h ≤ 1 is the level of efficiency in the use of
water, βSt
is the marginal cost of water pumped from the well, St is the stock of water in
1Although I believe that these decisions and costs are extremely important, I tried to simplifythe model in order to make the application with farmers easier.
19
the aquifer in period t, and k is the fixed cost of production. As commonly assumed in
the groundwater literature, only production costs related to groundwater are variable. It
is assumed that farmers already made all the decisions regarding the use of other inputs,
and their cost is already considered in the marginal cost β and the fixed cost k. Note
that the marginal cost of water pumped is inversely related to the stock of water in the
aquifer. If the stock of water increases, then the water table increases and farmers have
to pump water from a higher point in the well, which requires less electricity and reduces
pumping costs. Finally, there is no heterogeneity between farmers.
To specify the model in terms of water table instead of stock, I considered the
aquifer as a cylinder with a radius of R and height of D. Thus, the maximum capacity
of the aquifer is denoted by D × πR2. However, the stock of water in the aquifer will
change over time due to exploitation. Due to this, the stock can be observed using the
difference between the maximum depth of the aquifer, D, and the depth at which water
is pumped, dt. The stock of water at time t can be represented by: St =(D − dt
)×πR2.
With this identity, I can transform the current-period profit function to:
Bit = wit
(αh− β(
D − dt)× πR2
)− k
The equation of motion for the water table is given by:
dt+1 = dt +Wt
πR2 −f
πR2
20
Where Wt is the demand of water of the N farms, Wt =∑N
i=1wit, and f is the natural
recharge of the aquifer in period t. Since no water beyond D can be pumped, total water
use is limited to:
dt +Wt
πR2 ≤ D
Farmers’ decisions depend on behavioral assumptions. Types considered here are
myopic, rational and fully cooperative.
Given the functional form of the model, a myopic water user will pump the max-
imum possible amount of water in every period, as long as profits are positive, since
myopic water users do not internalize the future consequences of their water consump-
tion today. Because there are no contemporaneous externalities from other water users
in the model, the demand of a myopic user is given by:
wm =
w if dt ≤ D − β
πR2αh
0 otherwise
Where w is the maximum amount of water that can be pumped.
Alternatively, a rational water user will consider the future value of water in their
decisions. Since the decisions of others will affect the stock of water in the future, rational
21
users will also consider the choices of others. The rational water users problem is:
Vi1 = max{wit}Tt=1
[T∑t=1
δt−1Bit
]s.t
dt+1 = dt +1
πR2
N∑j=1
wjt + f
dt +
1
πR2
N∑j=1
wjt ≤ D
d1 given
Where δ is the discount rate. Assuming then that agent i can predict with certainty
other users’ choices, then user i maximizes the value function given the other users’ best
response2. Recalling the optimality principle, it is possible to write the Bellman equation
for agent i and period t as:
Vit (dt) = maxwit
[wit
(αh− β(
D − dt)× πR2
)− k + δVi,t+1 (dt+1)
]s.t.
dt+1 = dt +1
πR2 [wit + (N − 1)φ (dt) + f ]
dt +1
πR2 [wit + (N − 1)φ (dt)] ≤ D
d1 given
2Nevertheless, for empirical purposes, conjectures about other users’ decisions should varybetween individuals, depending on observable and unobservable variables.
22
Where φ (d) is the best decision taken by the other N − 1 firms and, as before, h < 1.
The solution of the problem will depend on the strategies that agents choose. Open-
loop strategies depend on time and not on the current state (dt), whereas feedback or
close-loop strategies will depend on both time and current state. Negri (1989) and other
authors argue that open-loop strategies are not time consistent, since agents will correct
their paths over time. Provencher and Burt (1993) show that the solution of this problem
involves two different types of externalities: strategic and stock. Strategic externalities
arise when feedback strategies are followed. These externalities negatively affect the
efficient allocation of the resource and could encourage the depletion of the resource. It
is important to mention that the myopic behavior will be rational if full open access is
guaranteed or if the user cost is very small. In other words, the full/rational behavior
will tend to to myopic if N increases (Provencher and Burt 1993)
A socially optimal (dynamically efficient) solution of the problem differs from the
individual problem in that the collective profits are maximized. Assuming homogeneity
of agents, the symmetric total profit maximization problem is:
NVit (dt) = maxwit
N
[wit
(αh− β(
D − dt)× πR2
)− k + δVi,t+1 (dt+1)
]s.t.
dt+1 = dt +1
πR2
[wit + (N − 1) φ (dt) + f
]dt +
1
πR2
[wit + (N − 1) φ (dt)
]≤ D
d1 given
23
Where ∼ denotes values at the social optimum. Given that V and V are concave,
Provencher and Burt (1993) show that the individual myopic or rational demands for
water are greater than the socially optimal demand, and lead to a lower steady-state
equilibrium stock of water. With a proper parametrization, it is possible to solve both
problems numerically.
3.1.2 Investment
Next I consider consider the problem when farmers can invest in new irrigation
technology. This new technology has an efficiency h of 1, meaning less water is required
to achieve the same profits exclusive of pumping costs, compared to the previous tech-
nology. This technology is adopted only once at a cost of I. The new technology also
requires maintenance cost of m every period3. The periodic benefits with the less ef-
ficient technology are denoted as B0 and are given by equation (3.1), whereas benefits
with the more efficient technology, without considering the investment cost, are given
by:
B1it
= wit
(α− β(
D − dt)× πR2
)− k −m
With the two technologies available, the farmer not only has to decide the op-
timal path of pumped water, but also the optimal moment to switch to more efficient
technology. These two situations can be combined as follows. In any period, say τ , the
3This additional cost can be interpreted as the cost incurred in hose and filter replacementfor drip irrigation technology.
24
farmer will choose whether or not to invest in the technology, in order to maximize the
present value of the utility, Viτ , taking into account the equation of motion of the stock
of water in the aquifer and the boundaries of wit:
Viτ = max{V 0iτ, V 1
iτ− I}
s.t.
dτ+1 = dτ +1
πR2 [wiτ + (N − 1)φ (dτ ) + f ]
dτ +1
πR2 [wiτ + (N − 1)φ (dτ )] ≤ D
d1 given
Where
V 0iτ
= B0iτ
+ δVi,τ+1
and
V 1iτ
=
T∑t=τ
δt−1B1it
Again, φ (·) denotes the best strategy of the other users. The present value of the utility
of not investing in τ , V 0iτ
, considers the possibility of investing in the new technology in
the next period τ + 1, whereas investment in τ is considered irreversible.
This problem can be solved using the two-step method proposed by Agaarwal
and Narayan (2004). The first stage involves the investment decision whereas the second
25
stage solves the optimal extraction path {wit}Tt=1. This problem is solved backwards,
starting from the second stage. It is possible to search for the optimal extraction path
conditional on the investment timing decision t, {wit(t)}Tt=1
, t = {1, 2, ..., T}. Each t will
yield a lifetime utility V(t)i1
. Now, the optimal investment time, t∗, can be represented
as:
t∗ = argmax{V(t)i1}, ∀t = {1, 2, . . . , T} (3.1)
Myopic agents do not care about the future, so they will not invest in the new
technology. Rational/strategic agents might be willing to invest in the new technology if
every user is willing to invest. However, there is the possibility of free-riding : Farmer i
will benefit from the water saving resulting from others’ investments. Therefore, farmer
i will have no incentive to invest if others do. If this is the case, then all the agents
will have the same strategy. Thus, Nash equilibrium will be the resulting equilibrium.
So two equilibria might arise, one in which everyone invests in the first period, and the
other, in which no one invests.
3.1.3 Parametrization, Myopic, Rational and Optimal Behavior
The total number of water users for each well considered in simulations is N = 4.
To facilitate the decision-making process of participants, I discretized the number of
hours of water that they can use. Thus, for this experiment, wit = {0, 1, . . . , 10}. The
irrigation technology efficiency is h = 0.5 for the less efficient technology, and h = 1
with the more efficient one. With this specification, 10 units of water will be required to
26
irrigate all the land with the less efficient technology, while only 5 units is required with
the more efficient one.
The planning horizon of participants is 5 production years. After year 5, they
retire from farming and receive their payoff (Vi1). Thus, it is not important for them
if there is water left in the aquifer4. The initial depth of extraction is set to d0 = 170
yards.
All the parameters that were used in the experiments are presented in Table
3.1. Also, tables 3.2, 3.3 and 3.4 present the revenues with the less-efficient technology,
highly-efficient technology and the costs of extraction. Note that revenues with the
highly-efficient technology increase with the number of units used up to five units. After
five units, revenues do not change. This is because farmers posses a fixed agricultural
area and, with the parameters used, all the area that they hold is irrigated with 5 units
(see Section 3.2.1). Also, note that the cost changes with each level of the depth of
extraction as well as number of water units required.
4Although I believe that it is important to give a value to that water, it would required thevaluation of the ecological benefits of that stock, and this valuation goes beyond the scope of thispaper.
27
Table 3.1.Parameters used in experiment
Parameter Value
α 10
β 390π
h 1 1
h 0 0.5
N 4
H 10
D 250
R 1
C 200
I 150
f 20π
m 9.460879
k 3
d 0 170
28
Table 3.2.Revenues with less-efficient technology
Hours Revenue
0 -3
1 7
2 17
3 27
4 37
5 47
6 57
7 67
8 77
9 87
10 97
Revenues by hours of water pumped
with flood irrigation
Table A
29
Table 3.3.Revenues with highly-efficient technology
Hours Revenue
0 -12
1 8
2 28
3 48
4 68
5 88
6 88
7 88
8 88
9 88
10 88
Table B
Revenues by hours of water pumped
with drip irrigation
30
Tab
le3.4
.P
um
pin
gcost
s
12
34
56
78
910
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Wa
ter
lev
el
24
92
48
24
72
46
24
52
44
24
32
42
24
12
40
23
92
38
23
72
36
23
52
34
23
32
32
23
12
30
22
92
28
22
72
26
22
52
24
22
32
22
22
12
20
21
92
18
21
72
16
21
52
14
21
32
12
21
12
10
20
92
08
20
72
06
20
52
04
20
32
02
20
12
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
390
195
130
98
78
65
56
49
43
39
35
33
30
28
26
24
23
22
21
20
19
18
17
16
16
15
14
14
13
13
13
12
12
11
11
11
11
10
10
10
10
99
99
88
88
8
780
390
260
195
156
130
111
98
87
78
71
65
60
56
52
49
46
43
41
39
37
35
34
33
31
30
29
28
27
26
25
24
24
23
22
22
21
21
20
20
19
19
18
18
17
17
17
16
16
16
1170
585
390
293
234
195
167
146
130
117
106
98
90
84
78
73
69
65
62
59
56
53
51
49
47
45
43
42
40
39
38
37
35
34
33
33
32
31
30
29
29
28
27
27
26
25
25
24
24
23
1560
780
520
390
312
260
223
195
173
156
142
130
120
111
104
98
92
87
82
78
74
71
68
65
62
60
58
56
54
52
50
49
47
46
45
43
42
41
40
39
38
37
36
35
35
34
33
33
32
31
1950
975
650
488
390
325
279
244
217
195
177
163
150
139
130
122
115
108
103
98
93
89
85
81
78
75
72
70
67
65
63
61
59
57
56
54
53
51
50
49
48
46
45
44
43
42
41
41
40
39
2340
1170
780
585
468
390
334
293
260
234
213
195
180
167
156
146
138
130
123
117
111
106
102
98
94
90
87
84
81
78
75
73
71
69
67
65
63
62
60
59
57
56
54
53
52
51
50
49
48
47
2730
1365
910
683
546
455
390
341
303
273
248
228
210
195
182
171
161
152
144
137
130
124
119
114
109
105
101
98
94
91
88
85
83
80
78
76
74
72
70
68
67
65
63
62
61
59
58
57
56
55
3120
1560
1040
780
624
520
446
390
347
312
284
260
240
223
208
195
184
173
164
156
149
142
136
130
125
120
116
111
108
104
101
98
95
92
89
87
84
82
80
78
76
74
73
71
69
68
66
65
64
62
3510
1755
1170
878
702
585
501
439
390
351
319
293
270
251
234
219
206
195
185
176
167
160
153
146
140
135
130
125
121
117
113
110
106
103
100
98
95
92
90
88
86
84
82
80
78
76
75
73
72
70
3900
1950
1300
975
780
650
557
488
433
390
355
325
300
279
260
244
229
217
205
195
186
177
170
163
156
150
144
139
134
130
126
122
118
115
111
108
105
103
100
98
95
93
91
89
87
85
83
81
80
78
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
Wa
ter
lev
el
19
91
98
19
71
96
19
51
94
19
31
92
19
11
90
18
91
88
18
71
86
18
51
84
18
31
82
18
11
80
17
91
78
17
71
76
17
51
74
17
31
72
17
11
70
16
91
68
16
71
66
16
51
64
16
31
62
16
11
60
15
91
58
15
71
56
15
51
54
15
31
52
15
11
50
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
88
77
77
77
77
66
66
66
66
66
55
55
55
55
55
55
55
55
44
44
44
44
44
44
44
15
15
15
14
14
14
14
13
13
13
13
13
12
12
12
12
12
11
11
11
11
11
11
11
10
10
10
10
10
10
10
10
99
99
99
99
98
88
88
88
88
23
23
22
22
21
21
21
20
20
20
19
19
19
18
18
18
17
17
17
17
16
16
16
16
16
15
15
15
15
15
14
14
14
14
14
14
13
13
13
13
13
13
13
12
12
12
12
12
12
12
31
30
29
29
28
28
27
27
26
26
26
25
25
24
24
24
23
23
23
22
22
22
21
21
21
21
20
20
20
20
19
19
19
19
18
18
18
18
18
17
17
17
17
17
16
16
16
16
16
16
38
38
37
36
35
35
34
34
33
33
32
31
31
30
30
30
29
29
28
28
27
27
27
26
26
26
25
25
25
24
24
24
23
23
23
23
22
22
22
22
21
21
21
21
21
20
20
20
20
20
46
45
44
43
43
42
41
40
40
39
38
38
37
37
36
35
35
34
34
33
33
33
32
32
31
31
30
30
30
29
29
29
28
28
28
27
27
27
26
26
26
25
25
25
25
24
24
24
24
23
54
53
52
51
50
49
48
47
46
46
45
44
43
43
42
41
41
40
40
39
38
38
37
37
36
36
35
35
35
34
34
33
33
33
32
32
31
31
31
30
30
30
29
29
29
28
28
28
28
27
61
60
59
58
57
56
55
54
53
52
51
50
50
49
48
47
47
46
45
45
44
43
43
42
42
41
41
40
39
39
39
38
38
37
37
36
36
35
35
35
34
34
34
33
33
33
32
32
32
31
69
68
66
65
64
63
62
61
59
59
58
57
56
55
54
53
52
52
51
50
49
49
48
47
47
46
46
45
44
44
43
43
42
42
41
41
40
40
39
39
39
38
38
37
37
37
36
36
35
35
76
75
74
72
71
70
68
67
66
65
64
63
62
61
60
59
58
57
57
56
55
54
53
53
52
51
51
50
49
49
48
48
47
46
46
45
45
44
44
43
43
42
42
41
41
41
40
40
39
39
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
Wa
ter
lev
el
14
91
48
14
71
46
14
51
44
14
31
42
14
11
40
13
91
38
13
71
36
13
51
34
13
31
32
13
11
30
12
91
28
12
71
26
12
51
24
12
31
22
12
11
20
11
91
18
11
71
16
11
51
14
11
31
12
11
11
10
10
91
08
10
71
06
10
51
04
10
31
02
10
11
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
44
44
44
44
44
43
33
33
33
33
33
33
33
33
33
33
33
33
33
33
33
33
33
33
33
88
88
77
77
77
77
77
77
77
77
66
66
66
66
66
66
66
66
66
66
65
55
55
55
55
12
11
11
11
11
11
11
11
11
11
11
10
10
10
10
10
10
10
10
10
10
10
10
99
99
99
99
99
99
99
88
88
88
88
88
88
8
15
15
15
15
15
15
15
14
14
14
14
14
14
14
14
13
13
13
13
13
13
13
13
13
12
12
12
12
12
12
12
12
12
12
12
11
11
11
11
11
11
11
11
11
11
11
11
11
10
10
19
19
19
19
19
18
18
18
18
18
18
17
17
17
17
17
17
17
16
16
16
16
16
16
16
15
15
15
15
15
15
15
15
15
14
14
14
14
14
14
14
14
14
14
13
13
13
13
13
13
23
23
23
23
22
22
22
22
21
21
21
21
21
21
20
20
20
20
20
20
19
19
19
19
19
19
18
18
18
18
18
18
18
17
17
17
17
17
17
17
17
16
16
16
16
16
16
16
16
16
27
27
27
26
26
26
26
25
25
25
25
24
24
24
24
24
23
23
23
23
23
22
22
22
22
22
21
21
21
21
21
21
21
20
20
20
20
20
20
20
19
19
19
19
19
19
19
18
18
18
31
31
30
30
30
29
29
29
29
28
28
28
28
27
27
27
27
26
26
26
26
26
25
25
25
25
25
24
24
24
24
24
23
23
23
23
23
23
22
22
22
22
22
22
22
21
21
21
21
21
35
34
34
34
33
33
33
33
32
32
32
31
31
31
31
30
30
30
29
29
29
29
29
28
28
28
28
27
27
27
27
27
26
26
26
26
26
25
25
25
25
25
25
24
24
24
24
24
24
23
39
38
38
38
37
37
36
36
36
35
35
35
35
34
34
34
33
33
33
33
32
32
32
31
31
31
31
30
30
30
30
30
29
29
29
29
28
28
28
28
28
27
27
27
27
27
27
26
26
26
Ta
ble
C
Pu
mp
ing
co
sts
by
wa
ter
lev
el
an
d p
um
pin
g h
ou
rs
9 10
Pu
mp
ing
ho
urs
Pu
mp
ing
ho
urs
Pu
mp
ing
ho
urs
4 5 6 7 810 0 1 2 35 6 7 8 90 1 2 3 40 1 2 3 4 105 6 7 8 9
31
The parameters were set so that it is not profitable to use water if there is less
in the aquifer than necessary to supply the maximum amount that users can require.
Thus, beyond dt = 210, it is more profitable to use zero hours of water and just cover
the fixed cost of production. With these parameters, the myopic, rational/strategic and
fully coordinated paths for the basic game were calculated.
Given that the decision variables are discrete and the functional forms are linear,
linear integer programming can be used to solve the problems numerically. A Branch-
and-Bound algorithm was used to find the optimal solutions. For the case of the social
optimum, a restriction requiring the same use of water for every farmer is imposed. For
Nash equilibrium, the steps presented below are followed:
1. Set the decisions of agent i to a random discrete number between 0 and 10
2. Set the decisions of agents j 6= i to a random discrete number between 0 and 10.These 3 agents have the same values but they are different to agent i.
3. Solve the problem for agent i.
4. Take these values and assign them to the decision variables of the other threeagents j 6= i (symmetric game).
5. Evaluate whether this solution is feasible for period t (i.e. dt + 4w∗t≤ D).
(a) If feasible ⇒ Go to next step.
(b) If not feasible ⇒ Turn all values for that period to zero and go to next step.
6. Repeat steps 3-5 until convergence of the value function
Given that the time span is short and that the action set is discrete and relatively
short, it is not difficult to find a stable solution for the Nash equilibrium. The trajectories
of units of water pumped, costs and well depth for each type of equilibrium are presented
in figures 3.1, 3.2 and 3.3. The total benefits from possible “fixed arrangements” in the
32
number of water units is calculated. This exercise could represent the situation in which
there is an agreement between users. The total benefits with arrangements from 0 to 10
hours of pumping were calculated. I considered zero hours of pumping whenever the cost
of extraction was too high and no production was more profitable. I consider 10 hours
for the last period, since the final well depth does not affect participant’s profits. The
results are presented in Figure 3.4. The equilibrium total benefits without including the
initial capital for myopic agents is 76.25; 108.75 for rational/strategic agents; and 165.82
for fully coordinated agents. Also, the value function is not linear for different fixed
arrangements. Moreover, with arrangements of 3, 4, 5, 6 and 7 units for each period, it
is possible to achieve net benefits higher than the Nash equilibrium. This indicates that
it is possible to be better-off than the Nash equilibrium if water users comply with those
fixed arrangements.
Fig. 3.1.Equilibrium Pumping hours for Myopic, Rational/strategic and Fully Coop-erative behaviors
33
Fig. 3.2.Benefits of pumping for Myopic, Rational/strategic and Fully Cooperativebehaviors
Fig. 3.3.Well depth for Myopic, Rational/strategic and Fully Cooperative behaviors
34
Fig. 3.4.Simulated benefits for Myopic, Rational/strategic and Fully Cooperative be-haviors, and fixed arrangements
In order to solve the model when the efficient technology is available, I first solved
the same problem in the case when only the highly-efficient technology is available. I
set the parameters in a way that it is possible to achieve the same social optimum with
the two technologies. This was done in order to avoid the introduction of a bias from
the parameters chosen. Then, I solved the second phase that involves the investment
decision, allowing the model to switch between the two technologies, given the efficient
path. As mentioned before, the model shows two equilibria: one in which all users adopt
the technology in the first period, and another in which none of the users adopt the
technology.
