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Furthermore, the laissez-faire Nash equilibrium outcome is still an admissible solution of the emission game if no further restrictions are imposed. This lead to.
Regulatory instruments for monitoring ambient pollution Gaston Giordana, Marc Willinger

Abstract: In a non-point source pollution situation, the regulator is unable to observe individual emissions, implying that conventional corrective policy instruments are not applicable. Collective penalties are efficient instruments for achieving a collective optimum. While such instruments are difficult to implement in the field (because individual performance cannot be taken into account) they represent a major challenge for the design of environmental policies. The aim of the survey is to assess the efficiency of such policies based on experimental findings. Key words : JEL references :

Outline

1. Introduction 2. Regulating non-point source pollution : a benchmark model 2.1. Emission and abatement decisions under laissez-faire 2.2. Incentive policies to cope with non-point source pollution 2.2.1. Individual incentives 2.2.2. Collective incentives 3. Collective incentives under certainty 3.1. Ambiant tax/subsidy and ambient tax 3.1.1. External damage 3.1.2. Internal damage 3.2. Group fines and random fining 3.2.1. External damage 3.2.2. Internal damage 4. Testing the robustness of collective incentives 4.1. Collective incentives in a stochastic environment 4.2. Information effects 4.2.1. Varying subjects’ information 4.2.2. Recommended play 4.3. Getting closer to the field : acceptability under “extreme” conditions 4.4. Collective incentives in market experiments 5. Individual incentives 5.1. The input tax 5.2. Using auctions to allocate subsidies to abatement projects 6. Collective instruments for monitoring stock externalities 7. Conclusion 8. References

1. Introduction When individual emissions of pollutants combine in an unpredictable way because of complex physical interactions and random perturbations, an ambient pollution problem arises. Water contamination is a widely studied case. Ambient or diffuse pollution occurs because complex processes (e.g. infiltration, agricultural practices) and random events (e.g. rainfalls) affect the concentration of pollutants in surface and ground waters. This contrasts to point source pollution, where effluents enter a river course at well-identified locations, such as pipe discharge. The use of pesticides and nitrogen in agriculture, emissions by mobile sources in the transportation sector, dumping in open sea, and at a large scale green-house gas emissions, are a few examples of the widespread phenomena of ambient pollution.

Traditional emission-based instruments, such as emission taxes, subsidies for abatement, standards and licences, which are based on individual emissions, do not readily apply to the ambient pollution case. The lack of monitoring technologies or costly monitoring prevents the identification of individual emissions. Emissions proxies, such as input use and firms’ characteristics (technology, size, ..) might be difficult to estimate and if available, they generally provide estimates of actual emissions that are too unreliable (Shortle and Horan, 2001) to be useful and acceptable for policy design. In the late eighties economists started exploring alternative instruments based on the level of ambient pollution which is generally more easy to measure. For example, nitrate concentration in groundwater, pesticide concentration in soil or atmospheric contamination by various substances can be measured with sufficiently high precision and reliability to provide undisputable indicators for setting policy targets.

Based on indicators of ambient pollution, economists have proposed several instruments which theoretically align private incentives with the regulator’s social objective. These instruments are designed in a way that the socially optimum level of emission can be implemented as a Nash equilibrium of the firm’s private emissions game. In her seminal paper Segerson (1988) proposed an instrument which combines a tax if ambient pollution is above the target level and a subsidy if ambient pollution is below the target level. Since individual emissions and abatement efforts are not observable, each firm is liable to the tax in case of

over-emissions and benefits from the subsidy in case of over-abatement. The tax/subsidy instrument proposed by Segerson (1988) has been improved in different ways by Hansen (1998), Shortle and Horan (2001) and others, who proposed instruments such as a pure tax, a pure subsidy and group fines. A major drawback with the original instrument is that it is not collusion-proof.

Furthermore, the laissez-faire Nash equilibrium outcome is still an

admissible solution of the emission game if no further restrictions are imposed. This lead to variants of the basic instruments and other instruments, such as random fining combined with subsidizing abatement (Xepapadeas, 1991). In section 2 of this paper we review the different variants of the general instrument that have been tested in the lab.

To our knowledge ambient pollution-based policy instruments have not yet been implemented in the field. One of the major obstacles is the policy-makers’ concern about the injustice that such instruments might create. Indeed, these instruments are based on “blind punishment” and “blind rewards”. Firms who engage in abatement activities might end up being fined, while firms who do not make any abatement effort might end up being rewarded. The problem becomes exacerbated under random fining. Such undesirable outcomes might create a general problem of acceptability and depending on the country, likely to be incompatible with prevailing rules of law. Besides the acceptability issue, the theoretical predictions under standard behavioural assumptions show that such instruments might be very efficient in achieving the social optimum. However, when carried over to the field they might prove less effective than predicted, because various dimensions might have been neglected, such as behavioural heterogeneity, limited information, and random factors affecting ambient pollution. This opens up a large avenue for running experiments to test the efficiency and reliability of these instruments under various settings.

The main goal of this survey, is to provide an overview of the various types of experiments that have been designed to evaluate the performance of alternative policy instruments to achieve a target level of emissions. In most of these experiments the target was set at the socially optimum level of emissions. A common finding of this growing literature is that among the instruments based on collective incentives, the ambient tax and the tax/subsidy scheme perform remarkably well. Efficient levels of emissions and abatements are observed under varying experimental settings, including heterogeneous players, limited information, stochastic ambient pollution or group size. Although treatment effects are observed at the

individual level, they affect only marginally group performance. This challenges the widespread view that such instruments can hardly carry over to the field.

