Quantity and Price Controls for the Correction of Externalities
under Uncertain Damages: Evidence from a Laboratory Experimenta
David R. Heresb
C.-Y. Cynthia Linc
March 30, 2012
Abstract
Economic theory predicts that quantity (e.g., tradable permits) and price (e.g., taxes) instruments for the control of
externalities will produce identical outcomes as long as certain conditions obtain - namely negligible transaction costs
and certainty about marginal control costs. This theoretical prediction explicitly renders irrelevant any uncertainties
from the perspective of the regulator regarding the marginal damages in determining the market equilibrium outcome.
At a different level, however, uncertainty about marginal damages may be important in practice due to citizen participation in the permit market that could trigger an array of behavioral responses not commonly observed in firms.
Through a laboratory experiment, the instruments’ equivalence is tested under different environments (including uncertainty about the marginal damages) that comply with the mentioned conditions. Results from the comparative
analysis of a tax and a tradable permit system in a market composed of individuals with induced heterogeneous
marginal abatement costs lend support to the equivalence of the instruments.
Keywords: damage uncertainty, experimental economics, externalities, price and quantity controls, tradable permit
systems
a This paper has not been submitted elsewhere in identical or similar form, nor will it be during the first three months after its submission to the
Publisher.
b Postdoctoral Researcher, Institute of Transportation Studies, University of California at Davis.
c Assistant Professor, Department of Agricultural and Resource Economics, University of California at Davis.
1
1
Introduction
For four decades the debate over the policy choice to correct for environmental externalities under uncertainty has
yielded several studies examining the circumstances that favor the implementation of either quantity or price controls
based on their respective expected welfare losses. Economic theory predicts that quantity (e.g., tradable permits) and
price (e.g., taxes) instruments produce identical outcomes as long as certain conditions obtain - namely negligible
transaction costs and certainty about marginal control costs (Adar, Griffin 1976; Stavins 1995; Weitzman 1974). Furthermore, the literature largely agrees that uncertainty over the marginal damage function (MDF) alone has no impact
on the price-quantity control equivalence and either approach performs equally in terms of their ex post efficiency. On
the contrary, uncertainties regarding the marginal control cost function (MCC) generate different policy prescriptions
depending on the relative slopes of the MDF and MCC curves - a relatively flat MDF would make more suitable a
price instrument whereas a relatively steep MDF would do the opposite (Adar, Griffin 1976; Weitzman 1974). The
extensions in Stavins (1996) require, to begin with, the existence of uncertainties about the marginal control cost function for the MDF uncertainties to play a role in the comparative advantage of instruments. Although this study focuses
on the uncertainties related to the MDF that regulatees experience and how these could affect their behavior, these
uncertainties (both about MDF and about regulatees’ behavior) would definitely translate to the regulator’s arena.
There are several reasons why the theoretical prediction that damage uncertainty does not matter might not hold.
Shrestha (1998) and Smith, Yates (2003) extended the standard results for the case when the victims of pollution
are allowed to participate in a market for pollution permits. Both studies conclude that when the ex ante number of
permits in the market is larger than the ex post social optimum level of pollution (due to a larger MDF realization
compared to its expectation), victims of pollution buy permits that are no longer used in production. It follows that,
when there is MDF uncertainty, the outcomes from a tax and a tradable permits system could differ even in the absence
of uncertainties about MCC. This will be made clear in Section 2, however the intuition is that under a tradable permits
system citizens could acquire permits to reduce total emissions creating a positive feedback on the price of the permits.
Even if an aggregate MCC could be estimated with accuracy, failing to account for the impact of citizens participation
in the permit market could break the equivalence between the two policies. In Smith, Yates (2003) the regulator is
not only uncertain about the MDF as in Shrestha (1998), but also about the ability of citizens to overcome a collective
action problem. Furthermore, conclusions from standard theory could turn out to be inaccurate due to what Shogren,
Taylor (2008) call behavioral failures, which for the present purposes represent an array of behavioral responses that
could be triggered in dissimilar fashion by the policy in place under uncertainty of the MDF. For instance, under MDFuncertainty and an environment where regulatees are also victims of the externality, some elements of prospect theory
(Kahneman, Tversky 1979) could be present, in contradiction to those of expected utility theory (EUT). Properties
of the former theory relevant to our discussion are aversion to losses and the weighting of events by magnitudes that
2
differ from their respective probabilities of occurrence, both of which could generate unequal outcomes between the
two policies.1
Lastly, even in the absence of uncertainty about either MCC or MDF, one policy could allow the realization of
desires that another policy would not, such as fairness considerations (Fehr, Schmidt 1999) and loss aversion which
may arise even if the environments are not risky (Tversky, Kahneman 1991).2 As will be shown in the theoretical model
section, disadvantageous inequity in terms of permit holdings or endowment effects could increase the equilibrium
price of permits and reduce the number of trades because there exists an heterogeneous value attached to each permit
beyond the profits from production that it allows to obtain.
To place the ideas above into context, consider a loss averse individual or firm who is concerned about the fairness of contributions to the externality and weighs the worst case scenario by a magnitude larger than the objective
probability occurrence. A tax instrument precludes such concerns from being fully reflected in the final decisions of
regulatees since an individual would not be able to affect the overall level of externality except from her own contribution.3 On the other hand, a tradable permits policy could let those carriers of utility (i.e., fairness, loss aversion and
risk attitudes) to play a bigger role on a final outcome, for example inducing individuals to buy permits to destroy them
or to show higher reluctance to sell.4 That is, a price control based on the desired level of emissions and the estimated
marginal benefits from polluting (or costs of emissions abatement) might not coincide with a quantity control where
fairness concerns, loss aversion and risk attitudes are unleashed to affect the market equilibrium. In other words, the
regulator could be confronted with different aggregate marginal benefits from polluting whether the policy is a tax or
a tradable permits system.
Notwithstanding the above discussion, permit markets with a large number of participants could ameliorate behavioral failures because, as with externality taxation, individuals could consider themselves unable to affect others’
behavior, such that the instruments’ equality could still hold. Through a laboratory experiment, we evaluate the equivalence of instruments by exposing participants to price and quantity controls under different environments that comply
with the traditional preconditions for the instruments’ equivalence to hold. In this study’s setting, subjects acting as
producers are given a marginal benefit schedule (MB) that shows the individual benefit from producing another unit of
the good which at the same time amounts to creating another unit of externality. Hence the MB can play the role of the
MCC in the previous discussion. Behavioral failures aside, standard conclusions about the equivalence of the instruments should follow because certainty about the induced MBs prevails in each of the treatments in which transaction
costs are negligible. The experiment sheds light on the causes driving responses of individuals with heterogeneous
induced benefits over the resource but who are equally affected by the externality. Analyzing individuals with heterogeneous marginal benefits does not only better represent an economy but is necessary for the experimental market
to motivate permit trading. Future work will be devoted to add another treatment where the amount by which each
individual is affected by a given level of externality differs (i.e., MDF heterogeneity).
3
Importantly, typical experiments on emissions trading have not been coupled with externalities, public goods or
common pool resource situations (for an early review on the subject see Issac, Holt (1999)). An exception is Plott’s
(1983) article where different externality-corrective policies, including tax and tradable permits, are compared. Part of
Plott’s motivation originates from the fact that some policy makers might not agree with the results from the policyfree standard externalities model based on the idea that “People are aware, sensitive, and concerned about others
so why should they behave in such an atomistic fashion? Intuitions, customs, ethics, and a host of instincts might
guide us individually and as groups to behavior other than that suggested by the model” (Plott 1983, p. 106). The
experimental design in this study is simpler than Plott’s original study in some respects such as the market structure,
however uncertainty over the MDF is added to the debate in order to test its impact on the role that intuitions, customs,
ethics and instincts could play in determining the behavior of individuals.5
It should be emphasized that in some cases the results from this experiment do not enable the identification of
each of the potential sources for discrepancy between instruments discussed above. The main interest, however, lies
in testing the instruments’ equality under MDF uncertainty that might not hold due to the existence of such effects. A
treatment in which both MCC and MDF are known with certainty serves as a control since, as the discussion above
recognizes, deviations from the equality could arise even in the absence of uncertainty due to fairness considerations
and endowment effects. We close this introductory section with a brief discussion of some of the implications from
current designs of market-based instruments for climate policy.
Indisputably, the significant impacts on both physical and biological systems that global climate change caused
by anthropogenic greenhouse gas (GHG) emissions is expected to have over this century have generated a renewed
interest in the debate over the optimal market-based policy (see Murray et al. (2009), Nordhaus (2007), and Stavins
(2008) for recent discussions of policy instrument choice in the context of climate change policy). An important aspect
of both currently operating and proposed carbon emissions markets such as the European Union Emissions Trading
Scheme and the California’s GHG Cap-and-Trade Program is that they allow third-parties’ or citizens’ participation
in the permit market. In the absence of a collective action problem, this provision would imply that the optimal level
of emissions is always reached regardless of the initial cap as long as the costs for third-parties to enter the market are
low. In a different version of a tradable permit systems (TPS), the participation of citizens is not only voluntary but
made compulsory by distributing emission allowances among households (i.e., personal carbon trading). This type
of system has been evaluated as an alternative to traditional cap-and-trade systems in the United Kingdom (Roberts,
Thumim 2006).