35
3.2 Experimental Design
3.2.1 Recruitment of Participants and Framing
Penn State undergraduate students were recruited through the Smeal College of
Business Laboratory for Economics Management Auctions (LEMA) recruitment system
for the laboratory experiments. A total of 200 students were recruited. Subjects could
participate in the experiment only once. The sessions were conducted between June 25
and July 15, and August 30 and September 17 of 2013.
Farmers from the State of Aguascalientes, Mexico were recruited for the framed
field experiments. Results from sessions with 256 farmers were used in LACEEP 1
(2014). For more information about the recruitment of the field experiment, please see
LACEEP 1 (2014).
Both experiments were framed as follows. Each participant holds H acres of land
devoted to agriculture. This land could be irrigated or not. The amount of land is fixed
over time throughout the game and it is the same for all participants. Each participant
shares a well among N . Participants are homogenous (i.e. have identical choice sets
and payoff) but they do not know for sure what the other users do (see below for a
description of the session).
Each period will represent one year of production. Water users decide the daily
amount of water they will use for the entire production year. Decisions on the amount
of water are expressed as hours of water/day pumped from the well, wit. Each irrigated
acre requires 12h hours of water/day from the well. For instance, to produce on the H
acres requires wit = H2h hours of water per day. The total level of water use depends on
36
the number of acres that are irrigated. Thus, the total irrigated land for the period will
depend on both the water requirements that they scheduled and the level of efficiency,
wit2h.
As mentioned above, changes in the depth of the water well will depend on the
amount of water that farmers use. For the sake of consistency all participants are told
that one hour of water pumped from the well will contribute to the depth of the well in
one yard . Finally, each farmer has an initial capital of C.
3.2.2 Treatments and Sessions
Treatments
The experimental design consists of two treatments:
Investment in technology (IN): In this treatment, participants will be allowed to invest
in irrigation technology. Participants are free to choose the time at which the investment
is done. The cost of investment is I.
Internal agreement (AG): Before participants make any decision regarding water con-
sumption, they agree on a fixed amount of water that they should pump in each period.
After participants make their agreements, they individually and anonymously decide
whether they comply with or deviate from the agreement.
The “Counterfactual” treatment (CF) refers to the sessions when the two treat-
ments are deactivated. Table 3.5 presents the distribution of sessions and participants
among the treatments for both field and laboratory experiments.
37
Table 3.5.Summary of sessions: Laboratory and field experiments
a. Laboratory
Treatment Sessions Groups Participants Periods
Counterfactual 14 23 92 920
Investment 7 14 56 560
Agreement 6 13 52 520
Total 27 50 200 2,000
b. Field
Treatment Sessions Groups Participants Periods
Counterfactual 7 21 84 840
Investment 8 21 84 840
Agreement 10 22 88 880
Total 25 64 256 2,560
Source: LACEEP 1 (2014)
Sessions
Games were played by groups of 4 participants. Each group represented a water
well and the four members of the group had to pump water from the same well. I
named the wells with colors: yellow, blue, orange, green and red. The number of wells
that participated in the session varied depending upon the number of attendants. Each
participant received a card of the color of the group membership. The card was randomly
assigned, but I ensured other participants with the same color did not sit nearby each
other. Each well was played independently. Wells did not compete for water and there
38
was no relationship between them. Finally, all experiments (both field and laboratory)
were paper-based.
All the sessions had at most 12 participants. Participants sat in individual cubicles
and members of the same well did not sit next to each other. Participants played for 15
periods. The first 5 periods (Round 1) corresponded to the baseline situation, in which
no investment nor agreement treatments were in place. After the first 5 periods, the
following 5 periods (Round 2) corresponded to a specific treatment. 3 types of sessions
in the experiments were applied. Participants were informed of the type of session
(CF,IN,AG) and corresponding instructions after the end of Round 1. After Round 2,
all the groups were randomly reshuffled and the same game as Round 2 was conducted.5.
Before participants made their pumping decisions for the first round, all group
members were informed of the initial well depth. This information was public throughout
the game and was the same for all the water wells.
Each participant had a revenue table for the case of the less-efficient technology
and, only for the case when the IN treatment is in place, participants had the revenues
of the two technologies, as shown in tables 3.2 and 3.3. They also had the cost table
presented in Table 3.4. Costs did not change between treatments. With this information,
participants could decide how many hours they pumped. They wrote down all their
decisions for the first period of Round 1 in their account sheet. Once all participants
made their decisions, calculated their income, cost and benefits for the first period (the
facilitator and assistants helped with these tasks), the facilitator proceeded to count how
5There is a variation in application of the CF session in Round 3, but that round will not beused in this study.
39
many hours were used by each participant for each well. This exercise was done in a
way that the other members of the well did not notice who their group partners were.
Then, I calculated the change in depth of each well (considering recharge) and made this
information public to proceed with the second period. This exercise was repeated four
more periods with the corresponding update well depth.
For Round 2, I started again from the initial well depth (170 yards). If the type
of session was “IN”, participants were able to invest in a highly-efficient technology.
All participants were informed of this opportunity before the round starts. However,
there was a cost of I to acquire the new technology. This payment was made only once
during the game. Thus, every period, they had to decide whether or not to invest in the
technology and the amount of water to pump. If the technology is adopted, they would
only calculate their benefits using the table of the highly-efficient technology, shown in
Table 3.3.
If the type of session is “AG”, the members of each well met for 10 minutes
before the game starts and discussed a fixed amount of water that they would request
for each period throughout the game. This agreement was written in their accounting
sheet. After the meeting, the participants proceeded to play a game similar to the
baseline. Participants could anonymously decide whether to comply with the agreement
or deviate, and no penalties were applied.
3.2.3 Rewards
As mentioned above, each participant received an initial endowment C which was
their show up fee. The payoffs at the end of each round were composed by C plus the
40
total net benefits from production that the participant earned through the five periods
minus I if the participant adopted the technology in the second (and third round for lab
experiments) of the “IN” sessions . At the end of the session, each participant drew a ball
from a bag with six balls, two of them marked with “1”, “2” or “3”,. The drawn number
indicated the round that was used to determine the reward. Participants received a
show up fee of $10 and the total earnings that participants received were between $10
and $226.
3.2.4 Survey
A short survey was conducted at the end of each session. The survey asked
about age, gender, major, minor, whether participants have taken courses in Economics,
Finances, Business Management, Psychology and Hydrology, and whether participants
had a farming background. The Cognitive Reflection Test (CRT) proposed by Frederick
(2005) was also included. This test is composed by three questions and it measures the
reflection capacity of agents, since the three questions could lead participants to give an
intuitive but wrong answer. Frederick (2005) mentions that the scores from the CRT is
correlated with patience, but also with less risk aversion.
Table 3.6 presents means and proportions of the variables gathered in the survey
for each treatment group, “Counterfactual”, “Investment” and “Agreement”. Most of
the students have a major related to “Business”, which includes Finance, Accounting,
Supply Chain Management and other similar majors, and also most of students have
6Some participants earned total benefits lower than the show up fee, however, the minimumreward was to $10.
41
taken a course in Economics. Also, there are no major differences between the groups,
with the exception of the percentage of male participants, participants with farming
background and participants that have taken courses in finance. The CRT survey results
show that, although on average participants obtained a low score, the sample is evenly
distributed between the “reflective” and the correct answers in Questions I and III, and
favors the “reflective” answer in Question II7.
Descriptive statistics of a survey conducted in the field experiment are presented
in Table 3.7. The survey consisted of five sections and farmers were asked about land
tenure, major crops and livestock, farmers’ experience and demographics, water access
and use, and irrigation technology available on the field.
7The CRT assigns a score of 1 to a correct answer and zero to a wrong answer. Therefore,the CRT final score has values of zero, one, two and three.
42
Table 3.6.Summary statistics of survey variables, laboratory experiment
Variable Counterfactual Investment Agreement Overall
Number of participants 92 56 52 200
Number of participants (%) 46.00 28.00 26.00 100.00
Mean of age (Years) 21.98 20.84 21.02 21.41
Male (%) 36.95 69.64 46.15 48.50
Farm background (%) 7.61 8.93 1.92 6.50
Courses (%):
Economics 85.87 89.29 84.62 86.50
Business Magement 48.91 69.64 61.54 58.00
Finance 53.26 75.00 59.62 61.00
Ag. Management 4.35 1.79 3.85 3.50
Environmental Economics 6.52 5.36 7.69 6.50
Psychology 42.39 46.43 51.92 46.00
Hydraulics 5.43 0.00 1.92 3.00
Major category (%):
Business 42.39 69.64 59.62 54.50
Education/Psychology 5.43 0.00 7.69 4.50
Energy/Environment 2.17 1.79 1.92 2.00
Engineering 5.43 3.57 1.92 4.00
Fundamental Sciences 7.61 3.57 7.69 6.50
Human development/medicine 3.26 1.79 7.69 4.00
Information Sciences 5.43 3.57 1.92 4.00
Liberal arts 7.61 5.36 9.62 7.50
Media 7.61 3.57 0.00 4.50
Natural Sciences 13.04 7.14 1.92 8.50
Cognitive Reflection Test (CRT)
Average Score (min:0, max:3) 1.59 1.04 0.96 1.27
Percentile 25 0 0 0 0
Median 2 0 0 1
Percentile 75 3 2 2 3
Answers Question I (%)
Answer = 5 57.61 33.93 34.62 45.00
Answer = 10 35.87 60.71 61.54 49.5
Question II (%)
Answer = 5 36.96 21.43 13.46 26.50
Answer = 100 45.65 58.93 71.15 56.00
Question III (%)
Answer = 47 43.48 35.71 26.92 37.00
Answer = 24 26.09 33.93 42.31 32.50
43
Table 3.7.Summary statistics of survey variables, field experiment
Variable Baseline Investment Agreement Overall
Mean of irrigated land (has.) 7.11 4.23 3.68 4.99
Mean of rain-fed land (has.) 5.11 4.82 3.66 4.52
Farmers with land in Ejido (%) 70.24 79.76 94.25 81.57
Owner farmers (%) 86.90 76.19 88.51 83.92
Renter farmers (%) 21.43 25.00 17.24 21.18
Farmers whose major crop is: (%)
Corn for food 27.71 69.05 41.38 46.06
Corn for Grazing 19.28 20.24 19.54 19.69
Alfalfa 12.05 8.33 22.99 14.57
Beans 9.64 2.38 6.90 6.30
Grapes 9.64 0.00 8.05 5.91
Farmers whose major livestock is: (%)
Bovine for dairy 53.70 42.11 34.92 43.10
Bovine for beef 22.22 36.84 47.62 36.21
Bovine for double purpose 5.56 7.02 0.00 4.02
Goat 9.26 8.77 7.94 8.62
Swine 3.70 3.51 3.17 3.45
Mean of age (Years) 54.42 46.19 54.98 51.91
Male Farmers (%) 92.86 90.48 95.45 92.97
Marital status (%)
Single 11.9 26.19 5.75 14.51
Married 79.76 66.67 79.31 75.29
Cohabitant 2.38 3.57 5.75 3.92
Widow 5.95 3.57 9.2 6.27
Education level (%)
Preschool/none 2.38 1.19 11.49 5.1
Incomplete Primary 34.52 22.62 27.59 28.24
Complet Primary 16.67 21.43 16.09 18.04
Incomplete Secondary 4.76 5.95 8.05 6.27
Complete Secondary 20.24 19.05 17.24 18.82
Incomplete Technician 1.19 5.95 4.6 3.92
Complete Technician 8.33 5.95 2.3 5.49
Incomplete agricultural technician 0 1.19 0 0.39
Complete agricultural technician 2.38 1.19 1.15 1.57
Incomplete upper secondary 1.19 0 0 0.39
Complete upper secondary 0 2.38 6.9 3.14
Incomplete undergraduate 2.38 4.76 1.15 2.75
Complete undergraduate 3.57 7.14 2.3 4.31
Graduate School 2.38 1.19 1.15 1.57
Source: LACEEP 1 (2014)
44
Table 3.7 (cont.)Summary statistics of survey variables, field experiment
Variable Baseline Investment Agreement Overall
Working regime (%)
Only on farm 41.67 38.10 54.02 44.71
Mostly on farm 20.24 20.24 6.90 15.69
Half-time on farm, half-time off-farm 26.19 30.95 31.03 29.41
Mostly off-farm 9.52 8.33 6.90 8.24
Only off-farm 0.00 1.19 0.00 0.39
Retired 2.38 1.19 1.15 1.57
Starting year (year) 1984 1992 1983 1986
Starting land (has.) 7.41 5.86 5.57 6.28
Major source of water (%)
Bordo 2.41 0.00 2.33 1.59
Water well 85.54 62.20 54.65 67.33
Dam 8.43 35.37 41.86 28.69
Other 3.62 2.43 1.16 2.39
Water well property
Private 3.57 0.00 0.00 1.18
Shared 82.14 58.33 55.81 65.35
Ejidal 4.76 10.71 1.16 5.51
No water well 9.52 30.95 43.02 27.95
Farmer is part of a water well association 90.79 81.03 95.92 89.07
Times of crop watering in first month 2.12 4.26 3.33 3.24
Times of crop watering in second month 2.12 3.77 3.32 3.07
Times of crop watering in third month 2.01 3.79 3.36 3.05
Hours for each watering 16.53 14.97 25.16 18.96
Farmers with irrigation technology (%)
Flood 69.88 74.70 65.12 69.84
Sprinkle 7.23 2.41 0.00 3.17
Drip 15.66 21.69 34.88 24.21
Micro Sprinkle 6.02 0.00 0.00 1.98
Other 1.20 1.20 0.00 0.79
Area with irrigation technology (has.)
Flood 3.99 2.64 2.35 2.99
Sprinkle 0.56 0.15 0.00 0.24
Drip 1.63 1.27 1.24 1.38
Micro Sprinkle 0.16 0.00 0.00 0.05
Other 0.04 0.04 0.00 0.02
Source: LACEEP 1 (2014)
45
Chapter 4
Results and discussion
This section summarizes the results of the laboratory experiment and those pre-
sented in ?. The experimental outcomes (pumping decisions) are presented first. They
show significant differences, on average, between the ones observed on the field and lab-
oratory experiment. Then, average treatment effects of the treatments are estimated
for each type of experiment. Effects of the treatments also differ between the two pop-
ulations, suggesting different reactions to the treatment. Finally, a deeper analysis is
conducted for each treatment: technology adoption and agreement compliance.
4.1 Experiment Outcomes
Tables 4.1 and 4.2 show the average values in each treatment, round and period
for the number of hours, benefits and well depth for both field and lab experiments.
Figures 4.1, 4.2 and 4.3 present the results graphically One noteworthy feature of the
results is that, in Round 1, the paths from the field experiment are very different from
the laboratory experiment. The average path of pumping hours in the field experiment
decreases in a smoother way than in the lab experiments, and similar differences are
observed on the average benefits and well depth. Also, important differences can also be
observed between the three treated groups of the field experiments in Round 1 when the
treatment has not been applied yet, whereas there are no significant differences between
46
the three treated groups of the lab experiments for the same round. These significant
differences are also shown in tables 4.1 and 4.2. Further, the average paths in Round 1
in both field and lab experiments greatly differ from the theoretical outcomes presented
in figures 3.1, 3.2 and 3.3.
47
Table 4.1.Average outcomes by type of session, round and period: Laboratory experi-ments
Period Treatment Round
Round 1 8.27 39.29 170.00
Round 2 8.83 42.18 170.00
Round 1 7.96 37.80 170.00
Round 2 7.23 *† 49.88 *† 170.00
Round 1 7.75 36.60 170.00
Round 2 5.85 *† 27.23 *† 170.00
Round 1 8.47 32.00 183.09
Round 2 8.99 32.43 185.30
Round 1 8.32 33.07 181.86 †
Round 2 6.91 *† 48.30 *† 178.93 *†
Round 1 8.02 31.58 181.00 *†
Round 2 5.06 *† 21.31 *† 173.38 *†
Round 1 8.01 18.29 196.96
Round 2 7.32 12.50 201.26
Round 1 7.82 19.71 195.14 †
Round 2 6.45 † 42.84 *† 186.57 *†
Round 1 8.13 22.37 *† 193.08 *†
Round 2 5.87 *† 24.67 *† 173.62 *†
Round 1 4.49 3.23 209.00
Round 2 3.29 1.70 210.52
Round 1 5.30 4.82 206.43
Round 2 5.66 *† 37.64 *† 192.36 *†
Round 1 6.38 *† 6.42 *† 205.62 *†
Round 2 5.83 *† 23.56 *† 177.08 *†
Round 1 6.14 7.63 206.96
Round 2 7.35 13.08 203.70
Round 1 4.84 4.16 207.64
Round 2 5.98 *† 38.82 *† 195.00 *†
Round 1 4.54 † 2.31 *† 211.15 *†
Round 2 8.38 30.44 *† 180.38 *†
Calculation of differences at 5% of error between CF and treatment for: * means (T-test)
and, † distributions (Mann-Whitney test)
3
4
5
Agreement
Counterfactual
Investment
Agreement
Counterfactual
Investment
Agreement
Counterfactual
Investment
Agreement
Counterfactual
Investment
1
2
Agreement
Hours of
pumpingBenefit Well Depth
Counterfactual
Investment
48
Table 4.2.Average outcomes by type of session, round and period: Field experiments
Period Treatment Round
Round 1 6.99 32.83 170.00
Round 2 7.24 34.26 170.00
Round 1 8.05 *† 38.19 *† 170.00
Round 2 5.61 *† 48.74 *† 170.00
Round 1 7.38 34.89 170.00
Round 2 7.15 34.09 170.00
Round 1 6.51 26.20 177.95
Round 2 6.95 28.52 178.95
Round 1 7.42 *† 28.25 182.19 *†
Round 2 5.46 *† 50.58 *† 172.43 *†
Round 1 7.26 *† 29.83 *† 179.50
Round 2 6.85 27.83 178.59
Round 1 6.58 22.88 184.00
Round 2 6.89 22.68 186.76
Round 1 7.18 18.40 *† 191.86 *†
Round 2 5.25 *† 51.54 *† 174.29 *†
Round 1 7.20 22.10 188.55 *†
Round 2 6.60 20.75 186.00
Round 1 6.60 16.92 190.33
Round 2 6.80 13.76 194.33
Round 1 6.90 7.75 *† 200.57 *†
Round 2 5.00 *† 50.12 *† 175.29 *†
Round 1 6.89 10.92 *† 197.36 *†
Round 2 6.40 10.88 192.41
Round 1 5.96 10.94 196.71
Round 2 6.46 5.40 201.52
Round 1 6.02 -5.00 *† 208.19 *†
Round 2 5.04 *† 51.96 *† 175.29 *†
Round 1 6.16 -2.08 *† 204.91 *†
Round 2 6.18 -19.08 198.00
Calculation of differences at 5% of error between CF and treatment for: * means (T-test)
and, † distributions (Mann-Whitney test)
Agreement
Counterfactual
Investment
Agreement
Agreement
Counterfactual
Investment
Agreement
Counterfactual
Investment
1
2
3
4
5
Counterfactual
Investment
Agreement
Counterfactual
Investment
Hours of
pumpingBenefit Well Depth
Source: LACEEP 1 (2014)
49
The results show important differences between the three groups in Round 2,
where the treatments are applied. For the field experiments, only the “IN” treatment
shows an improvement in the three variables analyzed with respect the counterfactual;
whereas for the lab experiments, both the “IN” and the “AG” treatments show significant
improvements with respect to the counterfactual in most of the periods. Finally, it is
worth noting that the average path of hours of pumping of the counterfactual group
of the lab experiments is very similar to the myopic theoretical behavior presented in
figure 3.1. This finding suggests that, after the first round, most participants notice the
behavior of their partners and decided to show this kind of behavior in opposition to a
more cooperative one. This result is not observed in the field experiments.
50
Fig. 4.1.Average individual hours pumped by period and treatment
a. Laboratory
b. Field
Source: LACEEP 1 (2014)
51
Fig. 4.2.Average individual benefits by period and treatment
a. Laboratory
b. Field
Source: LACEEP 1 (2014)
52
Fig. 4.3.Average well depth by period and treatment
a. Laboratory
b. Field
Source: LACEEP 1 (2014)
53
Turning to individual decisions, Figures 4.4 and 4.5 show histograms of pumping
hours for each period, round and treatment from the field and laboratory experiments,
respectively. The dispersion of choices from the field experiment is much higher than
from the laboratory experiment, which might reflect different degrees of game compre-
hension. However, when looking at the decisions of the field experiment in the first
period of the first round, that decisions are concentrated around 5 and 10 units, whereas
in the laboratory experiment they are mostly concentrated around 10 units, and a lesser
proportion is around 5 units. After period one, the distribution becomes flatter in the
field experiment, suggesting that farmers consider the potential cost of using high vol-
umes of the resource in early periods. In contrast, in the laboratory experiment, the
concentration around 10 units increases until period 4, where the distribution splits in
two parts, one around zero units and another around ten units. This is because it is not
profitable for some groups to use more water, given the depth of the well.