The paper is organised as follows. In section 2 we derive theoretical predictions about the performance of alternative policy instruments based on a simplified model of ambient pollution. Section 3 summarizes the main experimental findings about the performance of collective incentives instruments. Further results about treatment effects for these instruments are presented in section 4. Section 5 presents experimental findings on individual incentives policies that can be applied to ambient pollution. Section 6 extends collective instruments to stock externalities. Section 7 concludes.

2. Regulating non-point source pollution : a benchmark model In this section we introduce a simplified version of the general model of non-point source pollution, based on Segerson (1988), Hansen (1998), Shortle and Horan (2001) and others. This framework allows us to derive the basic theoretical predictions that are addressed by the experimental literature. Our framework is based on several simplifying assumptions: (i) we consider a single input/single output technology, (ii) we assume perfectly symmetric polluting firms, (iii) all pollutant emissions result from non-point sources, (iv) social damages of pollution are separable in internal and external damage, whenever they affect the polluters and the rest of the economy, and (v) whenever random shocks affect the level of ambient concentration of pollution we assume that it is in an additive manner and that shocks are not firm specific.

n identical risk-neutral firms, i = 1, …, n, produce a unique output by means of a unique input. Let yi be the level of output produced by firm i and vi the amount of its input use. We assume yi = f (vi ) where f is a strictly concave production function. Output is sold on a

competitive market at a fixed price p and inputs are bought in a competitive market at a fixed price q. The production activity of firm i generate a level of emission xi which creates a damage on other firms and on other agents in the economy, e.g. consumers. Firms can engage in a costly abatement activity to reduce their level of emission. The total cost for firm is denoted Ci = C (vi , ai , x ) and depends on the level of input use vi, the abatement effort ai, and the level of ambient pollution x. x corresponds to an externality affecting firms’ cost, which

we call internal damage. For example, excessive pumping irrigation water in a coastal aquifer by farmer, might generate saline intrusion which can render groundwater unusable for irrigation. We assume that C (vi , ai , x ) = C (vi , ai ) + I i (x ) where Ii(x) accounts for the internal damage: Cvi = ∂Ci ∂vi > 0 , Cai = ∂Ci ∂ai > 0 and C x = ∂I i ∂x > 0 . The i-th firm profit function is given by:

π i = pf (vi ) − Ci (vi , ai , x )

(1)

Let xi = h (vi , ai ) be the emission function, where hvi = ∂hi ∂vi > 0 and hai = ∂hi ∂ai < 0 . The relation between individual emissions and ambient concentration of pollution can be stochastic or deterministic. In the stochastic case, we define ambient pollution as n

x = ∑ xi + ~ e , where ~ e is a vector of random variables. For the sake of simplicity, let us i =1

2 assume homocedastic and independent shocks: E (~ e ) = 0 and E (~ e ) = σ , where σ is a

diagonal matrix of constants. The vector of stochastic variables e~ represents the physical uncertainty about the relationship between operating practices and the ambient level of pollutants that reflects the effect of a number of climatic and topographic conditions that cannot be predicted with certainty (e.g in agricultural non-point pollution of watersheds these may be the rainfall regime or some site factors affecting fate transport). This uncertainty impedes to infer behaviour from observed outcomes (i.e. given any level of abatement, the effects on environmental quality are uncertain, and vice-versa).

In the deterministic case we assume that the ambient concentration of pollution is simply the n

sum of individual emissions: x = ∑ xi . The non-point nature of pollution is due to i =1

prohibitive costs of monitoring individual pollutant emissions. Finally, let D(x) represent the external damage function of the ambient pollution, which affects other agents then the polluting firms. We assume D(0) = 0, D’(x) > 0 and D’’(x) ≥ 0.

In our simplified model ambient pollution can damage either consumers, the polluting firms themselves or both of them. We refer to these as external damage, internal damage, and mixed damage, respectively. This distinction allows us to capture most situations where the impossibility to observe individual actions (or to infer them from observed outcomes) produces a moral hazard problem that impedes attaining the optimal outcome (e.g. effort in a

work team, private contributions to a public good, withdrawals from a common pool resource, polluting firms’ emissions, …).

We assume that the social planner’s objective is to maximize expected social welfare W, defined as the firms’ aggregated profits minus expected total damages. In the deterministic n

case total damage is defined by the sum I(x) + D(x), where I ( x ) = ∑ I i ( x ) . In the stochastic i =1

case,

the

regulator

relies

on

the

total

expected

damage

I (x ) + D (x ) ,

where

  I ( x ) = E ∑ I i ( x ) and D (x ) = E [D (x )] . With these notations, social welfare in the  ∀i 

stochastic case becomes : n

[

]

W = ∑ pf (vi ) − Ci (vi , ai ) − I ( x) − D ( x ) , i =1

Since an obvious change of notation accounts for the deterministic case, we only give the first-order conditions for optimum emissions and abatements in the stochastic case. The regulator determines each firm’s optimal input use vi* and abatement effort ai* so as to maximize social welfare. In the symmetric case vi* = vˆ * and ai * = aˆ * for all i, that result in the optimal ambient pollution level x* = n ⋅ h(vˆ*, aˆ *) .The first-order conditions for optimal emissions and abatements are: pf vi − Cvi − (I ' ( x ) + D ' ( x )) ⋅ hvi = 0

(2)

− Cai − (I ' ( x ) + D ' ( x )) ⋅ hai = 0

for i = 1,…, n

The social optimum requires that each firm equalizes its marginal profit to the expected marginal social damage and the marginal abatement cost to the expected marginal social damage reduction.