Results from this experiment also add new evidence to the body of knowledge regarding behavioral changes that
could be expected to occur under a personal carbon trading system (or under a TPS in which transaction costs for
voluntary participation of citizen groups are low) but not within an standard upstream cap-and-trade system. Defra’s
report (DEFRA 2008) lists some of the research projects currently being carried out on the design, acceptability, and
4
behavioral impacts of a mechanism in which individuals are endowed with tradable carbon allowances. However,
among the studies focusing on the latter aspect, none has considered yet the use of experimental economics methods.
Since under an upstream TPS the cost of the permits is expected to be passed on through the productive chain to the
consumer, from the latter’s perspective traditional cap-and-trade is not different from a price control. As previously
mentioned, theory predicts that a personal carbon trading system (i.e., the quantity control) would provide the same
equilibrium as the upstream cap-and-trade (i.e., the pseudo price control). Nevertheless, proponents of the former
claim that these schemes will have a high impact on consumption patterns due the saliency of the measure, while
traditional cap-and-trade systems will encourage milder behavioral changes. Following this latter statement, even
when the overall allocated quota is equal in both TPS schemes, behavioral variations and different equilibria could be
observed between the two policy interventions. A recent study based on stated preference methodology found slight
differences in CO2 -mitigating behavior between a tax and a personal carbon trading regulation (Bristow et al. 2008) .
The results from that study show that participants would respectively reduce carbon emissions by 12% and 16%.
The remainder of this manuscript is structured as follows. Section 2 presents in more detail the economic model
and derives equilibrium conditions for the different policy scenarios both under the standard assumptions and allowing
for the presence of some of the behavioral responses. The experimental design is described in Section 3. The main
results from the experiment are presented in Section 4. Conclusions follow after a discussion of findings in Section 5.
2
Theoretical Model
The situation to be modeled in this analysis distinguishes from the common approaches in that the MDF affects
the regulatees’ behavior since they are the same entities suffering from those damages. In previous theoretical and
empirical work, these are typically specified as two unrelated affairs (i.e., regulated agents appear to be indifferent
to marginal damage costs and only the regulator sees such damages as a problem). Common-pool resources such
as fisheries, irrigation systems, land use, and road congestion can exemplify the situation under consideration. An
extreme example, due to the number of potential regulatees involved, is the case of climate change where the utility
of both firms and citizens could be affected by both the benefits and the damages from producing the externality.
Furthermore, the present design introduces treatments where the MDF is only known with uncertainty.6
In this study’s experimental market with externalities the two requirements for the equivalence of the instruments
to hold are fulfilled (i.e., transaction costs are negligible, and certainty about the marginal benefit prevails). However
it is possible that the corresponding level of emissions QE (price per emission permit PE ) predicted by a price control
(quantity control) can not be precisely inferred due to previously described behavioral responses that depend on the
particular policy/environment mix as hypothesized in Table 1.
The hypothesized directions of these effects follow from the previous discussion and a brief explanation is sketched
in the following lines, however the analysis that follows in this Section elaborates on the causes driving these conjec5
Table 1: Possible behavioral responses under different scenarios
Certainty
Uncertainty
Tax
No predicted deviation
Tradable Permits
Endowment effect (↑P) and (↓Q)
Fairness (↑P) and (↓Q)
Endowment effect (↑P) and (↓Q)
Fairness (↑P) and (↓Q)
Non-EUT risk attitudes (↓P or ↑P) and
(↓Q or ↑Q)
Risk-aversion (↑P) and (↑Q)
Non-EUT risk attitudes (↓Q or ↑Q)
Risk-aversion (↑Q)
tures. Responses based on fairness concerns and endowment effects can not arise under a price control setting due to
the individual’s inability to affect the total quantity produced (and thus the externality) by others and/or the distribution
of gains. That is, under a price control, a firm could choose to produce any quantity that its technology allows, but
affecting the tax level or precluding other firms from producing would be beyond its capabilities.
Under a tradable permits system these motives would increase the value of each permit compared to the case when
the value of the permit is only linked to the profits that can be obtained through production. This could ultimately
reduce the total quantity produced because a holder of a permit might not find attractive to use the permit nor to sell
it at the current market price. When market participants find themselves capable of affecting the total damage but no
endowment or fairness effects are present, the permit price is expected to increase, however the total quantity produced
should not be affected when the marginal damage is homogeneous across participants.
The ambiguity of the direction of the impacts of non-EUT risk attitudes is of particular interest. Prospect theory’s
S-shaped value function on gains and losses combined with overweighting of low probabilities events would imply
that: a) on the one hand bad states with assigned weights larger than their probability of occurrence would reduce
Q and P; b) on the other hand the convexity of the utility function over losses would imply risk-seeking behavior
therefore increasing Q and P. Unambiguously, when firms are risk averse, quantity could be shown to be smaller under
certainty for both price and quantity controls. Section 2.5 derives this result based on Sandmo (1971). Since the total
quantity is bounded from above under a quantity control, a possible effect is an increase in the equilibrium price of
permits.
Although fairness concerns play a small role in most markets due to their large number of participants, Fehr,
Schmidt (1999, p.834) argue that in some instances it is “...the impossibility of preventing inequitable outcomes by
individual players that renders inequity aversion unimportant in equilibrium”. Tax policies do not provide room to
disadvantaged players to affect outcomes. In a TPS however, disadvantaged players can affect the outcome through
their decisions in the permit market where they could incur costs to achieve more fair outcomes. Individuals could do
so by holding more permits than their optimal level of production, thus precluding others from producing more at the
6
cost of foregone income from further permit sales. Individuals incurring costs to punish agents taking unfair decisions
has been documented in studies such as Fehr, Gachter (2000).
In the case of a TPS between firms, severe loss aversion in the form of endowment effects is not expected to be
present since as Tversky and Kahneman acknowledge, loss aversion in the form of reluctance to sell (or endowment
effect) “...is surely absent in routine commercial transactions, in which goods held for sale have the status of tokens for
money” (Tversky, Kahneman 1991, p.1055).7 On the other hand, endowment effects could be more widespread in a
TPS between consumers who would not necessarily perceive permits as “tokens for money". As mentioned earlier, loss
aversion in the form of overweighting of uncertain states with negative consequences could similarly affect decisions
under the two policies regardless of whether the regulatees are firms or consumers.
Risk attitudes deviating from the EUT can affect both tax and TPS policies. However, with the latter alternative
potential damages can be further reduced by individual actions. As with actions to improve fairness, this requires that
individuals regard themselves as capable of affecting the relevant outcomes, or that the large numbers translate into
a small numbers case due to cooperation among the affected parties. It could be said that the smaller the number of
participants in the permit market, the higher the chances of observing the behavioral failures in Table 1.
In common with previous emissions permit experiments, this study’s experimental design resembles a market with
a large number of participants all of which are equally affected by the externality.8 However, gains from the activity
that generates the externality are not equal across individuals, such that the citizens in Shrestha (1998) and Smith,
Yates (2003) could be represented by those who are affected by the externality but who obtain little benefits from the
activity that creates it. From a different perspective, the market in this experiment could also be thought as one where
individuals trade permits to consume such as programs with individual tradable quotas.
Although the experimental design generates guidance about the causes producing a potential deviation from the
equivalence of the instruments, in some cases it does not allow a complete separation of them. By looking at Table 1 it
is clear that deviations from the instruments’ equality could be due to more than one hypothesis.9 Despite this caveat,
the main goal of the study is to compare the quantity outcomes of each policy intervention under certainty and uncertainty about the MDF. The following subsection elaborates on the solutions under alternative policies for the standard
model as well as on the potential causes underlying a hypothetical deviation from the instruments’ equivalence.
Preceded by the standard model case, the following subsections show the optimality conditions when potential
causes underlying a hypothetical deviation from the instruments’ equivalence are considered. More specifically the
following cases are presented: a) endowment effects over permits are present; b) fairness considerations are part of
the utility function, c) non-EUT risk attitudes arise as a response to uncertain damages; and d) risk-averse firms face
damage uncertainty. These four cases are analyzed in isolation in order to make the exposition clearer. In all these
variations but the uncertainty effects (cases c and d), results for the no-policy and the tax scenarios remain as in
7
the standard model, however, first order conditions will change under a TPS. This is because, as it was mentioned,
behavioral responses based on endowment effects and fairness concerns could only be enabled by a TPS.
2.1
Standard model
Let us assume that firms have a profit function πi (qi ) that is increasing in units of production qi (π0i (qi ) > 0) but at a
decreasing rate (π00i (qi ) < 0). To simplify the model, assume that the damage from group production (Q = qi + ∑Nj6=i q j )
is eQ, where it is assumed that the damage per unit is the same for everyone and that the marginal damage is constant.
Let the arguments of the utility function of each risk-neutral firm be the monetary amounts delivered by the profit
and damage functions:10
N
Ui (πi (qi ); Q) = Ui (qi ; ∑ q j ) = πi (qi ) − eQ
(1)
j6=i
2.1.1
Social Optimum
Assuming that each firm’s utility function is equally weighed, a social planner would maximize the difference ∑Ni=1 πi (qi )−
NeQ which yields the following N first order conditions:
π0i (qSO,i ) = Ne
(2)
Each firm’s marginal profit would be equated to the sum of marginal damages of the N firms (including itself).