The differences between the decisions of students and farmers might reflect struc-
tural differences in behavior. Farmers appear to be more pro-social than students, or at
least they consider a higher use value of the resource. Students tend to be more myopic
and selfish, and this behavior becomes stronger on the following rounds. These results
are consistent with other findings in the Behavioral Economics literature. For instance,
Belot et al. (2010) find that students are more likely to behave in accordance to the eco-
nomic theory than non-students in games that engage other-regarding preferences (such
as Trust Game or Public Good Game). Carpenter et al. (2005), Carpenter et al. (2008)
and Anderson et al. (2013) find similar results.
54
To fully account for the effects of each treatment on the use of the resource,
it is necessary to develop a deeper analysis of the different behaviors within the two
populations. This issue will be partially addressed in Part II of the dissertation.
55
Fig. 4.4.Histogram of pumping hours from laboratory experiment, by Round, Periodand Treatment
a. Counterfactual
b. Investment
c. Agreement
56
Fig. 4.5.Histogram of pumping hours from field experiment, by Round, Period andTreatment
a. Counterfactual
b. Investment
c. Agreement
Source: LACEEP 1 (2014)
57
For the case when the investment treatment is imposed (Round 2), the distribution
collapses to 5 units in the field experiment, meaning that most farmers chose to adopt
the technology, whereas in the laboratory experiment, the distribution splits into two
parts, one concentrated in 5 units and another in 10. This evidence confirms the results
from the theory, where two attraction points were found. Finally, when the agreement
treatment is imposed, the distribution of the field experiment is initially concentrated
around 5 and 7 units, and then becomes more dispersed and the concentration around
8 and 9 units increases. In the laboratory experiments, there are not any significant
changes in the distribution until the last period, when most of the participants switched
to 10 units.
The end-of-round outcomes of the experiment are also of interest. Tables 4.3 and
4.4 show the mean values for the three end-of-round variables for both field and labora-
tory experiments. Difference tests in both mean and distribution are performed between
rounds for each treatment (CF, IN and AG) in part a. of each table. The results show
that there are significant differences for the two treatments in the laboratory experi-
ments, whereas significant differences for the IN treatment are found only in the field
experiment. Difference tests between the counterfactual and each of the two treatments
within each round (Part b.) were also conducted. The results of the field experiment
show that there are some differences between the counterfactual and the IN treatment
in the total benefits in Round 1, and in the total hours pumped and final well depth
in Round 2. The differences in Round 1 suggest that, even though the treatments were
assigned randomly, there are some unobservable differences between the participants of
the sessions that has to be considered in the analysis.
58
Table 4.3.Average end-of-round outcomes by type treatment and round: Laboratoryexperiments
Total Benefits 299.27 323.73 *† 327.21 *†
Total hours
pumped34.83 32.23 *† 30.98 *†
Final Well Depth 209.31 198.93 *† 193.92 *†
Calculation of differences at 1% of error between Rounds for: * means (T-test) and, † distributions (Mann-Whitney test)
Total Benefits 299.27 323.73 *† 327.21 *†
Total hours
pumped34.83 32.23 † 30.98 *†
Final Well Depth 209.31 198.93 193.92 *†
Calculation of differences at 1% of error between CF and treatment for: * means (T-test) and, † distributions (Mann-Whitney test)
211.52
300.45
35.38
211.52
300.45
35.38
Investment Agreement Investment AgreementVariable
Round 2Round 1
Counterfactual Counterfactual
Round 2
Counterfactual Investment Agreement Counterfactual Investment Agreement
a. Differences for each treatment between Round 1 and Round 2
b. Differences between CF and other treatments within Round 1 or Round 2
207
299.57
34.25
207
299.57
34.25
213.09
301.89
35.77
213.09
301.89
35.77
VariableRound 1
Table 4.4.Average end-of-round outcomes by type treatment and round: Field experi-ments
Total Benefits 287.6 295.66 315.44 *† 274.47
Total hours
pumped35.57 34.88 26.36 *† 33.18
Final Well Depth 212.29 209.55 175.43 *† 202.73
Calculation of differences at 1% of error between Rounds for: * means (T-test) and, † distributions (Mann-Whitney test)
Total Benefits 287.6 *† 295.66 315.44 274.47
Total hours
pumped35.57 34.88 26.36 *† 33.18
Final Well Depth 212.29 209.55 175.43 *† 202.73
Calculation of differences at 1% of error between CF and treatment for: * means (T-test) and, † distributions (Mann-Whitney test)
207.38
304.63
34.35
207.38
304.63
34.35
Counterfactual
VariableRound 1 Round 2
Counterfactual Investment Agreement Counterfactual Investment Agreement
a. Differences for each treatment between Round 1 and Round 2
b. Differences between CF and other treatments within Round 1 or Round 2
200.57
309.77
32.64
200.57
309.77
32.64
Investment Agreement Investment AgreementVariable
Round 2Round 1
Counterfactual
Source: LACEEP 1 (2014)
59
For the lab experiments, there are no differences in the outcomes in Round 1,
between the CF and the treatments, which suggests that the samples are similar a priori.
On the other hand, in Round 2, all outcomes from the AG sessions are significantly
different from the CF treatment in both mean and median, whereas only the Total
Benefits from the IN sessions are significantly different from the CF sessions in both
mean and median. There are no significant differences in median for the Total Hours
pumped between IN and CF, whereas for the Final Well Depth, there are no significant
difference between IN and CF in either mean or median.
Figure 4.6 shows the average total net benefit and the theoretical equilibrium
values for each treatment and round. In both the field and laboratory experiments, the
three groups overcome, on average, the value of the Myopic theoretical result (275.25),
but do not reach the Nash solution in Round 1 (308.75). In Round 2, the total net
benefits of the CF group do not reach the Nash equilibrium in the field experiments,
whereas the benefits for the IN group barely reaches the Nash level, and the average net
benefits of the AG groups do not even reach those of the myopic benchmark. In the case
of the laboratory experiments, again the CF group does not reach the Nash. However, in
this case, both the IN and AG are significantly higher than the Nash. A similar pattern
is observed with total hours of pumping and final well depth (Figures 4.7 and 4.8).
60
Fig. 4.6.Average individual total benefits by round and treatment
a. Laboratory
b. Field
Source: LACEEP 1 (2014)
61
Fig. 4.7.Average individual total hours pumped by round and treatment
a. Laboratory
b. Field
Source: LACEEP 1 (2014)
62
Fig. 4.8.Average final well depth by round and treatment
a. Laboratory
b. Field
Source: LACEEP 1 (2014)
63
4.2 Treatment Effects
A key interest of this study is the analysis of how access to efficient technology
and communication affect water consumption and welfare. Three outcomes of interest
are the three end-of-stage outcomes: individual total hours pumped, individual total
benefits and final well depth.
As mentioned before, there are some intrinsic differences between the treated
groups. If these differences are not taken into account, any estimation of the impact
of the treatment will be biased. Moreover, participants learn about the game between
rounds. Then, it is also necessary to control for learning effects. In order to obtain reliable
estimates of the impact of the treatment, I will estimate a difference-in-difference model.
In this case, I consider a reduced form approach to analyze the treatment effects.
Consider the outcome ygis
observed at the end of the round without treatment (s = 1) and
the round after treatment (s = 2) for three different treated groups: “Counterfactual”
(g = 0), “Investment” (g = 1) and “Agreement” (g = 2). Recall that for the case of
g = 0, there is no treatment imposed in both s = 1 and s = 2. The following linear
equation can be estimated:
ygis
= α+ δ + θ1D1 + θ2D2 + φ1D1 × δ + φ2D2 × δ + βXi + υi + εis
Where α is a constant, δ is a binary variable that takes the value of one if s = 1 and zero
otherwise, D1 is a binary variable that takes the value of one if g = 1 and zero otherwise,
D2 is a binary variable that takes the value of one if g = 2 and zero otherwise, Xi are
64
fixed individual (group) level observable variables, υi is a specific individual (group) level
random term and εis is a individual (group) and time level error term.
The average treatment effect is denoted by φg for each treatment, g = 1, 2, given
that:
φ1 = E[y1i2− y1
i1
]− E
[y0i2− y0
i1
]and
φ2 = E[y2i2− y2
i1
]− E
[y0i2− y0
i1
]
Estimation of this model with OLS would yield inconsistent estimates because
of the presence of unobserved heterogeneity represented by υi. A random-effects model
to estimate the equation presented above in order to account for specific individual and
treated-group effects. The full model which includes some of the variables gathered
through the survey was also considered to control for observable characteristics of par-
ticipants. Results are presented in Table 4.6 for the field experiments and Table 4.5 for
the laboratory experiments.
65
Table 4.5.Difference-in-Difference estimation of final outcomes in rounds 1 and 2: Labexperiments
(1) (2) (3) (4) (5)
Total pumping
hours
Total pumping
hours - FullTotal Benefits
Total Benefits -
FullFinal Well Depth
Treatment (Base = CF)
IN -1.130 -1.130 -0.874 -2.971 -4.522
AG -0.554 -0.554 -1.176 -2.682 -2.214
Round 2 0.391 0.391 1.446 1.446 1.565
IN x Round 2 -2.409 -2.409 22.72*** 22.72*** -9.637
AG x Round 2 -4.237*** -4.237*** 26.50*** 26.50*** -16.95***
Age 0.142 -0.0317
Female 1.105 1.147
Major group (Base = Business )
Education/Psychology -1.041 -6.991
Energy/Envionment 3.372 14.00
Engineering -0.761 -11.35
"Hard" Sciences -1.451 -2.517
Human Devlopment/Medicine -0.397 -7.784
Information Sciences -1.952 -7.364
Liberal Arts -0.660 -8.363
Media -3.186* -13.77*
Natural Sciecnes 0.797 -7.820
CRT answer correct
Question 1 0.823 2.092
Question 2 -1.078 -2.030
Question 3 0.257 2.974
Constant 35.38*** 32.10*** 300.4*** 303.2*** 211.5***
σu 3.187*** 2.924*** 10.23*** 8.604*** 0
σe 6.135*** 6.135*** 24.73*** 24.73*** 13.01***
Observations 400 400 400 100 100
Number of caseid 200 200 200 50 50
Equation (3) is estimated at the well (group) level
*** p<0.01, ** p<0.05, * p<0.1
Variables
F test performed for significancy of σu
66
Table 4.6.Difference-in-Difference estimation of final outcomes in rounds 1 and 2: Fieldexperiments
(1) (2) (3) (4) (5)
Total pumping
hours
Total pumping
hours - FullTotal Benefits
Total Benefits -
FullFinal Well Depth
Treatment (Base = CF)
IN = 1 2.929** 3.292** -22.18* -21.19** 11.71**
AG = 1 2.244* 3.204** -14.11 -21.91** 8.974*
Round 2 1.702* 1.821* -5.143 -6.154 6.810
IN X Round 2 -10.92*** -11.36*** 32.99** 35.44*** -43.67***
AG X Round 2 -3.407** -3.858*** -16.05 6.413 -13.63**
Age -0.434** -0.455
Age2 0.00330* 0.00237
Female 0.829 2.859
Starting Year 3.748 47.02
Starting Year2 -0.000946 -0.0119
Head of household -2.644 2.92
Marital Status (Base = Single)
Married 0.262 -13
Cohabitant 1.462 24.68
Widow 1.483 3.803
Working time (Base = Only on farm)
Mostly on farm -0.554 4.729
Half on farm, half off-farm -2.741** -5.044
Mostly off-farm -4.827*** -15.14
Only off-farm -19.36*** -106.0***
Retired -1.462 -5.008
Education level (Base = Preeschool/None)
Primary school -1.745 -5.281
Secondary school -2.078 1.196
Technical school/Preparatory -1.659 8.714
Agricultural Technical school 1.692 21.13
University and Graduate school -3.586 5.804
Irrigated hectares 0.762*** 3.633***
Irrigated hecatares2 -0.00998*** -0.0416***
Land is ejido 0.761 17.62*
Source of water (Base = Dam)
Only water from well 1.246 7.183
Both water from well and dam 1.046 3.191
Primary crop alfalfa -0.0794 -4.915
Primary crop vine 3.520* 9.321
Area with drip irrigation -0.410*** -2.031***
Municipality (Base = Pabellón de Arteaga)
Aguascalientes -1.092 24.5
Asientos -0.678 -42.51***
Calvillo -4.246 10.3
Cosio -1.214 10.55
El Llano 0.383 -7.745
Rincón de Romos -3.922** -2.355
San Francisco 0.349 -45.68
San José de Gracia -4.809** 30.34***
Tepezalá -0.932 -8.894
Constant 32.64*** -3689 309.8*** -46349 200.6***
σu 5.882*** 4.373*** 25.95*** 9.117**
σe 6.411*** 6.380*** 74.32*** 48.67*** 14.93***
Observations 512 474 512 474 128
Number of caseid 256 237 256 237 64
Equation (5) estimated at the well (group) level
*** p<0.01, ** p<0.05, * p<0.1
Variables
Likelihood-ratio test performed for significancy of σu
Source: LACEEP 1 (2014)
67
The coefficients of interest are “IN x Round2” for the effect of the “IN” treatment,
and “AG x Round2” for the effect of the “AG” treatment. For the field experiments, the
two treatments have a significant negative effect on the total pumping hours and final well
depth, whereas only the IN treatment has a positive effect on final total benefits. As the
authors of LACEEP1 mention, this could be explained by the fact that some participants
deviated from the agreement. Thus, even though the amount of water was reduced, it
did not increase benefits. Also, there are intrinsic differences in the total water used in
the groups, since the coefficients of “IN” and “AG” are significantly different from zero
in equation (1) and (2). This result shows the value of the DID approach.
The authors of LACEEP1 also present the full model including contextual and
individual variables. It seems that older people, people that participate more in non-
agricultural activities, and people with a larger area with drip irrigation installed tend
to use less hours of pumping within the experiment, whereas people with total larger
areas tend to use more. At the same time, people that work only off-farm and people
with drip irrigation tend to earn less benefits in the game, and people with more area
tend to earn more. These results suggest that some individual characteristics might be
related to the types of behavior that the participant show during the game.
With respect to the laboratory experiments, the two treatments only show an
effect on the total benefits earned by participants, and only the “AG” treatment shows
effects on total hours pumped and final well depth. This is because, as I will show
in the next section, several participants did not adopt the technology and “free-ride”,
68
taking advantage of the benefits generated by the adoption of technology by other par-
ticipants. I also included individual characteristics in the regressions, but none of them
are significant.
4.3 Technology Adoption
The results presented in the previous section suggested that participants of the
field experiment show higher rates of adoption than the laboratory experiment, since
the “IN” treatment did not have any effect on the latter, but an important effect on the
former. As mentioned before, this might suggest the presence of strategic behavior in
adoption for some participants of the laboratory experiments.
Figure 4.9 shows the cumulative technology adoption percentages in each period
of Round 2 for both field and laboratory experiments. 81 percent of participants in the
field experiments adopted the technology in the first period of Round 2, and adoption
increased up to 90 percent in the fifth period. In contrast, roughly 40 percent of partici-
pants of the laboratory experiments adopted the new technology in the first period, and
up to 60 percent in the fifth period.
Recall that the theoretical model shows that there are two equilibria for the
investment problem, one in which all adopted the technology in the first period, and
one in which no one adopted the technology. The empirical findings suggest that the
theoretical predictions hold in the laboratory, since the sample is divided into people that
adopted immediately and people that never adopted. This is also observed on the third
round of the laboratory experiment. Although in Round 3, most participants adopted
69
the new technology on the first period, the adoption rate slightly increased from 62 to
66 percent, as shown in Figure 4.10.
Fig. 4.9.Percentage of technology adoption by period and experiment
Source: LACEEP 1 (2014)
Fig. 4.10.Percentage of technology adoption by period and round: Laboratory exper-iment
70
It is possible to analyze the factors that affect adoption rates, such as the current
well depth or personal characteristics of participants, using a proportional hazard model.
Define the hazard function as the instantaneous probability of leaving a state conditional
on survival on time t (Cameron and Trivedi 2005):
λ(t) = lim∆t→0
Pr [t ≤ T < t+ ∆T |T ≥ t]∆t
In this case, λ(t) represents the instantaneous probability of adopting the technology,
given that it has not been adopted by period t. The proportional hazard rate model
considers the hazard rate as a product of an intrinsic hazard rate that only depends on
time, and a factor that depends on the covariates x:
λ(t|x, β) = λ0(t)φ(x, β)
Where the most common functional form of φ(x, β) is exp(x′β).
Results from the Cox proportional hazard model of adoption for Round 2 of the
laboratory experiment are presented in Table 4.7. Well depth increases the hazard rate
by 275 percent whereas the squared of the well depth decreases the hazard ratio by
0.4 percent. This last result, although significant, is very weak. Therefore, well depth
has almost a linear effect on the hazard rate of adoption. With respect to the individual
characteristics, to be enrolled in the Information Sciences major increases the hazard rate
by 248 percent with respect to the Business major. Finally, differences in the results of
the CRT test also affects the hazard rate of adopting. The hazard rate of participants
71
that obtained zero, one and two in the CRT test is lower in 65.6, 58.4 and 48 percent with
respect to the effect of having full score (three), respectively. This result is interesting,
since the CRT is correlated with both patient and less risk averse people (Frederick
2005). Thus, people with higher CRT tend to be more thoughtful about the decision of
investing, or are less risk averse and are willing to bear the risk of investing, even if they
know that other participants might free-ride.
Table 4.7.Cox proportional hazard model of investment: Laboratory experiments
Variables Hazard ratio
Well depth 3.755**
Well depth sq. 0.996**
Age 6.540
Age sq. 0.957
Female 0.855
Major group (Base = Business )
Energy/Envionment 0.000
Engineering 0.559
"Hard" Sciences 1.323
Human Devlopment/Medicine 0.792
Information Sciences 3.483***
Liberal Arts 0.350
Media 1.598
Natural Sciecnes 0.000
CRT score (Base: Score = 3)
Score = 0 0.3440***
Score = 1 0.416**
Score = 2 0.520*
Observations 56
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
72
Turning to the field experiment, a possible explanation of the high adoption rate is
the background information that farmers hold about efficient irrigation technologies. Ac-
cording to LACEEP 1 (2014), there are several institutions in the area that have exten-
sion programs and demonstration plots with which information about efficient irrigation
technologies is given to farmers. Also, the Government of the State of Aguascalientes is
conducting several programs that aim at the improvement of water use efficiency through
the adoption of better irrigation technologies. A major constraint for adoption is the
lack of funding and budget constraints that farmers face. Only richer farmers can adopt
the technology, but most farmers are willing to adopt. In contrast, college students do
not posses any prior information about irrigation technologies, and they will only use
the information in the game to make their decisions. They will not adopt if they believe
that it is not worth to adopt the technology and, moreover, if their behavior is such
that they believe that they can benefit from not adopting. This difference between field
and laboratory experiments is important. If the experiment is meant to test behavior in
response to policy, then the test should be done with populations representative of the
affected population, since people with different backgrounds will see the experiment in
different ways.
4.4 Agreement
As mentioned above, participants from the AG sessions were asked to meet for
ten minutes before Round 2 starts in order to agree on a fixed individual level of pump-
ing throughout the five periods. However, no penalties were applied if the participant
deviated from the agreement.
73
Figure 4.11 shows histograms with the agreed values of pumping hours. Panel a.
shows the agreements in the laboratory experiment in Round 2. More than 60 percent
of the groups agreed on a value of 5 hours, and 22 percent agreed on 7 hours in Round
2. Two groups are categorized as “zero” that actually agreed on a variable number of
hours that involved combinations 0 and 10 hours, or combinations of 3 and 10 hours.
These groups earned the highest profit of the round. Variable agreements can also be
observed in Round 3 of the laboratory experiments (Panel b.). In this round, after the
groups were reshuffled, three groups chose combinations of 0 and 10 hours, and 0 and 3
hours. Again, these three groups earned the highest total benefits, and the members of
one group earned $364, which is almost the value that participants would have earned
at the social optimum ($365).
74
Fig. 4.11.Histogram of agreed values of pumping hours in “AG” sessions
a. Laboratory - Round 2
b. Laboratory - Round 3
c. Field
Source: LACEEP 1 (2014)
75
In the field experiments (Panel c.), most of the agreements are of 5 and 7 units,
and no group chose less than 5 hours.