2.1 Emission and abatement decisions under laissez-faire

The “laissez faire” situation involves n firms interacting when no instrument is implemented. Each firm i determines

vi0

and

ai0

so as to maximize its expected payoff,

π (vi , ai , x ) = p ⋅ f (vi ) − C (vi , ai , x ) , assuming that the other polluters’ decisions v j and a j (j ≠ i) are fixed. With our assumptions, the vectors v 0 = (vi0 ,..., vn0 ) and a 0 = (ai0 ,..., an0 ) is the

unique Nash equilibrium in dominant strategies, in both the deterministic and stochastic cases. The first-order conditions are: pf vi − Cvi − I i ' ( x ) ⋅ hvi = 0 (3) − Cai − I i ' ( x ) ⋅ hai = 0 Note that when there is no internal damage ( I ( x ) = 0 ) the first order condition simplifies to equalizing marginal revenue and marginal cost for input choice and choosing a level of abatement for which marginal abatement cost is zero. As can be seen from the above expressions, the marginal social damage is not taken into account by polluting firms. At the Nash equilibrium, each firm chooses its input level to equalize its marginal profit to its expected marginal private damage. Since π is concave, v * < v 0 and a * > a 0 . Hence, in the absence of regulation firms use too much input and choose levels of abatement that are too low with respect to the social optimum, which advocates for regulatory intervention.

2.2 Incentive policies to cope with non-point source pollution

Since we assume that individual emissions and abatement decisions are non-observable, because of physical or financial constraints, policy instruments must rely on some alternative observable indicator. Indicators might be individual (e.g. input use) or collective (e.g. ambient pollution). We therefore distinguish between individual and collective incentives. The first group of instruments includes traditional policies (e.g. pigouvian taxes) which are based on estimated individual emissions, input use or whatever individual firms’ characteristics are correlated to emissions. Each firm is therefore liable for its estimated individual contribution to the total damages of pollution. The second group considers policy instruments that are based on group decisions (e.g. ambient tax, group fines). Each firm is then liable for the whole economic damage. In the following, we derive the conditions under which each of the instruments implements the first-best level of emissions as a Nash equilibrium.

2.2.1 Individual incentives

Traditional policies can be implemented to cope with non-point pollution if individual emissions can be estimated or if input use, correlated with non-point pollutant emissions, is observed (Griffin and Bromley, 1982). The efficiency of individual incentive policies may considerably vary depending on whether ambient pollution is affected by stochastic variables

or not. Unless the estimated emissions are perfect substitutes for measured emissions and emissions are non stochastic, policies based on firm specific incentives (e.g. pigouvian tax on estimated emissions) cannot achieve the first best outcome (Shortle and Dunn, 1986). On the contrary, input based incentive schemes can be designed to achieve the first best outcome even under stochastic and imperfectly estimated emissions (Griffin and Bromley, 1982, Shortle et al, 1998, Horan and Shortle, 2001). Then, a tax on the externality of non-point emissions can be replicated by taxing inputs that increase the externality and subsidizing inputs that reduce it. In our framework, this means that input use vi has to be taxed and abatement ai subsidized. In the case of pigouvian policies, firm i’s payoff can be written as: (4)

π (vi , ai , x ) = p ⋅ f (vi ) − C (vi , ai , x ) − τ i

As stated before, the shocks affecting ambient pollution concentration are homocedastic. Therefore, both in the deterministic and the stochastic case, the social optimum can be implemented as a unique Nash equilibrium. This requires choosing an input based tax/subsidy scheme equal to τ i = t vi + sai , where tvi corresponds to the input tax and sai to the subsidy for

    abatement, with t vi = ∑ I j ' ( x ) + D ' ( x ) ⋅ hvi ⋅ vi , and sai = ∑ I j ' ( x ) + D ' ( x ) ⋅ hai ⋅ ai . The  i≠ j   i≠ j  input tax tvi is equal to the marginal expected damage increase of the ambient pollution, and the subsidy for abatement sai is equal to the marginal expected damage reduction of the ambient pollution. In the deterministic case, a pigouvian tax on estimated emissions is a first best policy. If emissions can be estimated without forecasting errors, it can be shown that a ~ ~ first best tax on estimated emissions is equal to τ i = ∑ I j ' (x ) ⋅ h (vi , ai ) (where h (.) represents i≠ j

the unbiased estimated emissions). All these taxes internalize the externalities generated from excessive production and under abatement.

2.2.2 Collective incentives

Instruments based on collective incentives rely on the level of ambient pollution x that reflects group decisions. In this subsection we describe the characteristics and properties of ambient based policy instruments on the basis of Segerson (1988), Xepapadeas (1991) and Hansen (1998). The stochastic or deterministic nature of the ambient pollution does not considerably

underpin the efficiency of collective incentives policies. Thus, we assume in this subsection that the ambient concentration of pollution is deterministic and, by the end, we briefly discuss the stochastic case.

Segerson (1988) first proposed an ambient based policy that combines a fixed fine and a tax/subsidy proportional to the difference between the actual level of ambient pollution x and an exogenously fixed target level x : (5)

k + ti [x − x ] if x > x T (x ) =  if x ≤ x si [x − x ]

While Segerson considered the case where the tax rate and the subsidy rate are equal (si = ti) we rely here on the more general case. Note that si and ti are firm-specific to account for observable characteristics of firms, such as size or technology. Depending on the values of parameters k, ti and si various ambient based instruments can be defined: a pure tax/subsidy scheme (k = 0), a pure tax scheme (k = 0 and si = 0), a pure penalty scheme (ti = 0 and si = 0) or a mixed scheme which are combinations of pure instruments. Hereafter, we will refer to them as ambient tax/subsidy, ambient tax, group fine and mixed instrument. An interesting property of these instruments is that they are “profit-neutral” at equilibrium : whenever polluters’ choices achieve the target level of ambient pollution, no tax is collected and no subsidy is provided. In most cases, and almost systematically in experimental settings, the target level x is set at the socially optimum level of emissions, x*. However, in some cases, especially when ambient pollution is subject to random shocks, the efficient policy target level might differ from the social optimum level. This is further discussed below.