2.1.2
No Policy
A baseline scenario (BS) with no externality-correcting policy would yield a competitive equilibrium with the following first order conditions for each firm:11
π0i (qBS,i ) = e
(3)
This condition implies that each firm will produce up to where its marginal profit is equal to the marginal damage on
itself. Compared to the social optimum, these set of conditions clearly yield larger qi for every firm and therefore a
larger Q than at the social optimum since π00i (qi ) < 0 (i.e., the smaller π0i (qi ) is, the larger qi is).
2.1.3
Tax
Assume that an optimal tax of t = e(N −1) is charged for each unit produced. First order conditions for each individual
firm are:
π0i (qPS,i ) = e + t
which is equal to the first order conditions under the social optimum.
8
(4)
2.1.4
Tradable Permits
Under this policy there is no charge per unit produced but there is a cap on the total number of units that can be
produced by the N firms as a group. This cap (L) is equal to the resulting sum of units under the social optimum (i.e.,
under the optimal tax policy). L permits are distributed among the firms, and firms must hold a permit for each unit
they produce. Permits are tradable, and firms have the option of not using them for production. The initial endowment
of permits for each firm is denoted by Li . Following the assumptions made about the utility function, this would be
composed as follows:
Bi
Si
Ui = πi (qi ) − eQ − ∑ τbi lbi + ∑ τsi lsi
(5)
s=1
b=1
where τbi and τsi are the prices at which permits bi and si are respectively bought and sold by individual i, who buys
and sells a total of Bi and Si permits.
Let us now separate the damage into the part generated by the firm i itself, and that from others:
N
Bi
Si
Ui = πi (qi ) − eqi − e ∑ q j − ∑ τbi lbi + ∑ τsi lsi
j6=i
b=1
(6)
s=1
Si
It is convenient to call firm i0 s permit holdings Hi = Li + ∑Bi
b=1 lbi − ∑s=1 lsi . Note that the damage to firm i generated by
others is bounded from above by the total number of permits in the market minus the permits owned by firm i (L − Hi ).
This expression can take the place of e ∑Nj6=i q j in the last equation yielding:
Bi
Si
Ui = πi (qi ) − eqi − e(L − Hi ) − ∑ τbi lbi + ∑ τsi lsi
b=1
(7)
s=1
Each of the N firms maximizes this utility function subject to:
Bi
Si
Li + ∑ lbi − ∑ lsi − qi ≥ 0
b=1
(8)
s=1
yielding the following first order conditions:
π0i (qQS,i ) = e + µi
(9)
τbi = µi + e
(10)
τsi = µi + e
(11)
For each permit bought:
For each permit sold:
9
where µi is the Lagrange multiplier associated with (8), in other words, it is the willingness to pay for (to accept) one
more (fewer) permit. Conditions (10) and (11) imply that prices at which permits are sold and bought by firm i are the
same and thus a single τi can be substituted into (9) yielding:
π0i (qQS,i ) = τi
(12)
The permit price at which each firm is willing to buy or sell incorporates the marginal damage from production (i.e.,
derived from the potential use of the permit by others to produce and therefore generate an externality). This would
ultimately push the permit price in the market to τ = eN, which is above the optimal tax rate, however the quantities
produced by each firm would remain as under the tax policy.12 As it can be seen from equations (10) and (11) the lower
limit to the price of permits is e which would occur when the cap is above the quantity that would be produced in the
absence of any policy. Although the participation of affected parties in the permit market could result in destruction
of some permits, this would not occur as long as all market participants are affected equally by the externality and
L < ∑Ni qBS,i . This result follows because all firms would have a marginal willingness to pay for a permit at least equal
to the marginal damage and no firm would produce beyond the point at which the marginal benefit is lower than their
own marginal damage. Since our experimental design assigns equal marginal damages to all participants and specifies
a cap that is set at the optimal level, this type of behavior could only be triggered by other motivations such as those
examined below.
In sum, when L = ∑Ni qSO,i the optimal level of emissions could be achieved with a tax of t = e(N − 1) or a permit
price of τ = eN. This will become clearer in Section 3, in which a functional form is given to the profit function.
2.2
Endowment effect
In this section it is assumed that firms experience an endowment effect which is represented by a negative impact from
selling permits:
Bi
Si
Si
Ui = πi (qi ) − eqi − e(L − Hi ) − ∑ τbi lbi + ∑ τsi lsi − δi ∑
b=1
s=1
(13)
s=1
where δi > 0 First order conditions are as follows:
π0i (qEQS,i ) = e + µi
(14)
τbi = µi + e
(15)
τsi = µi + e + δ
(16)
For each permit bought:
However, for each permit sold:
10
Willingness to accept for a sold permit is larger than the willingness to pay for another permit for every firm. This could
ultimately reduce the number of transactions and increase the equilibrium price. Let us assume that there are only two
firms which at the initial permit endowment show π01 (q1 ) > π02 (q2 ). That is, the equilibrium has not been reached
according to the standard model, and there would be gains from trade. However, in order for permits to flow from firm
2 to firm 1, the condition that must be satisfied is π01 (q1 ) > π02 (q2 ) + δ2 , with an equilibrium at π01 (q1 ) = π02 (q2 ) + δ2 .13
The buying firm must pay to the selling firm an amount equal to the foregone income from production plus an amount
equal to the reduction in the utility of the latter due to endowment effects.
Interestingly, for a sufficiently large δ2 , one could find that no trades take place and some permits remain unused
even if π01 (q1 ) > 0 and π02 (q2 ) = 0 at the initial endowment.
2.3
Fairness concerns
This section introduces fairness concerns in the sense that inequity to the disadvantage of firm i negatively affects the
utility of firm i. It is assumed that this fairness view is self-centered and that the firm is not affected from disadvantage
that others might experience. The element that affects the utility in this fashion is the difference between the average
i
permit holdings of other firms and the number of permits owned ( L−H
N−1 − Hi =
L−NHi
N−1 ).
It is further assumed that
firm i cannot compare itself to all the other firms, but knows the average permit holdings of the latter because the
total number of permits and firms in the market are public information. Furthermore, it is assumed that advantageous
inequity does not increase utility, therefore the max function in the last term.
Bi
Si
L − NHi
Ui = πi (qi ) − eqi − e(L − Hi ) − ∑ τbi lbi + ∑ τsi lsi − γi max
,0
N −1
s=1
b=1
(17)
where γi > 0
The first order conditions are as follows:
π0i (qFQS,i ) = e + µi
(18)
For each permit sold or bought:
τi =


 µi + e
if
L−NHi
N−1

 µi + e + γi ( N )
N−1
if
L−NHi
N−1 >
≤0
0
The price at which each firm is willing to sell and buy depends on how it compares with others’ average in terms
of permit holdings. When the firm i has more or the same number of permits than the average number other firms
have, the price at which it will sell or buy is simply the extra utility from producing an extra unit (µi ) plus the avoided
damage from someone else producing (e). However, when firm i has fewer permits than the average of other firms, it
would buy (sell) for an amount equal to µi + e plus the gain (loss) in utility from experiencing less (more) inequality
N
to its disadvantage γi ( N−1
).
11
Assume as in the previous section that there are only two firms which at the initial permit endowment show
π01 (q1 ) > π02 (q2 ). If firm 1 has less permits than firm 2, trade will occur because in that case γ1 is added to the lefthand side of the inequality thus reinforcing the gains from trade. If the opposite is true, trade will occur as long as
π01 (q1 ) > π02 (q2 ) + γ2 . The following three conditions characterize the different equilibria that could occur depending
on the permit holdings distribution:
π1 = π2
if H1 = H2
N
π1 + γ1 ( N−1
) = π2
if H1 < H2
N
π1 = π2 + γ2 ( N−1
) if H1 > H2
If all gains from trade have been exhausted when permit holdings are equal across firms, the equilibrium price of the
permits would be as in the standard case. Conversely, if equilibrium occurs at any distribution of permits in which some
firms have more permits than others, the permit price would be higher than in the standard case. As with endowment
N
effects, for a sufficiently large γ2 ( N−1
), one could find that no trades take place and some permits remain unused even
if π01 (q1 ) > 0 and π02 (q2 ) = 0 at the initial endowment.
2.4
Risk attitudes: Prospect theory
The above discussion of equilibria has so far not introduced uncertainty about e (i.e., MDF). Under the expected
utility framework, the outcomes would be the same if uncertainty lies in the level of ẽ (now stochastic) and E[ẽ] =
peh + (1 − p)el = e, where eh and el respectively represent scenarios with high and low damages that occur with
probabilities p and (1 − p). However, expected utility theory (EUT) has been criticized for its lack of support from
experimental data (Kahneman, Tversky 1979). Alternatively, prospect theory assigns weights to the different states
of utility, based on underlying preferences for gains and losses under each scenario. According to this theory, low
probability events tend to be overweighted (not necessarily overestimated) by individuals (something that could be
reinforced if the low probability event involves a large loss due to loss aversion).14
The initial wealth serves as the reference point from which gains and losses are computed, and the utility over the
prospects could be expressed as follows under EUT assumptions:
E[Ui ] =
p(πi (qi ) − eh Q) + (1 − p)(πi (qi ) − el Q)
= πi (qi ) − eQ
where the second line follows from peh + (1 − p)el = e.