Figure 4.12 shows cumulative percentages of deviation from the agreement by
type of agreement. Groups with agreements of “zero” were excluded, since the agrement
involved variable values. It is clear that participants of the field experiment show higher
rates of deviation, in general, than participants of the laboratory experiment. This
explains in part why the treatment effect of the AG treatment was significantly higher
in the laboratory experiments than in the field ones. Moreover, participants of the field
experiments whose group chose values of six pumping hours deviate earlier than other
participants.
It might be possible that the well depth in each period, along with personal
characteristics might affect deviation rates. The authors of LACEEP1 test the influence
of other factors on deviation rates with a Cox proportional hazard model. Results from
the Cox proportional hazard model for the field experiment are taken from LACEEP1
and presented in Table 4.8. A Cox model was also ran with the data from the laboratory
experiment. However, the effects of all covariates was significantly different from zero
and deviations were mostly explained by the baseline hazard rate which depends only
on time.
76
Fig. 4.12.Agreement deviation percentages in “AG” sessions
a. Laboratory - Round 2
b. Laboratory - Round 3
c. Field
Source: LACEEP 1 (2014)
77
Table 4.8. Cox proportional hazard model of deviation from agreement:Field experiments
Variable Hazard rate
Well Depth 0.920*
Well Depth sq. 1.0002
Agrement (Base = 5)
Agreement = 6 2.953***
Agreement = 7 2.104
Agreement = 8 5.789***
Agreement = 9 1.542
Agreement = 10 1.365
Age 0.988
Education level (Base = Pre-school/None)
Primary school 0.372***
Secondary school 0.158***
Technical school/Preparatory 0.345**
Agricultural Technical school 1.401
University and Graduate school 0.207**
Irrigated hectares 0.899
Working time (Base = Only on farm)
Mostly on farm 2.915
Half on farm, half off-farm 1.234
Mostly off-farm 1.679
Retired 3.336*
Source of water (Base = Well)
Only water from dam 0.357*
Both water from well and dam 0.444
Land is ejido 0.224***
Primary crop alfalfa 0.532***
Municipality (Base = Pabellón de Arteaga)
Aguascalientes 1.005
Cosio 0.087***
El Llano 3.676*
San Francisco 3.142*
Tepezalá 1.183
Observations 83
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
For the field experiment, LACEEP 1 (2014) find that well depth and its square do
not influence the hazard rate of defection. This result is consistent with the results from
non-cooperative game theory, where agents will deviate from the agreement, regardless
the state of the resource. Turning to the constant variables, having an agreement of
78
“6” and “8” significantly increases the probability of deviation in 195 and 579 percent,
respectively. However, these values are very high and should be taken with caution,
since the number of groups that chose those values is small. Furthermore, some individ-
ual characteristics also affect the hazard rate of defection. For instance, education has
significant effects in reducing the hazard of defection, although not in a monotonic way.
Also, being part of an ejido and having alfalfa as major crop have very strong effects on
reducing the probability of defection, reducing the hazard rate in 77.6 and 46.8 percent,
respectively. An ejido is a legally recognized agricultural community in Mexico originally
created manage agricultural land as a community. However, farmers that are part of the
ejido currently possess individual property rights over their land. Nevertheless, in many
ejidos land and water use decisions are still discussed with all their members. According
to the authors, the fact that farmers that are part of an ejido tend to deviate less from
the agreement gives some insights about the importance of reputation and social values
when face-to-face communication is part of the negotiation.
4.5 Discussion
The results of the experiments presented in this study show that there are impor-
tant differences between the behavior of the participants from the field and laboratory
experiments. Some researchers may argue that it is a matter of time and as more rounds
are played, actions will converge to the equilibrium and participants field and laboratory
experiments will behave similarly. However, several authors have found that there are
structural differences between the behavior of pools of students and non-students in labo-
ratory experiments (Anderson et al. 2013; Belot et al. 2010; Carpenter et al. 2005, 2008).
79
The results obtained in the present study align with the results from those studies in
the sense that students tend to behave in accordance to economic theory and seem to be
more selfish in a game with other-regarding preferences than non-students. In addition,
the experiments have given some insights about the importance of background informa-
tion when making decisions in experiments. The difference in the results obtained in the
IN treatment are very clear. The level adoption of new technology by farmers is very
high, even though there are incentives for not adopting. Moreover, the failure of the
efficient technology to improve the benefits in the laboratory experiment suggests the
presence of strategic behavior of participants, who do not have background information
about the technology.
Background information is extremely important when analyzing the behavior of
people in experiments. This is a key issue for policy design. When local authorities are
willing to design a program that helps to preserve a common-property resource, it is
imperative to work with communities and consider local traditions and history to build
institutions. Theoretical results are important as a benchmark, but local norms and the
way they evolve with the provision of the natural resource are fundamental.
Turning to the laboratory experiment, an interesting result from the IN treatment
was that the probability of adoption in the laboratory setting was highly correlated with
the results of the Cognitive Reflection Test (CRT), which is usually correlated with
patient and/or less risk-averse participants. This result suggests that participants that
adopt the technology are willing to bear risk of obtaining lower benefits due to potential
free-riding from other users.
80
The LACEEP1 study also shows that participants of the field experiment are less
likely to comply with the agreement, in comparison to those of the laboratory experiment.
This is surprising, since one would expect that social norms are more important in the
field than in the lab. The results show that farmers that are part of an ejido are more
likely to comply than other farmers. This result partially confirms that importance of
social norms in these settings.
Finally, it is necessary to mention that unobserved heterogeneity has not been
considered in the analysis . As shown in several figures, there is a high degree of hetero-
geneity in decision making among participants of the field experiment, and in a lesser
extent in the laboratory experiment. The presence of heterogeneity might reflect differ-
ent attitudes on the use of the resource. As mentioned before, some individuals might
behave more cooperatively and other more competitively. To identify those attitudes
and analyze whether they are correlated with some individual characteristics is funda-
mental for policy design based on economic experiments. The success of institutions
in common-pool resources management relies on the matching between its design and
user’s behavior. To identify these different behaviors and decision rules is the aim of the
second part of the dissertation.
Part II
81
82
Chapter 5
Dynamic Decision-making in the Groundwater
Experiment
5.1 Unbounded Rationality, Bounded Rationality and CPR
Economists traditionally assume that economic agents make choices “as if” they
are unboundedly rational, meaning that the potential to develop rational thinking, given
the information on hand, has no limits (Conlisk 1996). These assumptions have be-
come the keystone of scientific and policy-driven economics, and its power relies on the
formality with which behavior can be represented by formal models.
Nevertheless, since the late 1950’s, several economists have started to question the
rationality assumption. Many concepts such as “bounded rationality”, “heuristics” and
“rules of thumb” started to appear in economic studies as alternative behaviors (Simon
1955). Most of the critiques of rational behavior rely on the idea that the process of
choosing economically rationally (i.e. through profit or utility optimization) is complex,
and individuals have to rely on other criteria to make decisions (Simon 1955; Conlisk
1996). Moreover, some authors emphasize that the cost of acting in such a way is too
high. People incur a deliberation cost to process all the information available in order
to maximize the subjects utility and choose the optimal solution, and this deliberation
cost may be very high (Simon 1955; Conlisk 1996). Indeed, there is evidence that our
capability of making fully rational choices is context-dependent, since individuals show
83
a diminished cognitive performance when facing temporal adverse situations (Mani et
al. 2013).
Conlisk (1996) reviews several studies that make evident the presence of bounded
rationality in decision making. He discusses the arguments that traditional economists
make to defend the unbounded rationality assumption, and concludes that there is
enough evidence to switch to alternative theories that do not assume unbounded ra-
tionality. Camerer (1998) also emphasizes the necessity of exploring new theories of
individual decision. He focuses on the expected utility theory, and considers that the
prospect theory proposed by Kahneman and Tversky (1979) is a superior theory be-
cause it includes the traditional theory of expected utility and, at the same time, allows
other behaviors, such as loss adversity. Ellison (2006) gives an extensive exploration
of theory and evidence that implies bounded rationality specifically for industrial or-
ganization. Given the evidence that he found, he considers that a boundedly rational
behavior could be more realistic in some setups, and theory based on bounded ratio-
nality could be more flexible, which allows the incorporation of additional features to
models. In a recent article, Harstad and Selten (2013) discuss the reasons why neoclas-
sical economics is currently the prominent way of thinking in economics, and encourage
behavioral economists to pursue a formal and unified model with which it is possible to
compete with the traditional path. They identify some approaches as potential competi-
tors of unbounded rationality if a coherent set of tools that allow comparative statics
and stationary behavior is developed (Harstad and Selten 2013)
Most of the studies that have focused on alternative decision-making theories
have conducted economic laboratory experiments. (Houser and Winter 2004) estimate
84
discounting rates in an experimental setup using two different estimations strategies:
The first one is based on the usual rationality assumptions, whereas the second one uses
weaker behavioral assumptions. They define several decision rules based on heuristics and
estimate discount rates using these decision rules. They found that the estimation based
on decision rules gives a better prediction of the outcomes than rational expectations.
Goree and Holt (1999) discuss the results of three laboratory experiments and compare
the traditional predictions with those obtained using three different estimation strategies:
learning dynamics, logit equilibrium and iterated noisy introspection. By relaxing the
assumptions of perfect (unbounded) rationality and perfect foresight in the estimation,
they obtain a significant improvement in predicting the outcomes of their experiments.
Other studies have focused on the modeling and identification of classes of subjects.
Lettau et al. (1999) consider different types of agents and propose a theoretical model
in which individuals choose the best of several decisions rules, based on the state and
comparison over past experiences. Similarly, Suleimain and Rapoport (1997) consider
three types: Those concerned with equity, those who maximized utility and those that
cannot be categorized. Moreover, Fischbacher et al. (2001) find that a significant number
of agents that participated of a laboratory experiment can be categorized as “conditional
cooperators”.
A slightly more general approach is the one followed by El-Gamal and Grether
(1995). They propose a pre-defined set of behaviors that participants might show and
then classify participants according to their actions and how close they are to the out-
comes of the pre-defined theoretical behaviors. A more flexible approach is one in which
researchers “let the data speak”, and types of behavior are clustered according to the
85
actions agents make. After the clustering process, one can categorize the different be-
haviors existent in the population. This approach is followed by Houser et al. (2004).
For the case of natural resource and environmental economics, the question of
whether agents behave unboundedly rational or not is relevant and very important.
Shogren and Taylor (2008) discuss several issues regarding research on “imperfect ra-
tional behavior”, or “behavioral failures” as the authors call deviations from the eco-
nomically rational behavior. They discuss the relevance of these types of behaviors on
environmentally-related economic issues and the relation between behavioral and market
failures, which are common in environmental setups. They bring the question that, given
the specialities related to economics in environmental setups, is the lack of environmental
markets the cause of the existence of behavioral failures? How is it possible to “correct”
for environmental failures in order to have markets that work properly?
Nevertheless, some authors recognize that markets emerge from the interactions
of individuals with different types of behavior that try to exchange a specific good/bad
(Conlisk 1996). These authors propose that markets are self-organizing, and their func-
tionality rely on population heterogeneity. If self-organizing markets do not emerge,
it should be because the behavior of individuals does not allow their creation, or the
goods/bads in mind have some peculiarities that does not allow its exchange (e.g. trans-
action costs), or both. Thus, it is not clear whether behavior “correction” is possible
in order to obtain well-functioning markets, and therefore other types of institutions
have to emerge. Market-oriented policies will not necessarily work if the agents that
are involved are not “economically rational”, as pointed out by Gsottbauer and van den
Bergh (2011). The authors review models that depart from “unbounded” rationality and
86
analyze the possibilities of applying those models to environmental problems and policy
design. In their review, Gsottbauer and van den Bergh (2011) consider previous studies
that analyze departures from economic rationality and propose that environmental pol-
icy should go beyond price-based regulation or market-based instruments. For instance,
they mention that policy strategies can include social reward or punishment, which could
affect reputation and a consequent change in behavior. Gsottbauer and van den Bergh
(2011) also emphasize the lack of research on behavioral models applied to adaptation to
climate change. In addition, Shogren et al. (2010) note that behavioral economists have
clearly shown two important facts of economic behavior not allowed by the traditional
economic perspective: i) preferences are context-dependent, and ii) social preferences
have an important role in economic choice. The challenge is to incorporate these facts
on the analysis conducted by environmental and natural resource economists, where an
unbiased valuation of environmental non-market goods and the design of institutions
and mechanisms that promote cooperation in a CPR context are needed.
Literature, in general, recognizes the presence of agents whose behavior depart
from homo economicus. However, there is no agreement on whether these types of
behaviors have impacts on market outcomes, if existent. Nevertheless, to identify these
types of behavior in the population is crucial, since the presence of different types of
behaviors in the population might open the door to ways of avoiding the tragedy of the
commons, and facilitates the design of policy and institutions that would help to preserve
the resource, especially when markets are non-existent. This is key in a CPR context,
since the composition of the group might have important effects on the final state of the
resource and well being of users.
87
In summary, allowing behavior to depart from economic rationality implies not
only the need for theories that might explain the behavior of agents in a better way,
but also the need to identify these behaviors in a heterogenous population. Given that
relaxing the rational behavior assumption opens the door to many other behavioral the-
ories that, in addition, allow context-dependent preferences, the identification of agents
following one or another behavior seems to be a necessary but difficult task to pursue.
This part of the dissertation aims to identify different types of behavior in the
experiment. Data from both field and laboratory economic framed experiments was used
on the context of groundwater management to analyze users’ choices and endogenously
cluster the population on different groups, based on their choices during the game. For
that purpose, a Bayesian classification procedure based on the one proposed by Houser
et al. (2004) was used. The field experiment is presented in LACEEP 2 (2014) and
results from that study are presented here.
5.2 Behavioral Heterogeneity
According to the theoretical model presented in Chapter 3 , an optimum forward-
looking behavior fully internalizes the use value of the resource when a decision about
the demand for water is made. Then, at the beginning of the game, on the one hand,
fully-coordinated agents define the optimum path, which will depend only on time, given
that there is no uncertainty in the game. On the other extreme, fully-myopic agents will
disregard the use value of water remaining in the aquifer, and will decide according to
the current marginal benefits and costs.
88
Nevertheless, many people might base their decisions on heuristics, or follow “rules
of thumb”, especially when the consequences of their actions are not fully clear. Then,
it might be possible to identify some “types” of participants that lie in the range of
fully-myopic and forward-looking. This section aims at the identification of those types
of participants. In other words, I will try to identify clusters of participants based on
the decisions they make in the experiment.
Figure 5.1 shows the average paths of rounds 1 and 2 of both the field and lab-
oratory experiments. In Round 1, the resulting paths of the field experiment are very
different to those of the laboratory experiment. The average path of pumping hours
in the field experiment decreases in a smoother way than in the lab experiment, which
decreases abruptly at period 4. In Round 2, participants of the field experiment, on
average, used more water than in Round 1, but the paths are very similar. On the other
hand, the average path of the laboratory experiment changed drastically, showing now a
steep drop in period 9. In addition, the average paths obtained in the field experiments
significantly differ from the theoretical benchmarks. However, the average path of the
laboratory experiment in Round 2 resembles the “myopic” path.
89
Fig. 5.1. Average individual hours pumped by experiment and period
Source: LACEEP 1 (2014)
Although average values per period give us a general picture of the behavior
over time, a different scenario is observed when the distribution of choices is analyzed.
Figure 5.2 shows the histograms of the pumping hours chosen during rounds 1 and 2 for
the laboratory experiment, and Figure 5.3 for the field experiment. In the laboratory
experiment, the majority of choices are concentrated around “10” hours in periods 1
through 3 in Round 1, and then split between “0” and “10”, but there are several
participants that chose values between “3” and “9”. In Round 2, the concentration of
choices increased at “10” and, overall, there are less participants choosing intermediate
values. This change in the distribution might be a response to the learning process that
participants face during the game between rounds 1 and 2. With respect to the field
90
experiment, the choices are more dispersed and, in Round 1, the value of “5” concentrates
an important proportion of choices, along with the value of “10” in the initial periods,
and then dissipates towards intermediate values. In Round 2, a similar behavior but
with a higher concentration at “10” is observed, suggesting, as in the lab experiment,
that participants are adopting a competitive behavior during the game, but in this case,
the learning process is much slower.
91
Fig. 5.2. Hours of pumping by period: Laboratory experiment
a. Round 1
b. Round 2
92
Fig. 5.3. Hours of pumping by period: Field experiment
a. Round 1
b. Round 2
Source: LACEEP 1 (2014)
93
Another way to show heterogeneity in the data is mapping the choices against
another variable, such as well depth. Figure 5.4 shows the average number of pumping
hours for each depth level for each period of Round 2. A kernel-weighted polynomial
function estimated with the actual data is also shown. In the case of the laboratory
experiment, there is no clear pattern between choices and well depth. Initially, choices
are positively correlated with well depth, but then the relationship becomes negative
until the fifth period, where the sample is divided in two parts, one at the top and one
at the bottom. For the case of the field experiment, a positive relationship between
pumping hours and well depth is shown, but this relationship gets weaker over time and
choices become more dispersed.
94
Fig. 5.4. Average individual hours pumped by well depth
a. Laboratory
b. Field
Source: LACEEP 1 (2014)
95
Figure 5.4 also shows the choices made by four members of a randomly-selected
well from both the laboratory and field experiment. With respect to the laboratory exper-
iment, some initial differences in the behavior of participants is observed. For instance,
participant 12076 starts low and then increases the number of hours. On the other hand,
participant 12073 starts high and in period three abruptly decreases to zero, even when
it is still profitable to pump water. This behavior resembles the “rational/strategic” be-
havior of the theoretical model. In the field experiment, participant 16199 consistently
reduces its water demand until period four, and in period five its demand increases. At
the same time, the demand of water of participant 16200 consistently increases, again
until period four, and in period five it is reduced.
These differences in individual behavior could be identified if a more general
framework than the one proposed by the theoretical model is used. For instance, it might
be possible that not all agents behave as if they were unboundedly rational, suggesting
that some agents might use heuristics or “rules of thumb” to make decisions. These
differences are important since most of the theoretical models related to groundwater
management presume that all agents are either myopic or rational.
Houser et al. (2004) develop a methodology in which several “types” of agents
can be identified in a dynamic decision problem. They combine the flexible dynamic
model proposed by Geweke and Keane (2000) with a binary choice finite mixture model
estimated using Bayesian methods. The approach is based on Houser et al.’s application,
but some further steps were taken. First, a common-pool game was considered, in which
participants interact through the environment, and beliefs about other’s actions have to
be included in the model. Second, a discrete choice model as in Houser et al. (2004)
96
was used, the model is extended to a multinomial probit, since participants can make
choices on the number of hours between 0 and 10. The multinomial probit is a complex
model to estimate with traditional methods, but it is possible to estimate with Bayesian
methods.
5.3 Structural Model
Consider the Bellman equation of farmer i in the groundwater game presented
above:
Vi(dt) = B (wit, dt) + V(dt+1
∣∣∣dt, Wit, wit, t)
Where B (wit, dt) = wit
(α− β
D−dt
)− k are the current-period benefits defined
in the theoretical model, which depend on both the choice of hours of pumping and the
current well depth, and Wjt represents the beliefs of agent i of the total pumping hours
that the other members of the well will use.
As mentioned above, agents could have different behaviors. A rational agent
would solve a maximization problem and choose the level of wit that maximizes the
Bellman equation, considering his/her beliefs about the behavior of the other agents.
However, a myopic agent will use the maximum amount of water as long as Bit is positive,
whereas a cooperative agent will solve a maximization problem in which all agents are
considered altogether in the solution. Moreover, other agents might not make decisions
according to the behaviors presented in the theory. As mentioned above, researchers have
increasingly paid attention to decisions rules based on “rules of thumb” or heuristics.
97
In order to define a general equation with which all these behaviors could be
represented, Geweke and Keane (2000) consider a general functional form for the “future
function” Vi,t+1:
Vi(dt) = B (wit, dt) + F(dt+1, t+ 1
∣∣∣dt, Wit, wit, t)
Where F (·) is a general function that can be approximated by a N−order poly-
nomial. Note that the equation of motion of the state variable dt+1 and time t + 1 are
considered in the equation. Geweke and Keane (2000) show that, given a proper polyno-
mial approximation, this specification fits data generated with a dynamic programming
algorithm very well. Therefore, according to the authors, it is not necessary to solve
the dynamic programming problem with this specification. Moreover, this specification
gives us the necessary flexibility to analyze other types of behavior that depart from the
forward-looking rational one, since it is not necessary to make any assumption about
how agents form expectations.
Suppose now that there areK types of behavior or decision rules in the population.