If damages are a linear function of ambient pollution the regulator only needs to know the marginal damage to appropriately specify a first best linear tax: t i = D ' (x * ) . In this case the optimum is implemented as a Nash equilibrium in dominant strategies under the ambient tax/subsidy and the mixed instrument. For the group fine to achieve the first best outcome a

threshold equal to x* (the optimal ambient pollution) is required. The group fine allows for multiple Nash equilibria, since many combinations of individual emissions can achieve the target. Moreover, the laissez faire symmetric Nash equilibrium may still be a Nash equilibrium under the group fine.

Xepapadeas (1991) proposed a mechanism that combines subsidies and fines. Whereas the subsidies are proportional to the aggregate reduction of emissions, the fine is only charged in case that the ambient level of pollution exceeds the target set by the regulator. Two different fining regimes are studied in Xepapadeas (1991): collective and random fining. The collective fine is similar to the group fine described before: all the firms are charged with the fine

whenever the observed ambient pollution level lies above the target. Under the random fine scheme a single firm is randomly chosen and is liable to pay the total fine for the group, even if it is not responsible for the group’s deviation from the target. Whereas Xepapadeas claims his mechanism to be budget balancing, when the collected fines are redistributed among all the firms, the mechanism is not incentive compatible (Kritikos, 1993) and contradicts Holmström’s (1982) result (Herriges et al, 1994). Nevertheless it might induce compliance with the target if firms are sufficiently risk averse. Moreover, if the subsidy rate is equal to the marginal social benefits of abatement, choosing a fine sufficiently high and breaking the budget balance condition, allows implementing the efficient allocation of abatement efforts as a Nash equilibrium with both, the collective and random fines. Likewise to the group fine, the collective and random fines suffer from a multiplicity of asymmetric equilibria that

inefficiently meet the threshold. Besides this, there is an inefficient symmetric Nash equilibrium where every firm under-abates. As a consequence of the budget breaking characteristic of the ambient based mechanisms (Holmström, 1982), the ambient tax/subsidy and the mixed scheme introduce stronger incentives to over-abate as the tax threshold gets lower. Moreover, under these policies firms can significantly increase their earnings if they tacitly coordinate on a lower level of emission, with respect to the optimum, in order to maximize the sum of the group payoff. Overabatement renders the ambient based mechanisms inefficient, thus the scope for a “cooperative” solution or collusion ought to be evaluated. Unlikely, the ambient tax, the group, collective and random fine schemes are “collusion proof” because the maximisation of

the group payoff under the policy results in compliance with the threshold.

When damages are a non linear function of ambient pollution, the regulator can still correctly specify the tax or subsidy rate only knowing the damage function. Hansen (1998) showed that a tax equal to total economic damages of pollution, T ( x ) = D( x ) , can induce the optimum outcome as a Nash equilibrium in an informational efficient manner. But, in the absence of a tax threshold, the Nash equilibrium is not induced in dominant strategies because the marginal

tax that each polluter faces is directly affected by the decisions of all other polluters. Moreover, this interdependence gives incentives to form coalitions among the polluters aiming to increase abatement above the level that is individually optimal. In order to mitigate collusive outcomes, Hansen (1998) added a cut-off level to Segerson’s mechanism under which further damage reduction does not result in reduced tax payment. Therefore, when the damage function is non linear, the informational efficient ambient tax is set equal to: (6)

 D( x ) − D( x ) if x > x T (x ) =  if x ≤ x 0

If the tax threshold x is fixed sufficiently below the social optimum level of pollution, the

ambient tax implements the optimum as a Nash equilibrium in dominant strategies, for the linear case, and in Nash strategies in the non linear case. This derives from the stochastic nature of the link between individual decisions and ambient pollution because a sufficiently low threshold weakens the probability of meeting the threshold even if firms under-abate. However, when ambient pollution is a deterministic function of firm emissions, setting the threshold equal to the social optimum theoretically induces the social optimum in both when firms behave cooperatively or not. This also applies to the group and random fines schemes.

3. Collective incentives under certainty From a general perspective, collective incentives are instruments based on group performance. Nalbatian & Schotter (1997) where the first to investigate performance-based instruments, and found that such incentives perform poorly when the target is imposed exogeneously to the group. In contrast, endogenous targeting by group members, on the basis of relative performance do better at stimulating group output than those that are externally stipulated. Experimental findings about group incentives reviewed in this section are in sharp contrast with Nalbatian and Schotter’s early findings. Exogenous targeting works pretty well in achieving the target emission level for several instruments such as the ambient tax and the ambient tax/subsidy.

In this section we concentrate on instruments that are variants of the mechanism proposed by Segerson: k + t [x − x *] if x > x * T (x ) =  if x ≤ x * s[x − x *]

Mis en forme : Non Surlignage

Unless specified, x* will correspond to the socially optimum level of emissions defined as the amount of total emissions that maximizes social welfare. Depending on values set for t, s and k, many variants of T(x) are conceivable. The experimental literature focused on the comparison between the tax/subsidy instrument (k = 0, t > 0, s > 0), the tax instrument (k = s = 0, t > 0) and the group fine (k > 0, t = s = 0). A few papers also considered combinations of these basic instruments.