12
(19)
Alternatively, under prospect theory the following would be the utility function over the prospects:
Vi
= wi (p)(πi (qi ) − eh Q) + wi (1 − p)(πi (qi ) − el Q)
(20)
= πi (qi ) − (wi (p)eh Q + wi (1 − p)el Q)
= πi (qi ) − φi eQ
where φi > 1. This follows from the fact that the weights associated with the high and low damage events are respectively wi (p) > p and wi (1 − p) < (1 − p), and for simplicity it has been assumed that wi (p) + wi (1 − p) = 1.15
Summarizing, assuming EUT, the first order conditions derived in previous sections would simply substitute e with
the expected value of ẽ that have been assumed to be equal. However, under the alternative non-EUT assumptions, e
would be substituted with φi e where φi ≥ 1 clearly modifying the equilibria for all the policy scenarios (e.g, reducing
the equilibrium quantity produced). In the TPS scenario where firms find themselves capable of reducing maximum
potential damage from others, the discrepancy between the equilibrium permit price and the corresponding tax would
be larger as can be verified by substituting e for φi e in equations (10) and (11).
2.5
Risk attitudes: Risk-aversion a la Sandmo
Up to this point the assumption that firms are risk-neutral has been maintained. If this assumption is modified and
instead allow utility to be increasing in earnings but at a decreasing rate conclusions could change. These properties
of an utility function imply risk aversion and can be represented by a concave function, such that U 0 (Π(q; ẽ)) > 0 and
U 00 (Π(q; ẽ)) < 0, where Π represents net earnings. The derivations in this section are for the price control and follow
Sandmo’s steps who analyzed firm behavior under price uncertainty (Sandmo 1971).16
Let Π for every firm be:
Π(q; ẽ) = π(q) − ẽQ − tq
(21)
E[U 0 (Π)](π0 (q) − t − e) ≤ 0
(22)
π0 (q) ≤ t + e
(23)
Then, following Sandmo (1971),
Since U 0 (Π) is always positive, then:
Which compared to the equilibrium condition for the price control in the standard case, would yield a larger q for
every risk-averse firm. For example, for an specification of the form π(q) = Aq − 0.5αq2 , it could be shown that
q≥
A−t−e
α
for risk-averse firms, while risk-neutral firms would meet that condition with equality. This result might
13
seem counterintuitive, however note that if the damage part of the benefits function is uncertain, firms might prefer to
pay the certain tax than restrict production at perhaps a larger cost (or foregone income).
3
Experimental Design
3.1
General design and procedures
The central hypothesis tested in this experiment is that the quantity and price control equivalence is not affected by the
uncertainty over the MDF. Summarized in Table 2, the experimental procedure allows for testing this hypothesis by
means of comparing quantities and prices in groups exposed to different policies and marginal damage environments.
The policies imposed were a baseline scenario with no regulatory intervention (BS), a tax policy scenario (PS), and
a tradable permits policy scenario (QS). In addition, some of the participants played games where the MDF was
uncertain. Although our interest lies simply on the occurrence or not of the equivalence of instruments, based on the
observed outcomes we could derive some conjectures regarding the potential causes driving results.
Table 2: Summary of experimental design and procedures
Subjects
Ninety-six undergraduate students from the University of California. Average payment per
subject was USD 15 USD that included a USD 5 fee for showing up to the experiment.
The rest of their earnings depended on their cumulative performance in the three games.
Experimental subjects were only allowed to participate in one session.
Groups
Twelve 8-person independent groups.
Sessions
Seven 1-hour sessions conducted in a computer room at the University of California, Davis.
Five 2-group sessions and two single-group sessions (groups U3 and U4).
Treatments
Combination of the following policy and MD-environment treatments: BS, PS, and QS
(played by all groups), and C, Ub, and Ue (each group played only under one of these with
four groups under each MD-environment).
Stages
Policy treatments played in one of two orders: BS-PS-QS or BS-QS-PS. Both BS and PS
consisted of a single 20-second production-decision stage followed by screening of results for
10 seconds. In the QS treatment, the production stage was preceded by a permit market (90
seconds) and the screening of results after the production-decision stage lasted 20 seconds.
Every policy treatment consisted of 9 rounds including an initial trial round. Participants did
not know in advance the total number of rounds in each game.
MD types
C: e = 3; Ub: el = 0 or eh = 6 with 1/2 probability each; Ue: el = 2 or eh = 12 with probabilities 9/10 and 1/10 respectively. The expected values of e under the two uncertainty treatments
were equal to that from the certainty treatment.
MB types
MB schedules derived from linear functions πi = Ai − αi qi where i=L, ML, MH and H with
respective parameters Ai = (35, 30, 55, 50), and αi = (10, 5, 10, 5). The functions were truncated at zero profits and q0i s were restricted to positive integers (see Table 3).
14
The experiment was programmed and conducted with the experimental software z-Tree (Fischbacher 2007). Experimental subjects received detailed and identical instructions which were read aloud by the experimenter at the
beginning of each session and prior to each policy intervention (detailed instructions and screenshots from the participants’ interface are available from the authors upon request). Experimental subjects anonymously interacted with
other subjects within only one group during the whole experimental session through computer terminals. Participants
were endowed with experimental cash (Mi ) every round that, where applicable, could be used to pay for units produced
(q) (only under PS), buy permits (l) (only under QS) or for them to keep it. They also received a schedule with profits
from the production of units of a fictitious good (i.e., a marginal benefits table or MB). Participants were given one
of four types of these profit schedules classified as low, medium-low, medium-high, and high (L, ML, MH, and H
respectively, with two individuals per group in each category). Inducing valuations for fictitious goods in this manner
is common practice in economic experiments and has been formally justified in Smith (1976). Table 3 shows the
unit profits for the four types of MB, as well as the permit and experimental cash endowment, and quantity produced
from theoretical predictions for each policy scenario. Although parameters may differ across subjects in a group, each
subject only knew her (his) own valuations that remained constant during the 9 rounds of each of the policy treatments.
Importantly, the number of units each member of the group decided to produce created negative impacts on the
rest of the group. In order to simplify the decision-making, the damage (e) was specified as a constant for each unit
produced in the group (the actual value of that constant being revealed either before or after the production decision
was made depending on the marginal damage environment). Initial endowment, MB, deductions, and prices, were all
defined in terms of tokens - the experimental currency. Tokens had a corresponding value in dollars announced prior
to the beginning of the experiment and used to convert experimental earnings to their dollar value.
As described in Table 2 groups played under different environments regarding the damage function (MD environments or treatments). The damage (e = 3) was known with certainty in four of the groups (certainty treatments, C).
In eight other groups the damages were uncertain with a state (el ) being less adverse than the other (eh ), however, the
expected value of e under the uncertainty treatments was equal to that from the certainty treatment. In four of these
eight groups the two states would occur with equal probabilities (balanced uncertainty treatment, Ub), while in the
other four the two states were assigned extreme probabilities (extreme uncertainty treatment, Ue).
All twelve groups were exposed to the three policy scenarios BS, PS, and QS with the BS game always played
first. Under trade regimes, the group quota was distributed as personal tradable permits among individuals. Permits
allowed participants to produce units of the good (q) which delivered cash gains as described in Table 3. Although
the distribution of permits was not equitable as shown in Table 3, the symmetric partition of the group into high
and low MB minimized the possibility of agents exerting market power in nonmonopolized double-auction markets.
Most experimental evidence shows that this type of trading institution, further described below, produces competitive
outcomes under a wide range of market structural variations (Davis, Holt 1993; Holt 1995). Godby (1999) finds that
15
the results from an experiment conducted in two Canadian universities are better explained by non-competitive models
when there is a single dominant firm. The latter is not the case of the present design in which all participants receive a
permit endowment.
Each policy treatment consisted of nine rounds (including an initial trial round) in which individuals chose the
number of units of the good they wanted to produce. In the permit-trading stage of each round of the QS treatments,
individuals were allowed to sell and buy permits under a continuous double auction mechanism prior to entering the
production decision stage.17 In this experiment, current valid bids (asks) were shown ranked from highest to lowest
(lowest to highest) at every point in time and trade occurred when a buyer (seller) accepted the current ask (bid).18
Once an agreement was reached the new highest bid and lowest ask were shown on top of their respective lists. In
the production decision stage, individuals could only produce a quantity of the good that was equal or less than the
number of permits they hold, which precluded the development of strategies involving non-compliance.
Table 3: MB schedules, endowments, and predicted quantities
Unit
1
2
3
4
5
6
7
8
9
10
qBS
qPS = qQS
Token endowment (BS and PS)
Token endowment (QS)
Permit endowment (QS)
L
25
15
5
0
0
0
0
0
0
0
3
1
160
120
4
ML
25
20
15
10
5
0
0
0
0
0
5
1
140
160
3
MH
45
35
25
15
5
0
0
0
0
0
5
3
90
150
2
H
45
40
35
30
25
20
15
10
5
0
9
5
10
180
1
The policy scenarios played by the twelve groups are further described below. The aggregate demand for units
results from adding the inverse marginal benefit schedules of the eight subjects. Setting the aggregate demand for units
equal to the aggregate marginal damage of 24 (3 tokens times 8 subjects), the social optimum is reached at 20 units
produced in the group (44 units being the competitive equilibrium in the absence of correcting policies). This optimal
quantity could be achieved by imposing a limit to production of 20, or by charging a tax between 18 and 21. Note that
the tax could not be equal to aggregate marginal damage (24) for subjects internalize the marginal damage inflicted on
themselves. The tax was set at $21 which is equal to the sum of individual damages on the rest of the group per unit
produced. From Table 3 one can verify that such tax level would yield the respective qPS for each subject based on the
parameters of their respective MB, and the personal deduction of e = 3 on each unit produced.