These types affect the way how agents form expectations about the future. Then, the
function F for each type of decision rule k will be defined by a a set of parameters βik:
Vi(dt) = B(wit, dt
)+ F
k(dt+1, t+ 1
∣∣∣dt, Wit, wit;βik
)
98
Where the subscript ik denotes that individual i is classified in type k. For
instance, the third-order polynomial for the approximation of Fk
is:
Fk(wit = h) = β0ik
+ β1ik
(dt+1
∣∣dt, Wit, t, h)
+ β2ik
(d
2
t+1
∣∣dt, Wit, t, h)
+ β3ik
(dt+1
∣∣dt, Wit, t, h)
(t+ 1)
+ β4ik
(dt+1
∣∣dt, Wit, t, h)
(t+ 1)2
+ β5ik
(d
2
t+1
∣∣dt, , Wit, t, h)
(t+ 1)
+ β6ik
(d
3
t+1
∣∣dt, Wit, t, h)
+ β7ik(t+ 1) + β8ik
(t+ 1)2
+ β9ik(t+ 1)
3
The expression of Fk
will depend on the assumptions made about the beliefs of the
actions of other agents, Wjt. For now, it is assumed that agents have symmetric beliefs,
then Wit = 3h1. After inserting the equation of motion of dt+1, the future function for
1It is possible to consider a model of expectations, in which expectations vary with alternativesand states. This is another model that can be simultaneously estimated. Also, it is possible toinclude people beliefs in the equation. This exercise will not be conducted in this study
99
a 3rd-order polynomial is represented by:
Fk(wit = h) = β0ik
+ β1ik
[dt + 4h− r
]+ β2ik
[d
2
t+ 16h
2+ r
2+ 8dth− 2dtr − 8hr
]+ β3ik
[dt + h+ Wit − r
](t+ 1)
+ β4ik
[dt + h+ Wit − r
](t+ 1)
2
+ β5ik
[d
2
t+ 16h
2+ r
2+ 8dth− 2dtr − 8hr
](t+ 1)
+ β6ik
[d
3
t+ 64h
3 − r3+ 12d
2
th− 3d
2
tr + 48h
2dt − 48h
2r
+3r2dt + 12hr
2 − 24dthr]
+ β7ik(t+ 1) + β8ik
(t+ 1)2
+ β9ik(t+ 1)
3
Where h ∈ {0, 1, ..., 10} are the alternatives the agents face. Polynomials of order
3, 4, 5 and 6 are also specified in this study, and the one that best fits that data according
to a model selection criteria will be selected. In appendix A, the functional forms of the
polynomials of orders 4, 5 and 6 are presented.
100
Chapter 6
Empirical Specification and Estimation
6.1 Discrete Mixture Models
Unobserved heterogeneity in statistical models has been treated in different ways.
One way to overcome problems of parameters identification due to unobserved hetero-
geneity is through using discrete mixture models. Discrete mixture models consider that
the parameters of the behavioral model, which determine the data likelihood, are drawn
from a combination of a discrete number of distributions. For instance, instead of di-
rectly modeling a multi-modal distribution, flexibility is introduced if the distribution is
modeled as a combination of distributions.
Discrete mixture models are considered a model-based clustering algorithm. Tra-
ditional clustering algorithms (e.g. k-means or hierarchical clustering) are based on the
clustering criterion, usually the minimization of the distances to a centering measure
(mean or median). In contrast, model-based cluster algorithms assume a probabilistic
model from which multivariate observations of some variable are generated by a multi-
variate probability distribution.
Discrete mixture models can consider a point process (fixed coefficients drawn
from a base distribution), and its generalization, a mixture of distributions, from which
random parameters are drawn, and the parameters that define each distribution are
fixed or obtained from a baseline distribution (if allowed by the data). In contrast,
101
the continuous mixed model, which is commonly use with multinomial logit models,
considers a single continuous distribution from which the parameters are drawn. Figure
6.1 illustrates the approaches usually taken in the literature. On one extreme, the fixed
coefficient model considers a single coefficient for the entire population. Then, the model
can be generalized to several types of coefficients, a single family from which random
coefficients are drawn, and several families from which random coefficients are drawn.
102
Fig. 6.1. Single vs. Mixed Distributions
a. True distribution
b. Fixed effect c. Point process
d. Random effects e. Mixed distributions
103
More specifically, a discrete mixture distribution can be represented by:
p(yi|θ,π
)=
K∑k=1
πkf(yi|θk)
Where K is the number of latent classes, clusters or types considered in the model, f(·)
are the distributions to be mixed, θ are the parameters that define each distribution and
π denote the proportions of the population that come from each class. It is possible
to introduce an unobserved indicator that denotes the class membership. Consider the
indicator ζi ∈ {1, 2, ...,K}, and:
I(ζik
)=
1 if ζi = k
0 otherwise
Then, the model in equation 6.1 is equivalent to:
p(yi, ζik
|θ,π)
= p(ζik
)p(yi|θ,π
)=
K∏k=1
(πkf
(yi|θk
))I(ζi)
And the complete data likelihood is represented by:
p (y, ζ|θ,π) =
N∏i=1
K∏k=1
(πkf
(yi|θk
))I(ζik)
Finite mixture models are used in several disciplines (see Congdon (2010); Fruwirth-
Schantter (2006); Gelman et al. (2012)). In economics, one of the most prominent articles
that discussed finite mixture models theoretically is Heckman and Singer (1984). They
104
estimate a proportional hazard model with a mixture model for unobserved heterogene-
ity. Other studies that have used finite mixture models in economics are Greene and
Hensher (2003); Hess et al. (2011); Howard and Roe (2013) and Scherenberg et al. (2014)
Estimation of finite mixture models is difficult due to the multi-modal shape of the
likelihood. Traditional methods such as maximum likelihood are not suitable for these
types of distributions (Fruwirth-Schantter 2006). Over the last twenty years, researchers
have taken advantage of the computational improvements, and other methods are being
used, such as Expectation-Maximization (EM) and Markov Chain Monte Carlo (MCMC)
Bayesian methods. In this study, Bayesian methods for estimation will be used. The
method is presented in section 6.3.
6.2 Multinomial Probit
In order to identify the classes or “types” of agents in the experiments, it is
necessary to estimate the set of parameters βikthat define the utility function of each
agent. The empirical strategy used by Houser et al. (2004) is based on a random utility
mixture model, where both a point process for coefficients and normal distributions
for the error term are assumed. In other words, Houser et al. (2004) assume that the
coefficients of the future function are drawn from a normal distribution but fixed for
each class, whereas the error term varies between agents, alternatives and classes. The
error term represents any type of information that is unobserved by the econometrician
and that agents might use to make their decisions.
Allowing the error term vary among classes implies that their variances also vary
with classes. Some types will therefore show more dispersion in their error. This is a
105
strong assumption that might heavily affect the estimates if wrong. Thus, a more con-
servative approach is considered. It is assumed that the error terms are not drawn from
a mixture of distributions. Instead, the error terms of the choice model are considered
iid distributed with mean zero and fixed covariance matrix, and only the coefficients
follow a mixed point process.
Consider the iid normally distributed error term νit(h), with mean zero and co-
variance matrix Σ, and the empirical specification of the value function for alternative h
as:
Vit(dt+1|h) = Bi(h, dt
)+ F
k(dt+1
∣∣∣dt, Wit, h, t;βik
)+ νit(h)
The utility levels are not observed directly. However, the choices that agents make
are. Thus, it is assumed that those decisions that are chosen yield the highest utility
among all the alternatives:
wit = h ⇐⇒ Vit(h) = max {V (j),∀j = {0, 1, . . . , 10}}
Given the empirical specification used, a multinomial probit is the adequate choice
for the estimation of the structural parameters.
It is well known that the multinomial probit model is not identified for levels
(Albert and Chib 1993; Geweke et al. 1994; McCulloch and Rossi 1994; McCulloch et al.
2000; Nobile 1998), so it is necessary to specify the model in relative terms. The utility
106
of 10 pumping hours (h = 10) is used as the base category. Then, for every h 6= 10:
Vit(h) = Vit(h)− Vit(10)
= Bit(h, dt
)−Bit
(10, dt
)+F
k(dt+1
∣∣∣dt, Wit, h, t;βik
)− F k
(dt+1
∣∣∣dt, Wit, 10, t;βik
)+νit(h)− νit(10)
= Bit(h, dt
)+ F
k(dt+1
∣∣∣dt, Wit, h;βik
)+ ηit(h)
Where η(h) = ν(h)− ν(10) are normally distributed.
107
Assuming symmetric beliefs and considering a polynomial of order 3, the relative
value function V k is represented by:
Vit (h) = Bi(h, dt
)+ β1ik
(h− 10)
+ β2ik(h− 10)
[2 (h+ 10) + dt − r
]+ β3ik
(h− 10) (t+ 1)
+ β4ik(h− 10) (t+ 1)
2
+ β5ik(h− 10) (t+ 1)
[2 (h+ 10) + dt − r
]+ β6ik
(h− 10)[3(dt − r)
2+ 12(h+ 10)(dt − r) + 16
(h
2+ 10h+ 100
)]+ η(h)
Where β are multiples of the original β. Note that several terms of the polynomial cancel
out when taking the difference. More specifically, any term that is not multiplied by the
the alternative h will be eliminated. The functional form of polynomials of degrees 4, 5
and 6 are presented in appendix A.
In addition to the location constraint, it is necessary to impose another constraint
on the covariance matrix Σ for scale identification (Albert and Chib 1993; Geweke et
al. 1994; McCulloch and Rossi 1994; McCulloch et al. 2000; Nobile 1998). The first
term of the covariance matrix has to be fixed at 1. This is problematic, since it is not
straightforward to sample random matrices with this restriction. In order to be able to
108
identify the covariance parameters, a method proposed by Chib et al. (1998) is used (see
Section 6.3).
The traditional estimation of the multinomal probit model relies on the probability
of choosing an option as the alternative that yields the highest utility. This requires the
calculation of several integrals, which makes the estimation extremely difficult. For this
study, data augmentation (Albert and Chib 1993; McCulloch and Rossi 1994; McCulloch
et al. 2000; Nobile 1998) will be used to avoid the complexity of the estimation of the
multinomial probit. With this method, the problem reduces to a truncated multivariate
normal model:
yit ∼ TN(µy,Σ
)µy = Bi
(h, dt
)+ F
k(dt+1
∣∣∣dt, Wit, h;βik
)
Where yit is the latent relative utility. A truncated normal distribution is considered
because only values that meet the data constraints can be sampled from the normal
distribution. In this case, the data constraints are determined by the chosen alternative.
In other words, the sampled value of y(h) has to be consistent with the condition that, if
alternative h is chosen, then y(h) has to meet the condition that y(h) = max (y(j), ∀j).
The procedure proposed by Chib et al. (1998) is used to sample from the truncated
normal distribution. This method is presented in Section 6.3.
Finally, clusters of participants are formed assuming that βik= bk. In other
words, only heterogeneity between clusters is consider, leading to a point process model.
109
Group membership is denoted by the latent index variable ζik, and underlying group
proportions are denoted by λk.
6.3 Estimation
The empirical model that will be estimated is a discrete choice model with hetero-
geneity considered as a discrete point process. Traditional methods of estimation, such
as Maximum Likelihood, have shown problems when estimating mixture models. More-
over, it is well known that the multinomial probit is not easily estimated via Maximum
Likelihood, and that it can only be estimated up to 3 categories. Beyond this number,
it is necessary to use simulation methods, such as Simulated Maximum Likelihood. Re-
cently, researchers started to use two methods for these type of models. EM algorithm
and Bayesian. In this study, Bayesian methods to estimate the parameters of the model
are used. A brief explanation of the nature of Bayesian methods and the idea behind
the use of Monte Carlo Markov Chains is presented below. Then, the specific algorithm
that will be used in the study is explained.
6.3.1 Bayesian Methods
Bayesian inference relies on Bayes’ rule to set up a full probability model for the
data and parameters, and then, after conditioning on the data, calculate a posterior
distribution of the parameters (Gelman et al. 2012). The main idea behind Bayes’ rule
is that the joint probability density of two random variables (y and θ) can be written as
110
the product of two densities:
p (y, θ) = p (y|θ) p (θ)
Researchers often refer to p (y|θ) as the sampling or data distribution, and p (θ)
as the prior distribution. Then, conditioning on the data y, the posterior distribution
of θ is:
p (θ|y) =p (y, θ)
p (y)=p (y|θ) p (θ)
p (y)
Where p (y) =∫p (y|θ) p (θ) dθ. This term is fixed given the parameter θ, thus, the
literature usually refers to the unnormalized posterior density for Bayesian inference:
p (θ|y) ∝ p (y|θ) p (θ)
This rule indicates that the data y affects the posterior inference of the parameter
θ only through p (y|θ) which, when combined with a probability model, is called the data
likelihood. Traditional methods rely only on the data likelihood for inference. Maximum
Likelihood methods find the parameter θ that maximizes the function p (y|θ). Bayesian
inference uses the data likelihood to update prior information about the parameter. The
prior reflects the state of knowledge about the parameter, which can be informative
or non-informative. The degree of information carried by the prior will determine the
dependence of the posterior on the prior. In other words, a highly informative prior will
yield a very similar posterior since the data does not have an effect on it. Researchers
111
usually consider non-informative priors for estimation, in order to let the data speak.
However, in some applications, it is necessary to add some information in order to obtain
reliable posterior distributions.
The process of updating information from the prior with the observed data is
usually called Bayesian updating. If this process is done iteratively, given some properties
of the prior and likelihood and a sufficiently high number of iterations, it is possible to
obtain estimates of posterior density characteristics, such as moments and quantiles.
This iterative process is done using Monte Carlo Markov Chains (MCMC). To construct
the MCMC, the parameters have to be sampled from the estimated posterior distribution
in each iteration. The key to MCMC simulation is to create a Markov process whose
stationary distribution is the posterior p (θ|y) (Gelman et al. 2012).
Ideally, one would build the MCMC with direct samples from the posterior distri-
bution. However, this is computationally difficult in most cases and sampling algorithms
that approximate the posterior have to be used (Gelman et al. 2012). The baseline for
MCMC sampling schemes is the Metropolis-Hastings (M-H) algorithm. Intuitively, the
M-H algorithm “builds” the posterior distribution using draws from a proposal distribu-
tion (chosen a priori) and comparing the posterior density from the last updated draw
with that from the previous draw. These draws compose the MCMC, and the higher
the number of draws, the more similar the resulting distribution it is to the target dis-
tribution, the posterior. To determine whether the obtained distribution in each draw is
112
getting closer to the target distribution, the algorithm uses an acceptance rate:
α(θ∗|θ(t)
)= min
1,p(θ∗|y)f(θ
(t)|θ∗)
p(θ(t)|y
)f(θ∗|θ(t)
)
Where f(·) is the proposal distribution, p(·) is the target distribution, and θ∗
is the
proposal parameter sampled from f(·). Then, the MCMC updates to the next value:
θ(t+1)
=
θ∗
with probability min (r, 1)
θ(t)
otherwise
Details on how to choose f(·) and θ∗
can be found in Gelman et al. (2012) and Congdon
(2010).
The other commonly used sampling algorithm is the Gibbs sampler. This algo-
rithm is considered a special case of the M-H. The advantage of the Gibbs sampler is
that it allows sampling independent blocks of parameters. In other words, it is possible
to sample each parameter separately, conditional on the sampled values of the other pa-
rameters. Thus, each iteration of the MCMC with the Gibbs sampler consists on several
sampling steps, one for each parameter. In contrast, M-H samples the joint distribution
of the parameters simultaneously.
With the M-H, it is possible to sample from any posterior distribution. In contrast,
the Gibbs sampler can only be used whenever the prior and the posterior are conjugate
distributions, meaning that the posterior distribution is in the same family as the prior,
given the specification of the likelihood function. It is very common to combine Gibbs
113
sampling with M-H for those parameters that do not posses the conjugacy property
(Gelman et al. 2012).
There are several statistics and methods to analyze convergence of MCMC sam-
ples. The most commonly used method is the Brooks-Gelman-Rubin statistic, which
compares several interval lengths of different sampled MCMC for one parameter. Con-
vergence is achieved when the ratio of the mean of the chosen length of the chains is
equal to 1. Another method to assess convergence is the Geweke chi-square tests. This
procedure uses different portions of the MCMC and evaluates whether the two portions
can come from the same distribution. Graphical assessment is also possible through the
analysis of the MCMC trace and MCMC quintiles.
6.3.2 Data Likelihood and Parametrization
The first step to apply Bayesian inference to this case is to to define the data
likelihood. In the model, both the utility levels y and the class indicator ζ are not
observed in the data, but could be inferred (indeed, the major purpose of the study is
to estimate the class indicator ζ). Traditional methods rely on the “observed” likeli-
hood to estimate the parameters. This likelihood is incomplete, since y and ζ are not
observed. Nevertheless, since Bayesian methods rely on a complete probability model
for both parameters and data, it is possible to specify the “complete” data likelihood
as if the latent variables are observed, and then estimate those parameters from the
MCMC simulations. This procedure is called data augmentation (Albert and Chib 1993;
McCulloch and Rossi 1994; McCulloch et al. 2000), and is commonly used with Bayesian
methods.
114
Considering the probit model presented in Section 6.2, the complete data likeli-
hood of the model is represented by:
L (y, ζ|Σ, b, λ) = p (ζ|Σ, b, λ) p (y|ζ, λ,Σ, b)
=
N∏i=1
T∏t=1
p(ζi|Σ, b, λ
)p(yit|ζ, λ,Σ, b
)=
N∏i=1
T∏t=1
K∏k=1
[λkp
(yit|Σ, bk
)]I(ζi)=
K∏k=1
∏ik
T∏t=1
p(yit|Σ, bk
)( K∏k=1
λNk(ζ)
k
)(6.1)
Where Nk(ζ) is the number of individuals in category k and p(yit|Σ, bk
)is the
truncated multivariate normal:
p(yit|Σ, bk
)= (2π)
−H2 |Σ|−
12 exp
[−1
2
(yit −Bit − F
)′Σ−1 (
yit −Bit − F)]× I
(Sit)(6.2)
In equation 6.2, Sit denotes the support of the truncated normal distribution,
which is defined by the data (the chosen alternatives). Taking advantage of the Gibbs
sampler, Chib et al. (1998) and Geweke and Keane (2000) propose sampling the latent
utilities yit(h) from a truncated univariate normal distribution, given the values of the
latent utilities of the other alternatives. Thus, the support of the truncated normal
distribution is defined by:
Sit(h) =
(max{0,max{yit(−h)}},∞
)if wit = h, h = 1, 2, ...,H(
−∞,max{yit(−h)})
if wit 6= h, h = 1, 2, ...,H
(−∞, 0) if wit = H
115
Before describing the priors and the sampling algorithm, it is necessary to describe
the parametrization of the covariance matrix Σ. Recall that, to ensure identification, the
multinomial probit requires one of the diagonal elements of the covariance matrix to be
one. Usually, the first element of the matrix is chosen. As mentioned before, to obtain
random matrices with this restriction is a difficult task. Chib et al. (1998) propose a
Choleski decomposition to represent and sample free elements of Σ. Let Σ = LL′, where
L is a (J − 1) × (J − 1) lower triangular matrix with the first element equal to one
(l11 = 1). Chib et al. (1998) prove that the remaining elements can be sampled from
unrestricted univariate normal distributions with the following structure:
θ =(l21, log(l22), l31, l32, log(l33), ..., log(lH−1,H−1)
)
In other words, all the elements can be sampled from normal distributions, but those
elements that compose the diagonal of L are exponentiated. This method ensures a
positive-definite covariance matrix.
6.3.3 Priors and Sampling Algorithm
The set of parameters to estimate is composed by ψ = {b, λ, θ, {ζ}, {y}}, where
{} denote a latent variable.
116
The following priors for the parameters were considered:
b ∼ N(µb,Σb)
θ ∼ N(0, 0.001)
λ ∼ Dirichlet(α), αk = 2
And the latent variables are sampled, as mentioned before, from:
yit ∼ N(Bit + F ,Σ)I(Sit(h))
ζi ∼ Categorical(λ)
Note that the hyperparameters that define the prior of the parameters (b), µb and
Σb are allowed to be random. Thus, the baseline distribution of the coefficients of the
future function will be endogenously identify . The hyperpriors considered are:
µb ∼ N(µ0,Σ0)
Σb ∼ InverseWishart(M,ρ)
Where µ0 is a V x1 vector of zeros, where V is the number of terms in the future
function, Σ0 is the identity matrix, M is also the identity matrix, and ρ = V . With
the exception of θ, all the priors chosen are the natural conjugate priors. Also, with the
exception of α, relatively non-informative priors are considered.
117
The Gibbs sampling algorithm is based on the procedures presented in Fruwirth-
Schantter (2006) and Houser et al. (2004) combined with the sampling procedure for the
covariance matrix proposed by Chib et al. (1998):
1. Draw the latent utilities yit(h) from p(yit(h)|yit(−h), b,Σ, λ, ζ)I(Sit(h))
2. Draw the coefficients of the future function bk, for all k = 1, ..,K from the marginalposterior p(bk|y,Σ, λ, ζ), which is proportional to the likelihood in equation (6.1)times the prior of bk.