To ease the exposition of experimental findings we distinguish the experiments according to two criteria : i) market versus standard experiments and ii) internal versus external damage. In

market experiments, firms sell units of output in a competitive auction market, following the seminal paper by Plott (1983). The only available abatement technology is output reduction. In standard experiments there is no market interaction among firms, but links among agents are created through the negative externality created by ambient pollution. When the damage is purely external, there is no interaction among polluting firms under laissez-faire (no externality). On the other hand, under under internal damage, under laissez-faire each firm’s output or abatement decision affects the profit of other firms. Adding a corrective instrument, based on ambient pollution, creates therefore a further externality among firms.

In most experiments, there is no clear distinction between input and output choice or between abatement and emission decisions. In many experiments abatement is taken as output reduction and output is liken to emissions. Depending on the experimental setting, we shall rel on the most appropriate notations introduced in section 2,.

In order to compare the performance of various instruments.a common normalized efficiency measure is employed in most experiments. The efficiency measure is based on social welfare as defined previously, i.e. joint profit minus damage. The corresponding performance measure is defined as

E =



W LF

W OPT −

W LF

W

, where W is the realized level of welfare, WLF is the

predicted level under laissez-faire and WOPT the maximal attainable level of welfare. In this expression WOPT – WLF measures the achievable welfare gain and W − W LF measures the realized welfare gain with the implemented policy instrument.

In this section we present only the results of standard experiments without random random shocks. The introduction of a stochastic environment and of market interactions will be discussed in the next section, which is devoted to “robustness” of the basic findings presented in section 3. In subsection 3.1 we compare experimental results for the tax/subsidy and the ambient tax, and in subsection 3.2 we discuss group fines and random fining. 3.1 Ambient tax/subsidy and ambient tax 3.1.1 External damage

The seminal experiment by Spraggon (2002) involves groups of 6 players with symmetric individual profit functions πi (xi) = 25 – 0.002(ximax - xi )2, i = 1, …, 6, where xi measures firm i’s level of emission and ximax correspond to its maximum emission capacity. Note that could also be interpreted as input or output choice. ximax was set at 100 for all firms, implying that individual profit is increasing in emissions up to 100 and decreases for larger levels. Therefore, under laissez-faire each firm maximises it’s profits by choosing the uncontrolled level of emission xi = 100. This generates a level of total emissions equal to x = 600. The 6

external damage function is D(x) = 0.3x where x = ∑ xi . The optimum level of emissions is i =1

6

obtained by maximizing social welfare W = ∑ π i ( xi ) − D( x ) , which implies that each firm i =1

emits exactly xi* = 25 leading to a social optimum level of emissions x* = 150. Two variants of the ambient tax are compared : a tax/subsidy instrument and a pure tax instrument. The tax/subsidy instrument, T(x) = 0.3(x – 150), provides a subsidy if x is below the target x* = 150 and a tax above the target. Plugging this incentive scheme into each player’s profit function creates strategic interaction among firms leading to a regulated profit for firm i equal to πi (xi, x-i) = 25 – 0.002(100 - xi )2 – 0.3(x – 150). Each firm has a dominant strategy level of emission xi* = 25 which corresponds to the individual socially optimum level of emission. If all firms choose xi* = 25 the individual level of profit is πi (25, 125) = 13,75. However, firms can try to collude to capture a large subsidy by choosing xi = 0 leading to the profit level πi (0, 0) = 50. To prevent such a possibility, the tax instrument was designed to eliminate the subsidy part of the tax/subsidy instrument. This is done by defining the tax as T(x) = 0.3(x – 150) is x > 150, and T(x) = 0 for x ≤ 150. The unique dominant strategy

equilibrium is for each firm xi* = 25. A computerized experiment was run with one group per session, facing each one two different instruments. The constituent game was repeated for 25 periods for each instrument. The experiment allows to control for order effects and experience effects (subjects are called “experienced” when they face the second instrument). The main finding is that the tax/subsidy scheme does slightly better than the tax scheme with an average total emission close to the social optimum level (158.44 vs 209.99 for tax) and a high level of efficiency (98.12% vs 86.67% for tax). For these two instruments the total emission is very close to the optimum, and neither order nor experience affect the performance of these instruments. Furthermore, the tax/subsidy and the tax perform better than collective fines as discussed in the next subsection. However, since with collective incentives instruments, firms are individually liable for the total damage, large individual costs might be generated when the target is not met, leading to losses (bankruptcy). Although the likelihood of ending up bankrupt was mitigated by providing subjects with an opening balance, bankruptcy was observed in sessions with experienced subjects with all instruments.

In Camacho & Requate (2004) groups of 5 subjects had to choose simultaneously an abatement decision. Abatement cost is increasing with the level of abatement at an increasing rate. A cost schedule for units of abatement was provided to the subjects (see table 1 below). If a firm chooses not to the default profit is π0 =

200. Total emissions are given by

x = ∑ (x max − ai ) where x max = 4 corresponds to the level of emission without abatement. 5

i =1

Since the damage function is D(x) = 50x, social welfare is maximized if each firm chooses to 5 5   abate exactly 2 units. This can be seen by writing W = 5 × 200 − ∑ C ( ai ) − 5020 − ∑ ai  . At i =1 i =1  

the optimum level of abatement each firm incurs a marginal cost equal to 50. Given the integer restriction (see table 1) the socially optimum level of abatement is a* = 2 for each firm.

5

The authors test the tax/subsidy instrument with T(x) = 50x = 50(10 – a) where a = ∑ a i . i =1

On average subjects chose to abate 2.06 units, which is almost the optimum level of abatement. As in Spraggon (2002) each subject was involved in two treatments. There is a

significant difference between experienced (first treatment) and inexperienced subjects (second treatment) : the optimal level of abatement was chosen 50% of the time by inexperienced subjects compared to 41.8% for experienced subjects. Both types of subjects tend to over-abate, a fact that can be interpreted as attempts to collude for being subsidized. Efficiency rates are 79% (75%) for inexperienced (experienced) subjects, a bit lower than in Spraggon (2002). Repetition leads to more over-abatement and experience increases abatement. Although the setting differs in many respect from Spraggon (2002) the authors’ findings confirm his results.