16
3.2
Theoretical predictions for each policy treatment
Theoretical predictions for each policy treatment are obtained from the assumptions underlying the model of Section
2.1 together with the benefit function from producing the fictitious good for participant i in equation (24).
πi (qi ) = Ai qi −
αi q2i
2
(24)
The predicted outcomes from qi below are contrasted to actual outcomes in Section 4. Importantly the token
endowment Mi received by each subject is enough to guarantee a non-binding token constraint when required to pay
taxes or to have permits for each unit produced.
(A) No policy (BS) This is the baseline scenario with no policy to reduce the externality. There is no cost for producing
units of the good and the individual before-damage earnings in each round are the sum of the unit profits. Tokens
are deducted from each subject’s account based on the total number of units produced in the group (Q, which
is the sum of what the 8 participants in the subject’s group decided to produce). After each of the nine rounds,
participants could observe for ten seconds what Q was and how their earnings were calculated. The final individual
payout (Πi ) in each 30-second round was the result of the sum of the profits from units produced, plus the initial
endowment, less the tokens deducted from group production. In the following formulae, πi (qi ) represents the
sum of unit profits where qi is the number of units produced. The derivative of this profit function is equal to the
individual MBs described in tabular form in Table 3. As it was mentioned before, subjects were allowed only to
produce units in whole numbers. The individual optimal predicted qi is given by:
qBS,i =
Ai − e
αi
(25)
with resulting payout equal to:
ΠBS,i = πi (qBS,i ) + Mi − eQ
(26)
(B) Price control scenario (PS) A fee (t = 21) for each unit produced of the fictitious good was announced and each
individuals’ earnings would be reduced by tqi . The rest of characteristics from (A) remained equal. The individual
optimal predicted qi is given by:
qPS,i =
17
Ai − e − t
αi
(27)
The final individual payout in each 30-second round is the result of the sum of the profits from units produced,
plus the initial endowment, less tokens paid, less tokens deducted from group production:
ΠPS,i = πi (qPS,i ) + Mi − tqPS,i − eQ
(28)
(C) Quantity control scenario (QS) As in (A), there is no price to be paid per unit produced of the fictitious good.
However, a limit on the total amount of units that can be produced (Q = 20) was introduced. This quantity is
based on the aggregate marginal benefit function and corresponds to the amount that would be produced if t was
the fee charged for producing units. A number of permits that give the right to produce units was distributed to
every member of each group according to the quantities in Table 3. Subjects were allowed to make bids to buy
a permit from others and make offers to sell a permit to others, and/or accept offers/bids from others. This is
translated into the constraint in equation (29) that requires that the initial number of permits (Li ), plus permits
bought (lBi ), less permits sold (lSi ) must be greater or equal than qi . This inequality allows in principle for the
possibility that individuals do not use all the permits they hold.
Bi
Si
Li + ∑ lbi − ∑ lsi − qi ≥ 0
(29)
s=1
b=1
The permit market was opened for 90 seconds prior to the production decision stage each round. After the permit
market closed each round, individuals had 20 seconds to decide how many units of the good they wanted to
produce just as in (A) and (B).
The final individual payout in each 120-second round was the result of the sum of the profits from units produced,
plus the initial endowment, less tokens deducted from group production, less tokens paid for buying permits, plus
tokens received from selling permits:
Bi
Si
ΠQS,i = πi (qi ) + Mi − eqi − e(L − Hi ) − ∑ τbi lbi + ∑ τsi lsi
b=1
(30)
s=1
Since the prices at which permits are bought and sold (τbi and τsi respectively) are not fixed, bi and si index for
the specific trades , while Bi and Si represent number of permits bought and sold respectively by individual i.
Maximizing (30) with respect to q assuming (24) and subject to (29) yields the following first order conditions:
Ai − αi qi − e − µi = 0
18
(31)
where µi is the Lagrange multiplier associated with (29) and represents both the marginal willingness to pay and
the marginal willingness to accept for a permit.
for every lbi :
− τbi + e + µi = 0
(32)
τsi − e − µi = 0
(33)
for every lsi :
From (32) and (33), prices at which individual i buys and sells permits should be equal for all transactions and
thus a single τi can be substituted in (31):
qQS,i =
A i − τi
αi
(34)
Equation (34) characterizes every individual’s production decision. The components of this function are all given
except for τi which is endogenously determined in the market for permits. Since µi + e = τi > 0 for every individual, then (29) is a binding constraint and it follows that ∑Ni Li = ∑Ni qi . The last equality allows us to predict
the market equilibrium price for permits (τM ) when it is combined with the equilibrium condition τi = τM for all
i. The N functions represented by (34) are added up and set equal to the total number of permits in the market to
finally solve for the unique unknown τM .
Adding up the N functions in (34), setting them equal to L = ∑Ni Li and solving for a single µ = τM :
τM =
Ai
αi − L
∑Ni α1i
∑Ni
(35)
Under no uncertainty about e and no other behavioral deviations, the different individual τ0i s should converge
to a single market price for the permits τM = t + e. Adding up (27) across i assuming t = (N − 1)e (i.e., the
optimal tax), would yield the optimal total production QPS = ∑Ni
Ai
αi
− eN ∑Ni
1
αi .
Substituting L in (35) for QPS
produces an equilibrium permit price τM = eN = t + e. If risk attitudes (in the case of uncertainty about e), and
other behavioral responses based on fairness grounds and loss aversion depend on the policy/environment mix,
convergence to τM = t + e might be affected.
4
Results
Table 4 shows the average group quantity and standard deviation for all and last rounds (1-4 and 5-8 respectively) in
the different treatment combinations. As expected, in the absence of any regulation, the quantity is larger, approaching
the competitive equilibrium of 44 units. Interestingly, quantities seem to be larger under uncertainty with equal probabilities (Ub) for all policies. The numbers in the table also suggest that the difference between the quantity under PS
19
and QS interventions is smaller when the MD is known with certainty. Similar numbers are found to those in Table 4
if only observations for the unregulated game and the game immediately played after it are considered.
Table 4: Average group quantity per round by treatment combination
MD Environment
Certainty (C)
Uncertainty-b (Ub)
Uncertainty-e (Ue)
BS
All
Last
31.81 35.19
(7.62) (6.86)
36.5 39.25
(7.41) (7.59)
33.03 34.38
(7.64) (7.06)
PS
All
18.44
(5.23)
23.44
(5.67)
20.44
(4.91)
Last
18.38
(3.69)
21.94
(5.51)
20.25
(4.84)
QS
All
Last
18.28 18.81
(1.44) (1.22)
19.09
19.5
(1.15) (0.73)
18.16 18.38
(1.83) (1.71)
However, the difference in the means presented in Table 4 could be the result of sampling errors and not of
the different treatment combinations. Average group quantities in the last four rounds for each group were used to
perform t-tests (assuming that observed quantities come from normally-distributed population) and non-parametric
(or distribution-free) statistical tests suitable for inferences based on small samples were performed. These tests
require observations to be independently distributed, therefore only one observation per group and policy treatment
can be used. We decided to use the group quantity average of the four last rounds in each policy treatment since as
experimental subjects gain experience their decisions are expected to be made with fewer errors. Details about the
steps involved in conducting the Wilcoxon rank can be found in Conover (1971) and Siegel, Castellan (1988).
Wilcoxon-Mann-Whitney rank and t-tests were also conducted to test the hypothesis of equal differences between
PS and QS regardless of the order in which they were played. The hypothesis can not be rejected for any of the MD
environments (p-values of the t-test are 0.32, 0.60, and 0.47 for the C, Ub, and Ue treatments respectively; 0.22, 1.00,
and 0.439 for the Wilcoxon-Mann-Whitney test). Similarly, the hypothesis of the equality between prices and trade
volume (N) based on the order in which the QS game was played can not be rejected (p-values for the t-test for N: 0.56,
0.82, 0.53; for prices: 0.82, 0.50, 0.78). This allows us in principle to treat each policy treatment as an independent
observation, yielding twelve observations per policy treatment, and four per policy/MD environment mix.
4.1
Observed outcomes against theoretical predictions
Result 1: QObs
MD,BS < QMD,BS for MD = C,Ub,Ue
Support: Even though observed group quantities QObs are clearly larger under a no-policy scenario compared to regulated treatments (Table 4), statistical tests for related samples from Table 5 show that the null hypothesis that the
quantities under BS are as large as those predicted by the theoretical model for any MD environment (QMD,BS = 44)
should be rejected.19 This result is in line with findings from several common-pool resource experiments in which
the resource is exploited above the optimal level, but does not reach the predicted non-cooperative equilibrium even
20
without any facilitating institutions to cooperate such as communication and sanctioning (Ostrom 1998).