3. Draw the parameters θ that compose the covariance matrix Σ from p(θ|y, b, λ, ζ)
4. Draw the type proportions λ from the marginal posterior p(λ|ζ) = Dirichlet(α0 +Nk(ζk),∀k)
5. Draw the type membership indicator ζi from p(ζi|y, b,Σ, λ, ζ−i) ∝ p(yi|ζi, ζ−i)p(ζi|ζ−i)
Two steps have to be added in order to make inference about the hyperparameters
µb and Σb:
6. Draw the hyperparameter µb from the marginal posterior p(µb|b,Σb)
7. Draw the hyperparameter Σb from the marginal posterior p(Σb|b, µb)
With the exception of b, the remaining parameters are sampled directly from
the resulting conjugate posteriors. For the case of b, it is necessary to include a M-H
sampling within the Gibbs sampling, as shown in Section 6.3.1.
All the MCMC were run using JAGS on the lionfx computer core at Penn State.
118
Chapter 7
Results and Discussion
MCMC simulations were performed to approximate the posterior distributions of
the parameters and obtain the classification index ζ in order to cluster participants of the
laboratory experiment into groups. Two different chains for each model were simulated,
and used 20,000 iterations from those chains after considering an adaptation period of
20,000 iterations in which the samplers gain efficiency, and 60,000 iterations of burn-in.
We also discuss the results obtained in the field experiment presented in LACEEP 2
(2014). The results from the two experiments are compared.
7.1 Deviance Information Criteria and Group Number
One key issue that has not been discussed is the way the number of groups is
determined. Houser et al. (2004) performed simulations with several number of groups
and different model specifications (based on the degree of the polynomial of the future
function). For each model, they calculated the marginal likelihood in order to assess the
performance of the model. Once all the models are evaluated, they chose the model with
the best performance in order to obtain the classification.
Even though there are methods with which it is possible to identify the optimal
number of classes, a similar path to Houser et al. (2004) is pursued in this study, with the
difference that, instead of the calculation of the marginal likelihood, model assessment is
119
based on the Deviance Information Criterion (DIC) (Spiegelhalter et al. 2002). Once the
best specification is identified, identification of the typology of participants is possible.
The DIC is the parallel of the Akaike Information Criteria applied to Bayesian
inference. Consider the deviance defined as D(y, θ) = −2log[p(y|θ)]. The expected value
of D(·), D is a measure of how well the model fits the data, with a better performance the
lower D is. It is always possible to increase the number of parameters and improve model
fitting. The DIC penalizes the model performance adding a measure of complexity. This
measure of complexity, represented by pD = D −D(θ), measures the effective number
of parameters in the model. Thus, pD measures the gap between the average deviance
and the “reference” deviance (Congdon 2010). The reference deviance as the deviance
evaluated with the “true” parameters, θ, is taken. Then, the DIC is calculated as:
DIC = D + pD
MCMC’s with models of 3,4,5 and 6 groups were simulated, and polynomial de-
grees of 3,4, 5 and 6. Table 7.1 presents the DIC for each model. The model with the best
performance in the laboratory experiment has 6 groups with a polynomial of degree 3,
whereas the model with the best performance in the field experiment has 6 groups with
a polynomial of degree 4, as presented by LACEEP 2 (2014). Henceforth, the analysis
will be based on those models. Table 7.2 presents the number of members in each group
for each experiment. Although the number of categories allowed was 6 and 4 clusters in
the laboratory and field experiments, respectively, not all the categories have members
120
in it. In both the laboratory and field experiments, only three groups have members in
each experiment.
Table 7.1. Deviance Information Criterion
1 2 1 2 1 2 1 23 17,413 17,415 - - 19,503 20,614 18,344 18,3494 17,321 17,451 19,956 17,663 20,084 19,802 18,401 18,3415 17,615 17,440 17,738 19,291 - - 18,253 18,3786 16,823 16,678 19,723 17,389 20,149 20,474 18,313 18,366
6Groups
Degree
Chain3 4 5
a. Laboratory
1 2 1 2 1 2 1 23 21,350 23,303 25,824 24,951 89,234 65,331 66,969 68,3774 27,512 22,638 25,688 21,864 65,398 69,083 61,272 76,8185 - - 21,351 20,902 63,676 94,259 56,128 62,4896 25,117 20,746 25,026 20,202 69,057 68,714 63,233 82,353
Groups3 4 5 6
Chain
Degree
b. Field
Source: LACEEP 1 (2014)
121
Table 7.2. Distribution of groups
N % N %
Group 1 69 82.1 31 33.7
Group 2 15 17.9 28 30.4
Group 3 - - 33 35.9
Total 84 100.0 92 100.0
Field LaboratoryGroup
Source: LACEEP 1 (2014)
7.2 Parameter Statistics and Convergence
Tables 7.3 and 7.4 show the mean, standard deviations, minimum and maximum
values of the estimated posterior distributions of the parameters. Although very close,
in most cases the parameters are significantly different from zero, since the range of the
distribution does not cross the origin. The size of the parameters is very small because
the variables that enter into the future function are powers of the well depth and time,
which could take very high values if the choices taken are among the highest.
122
Table 7.3. Descriptive statistics of posterior distributions: Field experiment
Parameter N Mean SD Min Max Gewekebeta 1 20001 -0.000045 0.000002 -0.000050 -0.000038beta 2 20001 -0.000004 0.000004 -0.000014 0.000003 ***beta 3 20001 -0.000002 0.000007 -0.000015 0.000012 ***beta 4 20001 0.000029 0.000003 0.000022 0.000037 ***beta 5 20001 0.000010 0.000003 0.000002 0.000018beta 6 20001 -0.000329 0.000005 -0.000341 -0.000319 ***beta 7 20001 0.000029 0.000000 0.000028 0.000030 ***beta 8 20001 0.000113 0.000003 0.000108 0.000121beta 9 20001 0.000152 0.000013 0.000127 0.000174 ***beta 10 20001 -0.000013 0.000002 -0.000017 -0.000007
Parameter N Mean SD Min Max Gewekebeta 1 20001 -0.000135 0.000007 -0.000161 -0.000119 ***beta 2 20001 0.000062 0.000004 0.000050 0.000074beta 3 20001 0.000028 0.000018 0.000001 0.000071beta 4 20001 0.000131 0.000011 0.000110 0.000153beta 5 20001 0.000143 0.000009 0.000125 0.000169 **beta 6 20001 -0.000586 0.000019 -0.000628 -0.000557 ***beta 7 20001 0.000047 0.000001 0.000044 0.000050beta 8 20001 0.000314 0.000012 0.000283 0.000337 ***beta 9 20001 0.000534 0.000011 0.000510 0.000554 ***beta 10 20001 0.001100 0.000008 0.001082 0.001115 ***
Group 2
Group 1
***=0.01, **=0.05, *=0.1
Source: LACEEP 1 (2014)
123
Table 7.4. Descriptive statistics of posterior distributions: Laboratory ex-periment
Parameter N Mean SD Min Max Gewekebeta 1 20001 -0.00053 0.00020 -0.00095 -0.00020 ***beta 2 20001 -0.00037 0.00019 -0.00074 -0.00005beta 3 20001 0.00430 0.00017 0.00399 0.00465 ***beta 4 20001 0.00536 0.00022 0.00495 0.00582beta 5 20001 0.01775 0.00043 0.01686 0.01853 **beta 6 20001 -0.00067 0.00001 -0.00069 -0.00065 ***
Parameter N Mean SD Min Max Gewekebeta 1 20001 0.00138 0.00011 0.00108 0.00165beta 2 20001 0.00549 0.00011 0.00518 0.00577beta 3 20001 0.00694 0.00026 0.00654 0.00749beta 4 20001 0.00962 0.00021 0.00906 0.01005beta 5 20001 0.02808 0.00054 0.02706 0.02911 ***beta 6 20001 -0.00023 0.00004 -0.00034 -0.00017 **
Parameter N Mean SD Min Max Gewekebeta 1 20001 -0.00054 0.00019 -0.00104 -0.00027 ***beta 2 20001 -0.00218 0.00013 -0.00241 -0.00183 ***beta 3 20001 0.00317 0.00016 0.00269 0.00342beta 4 20001 -0.00686 0.00008 -0.00708 -0.00665beta 5 20001 0.01992 0.00031 0.01938 0.02050beta 6 20001 -0.00066 0.00001 -0.00067 -0.00064 ***
Group 1
Group 2
Group 3
***=0.01, **=0.05, *=0.1
Figures 7.1 and 7.2 show the estimated posterior distributions. Several parameters
show multimodal distributions, which is a sign of non-convergence. Also, some of the
estimated posterior distributions overlap, which is a sign that discrimination of groups
is not fully achieved.
124
Fig. 7.1. Estimated posterior distributions of parameters: Field experiment
Source: LACEEP 1 (2014)
125
Fig. 7.2. Estimated posterior distributions of parameters: Laboratory ex-periment
Convergence of chains is important in order to obtain reliable estimates of the
posterior distributions. One way to assess whether the chains have converged or not is
through tracing the Deviance. Figure 7.3 shows the estimated deviance of the two chains
of each experiment. All the chains are still decreasing but close to achieve a lower bound.
This means that the models would have converged if more iterations would have been
ran.
126
Fig. 7.3. Trace of deviance, two chains
a. Field
b. Laboratory
Source: LACEEP 1 (2014)
Another way to assess convergence is using Geweke’s convergence test. This test
compares the mean values of the initial and ending parts of the chain. If these averages
are significantly different, then the chains have not converged. Tables 7.3 and 7.4 show
127
the level of significance of the Geweke’s test. Several parameters have not converged.
However, given the small values of the parameters, it is very unlikely that the stationary
values of the parameters are too different from the current estimates. Traces of the
parameters for each experiment are presented in Appendix B.
7.3 Classification and Characteristics of Groups
Although convergence have not been fully achieved, it is still possible to use the
classification algorithm to cluster participants according to their choices, since several
parameters already converged and correctly discriminated groups. Figure 7.4 shows
the average paths of the hours of pumping for the second round of the experiment for
each type and experiment. In the field experiment, Group 1 starts pumping water at
around 7 units and its consumption does not change significantly over the game. On the
other hand, Group 2 shows a significantly higher use of water during the game, with an
important reduction by the end.
128
Fig. 7.4. Average individual hours pumped by period and type
a. Field
b. Laboratory
Source: LACEEP 1 (2014)
129
Fig. 7.5. Average individual pumping costs by period and type
a. Field
b. Laboratory
Source: LACEEP 1 (2014)
130
With respect to the laboratory experiment, Group 1 could be labeled as “Quasi
myopic”, since they follow a similar pattern to the one followed by the myopic prediction
of the theoretical model. This group keeps a high level of consumption until period
9 when they decrease their consumption to very low levels. Group 2 also follows a
similar patter to the myopic behavior from the theoretical model, as Group 1. It will be
shown that, although clustered in different groups, there are not significant differences
in the final outcomes of these two group. Finally, with respecto to Group 3, this group
follows a similar patter to the rational/strategic theoretical prediction: they keep a high
consumption until period 8 when they drastically reduce their pumping hours without a
severe rise on costs. Then, they raise their number of pumping hours again for the rest
of the game.
It is worth mentioning the differences between figures 5.1 and 7.4, especially for
the field experiment. Once the population is clustered, the nice and smooth path pre-
sented in Figure 5.1 disappears, yielding a more realistic path with more variance. Thus,
researchers should be careful of making inference about the behavior of participants
based on averages, since many unobserved structures could be hidden.
Looking at individual decisions, figures 7.6 and 7.7 show histograms of the choices
taken by participants by period and cluster. As mentioned before, choices of Group 1
in the field experiment show a bimodal distribution in the initial periods, becoming
flatter in latter periods, whereas Group 2 shows values concentrated around the highest
values. With regard the laboratory experiment, both groups 1 and 2, the “myopic”
groups mostly chose 10 units, with the exception of period 4, whereas Group 3 shows
more diversity.
131
Fig. 7.6. Histogram of choices by cluster and period: Field experiment
Source: LACEEP 1 (2014)
Fig. 7.7. Histogram of choices by cluster and period: Laboratory experiment
132
Moving towards the end-of-stage variables (total hours, total benefits and final
well depth), Table 7.5 shows important differences between groups in both the field and
laboratory experiments. In the field experiment, Group 2, the “greedy group”, ended
up earning significantly less than Group 1, since its pumping costs increased. With
respect to the laboratory experiment, groups 1 and 2, which used a relatively high
amount of water on average, are the groups that earned the most, whereas Group 3
earned significantly less than the other two groups, even though they used less water.
As mentioned before, there are no significant differences between Group 1 and Group 2
in the laboratory experiment.
Table 7.5. Total benefits and final well depth
Group 1 33.17 315.10 202.55 38.35 309.74 216.77
Group 2 39.73 ** 256.47 *** 229.60 *** 38.75 303.50 219.29
Group 3 - - - 30.82 *** 293.15 *** 204.36 ***
Mean difference tests (T-tests) with respecto to Group 1
GroupHours Benefit Well depth Hours Benefit Well depth
LaboratoryField
Source: LACEEP 1 (2014)
Given these results, it is necessary to note that the composition of the groups is
an important determinant of the the final outcome. In the laboratory experiment, the
dominant behavior is the one from groups 1 and 2, with 64% of participants. This group
shows high extraction rates and, at the end, will also affect the benefits from the other
groups. On the other hand, the dominant behavior in the field experiment is the one
133
from Group 1, which shows low extraction rates. In this case, total benefits of most of
the participants are improved. They do not achieve social efficiency (365), but surpass
the level of the Nash equilibrium (308).
7.4 Discussion
This part of the dissertation tries to reveal the “hidden behaviors” of the partici-
pants of the experiment. This has been done in way that “the data is allow to speak”, in
opposition to more directed ways of testing behavior, as in experimental economics. In
order to identify and classify different behaviors in the population, a Bayesian classifica-
tion algorithm is used, based on the one proposed by Houser et al. (2004), but adapted
to this case.
The results suggest that it is possible to identify different groups with the method.
Three clear groups in the field experiment were identified: one “greedy” group that
consumes most of the resource at the beginning of the game, a “patient” group that
starts using a relatively low amount of the resource and then increased the quantity
consumed, and a third group that starts with the lower amount of water and remains
low on the following periods. For the case of the laboratory experiment, we found a group
that resembles the prediction of the myopic behavior in the theory. This group starts
with a very high consumption and abruptly reduces it to very low levels, switching again
to higher levels at the last two periods. We also found another group that resembles the
rational/strategic behavior predicted by the theory. Besides the water pumping path,
we also found significant differences in both the total earnings and final well depth of
134
the groups. Moreover, some groups consumed very similar amounts of the resource at
the end of the game, but the total earnings are significantly different.
As before, the results align with what is found in the literature: non-student par-
ticipants tend to show a more pro-social behavior than the student population. However,
in the field experiment, we were able to identify a small group of participants that did
not behave in this manner. Identifying these different behaviors is crucial for the design
and success of institutions.
It is worth mentioning some comments about the classification method. First, to
achieving convergence is difficult. Some strategies that might help achieving convergence
include a reparametrization of the model and considering more informative priors. The
first strategy is difficult to perform since the empirical model is based on a structural
model that is already very flexible. A reparametrization of the model might change
the structural form from a random utility-based choice model to something else. The
strength of the model relies on the fact that it is random-utility based. The second
strategy is also difficult to apply since it is not possible to obtain more prior information.
Nevertheless, the results suggest that convergence might be achievable, and that reliable
estimates of the posteriors can be obtained, given that some chains did converge.
135
Chapter 8
Concluding Remarks
This dissertation summarizes the results obtained from economic framed experi-
ments conducted with both farm water users from Mexico and undergraduate students.
Few studies have compared the results of artefactual experiments with the two popu-
lations. As discussed in previous chapters, there are several differences in the behavior
of the two populations, which confirms the results obtained by other researchers. Thus,
it is imperative for experimental economists to replicate experiments with several types
of populations in order to ensure the external validity of the study, especially if the
experiment is framed, as in this case.
The first part of this dissertation presents a dynamic CPR experiment framed as
a groundwater game. This frame allows the analysis of dynamic decisions in CPR, and
does not rely on the analysis of steady state equilibrium outcomes, as most dynamic
experiments do. This is an innovative design, since previous studies do not consider
the groundwater problem in experimental settings, with the exception of Suter et al.
(2012). Moreover, this is the first study that conducts a groundwater experiment with
farm groundwater users.
The results obtained in Part I are very suggestive on the idea that the kinds
of participants are an important issue usually overlooked by researchers. These results
confirm that external validity of experiments is difficult to achieve, and it is only possible
136
to derive conclusions about the target population. External validity is an important
property that must be sought if the intention is to use the results of experiments as
benchmarks for policy design in a broader population.
In addition, these results suggest that farmers bring to experiments prior infor-
mation that affect their choice behavior. This goes in line with what is proposed by
Cardenas and Ostrom (2004). Even though students tend to behave more in line with
what traditional economic theory proposes, exceptions are consistently found in exper-
imental setups and researchers are trying to explain, with alternative theories, these
departures from the traditional economic benchmark. The setup becomes more compli-
cated on the field, not only because of comprehension issues (which could be overcome
with more practice rounds, simpler and concise instructions, etc.), but also because of
the information that farmers bring to the session.
As Cardenas and Ostrom (2004) mention, there are three layers of information
that participants in a social dilemma experiment might take into account to make their
choices: i) Material payoff game layer, ii) Group-context layer and, iii) Identity layer.
The results obtained in the investment treatment in the field experiment give insights
about the importance of the identity layer when compared with those obtained in the
laboratory experiment, since farmers have more experience and are more familiar with
irrigation technologies than students.
Another challenge is identifying and classifying different types of behaviors within
a heterogenous population. This is key in a CPR context, since the composition of groups
might have important effects on the final state of the resource and well being of users.
Moreover, since usually CPR users interact in a dynamic setup, and preferences are
137
context-dependent, agents might switch their behavior based on the partial results of the
“game”. Then, users with a “dominant” behavior might exert their influence on users
with other behaviors, which might result in the outcomes predicted by the dominant
behavior even though the population was originally heterogenous.
It is possible, in experimental contexts, to design the experiment and apply the
treatments in order to verify whether participants behave according to a given theory or
not. Nevertheless, this strategy does not exclude the possibility that other behavioral
theories are at stake, and that these theories could offer better explanations than the ones
considered in the study. Departing from the traditional economic rational framework
opens a whole new set of behavioral motives that should be investigated. The problem
is that there are no limits on the size of the set of alternatives.
In this study, we clearly found two groups. In the field experiment, a small group
of participants try to consume most of the resource at the beginning of the game, whereas
the majority of participants are characterized for being more cautious. In contrast, in
the laboratory experiment, most of participants are categorized as myopic, and a small
group resembles the behavior of the rationa/strategic agent from the theory.
The ultimate purpose of the classification exercise is to analyze the effects of
policies on the different groups that compose the populations. Groups with some type
of behavior will react in different ways to a certain policy than other groups. Moreover,
the analysis of the interaction of these groups and the resulting wellbeing is a major task
to do.
Further research should incorporate the analysis of switching behaviors in the
population. As mentioned before, some groups with a given behavior could be more
138
dominant than others. In a dynamic setup, this might lead to changes in the behavior of
others, since agents learn about the process and the attitude of the other agents. Some
researchers are starting to analyze economic complex systems under this evolutionary
approach. Some tools that, traditionally, were used by biologists or ecologists, such as
Agent-based models and system dynamics, are becoming more popular among environ-
mental and natural resource economists. The analysis of the properties of the steady
state equilibrium as a general characterization of the economic system is becoming less
useful when a heterogenous population constantly interacts in a changing environment.
Nevertheless, in order to conduct research on complex and evolutionary systems, it is
necessary to establish analytical boundaries that allow identification of causal effects.
This is a hard task with complex systems.
Finally, it is important to mention the potential benefits of using economic framed
field experiments as a pedagogical tool. Some researchers are starting to conduct projects
in order to assess the effectiveness of these research methods for strengthening collective
action in communities in developing countries (IFPRI 2013). Although it was not pos-
sible to perform a formal evaluation in this project, participants of the field experiment
manifested their “gratitude” for showing them in “simple terms” the groundwater prob-
lems that they are facing, and for making them think about how severe these problems
are. As mentioned in LACEEP 2 (2014), farmers at the end of all the sessions started
a discussion about the groundwater problems in Aguascalientes without any encourage-
ment from the facilitator. Although I do not expect that these sessions generated any
significant change in the behavior of farmers and the way they use water, it was ex-
tremely rewarding to see that my work helped at least a small bit in the comprehension
139
of the commons problem and how to avoid the commons tragedy in the study region.
Ultimately, this is the aim of economic research: to generate knowledge to aid the critical
thinking of decision makers.