Abated units

Marginal cost

Total cost

0

0

0

1

20

20

2

40

60

3

60

120

4

80

200

Table 1 : abatement cost in the experiment by Camacho & Requate (2004)

3.1.2 Internal damage

In Cochard et al. (2005) the damage affects only polluters themselves, and no external damage occurs. Therefore, strategic interaction among firms occurs even under laissez-faire. Groups of 4 firms are involved in a polluting activity. Under laissez-faire the profit of firm i is given by πi (xi, x-i) = -3xi2 + 108xi –10x-i , i = 1, .., 4, where xi is interpreted as firm i’s level of emission. D(x-i) = 10x-i corresponds to the damage on firm i generated by other firms’ emissions. Under laissez-faire there is a unique dominant strategy equilibrium level of emission where each firm chooses xi = 18 leading to an aggregate level of emission x = 72. The

optimum 4

4

i =1

i =1

level

of

emissions

is

achieved

by

maximizing

social

welfare

W = ∑ π i = ∑ ( −3xi2 + 108 xi − 10 x−i ) leading to individual optimal emissions xi* = 13 and x* = 52. Two instruments are compared : a tax/subsidy instrument, T(x) = 30(xt – 52), and a tax instrument, T(x) = 30(xt– 52) if x > 52 (and 0 otherwise). Both instruments induce a unique dominant strategy equilibrium, where each firm chooses the optimum individual level

of emission xj* = 13. As in previous experiments, the tax/subsidy instrument involves an incentive for firms to collude to catch the subsidy.

Acknowledging the vast literature on voluntary contributions to a public good - or positive externality -, subjects might cooperate to achieve the social optimum. Similarly, since emissions generate a public bad for polluters, subjects with other-regarding preferences will reduce their level of emission below their equilibrium level. Therefore the authors run a baseline treatment to evaluate the extent of cooperation under laissez-faire. If subjects already cooperate to avoid damaging others, the introduction of incentives might crowd out individual efforts to abate emissions.

A computerized experiment was run with groups of 4 subjects, each subject being assigned to only one treatment. The constituent game was repeated 20 periods. In each period, subjects had a 20 tokens endowment that they could invest in their polluting activity. Under laissezfaire the observed level of emissions gets very close to the predicted Nash equilibrium level, and accordingly efficiency is close to zero. The authors estimate asymptotic efficiency E∞ with a panel data regression Ejt = E∞ + E0 1 + uj + εjt, where Ejt is the level of efficiency t observed for group j in period t, and uj and εjt are error terms. As t increases, the second term becomes negligible, providing an estimate of asymptotic efficiency E∞. Likewise E∞ + E0 provides an estimate of initial efficiency (t = 1). Comparing the two instruments, Cochard et al. (2005) found that the tax instrument performs much better than the tax/subsidy instrument. Average emissions are around 40 for the tax/subsidy and around 54 for the tax instrument. Average efficiency is negative in the TS treatment, while it reaches a level of 80.08% for the T treatment. Estimated asymptotic efficiencies confirm these findings, in sharp contrast with Spraggon (2002) who found that the ambient tax/subsidy is almost perfectly efficient under external damage.

Cochard et al. (2005) also introduce a reliability measure accounting for the variability of the instrument in meeting the target. The reliability indicator measures both the variability in efficiency across groups for a given period, and over time for a given group. The former measures “inter-group” reliability, and the latter “inter-period” reliability. Inter-group reliability is measured by the inverse of the standard deviation of efficiency between groups

in each period t.1 The larger the variance, the lower the inter-group reliability. Inter-period reliability for a given group between periods t and t-1 is assessed by considering |∆Eit| = |Eit – Eit-1|, the absolute variation of efficiency between these two periods. The smaller |∆Eit|, the higher the inter-period reliability of the instrument between periods t-1 and t. While the tax instrument exhibits high inter-group and inter-period reliability, the tax/subsidy instrument generates large variations across groups and over time in each group. Also, under laissezfaire, variations are low, both across groups and over time within groups.

The above findings indicate that the type of damage – external or internal –affect instruments’ performance. While the ambient tax/subsidy and the ambient tax perform equally well under external damage, the tax/subsidy instrument is inefficient under internal damage (not different from laissez-faire) while the tax instrument approaches full efficiency . This seems to indicate that adding a second externality by means of a collective incentive to a previously existing externality might strengthen the incentive for firms to collude, whenever the instrument does not prevent such an issue. Note that Spraggon (2002) tested also a forcing contract inspired by Holmstrom (1982) by providing a subsidy if abatement reduces emissions below the target (0.3(x – 150) – 22.5 if x ≤ x* and 0 otherwise). This instrument, performed very badly in achieving the social optimum, mainly due to a coordination problem because of multiple Nash equilibria. The issue of multiple equilibria is further discussed in the next sub-section.

3.2 Group fines and random fining

Group fines offer a simple and easy-to-understand tool for achieving the socially optimum level of emissions, and therefore they have been extensively studied. In constrast to the tax/subsidy, collusion is avoided by the group fine. However group fines generate multiple Nash equilibria implying a coordination issue. Two types of group fines have been compared in the experimental literature : a collective group fine for which all polluters are liable to pay a fine if x > x* and a random fine, where only one randomly selected player is liable for the fine. A general finding is that group fines, either collective or random, are less efficient than the tax or the tax/subsidy instruments.

3.2.1 External damage

1

SGt = (1/4)*Σi(Eit – Etm)² where Etm = (1/4)*ΣiEit.