Table 5: H0 : Observed Q is equal to theoretical prediction (p-values)
t-test
Wilcoxon Rank test
HA :
<Q
6= Q
>Q
<Q
6= Q
>Q
QC,BS
0.016* 0.031* 0.984 0.063† 0.125 0.938
QUb,BS 0.140
0.280
0.860 0.063† 0.125 0.938
QUe,BS 0.016* 0.032* 0.984 0.063† 0.125 0.938
QC,PS
0.120
0.240
0.880 0.125
0.250 0.875
0.625 0.313
QUb,PS 0.751
0.499
0.249 0.688
QUe,PS 0.538
0.924
0.462 0.375
0.750 0.625
QC,QS
0.058† 0.117
0.942 0.063† 0.125 0.938
QUb,QS 0.101
0.201
0.900 QUe,QS 0.056† 0.111
0.945 0.063† 0.125 0.938
Reject H0 in favor of the respective HA at the 5% (*) and 10% level (†)
Result 2: QObs
MD,PS = QMD,PS for MD = C,Ub,Ue
Support: The null hypothesis of quantities under PS being equal to the theoretical prediction (QMD,PS = 20) can not
be rejected at any conventional level of significance for any MD environment. The finding for the certainty treatment
is in agreement with the hypothesized absence of behavioral responses previously presented in Table 1. Under the
uncertainty treatments, the results might suggest that different individual risk attitudes counterbalance each other, or
that subjects in fact maximize an expected utility function.
Result 3: QObs
MD,QS < QMD,QS for MD = C,Ue
Support: From Table 5, the null hypothesis that group quantity is equal to 20 under QS for the C and Ue environments
is rejected at the 10% level.20 Since the null hypothesis is rejected even under certainty, some support would be lent
to the existence and impact of fairness concerns and endowment effects. For the case of Ue, it is not possible from
these tests to disentangle the effects of risk attitudes from fairness concerns and endowment effects. In Section 4.2 we
explore other approaches to assist in the comparison between treatments.
Obs = P
Obs
Result 4: PMD
MD for MD = C,Ub,Ue and SUb,QS > SUb,QS
Support: Table 6 shows average permit prices and volume traded or sales for the last four rounds. Both appear close
to their theoretical prediction (24 and 10) in every case except for sales under Ub. Statistical tests were performed to
test the null hypothesis that observed prices and volumes are equal to the theoretical prediction. We can not reject the
null in the case of prices under any MD environment. In Table 7 we only present results for the tests on sales. These
21
Table 6: Average price and permit sales per round by MD environment
MD environment
Certainty (C)
Uncertainty-b (Ub)
Uncertainty-e(Ue)
Price
All
Last
26.14 24.72
(7.40) (7.22)
24.80 25.13
(5.59) (3.66)
24.69 24.67
(8.00) (7.96)
Permit sales
All
Last
9.91 10.63
(5.56) (6.45)
13.63 13.56
(3.41) (3.18)
11.50 10.38
(5.26) (4.84)
Table 7: H0 : Observed S is equal to theoretical prediction (p-values)
t-test
Wilcoxon Rank test
HA : <S
6= S
>S
<S
6= S
>S
C
0.609 0.781
0.391
0.563 0.875 0.438
Ub 0.964 0.071† 0.036* 0.938 0.125 0.063†
Ue
0.603 0.794
0.397
0.438 0.875 0.563
Reject H0 in favor of the respective HA at the 5% (*) and 10%
level (†)
show that only under the Ub environment volume traded would be different from the predictions (larger than predicted).
4.2
Policy treatment effects
The empirical analysis in this section makes complete use of the variation across individual observations under the
two policy interventions. Our estimates are based on the units produced by each subject each round in the PS and
QS treatments. This strategy allows us to implement panel data methods to a much larger sample size than that used
in the previous section and to test hypothesis with a higher degree of confidence. Due to the larger sample sizes it
is also possible to restrict the analysis to policy treatments based on their order of implementation and to incorporate
a number of control variables without losing degrees of freedom. Furthermore, it is appropriate to assume a random
effects model in which the unobserved heterogeneity is not correlated to regressors. We report estimates from a
population-averaged panel Poisson model with a first order autocorrelation error structure using different portions of
our dataset in Table 8. Count data methods such as the Poisson regression model are suitable for cases in which the
dependent variable takes only non-negative integer values as it is the case with units produced. Each panel is the
result of a subject-treatment combination and therefore we have 192 (96 subjects times 2 treatments) panels with eight
periods each when all policy treatments are considered and 96 panels when only data on the first or the second policy
intervention are used. The regressions control for policy treatment/MD environment combination, order of policy
treatment, round number and subject characteristics such as MB-type, gender, years of college education, experience
22
in experiments, major, and degree of fairness and environmental concern measured by two questions asked at the end
of the experimental session.
Of main interest is the difference between policy treatments under a given MD environment. Tests on the equality
of the coefficients c-p and c-q; ub-p and ub-q; and ue-p and ue-q were performed for each regression (c-p is the base
case, therefore a test of c-p=c-q reduces to a significance tests of the c-q coefficient). From the sample that includes
data from both first and second policy treatments the units in the the two policy interventions in the Ub environment
would be statistically different at the 5% level in the first rounds. This difference, however, vanishes in later rounds.
Tests applied to the samples for the first and the second policy treatment only show a statistical difference at the 10%
level in later rounds of the first policy intervention. This difference also vanishes as it is not significant in neither
earlier nor later rounds of the second policy intervention. When observed, the differences indicate that units would be
lower in QS than in PS. Examined more closely, average units by MB-type are always closer to the predicted amount
under PS than under QS for the four types of subjects. Under QS, subjects with LO and ML marginal benefits, produce more units than optimal, while the opposite is true for MH and HI subjects. Considering that the difference is not
significant in the second policy treatment regressions suggests that this divergence occurs when subjects are first faced
with the policy/environment mix. In other words„ behavioral considerations that affect units production may be not be
as relevant in later rounds when subjects have assimilated the mechanics of the policy in place and better understood
the range of uncertainty of the consequences of their decisions.
Result 5: Individual quantities are not different across policy treatments under any MD environment.
Support: Based on the tests of equality between the policy/environment combination coefficients in Table 8 individual
quantities under PS are not significantly different from those under QS regardless of the MD environment. This result
does not add support to the findings from Results 2 and 3 where the group quantity under PS was not affected by the
MD environment but it was under QS.
4.3
MD Environment effects on permit prices and sales
In this section we analyze the impact of the MD environment on the permit market outcomes. More specifically, we
estimate the number of permit sales by each subject each round using the same model and specification as those implemented for units produced. The sample size is however smaller since these regressions are only based on data from
the QS treatments. In the case of permit prices we perform regression analysis suitable for long panels that allows a
more flexible error structure. The time variable in the permit price regressions is given by the order in which trades
were completed within a group during the whole treatment (i.e., not re-started every round). Although the regressions
in Table 9 control for several characteristics of both the seller (s) and the buyer (b) of each transaction, we only present
the coefficients for the MB-type. Tests of linear hypothesis were implemented for c=ub, c=ue and ub=ue in every case
23
Table 8: Units produced: Poisson population-averaged model with AR1 error
Explanatory
variablesa
c-q
ub-p
ub-q
ue-p
ue-q
qfirst
round
ml
mh
hi
Constant
Dependent variable: Units produced
All policy treatments
First policy treatment
Second policy treatment
Rounds 1-4 Rounds 5-8 Rounds 1-4 Rounds 5-8 Rounds 1-4 Rounds 5-8
-0.022
(0.119)
0.324**
(0.118)
0.014
(0.128)
0.112
(0.111)
-0.035
(0.130)
-0.091
(0.079)
-0.030
(0.019)
-0.114
(0.130)
0.169
(0.112)
0.547**
(0.119)
0.725**
(0.221)
0.012
(0.124)
0.204
(0.141)
0.085
(0.136)
0.086
(0.125)
-0.002
(0.137)
-0.073
(0.083)
-0.005
(0.015)
-0.048
(0.133)
0.305**
(0.101)
0.674**
(0.112)
0.889**
(0.264)
-0.175
(0.181)
0.191
(0.181)
-0.091
(0.171)
0.006
(0.147)
-0.231
(0.178)
-0.037
(0.195)
0.128
(0.201)
0.076
(0.191)
0.131
(0.164)
-0.135
(0.165)
0.123
(0.156)
0.369*
(0.152)
0.205
(0.210)
0.246
(0.153)
0.129
(0.204)
0.043
(0.165)
0.157
(0.183)
0.200
(0.201)
0.080
(0.183)
0.059
(0.239)
-0.042
(0.027)
-0.105
(0.179)
0.064
(0.154)
0.473**
(0.159)
0.653*
(0.308)
0.000
(0.023)
0.083
(0.186)
0.358**
(0.131)
0.737**
(0.153)
0.564†
(0.339)
-0.017
(0.025)
-0.137
(0.174)
0.277†
(0.149)
0.615**
(0.167)
0.722*
(0.290)
-0.011
(0.018)
-0.196
(0.180)
0.253†
(0.145)
0.606**
(0.149)
1.169**
(0.394)
Plus other variables controlling for characteristics of subjectsb
Observations
768
768
384
384
384
384
Subjects
192
192
96
96
96
96
Robust standard errors in parentheses
** p<0.01, * p<0.05, † p<0.10
a Binary variables equal 1 if: marginal damage (MD) environment was C and policy treatment was
QS (c-q); MD environment was Ub and policy treatment was PS (ub-p); MD environment was Ub
and policy treatment was QS (ub-q); MD environment was Ue and policy treatment was PS (ue-p);
MD environment was Ue and policy treatment was QS (ue-q); QS treatment was played first (qfirst);
subject had a medium-low marginal benefit schedule (MB) (ml); subject had a medium-high MB
(mh); subject had a high MB (hi).
b These variables are age, gender, years of college, major, experience in experiments, and two variables that measure subjects’ social and environmental concern.