140
A Functional Forms of Polynomials of a Higher Degree
In this appendix, we will present the functional forms of the polynomials of order4, 5 and 6.Degree = 4The future function of the polynomial of degree 4 is represented by:
Fk(wit = h) = β0ik
+ β1ik
(dt+1
∣∣dt, Wit, t, h)
+ β2ik
(d
2
t+1
∣∣dt, Wit, t, h)
+ β3ik
(dt+1
∣∣dt, Wit, t, h)
(t+ 1) + β4ik
(dt+1
∣∣dt, Wit, t, h)
(t+ 1)2
+ β5ik
(d
2
t+1
∣∣dt, Wit, t, h)
(t+ 1) + β6ik
(d
3
t+1
∣∣dt, Wit, t, h)
+ β7ik(t+ 1) + β8ik
(t+ 1)2
+ β9ik(t+ 1)
3+ β10ik
(d
4
t+1
∣∣dt, Wit, t, h)
+ β11ik
(dt+1
∣∣dt, Wit, t, h)
(t+ 1)3
+ β12ik
(d
2
t+1
∣∣dt, Wit, t, h)
(t+ 1)2
+ β13ik
(d
3
t+1
∣∣dt, Wit, t, h)
(t+ 1)
+ β14ik(t+ 1)
4
141
After considering the assumption of Wit = 3h and plugging in the equation ofmotion of well depth, we get:
Fk(wit = h) = β0ik
+ β1ik
[dt + 4h− r
]+ β2ik
[d
2
t+ 16h
2+ r
2+ 8dth− 2dtr − 8hr
]+ β3ik
[dt + 4h− r
](t+ 1)
+ β4ik
[dt + 4h− r
](t+ 1)
2
+ β5ik
[d
2
t+ 16h
2+ r
2+ 8dth− 2dtr − 8hr
](t+ 1)
+ β6ik
[d
3
t+ 64h
3 − r3+ 12d
2
th− 3d
2
tr + 48h
2dt − 48h
2r + 3r
2dt
+12hr2 − 24dthr
]+ β7ik
(t+ 1) + β8ik(t+ 1)
2+ β9ik
(t+ 1)3
+ β10ik
[d
4
t+ 16hd
3
t− 4rd
3
t+ 96h
2d
2
t− 48hrd
2
t+ 6r
2d
2
t+ 256h
3dt
−192h2rdt + 48hr
2dt − 4r
3dt + 256h
4 − 256h3r + 96h
2r
2
−16hr3
+ r4]
+ β11ik
[dt + 4h− r
](t+ 1)
3
+ β12ik
[d
2
t+ 16h
2+ r
2+ 8dth− 2dtr − 8hr
](t+ 1)
2
+ β13ik
[d
3
t+ 64h
3 − r3+ 12d
2
th− 3d
2
tr + 48h
2dt − 48h
2r + 3r
2dt
+12hr2 − 24dthr
](t+ 1)
+ β14ik(t+ 1)
4
142
And the relative future function, Fk
i represented by:
Fk
(h) = β1ik(h− 10)
+ β2ik(h− 10)
[2 (h+ 10) + dt − r
]+ β3ik
(h− 10) (t+ 1)
+ β4ik(h− 10) (t+ 1)
2
+ β5ik(h− 10) (t+ 1)
[2 (h+ 10) + dt − r
]+ β6ik
(h− 10)[3(dt − r)
2+ 12(h+ 10)(dt − r) + 16
(h
2+ 10h+ 100
)]+ β7ik
(h− 10)[(dt − r)
3+ 6(h+ 10)(dt − r)
2
+16(h
2+ 10h+ 100
)(dt − r)− 16
(h
3+ 10h
2+ 100h+ 1000
)]+ β8ik
(h− 10) (t+ 1)3
+ β9ik(h− 10) (t+ 1)
2 [2 (h+ 10) + dt − r
]+ β10ik
(h− 10) (t+ 1)[3(dt − r)
2+ 12(h+ 10)(dt − r) + 16
(h
2+ 10h+ 100
)]
143
Degree = 5The future function of the polynomial of degree 5 is represented by:
Fk(wit = h) = β0ik
+ β1ik
(dt+1
∣∣dt, Wit, t, h)
+ β2ik
(d
2
t+1
∣∣dt, Wit, t, h)
+ β3ik
(dt+1
∣∣dt, Wit, t, h)
(t+ 1) + β4ik
(dt+1
∣∣dt, Wit, t, h)
(t+ 1)2
+ β5ik
(d
2
t+1
∣∣dt, Wit, t, h)
(t+ 1) + β6ik
(d
3
t+1
∣∣dt, Wit, t, h)
+ β7ik(t+ 1) + β8ik
(t+ 1)2
+ β9ik(t+ 1)
3+ β10ik
(d
4
t+1
∣∣dt, Wit, t, h)
+ β11ik
(dt+1
∣∣dt, Wit, t, h)
(t+ 1)3
+ β12ik
(d
2
t+1
∣∣dt, Wit, t, h)
(t+ 1)2
+ β13ik
(d
3
t+1
∣∣dt, Wit, t, h)
(t+ 1)
+ β14ik(t+ 1)
4
+ β15ik
(d
5
t+1
∣∣dt, Wit, t, h)
+ β16ik
(dt+1
∣∣dt, Wit, t, h)
(t+ 1)4
+ β17ik
(d
2
t+1
∣∣dt, Wit, t, h)
(t+ 1)3
+ β18ik
(d
3
t+1
∣∣dt, Wit, t, h)
(t+ 1)2
+ β19ik
(d
4
t+1
∣∣dt, Wit, t, h)
(t+ 1)
+ β20ik(t+ 1)
5
144
After considering the assumption of Wit = 3h and plugging in the equation ofmotion of well depth, we get:
Fk(wit = h) = β0ik
+ β1ik
[dt + 4h− r
]+ β2ik
[d
2
t+ 16h
2+ r
2+ 8dth− 2dtr − 8hr
]+ β3ik
[dt + 4h− r
](t+ 1)
+ β4ik
[dt + 4h− r
](t+ 1)
2
+ β5ik
[d
2
t+ 16h
2+ r
2+ 8dth− 2dtr − 8hr
](t+ 1)
+ β6ik
[d
3
t+ 64h
3 − r3+ 12d
2
th− 3d
2
tr + 48h
2dt − 48h
2r + 3r
2dt
+12hr2 − 24dthr
]+ β7ik
(t+ 1) + β8ik(t+ 1)
2+ β9ik
(t+ 1)3
+ β10ik
[d
4
t+ 16hd
3
t− 4rd
3
t+ 96h
2d
2
t− 48hrd
2
t+ 6r
2d
2
t+ 256h
3dt
−192h2rdt + 48hr
2dt − 4r
3dt + 256h
4 − 256h3r + 96h
2r
2
−16hr3
+ r4]
+ β11ik
[dt + 4h− r
](t+ 1)
3
+ β12ik
[d
2
t+ 16h
2+ r
2+ 8dth− 2dtr − 8hr
](t+ 1)
2
+ β13ik
[d
3
t+ 64h
3 − r3+ 12d
2
th− 3d
2
tr + 48h
2dt − 48h
2r + 3r
2dt
+12hr2 − 24dthr
](t+ 1)
+ β14ik(t+ 1)
4
+ β15ik
[d
5
t+ 20hd
4
t− 5rd
4
t+ 160h
2d
3
t− 80hrd
3
t+ 10r
2d
3
t+ 640h
3d
2
t
−480h2rd
2
t+ 120hr
2d
2
t− 10r
3d
2
t+ 1280h
4dt − 1280h
3rdt
+480h2r
2dt − 80hr
3dt + 5r
4dt + 1024h
5 − 1280h4r
+640h3r
2 − 160h2r
3+ 20hr
4 − r5]
+ β16ik
[dt + 4h− r
](t+ 1)
4
+ β17ik
[d
2
t+ 16h
2+ r
2+ 8dth− 2dtr − 8hr
](t+ 1)
3
145
+ β18ik
[d
3
t+ 64h
3 − r3+ 12d
2
th− 3d
2
tr + 48h
2dt − 48h
2r + 3r
2dt
+12hr2 − 24dthr
](t+ 1)
2
+ β19ik
[d
4
t+ 16hd
3
t− 4rd
3
t+ 96h
2d
2
t− 48hrd
2
t+ 6r
2d
2
t+ 256h
3dt
−192h2rdt + 48hr
2dt − 4r
3dt + 256h
4 − 256h3r + 96h
2r
2
−16hr3
+ r4]
(t+ 1)
+ β20ik(t+ 1)
5
146
And the relative future function, Fk
i represented by:
Fk
(h) = β1ik(h− 10)
+ β2ik(h− 10)
[2 (h+ 10) + dt − r
]+ β3ik
(h− 10) (t+ 1)
+ β4ik(h− 10) (t+ 1)
2
+ β5ik(h− 10) (t+ 1)
[2 (h+ 10) + dt − r
]+ β6ik
(h− 10)[3(dt − r)
2+ 12(h+ 10)(dt − r) + 16
(h
2+ 10h+ 100
)]+ β7ik
(h− 10)[(dt − r)
3+ 6(h+ 10)(dt − r)
2
+16(h
2+ 10h+ 100
)(dt − r)
−16(h
3+ 10h
2+ 100h+ 1000
)]+ β8ik
(h− 10) (t+ 1)3
+ β9ik(h− 10) (t+ 1)
2 [2 (h+ 10) + dt − r
]+ β10ik
(h− 10) (t+ 1)[3(dt − r)
2+ 12(h+ 10)(dt − r) + 16
(h
2+ 10h+ 100
)]+ β11ik
(h− 10)[5(dt − r)
4 − 40(h+ 10)(dt − r)3
+160(h2 − 10h+ 100)(dt − r)
2
+320(h3
+ 10h2
+ 100h+ 1000)(dt − r)
+256(h
4+ 10h
3+ 100h
2+ 1000h+ 10000
)]+ β12ik
(h− 10) (t+ 1)4
+ β13ik(h− 10) (t+ 1)
3 [2 (h+ 10) + dt − r
]+ β14ik
(h− 10) (t+ 1)2[3(dt − r)
2+ 12(h+ 10)(dt − r) + 16
(h
2+ 10h+ 100
)]+ β15ik
(h− 10) (t+ 1)[(dt − r)
3+ 6(h+ 10)(dt − r)
2
+16(h
2+ 10h+ 100
)(dt − r)
−16(h
3+ 10h
2+ 100h+ 1000
)]
147
Degree = 6The future function of the polynomial of degree 5 is represented by:
Fk(wit = h) = β0ik
+ β1ik
(dt+1
∣∣dt, Wit, t, h)
+ β2ik
(d
2
t+1
∣∣dt, Wit, t, h)
+ β3ik
(dt+1
∣∣dt, Wit, t, h)
(t+ 1) + β4ik
(dt+1
∣∣dt, Wit, t, h)
(t+ 1)2
+ β5ik
(d
2
t+1
∣∣dt, Wit, t, h)
(t+ 1) + β6ik
(d
3
t+1
∣∣dt, Wit, t, h)
+ β7ik(t+ 1) + β8ik
(t+ 1)2
+ β9ik(t+ 1)
3+ β10ik
(d
4
t+1
∣∣dt, Wit, t, h)
+ β11ik
(dt+1
∣∣dt, Wit, t, h)
(t+ 1)3
+ β12ik
(d
2
t+1
∣∣dt, Wit, t, h)
(t+ 1)2
+ β13ik
(d
3
t+1
∣∣dt, Wit, t, h)
(t+ 1)
+ β14ik(t+ 1)
4
+ β15ik
(d
5
t+1
∣∣dt, Wit, t, h)
+ β16ik
(dt+1
∣∣dt, Wit, t, h)
(t+ 1)4
+ β17ik
(d
2
t+1
∣∣dt, Wit, t, h)
(t+ 1)3
+ β18ik
(d
3
t+1
∣∣dt, Wit, t, h)
(t+ 1)2
+ β19ik
(d
4
t+1
∣∣dt, Wit, t, h)
(t+ 1)
+ β20ik(t+ 1)
5
+ β21ik
(d
6
t+1
∣∣dt, Wit, t, h)
+ β22ik
(dt+1
∣∣dt, Wit, t, h)
(t+ 1)5
+ β23ik
(d
2
t+1
∣∣dt, Wit, t, h)
(t+ 1)4
+ β24ik
(d
3
t+1
∣∣dt, Wit, t, h)
(t+ 1)3
+ β25ik
(d
4
t+1
∣∣dt, Wit, t, h)
(t+ 1)2
+ β26ik
(d
5
t+1
∣∣dt, Wit, t, h)
(t+ 1)
+ β27ik(t+ 1)
6
148
After considering the assumption of Wit = 3h and plugging in the equation ofmotion of well depth, we get:
Fk(wit = h) = β0ik
+ β1ik
[dt + 4h− r
]+ β2ik
[d
2
t+ 16h
2+ r
2+ 8dth− 2dtr − 8hr
]+ β3ik
[dt + 4h− r
](t+ 1)
+ β4ik
[dt + 4h− r
](t+ 1)
2
+ β5ik
[d
2
t+ 16h
2+ r
2+ 8dth− 2dtr − 8hr
](t+ 1)
+ β6ik
[d
3
t+ 64h
3 − r3+ 12d
2
th− 3d
2
tr + 48h
2dt − 48h
2r + 3r
2dt
+12hr2 − 24dthr
]+ β7ik
(t+ 1) + β8ik(t+ 1)
2+ β9ik
(t+ 1)3
+ β10ik
[d
4
t+ 16hd
3
t− 4rd
3
t+ 96h
2d
2
t− 48hrd
2
t+ 6r
2d
2
t+ 256h
3dt
−192h2rdt + 48hr
2dt − 4r
3dt + 256h
4 − 256h3r + 96h
2r
2
−16hr3
+ r4]
+ β11ik
[dt + 4h− r
](t+ 1)
3
+ β12ik
[d
2
t+ 16h
2+ r
2+ 8dth− 2dtr − 8hr
](t+ 1)
2
+ β13ik
[d
3
t+ 64h
3 − r3+ 12d
2
th− 3d
2
tr + 48h
2dt − 48h
2r + 3r
2dt
+12hr2 − 24dthr
](t+ 1)
+ β14ik(t+ 1)
4
+ β15ik
[d
5
t+ 20hd
4
t− 5rd
4
t+ 160h
2d
3
t− 80hrd
3
t+ 10r
2d
3
t+ 640h
3d
2
t− 480h
2rd
2
t+
120hr2d
2
t− 10r
3d
2
t+ 1280h
4dt − 1280h
3rdt + 480h
2r
2dt − 80hr
3dt + 5r
4dt
+1024h5 − 1280h
4r + 640h
3r
2 − 160h2r
3+ 20hr
4 − r5]
+ β16ik
[dt + 4h− r
](t+ 1)
4
+ β17ik
[d
2
t+ 16h
2+ r
2+ 8dth− 2dtr − 8hr
](t+ 1)
3
+ β18ik
[d
3
t+ 64h
3 − r3+ 12d
2
th− 3d
2
tr + 48h
2dt − 48h
2r + 3r
2dt
+12hr2 − 24dthr
](t+ 1)
2
+ β19ik
[d
4
t+ 16hd
3
t− 4rd
3
t+ 96h
2d
2
t− 48hrd
2
t+ 6r
2d
2
t+ 256h
3dt
−192h2rdt + 48hr
2dt − 4r
3dt + 256h
4 − 256h3r + 96h
2r
2
−16hr3
+ r4]
(t+ 1)
149
+ β20ik(t+ 1)
5
+ β21ik
[d
6
t+ 24hd
5
t− 6rd
5
t+ 240h
2d
4
t− 120hrd
4
t+ 15r
2d
4
t+ 1280h
3d
3
t− 960h
2rd
3
t
+240hr2d
3
t− 20r
3d
3
t+ 3840h
4d
2
t− 3840h
3rd
2
t+ 1440h
2r
2d
2
t− 240hr
3d
2
t
+15r4d
2
t+ 6144h
5dt − 7680h
4rdt + 3840h
3r
2dt − 960h
2r
3dt + 120hr
4dt
−6r5dt + 4096h
6 − 6144h5r + 3840h
4r
2 − 1280h3r
3+ 240h
2r
4 − 24hr5
+ r6]
+ β22ik
[dt + 4h− r
](t+ 1)
5
+ β23ik
[d
2
t+ 16h
2+ r
2+ 8dth− 2dtr − 8hr
](t+ 1)
2
+ β24ik
[d
3
t+ 64h
3 − r3+ 12d
2
th− 3d
2
tr + 48h
2dt − 48h
2r + 3r
2dt
+12hr2 − 24dthr
](t+ 1)
3
+ β25ik
[d
4
t+ 16hd
3
t− 4rd
3
t+ 96h
2d
2
t− 48hrd
2
t+ 6r
2d
2
t+ 256h
3dt − 192h
2rdt
+48hr2dt − 4r
3dt + 256h
4 − 256h3r + 96h
2r
2 − 16hr3
+ r4]
(t+ 1)2
+ β26ik
[d
5
t+ 20hd
4
t− 5rd
4
t+ 160h
2d
3
t− 80hrd
3
t+ 10r
2d
3
t+ 640h
3d
2
t− 480h
2rd
2
t+
120hr2d
2
t− 10r
3d
2
t+ 1280h
4dt − 1280h
3rdt + 480h
2r
2dt − 80hr
3dt + 5r
4dt
+1024h5 − 1280h
4r + 640h
3r
2 − 160h2r
3+ 20hr
4 − r5]
+ β27ik(t+ 1)
6
150
And the relative future function, Fk
i represented by:
Fk
(h) = β1ik(h− 10)
+ β2ik(h− 10)
[2 (h+ 10) + dt − r
]+ β3ik
(h− 10) (t+ 1)
+ β4ik(h− 10) (t+ 1)
2
+ β5ik(h− 10) (t+ 1)
[2 (h+ 10) + dt − r
]+ β6ik
(h− 10)[3(dt − r)
2+ 12(h+ 10)(dt − r) + 16
(h
2+ 10h+ 100
)]+ β7ik
(h− 10)[(dt − r)
3+ 6(h+ 10)(dt − r)
2
+16(h
2+ 10h+ 100
)(dt − r)
−16(h
3+ 10h
2+ 100h+ 1000
)]+ β8ik
(h− 10) (t+ 1)3
+ β9ik(h− 10) (t+ 1)
2 [2 (h+ 10) + dt − r
]+ β10ik
(h− 10) (t+ 1)[3(dt − r)
2+ 12(h+ 10)(dt − r) + 16
(h
2+ 10h+ 100
)]+ β11ik
(h− 10)[5(dt − r)
4 − 40(h+ 10)(dt − r)3
+160(h2 − 10h+ 100)(dt − r)
2
+320(h3
+ 10h2
+ 100h+ 1000)(dt − r)
+256(h
4+ 10h
3+ 100h
2+ 1000h+ 10000
)]+ β12ik
(h− 10) (t+ 1)4
+ β13ik(h− 10) (t+ 1)
3 [2 (h+ 10) + dt − r
]+ β14ik
(h− 10) (t+ 1)2[3(dt − r)
2+ 12(h+ 10)(dt − r) + 16
(h
2+ 10h+ 100
)]+ β15ik
(h− 10) (t+ 1)[(dt − r)
3+ 6(h+ 10)(dt − r)
2
+16(h
2+ 10h+ 100
)(dt − r)
−16(h
3+ 10h
2+ 100h+ 1000
)]+ β16ik
(h− 10)[3(dt − r)
5+ 30(h+ 10)(dt − r)
4
+160(h2
+ 10h+ 100)(dt − r)3
+480(h3
+ 10h2
+ 100h3 − 1000)(dt − r)
2
+768(h4
+ 10h3
+ 100h2
+ 1000h+ 10000)(dt − r)
+512(h5
+ 10h4
+ 100h3
+ 1000h2
+ 10000h− 100000)]
151
+ β17ik(h− 10) (t+ 1)
5
+ β18ik(h− 10) (t+ 1)
4 [2 (h+ 10) + dt − r
]+ β19ik
(h− 10) (t+ 1)3[3(dt − r)
2+ 12(h+ 10)(dt − r) + 16
(h
2+ 10h+ 100
)]+ β20ik
(h− 10) (t+ 1)2[(dt − r)
3+ 6(h+ 10)(dt − r)
2
+16(h
2+ 10h+ 100
)(dt − r)
−16(h
3+ 10h
2+ 100h+ 1000
)]+ β21ik
(h− 10) (t+ 1)[5(dt − r)
4 − 40(h+ 10)(dt − r)3
+160(h2 − 10h+ 100)(dt − r)
2
+320(h3
+ 10h2
+ 100h+ 1000)(dt − r)
+256(h
4+ 10h
3+ 100h
2+ 1000h+ 10000
)]B MCMC of Parameters
In this appendix, we will present the MCMC of the parameters of the futurefunction.