Spraggon (2002) introduces the lump sum fine T(x) = - 24 if total emissions are above the target (x > x*) and T(x) = 0 otherwise. Recall that x* = 150 and x = 600 under laissez-faire. With the group fine the individual profit function becomes πi (xi, x-i) = 25 – 0.002(100 - xi )2 – 24 if x > 150 and πi (xi, x-i) = 25 – 0.002(100 - xi )2 if x ≤ 150. There is a symmetric Nash equilibrium where each player chooses xi* = 25. However, any asymmetric distribution of x = 150 among the 6 players is also a Nash equilibrium for this game. The group fine instrument performed very badly. Overall, efficiency is low compared to the tax and tax/subsidy instruments (about 54%) and average emissions are high : x = 358, more than twice the socially optimum level.

Alpizar et al. (2004) and Camacho & Requate (2004) compare collective and random fining. In Camacho & Requate’s experiment, the collective fine is defined with respect to total abatement a. If total abatement is above the target level a* each player receives a subsidy per unit of total abatement. Otherwise, a lump-sum fine is deduced from the subsidy. Specifically if a ≥ a* the individual subsidy is equal to 10a and if a < a* the individual subsidy is equal to 10a – f where f takes either value 60 or 90. Under random fining, the levels of these fines are multiplied by 5 since one firm is picked up randomly, with uniform probability, and becomes liable for the fine in case of under-abatement.

Under collective fining firm i’s profit is given by :

π i ( ai , a−i ) = 200 − C ( ai ) + 10a if a ≥ a* and

π i ( ai , a −i ) = 200 − C ( ai ) + 10a − f if a < a* With the cost schedule reported in table 1 and given that a* = 10, the symmetric equilibrium is a* = 2 for both values of f. Many asymmetric equilibria are compatible with a* = 10.

Under random fining, the profit function is unchanged if a ≥ a*. But if a < a*, two cases must be distinguished : with probability 4/5 player i’s profit is π (ai , a −i ) = 200 − C (ai ) + 10a , and with probability 1/5 his profit is π (ai , a −i ) = 200 − C (ai ) + 10a − 5 f . Two values are considered : f = 60 and f = 90. Under risk-neutrality the predictions for the random fine are the same as for the collective fine.

The main finding is in line with Spraggon (2002). Collective and random fining have a lower performance than the tax/subsidy instrument. Average abatement is between 1.13 and 1.28 depending on the treatment. Furthermore the average is lower for experienced subjects than for inexperienced subjects. The frequency distribution of abatement levels is bimodal for experienced subjects (either 0 or 2 units of abatement) as can be seen from the figure 1 below. Efficiency rates for collective and random fines are also clearly below the efficiency rate found for the tax/subsidy instruments, the difference being stronger for experienced subjects. For the collective fine average efficiency is 58% (68%) for inexperienced (experienced) for f = 60 and 76% (44%) for f = 90. For the random fine average efficiency is 63% (49%) for inexperienced (experienced) for f = 60, and 67% (52%) for f = 90.

Figure 1 : Frequency distribution of abatement efforts in Camacho & Requate (2004)

In Alpizara et al. (2004) subjects had to choose a level of abatement as in Camacho & Requate. The default profit, under laissez-faire, was π° = 34. The abatement cost schedule was the same as in Camacho & Requate (see table 1) except that maximum abatement was

restricted to 3 units per player. Player i’s profit is given by π i ( ai , a −i ) = 34 − if a ≥ a* and π i ( ai , a −i ) = 34 − C (ai ) +

[

1 C (ai ) + 50a 2

]

1 [50a − f ] if a < a*. Since the experiment involved 2

only two players, a* = 4, ai* = 2 and f = 34 implement the social optimum level of abatement. In case of under-abatement, the collective penalty corresponds to half of the fine for each player, while under random fining, the selected player had to bear the total fine f.

Alpizar et al. (2004) compare results from a student sample and a sample of managers of coffee mills, which are aware of the externality generated by their activity2. Both types of subjects where sampled in Costa Rica. Due to sample constraints for managers, the experiment was restricted to groups of two players. Subjects of the two samples had to perform two treatments, the collective fine treatment followed by the random fine treatment. Control for order effects was implemented for the student sample.

There is a tendency for the frequency of under-abatement to increase over time in the student sample, while its stays more or less constant in the manager sample. The within-sample analysis shows that the efficient outcome where the two players abate exactly 2 units is less than 50% for both samples. However there is clearly over-abatement in the manager sample under both instruments, while in the student sample over and under-abatement are observed with nearly the same frequency. Furthermore, the student sample exhibits an order effect. When the collective penalty is played after the random fining, a higher proportion of efficient outcomes is observed compared to the reverse order.

3.2.2 Internal damage

Recall that in Cochard et al. (2005) the damage affects only polluters, implying strategic interaction under laissez-faire. As in external damage experiments, a lump-sum tax can implement the first best level of emission if the level of the fine is large enough. Since player i’s profit function is given by πi (xi, x-i) = -3xi2 + 108xi –10x-i, where D(x-i) = 10x-i corresponds to the damage to firm i under laissez-faire, the dominant strategy for each firm is to choose xi = 18 , while the socially optimum level of emission is xi* = 13 individually and 2 Ambient water pollution by coffee mills comes from the fact that water is used to peel and wash the fruit in a common river basin and monitoring is imperfect or lacking due to budget constraints.

x* = 52 collectively. Any collective fine larger than f = 75 implements the social optimum. The authors considered a very large level for the fine (f = 600) as a stress test of the collective fine instrument.