24
(c being the baseline case). Results 6 and 7 below summarize findings.
Table 9: Permit prices: Generalized least squares with group-specific AR1 error
Explanatory
variablesa
ub
ue
qfirst
round
ml_b
ml_s
mh_b
mh_s
hi_b
hi_s
Constant
Dependent variable: Natural log of permit price
All policy treatments
First policy treatment
Second policy treatment
Rounds 1-4 Rounds 5-8 Rounds 1-4 Rounds 5-8 Rounds 1-4 Rounds 5-8
-0.177**
(0.058)
-0.323**
(0.076)
0.094†
(0.055)
-0.030
(0.019)
-0.058
(0.054)
0.026
(0.033)
-0.008
(0.048)
-0.096*
(0.045)
-0.107*
(0.051)
-0.134**
(0.050)
3.393**
(0.126)
0.396**
(0.066)
0.259**
(0.072)
-0.033
(0.042)
0.028*
(0.013)
0.173**
(0.045)
-0.034
(0.027)
0.136**
(0.043)
-0.132**
(0.042)
0.092*
(0.042)
-0.050
(0.040)
2.525**
(0.149)
-0.064
(0.130)
-0.006
(0.129)
0.387**
(0.076)
0.605**
(0.094)
-0.140†
(0.081)
-0.722**
(0.094)
-0.126†
(0.071)
-0.481**
(0.076)
-0.019
(0.024)
-0.047
(0.076)
-0.025
(0.055)
-0.018
(0.071)
-0.247**
(0.073)
-0.137†
(0.076)
-0.202**
(0.078)
3.467**
(0.248)
0.038*
(0.015)
0.098
(0.060)
-0.132**
(0.040)
-0.011
(0.054)
-0.151**
(0.054)
-0.085
(0.067)
-0.104*
(0.050)
2.408**
(0.183)
-0.004
(0.021)
-0.232*
(0.094)
0.032
(0.063)
-0.082
(0.087)
-0.103
(0.093)
-0.118
(0.084)
-0.150†
(0.089)
3.412**
(0.252)
0.014
(0.013)
-0.025
(0.074)
0.054
(0.047)
0.148*
(0.067)
-0.018
(0.082)
0.245**
(0.068)
-0.099
(0.067)
3.033**
(0.213)
Plus other variables controlling for characteristics of sellers and buyersb
Observations
568
553
289
282
279
271
Groups
12
12
6
6
6
6
Robust standard errors in parentheses
** p<0.01, * p<0.05, † p<0.10
a Binary variables equal 1 if: marginal damage (MD) environment was Ub (ub) ; MD environment
was Ue (ue); QS treatment was played first (qfirst); buyer had a medium-low marginal benefit schedule (MB) (ml_b); buyer had a medium-high MB (mh_b); buyer had a high MB (hi_b); seller had a
medium-low marginal benefit schedule (MB) (ml_s); seller had a medium-high MB (mh_s); seller
had a high MB (hi_s).
b These variables are age, gender, years of college, major, experience in experiments, and two variables that measure subjects’ social and environmental concern. The characteristics of both sellers
and buyers for each transaction were included.
Result 6: Permit prices are larger under uncertain MD environments.
Support: Differences in prices under different MD-environments are statistically significant from each other. In later
25
rounds, prices are largest under Ue and lowest under C when QS is the first policy treatment played. Conversely,
when QS is the second policy treatment played, prices are largest under C and lowest under Ue. In addition, the size
of the largest difference is reduced when QS is played second which would also call for a learning effect that limits
behavioral drivers of variations.
Result 7: Individual permit sales are not different across MD environments.
Support: Regression results for individual permit sales are presented in Table 10. Statistical tests of the null hypothesis of differences across environments equal to zero can not be rejected in all but one case. The only exception is
the comparison between sales under C and Ub when first rounds of all treatments are considered. In this case, sales
would be larger under Ub at the 5% level (sales would also be larger under Ue but only at the 10% level; the difference
between Ub and Ue is not significant). This difference which is only significant at the 10% level in first rounds of the
first policy treatment, vanishes in later rounds and it is not significant in the sample which played QS second.
5
Discussion
Parametric and non-parametric tests based on mean group quantities yielded some statistically significant evidence for
the divergence from theoretical predictions in the case of quantity controls under certainty and uncertainty with extreme
events. However, the same statistical tests showed no divergence from predicted quantities for the tax instrument. At
the same time, direct comparison of these two policies through regression analysis does not allow rejection of the
equivalence of instruments in terms of quantities produced.
Interestingly, when first faced with the interventions, production in an environment with extreme uncertain events
(Ue) is smaller under a TPS than under a tax scheme. This divergence vanishes in later rounds or when data from all
treatments are considered. A potential explanation to this finding in earlier rounds is given by prospect theory: riskseeking behavior in losses induces individuals to see permits more scarce than they are based on the expected damage,
yielding a higher price and inducing an exhaustive use of permits for production. However, when the uncertainty
embeds an event with extreme bad consequences but small probability, the risk-seeking behavior in losses is dominated
by an overweighting of small probability events that are extremely harmful and thus production occurs below what
would be when the damages from production are known with certainty. In an environment with uncertain damages
with equal probabilities (Ub) the overweighting of small probabilities is absent and risk-seeking behavior in losses
would lead to more production. An alternative explanation for the result under Ub is given by assuming that individuals
maximize a concave utility function that has the net monetary payoffs as an argument. Concavity of the utility function
results in risk-aversion which has been shown to induce overproduction at the individual optimum. It appears, that in
later rounds when the expected damage becomes more evident, these individual behavioral responses based on risk
attitudes are no longer present.
26
Table 10: Permits sales: : Poisson population-averaged model with AR1 error
Explanatory
variablesa
ub
ue
qfirst
round
ml
mh
hi
Constant
Dependent variable: Permit sales
All policy treatments
First policy treatment
Second policy treatment
Rounds 1-4 Rounds 5-8 Rounds 1-4 Rounds 5-8 Rounds 1-4 Rounds 5-8
0.448*
(0.198)
0.404†
(0.217)
0.059
(0.142)
0.027
(0.034)
-0.211
(0.187)
-0.735**
(0.270)
-1.076**
(0.217)
0.296
(0.460)
0.368†
(0.219)
0.177
(0.247)
-0.027
(0.163)
-0.035
(0.028)
-0.368
(0.239)
-1.108**
(0.307)
-1.233**
(0.293)
0.202
(0.501)
0.432†
(0.260)
0.327
(0.277)
0.267
(0.302)
-0.049
(0.330)
0.056
(0.051)
-0.336
(0.304)
-1.027**
(0.312)
-1.067**
(0.354)
0.392
(0.765)
-0.076†
(0.043)
-0.001
(0.303)
-1.063**
(0.379)
-0.609
(0.399)
-0.637
(0.749)
0.222
(0.485)
0.494
(0.337)
0.002
(0.044)
0.733
(0.508)
0.614†
(0.366)
0.005
(0.031)
0.046
(0.243)
-0.029
(0.259)
-0.189
(0.263)
0.493
(0.843)
-0.087
(0.258)
0.202
(0.296)
-0.698**
(0.235)
0.465
(0.940)
Plus other variables controlling for characteristics of the subjectsb
Observations
384
384
192
192
192
192
Subjects
96
96
48
48
48
48
Robust standard errors in parentheses
** p<0.01, * p<0.05, † p<0.10
a Binary variables equal 1 if: marginal damage (MD) environment was Ub (ub) ; MD environment
was Ue (ue); QS treatment was played first (qfirst); subject had a medium-low marginal benefit
schedule (MB) (ml); subject had a medium-high MB (mh); subject had a high MB (hi).
b These variables are age, gender, years of college, major, experience in experiments, and two variables that measure subjects’ social and environmental concern.
27
According to our regression analysis, permit prices in quantity control interventions are larger under Ub than C and
Ue when the last rounds of all treatments are considered. Fairness and endowment effects aside, given the potentially
smaller damages under the Ub treatments, standard competition to obtain permits for profit could be more prevalent
than overweighting of probabilities which as mentioned earlier could be reduced as subjects gain experience. On the
other hand, the number of individual sales is not affected by the MD environment.
A few lessons for climate policy where damages are uncertain can be drawn from this study. The most important:
a carbon tax or an upstream cap-and-trade program can deliver the same reductions as a personal carbon trading
system such as that proposed in the United Kingdom. Findings from the present exercise show that emissions under
a TPS would be undistinguishable from those from a price control after a number of rounds. This is in agreement
with findings from a Defra-commissioned study where the difference between price and quantity policies was positive
but small in magnitude (Bristow et al. 2008). Importantly, it is likely that the costs of implementing a personal
carbon trading system would hardly be outweighed by potential further reductions or individual utility gains based on
behavioral responses.
From another standpoint, prices are effective in carrying the message of scarcity or damage to the environment.
This also implies that the non-cooperative competitive equilibrium model predicts well the behavior of individuals
who due to a collective action problem would not restrain consumption below the competitive equilibrium where
individual marginal benefits equal marginal costs (i.e., full price with or without a tax). Importantly, both theoretically
and empirically we have shown that the price emerging from a permit market in which all participants are affected by
the externality would be larger than the optimal tax - therefore price-equality does not obtain from this context.