152
Fig. B.1. Trace of the MCMC of all the parameters of the future functionof the field experiment
Group 1
Group 2
153
Fig. B.2. Trace of the MCMC of all the parameters of the future functionof the field experiment - Group 1
154
Fig. B.3. Trace of the MCMC of all the parameters of the future functionof the field experiment - Group 2
155
Fig. B.4. Trace of the MCMC of all the parameters of the future functionin the laboratory experiment
Group 1
Group 2
Group 3
156
Fig. B.5. Trace of the MCMC of all the parameters of the future functionof the laboratory experiment - Group 1
157
Fig. B.6. Trace of the MCMC of all the parameters of the future functionof the laboratory experiment - Group 2
158
Fig. B.7. Trace of the MCMC of all the parameters of the future functionof the laboratory experiment - Group 3
159
Bibliography
Agaarwal, Rimjhim M. and Tulika A. Narayan (2004), Does inequality lead to greater efficiencyin the use of local commons? The role of strategic investment in capacity, Journal of Environ-mental Economics and Management, Vol. 47: 163-182.
Albert, James H. and Siddhartha Chib (1993), Bayesian analysis of binary and polychotomusdata, Journal of the American Statistical Association, Vol. 88: 669-679
Anderson, Jon, Stepehen V. Burks, Jeffrey Carpenter, Lorenz Gotte, Karsten Maurer, DanieleNosenzo, Ruth Potter, Kim Rocha and Aldo Rustichini (2013), Self-selection and variationsin the laboratory measurement of other-regarding preferences across subject pools: evidencefrom college students and two adult samples, Experimental Economics, Vol. 16: 170-189.
Bardhan, Pranab (2000), Irrigation and Cooperation: An Empirical Analysis of 48 IrrigationCommunities in South India, Economic Development and Cultural Change, Vol 48 (4): 847-865.
Barham, Bradford L., Jean-Paul Chavas and Oliver T. Coomes (1998), Sunk Costs and theNatural Resource Extraction Sector: Analytical Models and Historical Examples of Hysteresisand Strategic Behavior in the Americas, Land Economics, Vol. 74 (4): 429-448.
Belot, Michele, Luis Miller and Raymond Duch (2010), Who Should be Called to the Lab?: Acomprehensive comparison of students and non-students in classic experimental games, NuffieldCentre for Experimental Social Sciences Discussion Paper Series 2010-001.
Brill, Thomas C. and H. Stuart Burness (1994), Planning versus competitive rates of groundwaterpumping, Water Resources Research, Vol. 30(6): 1873-1880
Brown, Gardner Jr. and Robert Deacon (1972), Economic Optimization of Single-Cell Aquifer,Water Resources Research, Vol. 8(3): 557-564
Burt, Oscar R. (1964), Optimal Resource Use Over time with and Application to Ground Water,Management Science, Vol. 11(1) Series A: 80-93
Burt, Oscar R. (1967), Temporal Allocation of Groundwater, Water Resources Research, Vol.3(1): 45-56
Burt, Oscar R. (1970), Groundwater Storage Control undr Institutional Restrictions, WaterResources Research, Vol. 6(6): 1540-1548
Caldera Ortega, Alex Ricardo (2009), Gobernanza y sustenibilidad: Desarrollo institucional yprocesos polıticos en torno al agua subterranea en Mxico. Los casos del valle de Leon y delvalle de Aguascalientes, Ph.D. Dissertation in Political Sciences, Facultad Latinoamericanade Ciencias Sociales-FLACSO, Mexico City.
Camerer, Colin (1998), Bounded Rationality in Individual Decision Making, Experimental Eco-nomics, Vol. 1: 163-183
Cameron, A. Colin and Pravin K. Trivedi (2005), Microeconometrics: Methods and Applications,New York: Cambridge University Press.
Cardenas, Juan Camilo, Luz Angela Rodriguez and Nancy Johnson (2011), Collective Actionfor Watershed Management: Field Experiments in Colombia and Kenya, Environment andDevelopment Economics, Vol.16: 275-303.
Cardenas, Juan Camilo and Elinor Ostrom (2004), What do people bring into the game: Exper-iments in the field about cooperation in the commons, CAPRi Working Paper No. 32.
160
Carey, Janis M. and David Zilberman (2002), A Model of Investment under Uncertainty: Mod-ern Irrigation Technology and Emerging Markets in Water, American Journal of AgriculturalEconomics, Vol. 84 (1): 171-183.
Carpenter, Jeffrey, Stephen Burks and Eric Verhoogen (2005), Workers: The Effects of SocialFraming on Behavior in Distribution Games, Research in Experimental Economics, Vol 10:261-290.
Carpenter, Jeffrey, Cristina Connolly and Caitlin Knowles Myers (2008), Altruistic Behavior ina Representative Dictator Experiment, Experimental Economics, Vol. 11:282-298.
Chib, Siddhartha, Edward Greenberg and Yuxin Chen (1998), MCMC Methods for Fitting andComparing Multinomial Response Models, Working paper series, Washington University atSt. Lois
Congdon, Peter D. (2010), Applied Bayesian Hierarchical Methods, New York: Chapman andHall/CRC
Conlisk, John (1996), Why Bounded rationality, Journal of Economic Literature, Vol. 34(2), pp.669-700
Comite Tecnico de Aguas Subterrneas/Ojocaliente-Aguascalientes-Encarnacion (COTAS-OAE)(2006), Escenarios del Agua 2015 y 2030 en el Acuıfero Interestatal Ojocaliente-Aguascalientes-Encarnacion: acciones para un desarrollo con sostenibilidad ambiental, dowloaded fromhttp://www.cotas.org.mx/.
Coward, E.W. (1976), Principles in social organization in an indigenous irrigation system, Humanorganization, Vol. 38(1): 28-36.
Dayton-Johnson, Jeff (2000), Determinants of collective action on the local commons: a modelwith evidence from Mexico, Journal of Development Economics, Vol. 62, pp.181-208.
Dosi, Cesare and Michele Moretto (2010), Environmental Innovation, War of Attrition and In-vestment Grants, International Game Theory Review, Vol. 12 (1): 37-59.
El-Gamal, Mahmoud A. and David M. Grether (1995), Are people Bayesian? Uncovering behav-ioral strategies, Journal of the American Statistical Association, Vol. 90(432):1137-1145.
Ellison, Glenn (2006), Bounded Rationality in Industrial Organization, MIMEO
Food and Agriculture Organization (2003), Groundwater Management: The Search for PracticalApproachers, Water Reports, 25
Fischbacher, Urs, Simon Gachter and Ernst Fehr (2001), Are People Conditionally Cooperative?Evidence from a Public Good Experiment, Economic Letters, Vol. 71: 397-404
Frederick, Shane (2005), Cognitive Reflection and Decision Making, Journal of Economic Per-spectives, Vol. 19(4),pp:25-42
Fruwirth-Schantter, Sylvia (2006), Finite Mixture and Markov Switching Models, New York:Springer
Gelman, Andrew, John B. Carlin, Hal S. Stern and Donald B. Rubin (2009), Bayesian DataAnalaysis, Second Edition, New York: Chapman and Hall/CRC
Geweke, John, Michael Keane and David Runkle (1994), Alternative computational approachesto inference in the multinomial probit model, Review of Economics and Statistics, Vol. 76:609-632
Geweke, John and Michael Keane (2000), Bayesian Inference for Dynamic Discrete Choice ModelsWithout the Need for Dynamic Programming, in eds. Roberto Mariano, Til Schuermann andMelvyn J. Weeks, Simulation-Based Inference in Econometrics: Methods and Applications,Cambridge University Press
161
Gardner, Roy, Elinor Ostrom and James M. Walker (1990), The Nature of Common-Pool Re-source Problems, Rationality and Society, Vol. 2(3):335-358.
Geweke, John and Michael Keane (2000), Bayesian Inference for Dynamic Discrete Choice ModelsWithout the Need for Dynamic Programming, in eds. Roberto Mariano, Til Schuermann andMelvyn J. Weeks, Simulation-Based Inference in Econometrics: Methods and Applications,Cambridge University Press
Gisser, Micha and David A. Sanchez (1980), Comptetion Versus Optimal Control in GroundwaterPumping, Water Resources Research, Vol. 16(4):638-642.
Gobierno del Estado de Aguascalientes (2009), Sistema de Indicadores Ambientales del Estado deAguascalientes, Aguascalientes, Mexico: Gobierno del Estado de Aguascalientes and Institutodel Medio Ambiente.
Goree, Jacon K and Charles Holt (1999), Stochastic game theory: For playing games, not forjust doing theory, Procedures of the National Academy of Sciences, Vol. 96, pp. 10564-10567
Greene, William H. and David A. Hensher (2003), A latent class model for discrete choice analysis:contrast with mixed logit, Transportation Research Part B, Vol.37:681-698
Gosttbauer, Elisabeth and Jeroen C.J.M. van den Bergh (2011), Environmental Policy TheoryGiven Bounded Rationality and Other-ragarding Preferences, Environmental and ResourceEconomics, Vol. 49(2): 263-304
Hackett, Steven, Edella Schlager and James Walker (1994), The Role of Communication in Re-solving Common Dilemmas: Experimental Evidence with Heterogenous Appropriators, Jour-nal of Environmental Economics and Management, Vol. 27: 99-126.
Hardin, Garrett (1968), The Tragedy of the Commons, Science, 162: 1243-1248.
Harstad, M. Ronald and Reinhard Selten (2013), Bounded-Rationality Models: Tasks to BecomeIntellectually Competitive, Journal of Economic Literature, Vol. 51(2): 496-511.
Heckman, J. and B. Singer (1984), A Method for Minimizing the Impact of Distributional As-sumptions in Econometric Models for Duration Data, Econometrica, Vol. 52(2):271-320.
Hess, Stephane, Moshe Ben-Akiva, Dinesh Gopinath and Joan Walker (2011), Advantages oflatent class over continuos mixture of Logit models
Houser, Daniel (2003), Bayesian analysis of a dynamic stochastic model of labor supply andsaving, Journal of Econometrics, Vol. 113, pp: 289-335.
Houser, Daniel, Michael Keane and Kevin McCabe (2004), Behavior in a dynamic decision prob-lem: An analysis of experimental evidence using Bayesian type classification algorithm, Econo-metrica, Vol. 72 (3): 781-822
Houser, Daniel and Joachim Winter (2004), How Do Behavioral Assumptions Affect StructuralInference? Evidence From a Laboratory Experiment, Journal of Business & Statistics, Vol.22(1), pp:64-79
Howard, Gregory and Brian E. Roe (2014), Stripping Because You Want to Versus StrippingBecause the Money is Good: A Latent Class Analysis of Farmers Preferences Regarding Fil-ter Strip Programs, Paper presented at the 2013 AAEA and CAES Joint Annual Meeting,Washington, DC August 4-6, 2013
International Food Policy Research Institute, Experimental Games for Strength-ening Collective Action, http://www.ifpri.org/book-6330/node/9632 andhttp://wle.cgiar.org/blog/2013/10/14/ifpris-water-games-to-strengthen-collective-action/
162
Instituto Nacional de Estadıstica y Geografıa (2009), Estados Unidos Mexicanos, CensoAgropecuario 2007, VII Censo Agrıcola, Ganadero y Forestal, Mexico D.F.: INEGI.
International Water Management Institute (2010), Banking on Groundwater in Times of Change,Water Policy Brief, Issue 32
Janssen, Marco, John M. Anderies, J.C. Cardenas (2011), Head-enders as stationary banditsin asymmetric commons: Comparing irrigation experiments in the laboratory and the field,Ecological Economics, Vol. 70 (9): 1590-1598.
Jevons, W. S. (1865), The Coal Question, London: Macmillan and Co.
Kahneman, Daniel and Amos Tversky (1979), Prospect Theory: An Analysis of Decision underRisk, Ecnometrica, Vol. 47(2): 263-292
Koundouri, Phoebe (2000), Three Approaches to Measuring Natural Resource Scarcity: Theoryand Application to Groundwater, Doctoral Dissertation, University of Cambridge
Koundouri, Phoebe (2004), Current Issues in the Economics of Groundwater Resource Manage-ment, Journal of Economic Surveys, Vol 18(5): 703-740
Koundouri, Phoebe (2004), Potential for groundwater management: Gisser-Sanchez effect recon-sidered, Water Resources Research, Vol. 40, W06S16, doi:10.1029/2003WR002164.
Lee, Myoung-Jae (2005), Micro-Econometrics for Policy, Program and Treatment Effects, NewYork: Oxford University Press.
Lettau, Martin and Harald Uhlig (1999), Rules of Thumb versus Dynamic Programming, TheAmerican Economic Review, Vol. 89(1), pp:148-174
Lichtemberg, Erik (1989), Land Quality, Irrigation Development and Cropping Patterns on theNorthern High Planes, American Journal of Agricultural Economics, Vol. 71(1): 187-194.
Madani, Kaveh and Ariel Dinar (2012), Non-cooperative institutions for sustainable common poolresource management: Applications to groundwater, Ecological Economics, Vol. 74: 34-45.
Mani Anandi, Sendhill Mullainathan, Eldar Shafir and Jiaying Zhao (2013), Poverty ImpedesCognitive Function, Science, Vol. 341:976-980
McCulloch, Robert and Peter Rossi (1994), An exact likelihood analysis of the multinomial probitmodel, Journal of Econometrics, Vol. 64: 207-240.
McCulloch, Robert, Nicholas Polson and Peter Rossi (2000), A Bayesian Analysis of the multi-nomial probit model with fully identified parameters, Journal of Econometrics, Vol.99, pp:173-193
McGinnis, Michael D., ed. (2000), Polycentric Games and Institutions: Readings from the Work-shop in Political Theory and Policy Analysis, Ann Arbor, MI: The University of MichiganPress.
Moreno-Sanchez, Rocıo del Pilar and Jorge Higinio Maldonado (2010), Evaluating the role of co-management in improving governance of marine protected areas: An experimental approachin the Colombian Caribbean, Ecological Economics, Vol. 69: 2577-2567.
Moretto, Michele (2000), Irreversible investment with uncertainty and strategic behavior, Eco-nomic Modelling, Vol. 17: 589-617.
Nieswiadomy, Michael (1985), The Demand for Irrigation Water in the High Plains of Texas,1957-1980, American Journal of Agricultural Economics, Vol. 67(3): 619-626
Negri, Donald H. (1989), The Common Property Aquifer as a Differential Game, Water ResourcesResearch, Vol. 25 (1): 9-15.
163
Nobile, Agostino (1998), A hybrid Markov chain for the Bayesian analysis of the multinomialprobit model, Statistics and Computing, Vol.8: 229-242
Ostrom, Elinor (1986), Issues of definition and theory: some conclusions and hypothesis, Proceed-ings of the conference on common property management, National Research Council, Wash-ington D.C.: National Academy Press.
Ostrom, Elinor (1990), Governing the Commons: the evolution of institutions for collective ac-tion, New York: Cambridge University Press.
Ostrom, Elinor (1992), Crafting institutions for self-governing irrigation systems, San Francisco,CA: Institute for Contemporary Studies University Press.
Ostrom, Elinor and Roy Gardner (1993), Coping with Asymmetries in the Commons: Self-Governing Irrigation Systems Can Work, The Journal of Economic Perspectives, Vol. 7(4):93-112.
Ostrom, Elinor (2002), Chapter 24: Common-Pool Resources and Institutions: Toward a Re-vised Theory, in Bruce Gardner L. and Gordon C. Rausser (eds.), Handbook of AgriculturalEconomics, Vol. 2, Amsterdam: Elsevier Science B.V.
Peterson, Jeffrey M. and Ya Ding (2005), Economic Adjustments to Groundwater Depletionin the High Planes: Do Water-Saving Irrigation Systems Save Water?, American Journal ofAgricultural Economics, Vol. 87(1): 147-159.
Pfeiffer, Lisa (2009), Three Essays on the Economics of Groundwater Extraction for Agriculture:Property Rights, Externalities and Policy, Doctoral Dissertation, University of California -Davis.
Provencher, Bill and Oscar Burt (1993), The Externalities Associated with the Common PropertyExploitation of Groundwater, Journal of Environmental Economics and Management, Vol. 24:139-158.
Rodrguez-Haros, Benito and Jacinta Palerm-Viqueira (2007), Before transference: Handing overwater districts, Agricultura, Sociedad y Desarrollo, Vol. 4 (2): 105-125.
Rubio, Santiago J. and Begona Casino (2003), Strategic Behavior and Efficiency in the CommonProperty Extraction of Groundwater, Environmental and Resource Economics, Vol.26(1): 73-87
Salcedo, Rodrigo (2014), Dynamic decision making in common-pool resource economic experi-ments: Behavioral heterogeneity in the field and the lab, LACEEP Working paper
Salcedo, Rodrigo and Miguel Angel Gutierrez (2014), Cooperation makes it happen? A ground-water economic framed experiment, LACEEP Working paper
Scheierling, Susanne M., Robert A. Young and Grant E. Cardon (2006), Public subsidies forwater-conserving irrigation investments: Hydrologic, agronomic, and economic assessment,Water Resources Research, Vol. 42(3), W03428.
Sekhri, Sheetal (2011), Public Provision and Protection of Natural Resources: GroundwaterIrrigation in Rural India, American Economic Journal: Applied Economics, Vol. 3: 29-55
Shen, Junyi (2009), Latent class model over mixed logit? A comparison by transport choice data,Applied Economics, Vol. 41: 2915-2924
Scherenberg Farret, Ericka, Patrick T. Brandt and Catherine Eckel (2014), A finite mixturemodel of behavior in a Three-Person Trust Game, MIMEO
Shogren, Jason F., Gregory M. Parkhurst and Prasenjit Banerjee (2010), Two Cheers and aQualm for Behavioral Economics, Environmental and Resource Economics, Vol. 46: 235-247
164
Shogren, Jason F. and Laura O. Taylor (2008), On Behavioral-Environmental Economics, Reviewof Environmental Economics and Policy, Vol. 2(1): 26-44
Simon, Herbert A. (1955), A Behavioral Model of Rational Choice, Quarterly Journal of Eco-nomics, Vol. 69(1): 99-118
Spiegelhalter, David J., Nicola G. Best, Bradley P. Carlin and Angelika Van Der Linde (2002),Bayesian measures of model complexity and fit, Statistical Methodology, Vol. 64(4):583-639
Suleimain, R. and A. Rapoport (1997), Provision of step-level goods with continuous contribu-tions, Journal of Behavioral Decision Making, Vol 5: 133-153
Suter, Jordan F., Joshua M. Duke, Kent D. Messer and Holly A. Michael (2012), Behavior ina Spatially Explicit Groundwater Resource: Evidence from the Lab, American Journal ofAgricultural Economics, Vol. 94(5):1094-1112.
Swallow, Brent, Nancy Johnson, Rurth Meinzen-Dick and Anna Knox (2006), The challenges ofinclusive cross-scale collective action in watersheds, Water International, Vol. 31(3): 361-376.
Trawick, Paul (2003), Against the Privatization of Water: An Indigenous Model for ImprovingExisting Laws and Successfully Governing the Commons, World Development, Vol. 31(6):977-966.
Wang, Chenggang and Eduardo Segarra (2011), The Economics of Commonly Owned Groundwa-ter When User Demand Is Perfectly Inelastic, Journal of Agricultural and Resource Economics,Vol 36(1): 95-120
Ward, Frank A. and Manuel Pulido-Velazquez (2008), Water conservation in irrigation can in-crease water use, Proceedings of the National Academy of Science, Vol. 105(47): 18215-18220.
Worthington, Virginia E., Oscar R. Burt and Richard L. Brustkern (1985), Optimal Managementof a Confined Groundwater System, Journal of Environmental Econmics and Management,Vol. 12(3): 229-245
Vita
Rodrigo Salcedo Du Bois
Education
The Pennsylvania State University State College, Pennsylvania 2006–Present
Ph.D. in Agricultural, Environmental and Regional Economics
Universidad del Pacıfico Lima, Peru 1997–2002
B.S. in Economics
Awards and Honors
Latin American and Caribbean Environmental Economics Program (LACEEP) 2012Research Grant
Seminario Permanent de Investigacion Agraria 2005Research Fellow
European Association of Environmental and Resource Economists (EAERE),Fondazione Eni Enrico Mattei (FEEM) andVenice international University (VIU) 2012Grant to attend the European Summer School in Resource and EnvironmentalEconomics
Research Experience
Dissertation Research The Pennsylvania State University 2012–PresentResearch Advisor: Prof. James S. Shortle and Prof. David Abler
Graduate Research The Pennsylvania State University 2006–2012Supervisor: Prof. Jill L. Findeis
Undergraduate Research Universidad del Pacıfico 199?–199?
Working Experience
Research Assistant The Pennsylvania State University 2006–2012
Assistant Researcher Grupo de Analiss para el Desarrollo, Lima, Peru 2004-2006
Project Analyst Instituto Nacional de Investigacion Agraria, Lima, Peru 2003–2004
Project Analyst Ministerio de Agricultura, Lima, Peru 2001–2002