6
Conclusions
For several years there has been a debate between the advantages of two market-based policies to correct for externalities. The debate between taxes and tradable permits advocates has gained renewed momentum due to their potential
to contain global warming by cost-effectively reducing GHG emissions. Policy implementation issues left aside, both
policies would yield the same outcomes under certainty of the benefits from pollution (or costs of pollution abatement).
When the benefits from pollution are uncertain, conditions that favor one or the other policy have been based on the
relative slopes of the marginal damage and benefit functions. In comparing the two policies, theoretical analysis has
proved that the damage function is irrelevant.
Experiments were conducted to test the equivalence of the two policy instruments when the damage function is
only known with uncertainty. Further, the designed scenario let producers of the externality to be also affected by
the damages. An array of behavioral responses not commonly included in economic analysis were hypothesized
to potentially affect the equivalence between price and quantity controls for correcting externalities. Equilibrium
28
conditions were analytically derived under the existence of different behavioral responses showing that, when present,
the instruments’ equivalence would be affected.
Nevertheless, under both certainty and uncertainty of the marginal damage, results from this experiment lend
support to the quantity-equivalence of the two policy instruments. Although some statistical tests showed statistically
significant divergence from theoretical predictions, put together, the data generated from this experiment do not allow
rejection of the hypothesis that price and quantity controls yield the same quantity equilibrium. However, we have
shown both theoretically and empirically that price-equivalence does not obtain when all participants are affected by
the externality (i.e., permit price is larger than the optimal tax when optimal Q is the cap).
Potential extensions to this study abound. For instance, taxes and quantities could be set at levels that theoretically
would not yield a social optimum. This would permit to observe, within an experimental framework, subjects’ ability
to overcome a collective action problem in a tradable permit system where the tax or the cap is loosely set. Importantly,
future developments of the experimental design from this study could incorporate the specification of damage functions
that are more likely to arise under climate change. In particular, heterogeneity in the level of damage across individuals
could be introduced, while each of the individual marginal damage functions could allow for larger losses after a certain
threshold.
Notes
1 If
the expected value of the MDF under uncertainty is allowed to be equal to the certain MDF, EUT would predict the same outcomes for the
certain and uncertain scenarios. Moreover, prospect theory’s risk attitudes could not only affect the decisions under uncertainty but also do so in
different ways for the two policies, since a market for permits allows for further reductions of the maximum potential damage while a tax instrument
does not. These ideas become clearer in Section 2.
2 Although
studies such as Plott, Zeiler (2005), refute endowment effects (a consequence of loss aversion) found in Kahneman et al. (1990) as an
explanation to observed gaps between willingness to accept and willingness to pay measures for the same good, the controversy about the existence
of such effect in contingent valuation and other settings such as permits markets is not yet resolved.
3 Clearly,
under a tax regime an individual could produce or consume more in order to avoid experiencing disadvantageous inequity in terms of
externality contribution. However, damages to this individual (and to the rest of the society for that matter) would be increased at the same time,
diminishing the palatability of such actions to reduce this particular type of inequity.
4 Loss
aversion could introduce endowment effects which in this case are only present in the quantity control. It however can also be reflected
in an overweighting of negative consequences of individuals’ actions, such that the impact of the externality could be overstated under both type
of policies. Regarding the latter idea, Tversky, Kahneman (1991, p.1057) argue that: “Because of this asymmetry [between pain and pleasure] a
decision maker who seeks to maximize the experienced utility of outcomes is well advised to assign greater weight to negative than to positive
consequences”. This type of loss aversion that could be present under both certain and uncertain environments poses no major problem to the
regulator if the adjustment factor for the externality can be measured and incorporated into the MDF. In other words, by considering δe instead of
simply e as the negative impact on each individual, where δ > 1.
5 In
Plott (1983) an underlying market for a good generating externalities was constructed in addition to the permit market. The structure of the
laboratory market implemented for this study is more similar to the designs used in experiments dealing with specific aspects of permit markets
29
(for recent exercises see, for example, Cason, Gangadharan (2003); Murphy, Stranlund (2007)). However, in addition the damage part of the story,
which has been absent in the latter group of studies, is incorporated.
6 Under a risk-averse firms framework, Adar, Griffin (1976) derived a behavioral MCC higher than the expected and realized MCCs thus reducing
abatement. This idea is further elaborated in Section 2.5. Furthermore, shifts in different directions could be in place when considering MDF that
affects regulatees’ perceptions of risk and fairness. In Malueg, Yates (2006), Shrestha (1998) and Smith, Yates (2003) the victims of pollution (i.e.,
citizens) are explicitly incorporated in the theoretical analyses of permit markets. However, the first does not consider MDF uncertainty, while the
other two incorporate it assuming that the realized MDF is known before making permit-trading decisions. Among the experimental studies, Plott
(1983) designed a market in which traders are affected by the externality, however, uncertainty was not incorporated.
7 Yet
in a passage from their study on endowment effects it is also recognized that “Endowment effects can also be observed for firms and other
organizations. Endowment effects are predicted for property rights acquired by historic accident or fortuitous circumstances, such as government
licenses, landing rights, or transferable pollution permits.”(Kahneman et al. 1990, p.1345)
8 Each
of the experimental markets are composed of 8 subjects acting as firms. Muller, Mestelman (1998) note that between 8 and 12 individuals
are typically recruited for each experimental permit market. The studies included in Issac, Holt (1999) are not an exception to this convention.
9 Yet,
another cause for deviation from instruments’ equality not considered in this study is the theory of bounded rationality which implies that
subjects do not perform all the calculations necessary to achieve rational outcomes and instead apply heuristic rules in their decisions. In a tradable
permit systems this conditions could result in non-optimal exchanges and under uncertainty in miscalculations of expected values (Kahneman 2003).
Game misconceptions such as those analyzed in Plott, Zeiler (2005) are minimized through a careful revision of the instructions.
10 This
is, profit and damage enter linearly the utility function. This assumption is relaxed in Section 2.5 where the introduction of risk-aversion
affects the optimality conditions. Note that this model could be framed with consumers i and utility functions from consumption πi (qi ).
11 BS
stands for the baseline scenario with no policy, PS for the price or tax scenario, and qi with subscript QS represents the quantity under the
tradable permits policy or quantity control scenario.
12 The
equilibrium price would be greater (smaller) than eN when the cap is below (above) the optimal quantity.
13 This
condition arises from the fact that for a trade to take place, it must be that τb1 > τs2 . Substituting from the multipliers in (14) and recalling
that e is the same for every firm that condition follows. The possibility of firm 2 buying permits from 1 has been ruled out due to the assumption
π01 (q1 ) > π02 (q2 ) and δi > 0.
14 An
example would clarify the difference between overweighting and overestimating probabilistic events. Consider a consumer with a utility
2
function v = 100x − x2 − γx. Assume that γ can take the values 10 and 110 with probabilities 0.9 and 0.1 respectively, and that the consumer chooses
the level of x. Under the framework of EUT the optimal quantity would be x = 80. Let us now consider that the individual knows the probabilities,
that is, there is no under or over estimation of them. However, she is highly reluctant to experience losses and therefore she maximizes a function
with weights 0.7 and 0.3 instead of the probabilities 0.9 and 0.1 above. Under these assumptions, the optimal x would be 60.
15 If the event with a higher in magnitude risky component is overweighted and w
p +w1−p
= 1 the resulting value would be larger than the expected
value. Consider the prospect (ηx,p;x,1-p) where η > 1. The expected value of this prospect is E = pηx + (1 − p)x. Now, assume that instead of
probabilities, weights are assigned such that the prospect takes the following form: V = w p ηx + w1−p x. The difference V − E = (w p − p)(ηx − x)
is positive because w p > p and η > 1.
16 Here,
the tax level is assumed to be known with certainty, however uncertainty lies in the marginal damage that also affects the polluter.
Performing the respective modifications similar conclusions can be reached for the other two policy scenarios considered in this study. For the
no-policy scenario, simply drop the terms with the t from the derivations. If it is assumed that no other behavioral deviations from the standard case
occur under a tradable permits policy, equations (21) and (23) only require the substitution of τ (the equilibrium price of permits) for t.
17 Plott
and Gray consider that this type of market institutions require eight seconds per equilibrium transaction (Plott, Gray 1990). This study’s
design implies ten equilibrium transactions complying with this suggestion. From Table 3, each L subject sells three units, and each ML subject
sells two.
30
18 This
version of the continuous double auction institution that incorporates the so-called rank queue facilitates convergence towards equilibrium
(Smith, Williams 1983). See Friedman (1991) for an updated overview and history of this trading mechanism used for example in the New York
Stock Exchange. The layout of the permit market stage of this experiment builds upon that used in Zetland (2008, Ch.7) within the context of water
rights in southern California.
19 The
only case where there is no agreement between the two tests is in the Ub treatment where one would reject the null based on the Wilcoxon
Rank test, but would not be able to do so based on the t-test. It is also noteworthy that for our sample size of four groups in each treatment
combination, the lowest p-value possible in the Wilcoxon Rank test would be 0.0625.
20 The Wilcoxon Rank test could not be performed for the QS treatment under the uncertainty-b environment because the sample size was reduced
to two when null differences were dropped from the analysis. This is, observations for which the hypothesized value and the observed value are
equal can not be used for this type of test which requires at least four observations.
31
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