The average level of emission is very close to the social optimum : x = 51.68 with asymptotic estimated value nearly equal. Since the fine was very rarely implemented, subjects succeeded in maintaining total emissions below the target. However, the data shows that a fraction of the subjects chose emissions below the individually optimum level x* = 13, while others chose a higher level of emissions, probably by anticipating that very risk-averse subjects would act in a very cautious way. This lead to very unequal payoffs for subjects compared to other instruments. Average efficiency is about 60%, comparable to Spraggon (2002) and to the treatment f = 60 of Camacho & Requate (2004). Taking into account both asymptotic efficiency and asymptotic reliability, Cochard et al. (2005) observe that the group fine’s overall performance is pretty close to the ambient tax performance, better than the tax/subsidy (as well as an input tax, see below) to reach the socially optimum level of emissions.

To conclude the section, experiments on collective instruments under certainty showed that the ambient tax or the tax/subsidy perform rather well to achieve the social optimum, depending on the type of damage (internal and external) damage. As expected group fines and subsidies are less effective because of the difficulty to coordinate individual action on one of the multiple nash equilibria.

4. Testing for robustness of collective incentives In this section we present various treatment effects that were introduced to test the robustness of collective incentives, mainly the ambient tax. Treatment effects account for heteregoneity of polluting firms (Spraggon 2004b), stochastic ambient pollution (Spraggon, 2002), incomplete information of polluters (Spraggon 2007), and advice to players (Oxoby & Spraggon, forthcoming). Cochard et al. (2007) combine heterogeneity, random shocks, incomplete information and infinite time to test the ambient tax under conditions close to the field. Finally, the instruments have been tested by changing the institutional design, allowing polluting firms to compete on an output marke (Poe et al., 2004, Vossler et al., 2006).

Findings converge to the conclusion that the ambient tax is very robust in achieving the socially optimum level of emissions under various conditions.

4.1 Heterogeneity

Spraggon (2004b) considers the case of heterogeneous capacity firms Instead of 6 firms with equal emission capacities (ximax = 100), the experiment involves 3 low capacity firms (ximax = 75) and 3 high capacity firms (ximax = 125). Socially optimal levels of emissions are xl* = 0 for low capacity firms and xl* = 50 for high capacity firms, leading to a total level of emissions of 150 compared to 600 under laissez-faire, as in the homogeneous case. The main findings are that the aggregate emissions are close to the optimum with the tax/subsidy instrument. There is no significant difference in average emissions and efficiency between the heterogeneous case and the homogeneous case. An interesting finding is that the level of abatement is larger for large capacity than for small capacity firms, implying that the Nash equilibrium solution under the tax/subsidy instrument is a poor predictor of individual decisions (see also Spraggon, 2004a)

4.2 Random shocks

In Spraggon (2002) the regulator observes the level of total emissions x subject to random error ε~ , where ε~ a uniformly distributed variable over the integers between -40 and +40. In the stochastic setting firms face a risky situation : the group might be fined although total emissions are below the target, or it might be not fined although ambient pollution is beyond the target. The results show that in a context of random ambient pollution the tax/subsidy and the tax instruments perform equally well and are more able to meet the target than group fines. Furthermore, group fines lead to emissions that are significantly above the target.

4.3 Information effects

In this sub-section we present two types of information effects : varying subjects’ information about others and advising subjects about their objective. Knowledge of other players’ payoffs may affect the performance of various instruments. For example, it can affect the likelihood

that players tacitly collude under the tax/subsidy instrument. Advising subjects might reduce confusion and errors and lead to more compliance.

4.3.1 Varying subjects’ information

The experiment by Spraggon (2007), involves two treatment variables : the information condition (full, partial or no information), and the payoff functions (homogeneous or heterogeneous). Under the full information condition subjects know the payoff-function off all members in their group as in previous experiments. Under the partial information condition subjects only know the number of members in their group but have no information about their payoff functions. Finally, under the no information condition subjects only know their own payoff function and have no information about the number of members in the group. Heterogeneity of payoff functions was implemented with the same design as in Spraggon (2004b), allowing for 3 large and 3 small emission capacity firms.

The conjecture was that the no information condition would help groups to converge to the target outcome under the tax/subsidy scheme consistently with experimental findings by Marks and Croson (1999) and Rondeau et al. (1999) for threshold public goods games, and Cochard et al. (2007) for the tax/subsidy instrument.

The main result is that the information condition has no effect on total emissions under the tax/subsidy instrument. However, reductions in efficiency are observed, which are attributable to heterogeneity and limited information (table 2). Convergence to the optimum level of emission varies across conditions : in the heterogeneous case under no information, emissions converge to the optimum and variance decreases, while variability increases for the partial and full information conditions. In the homogeneous case however variance becomes lowest in the full information condition. Differences in efficiency are attributable to treatments effects on individual decisions. Heterogeneous subjects play more randomly under no information, while the opposite is true for homogeneous subjects who play more randomly under partial information. However the main finding is that the tax/subsidy instrument is robust to various changes, combining limited information and heterogeneity of emission capacities.

No Info

Information Partial Info

Full Info

Total

Heterogeneous

79.68% 2.80

82.41% 0.62

85.09% 4.88

82.39% 1.81

Homogeneous

89.16% 0.79

86.94% 2.84

96.33% 1.09

90.81% 1.68

Total

84.42% 2.49

84.68% 1.65

90.71% 3.36

86.60% 1.57

Table 2 : Mean Efficiencies by Treatment (Spraggon, 2007)

4.3.2 Recommended play

Drawing on findings by Croson & Marks (2001) about the effects of recommended play on voluntary contributions to a public good, Oxoby & Spraggon (forthcoming) investigated the effect of recommended play on compliance with ambient pollution instruments. Croson & Marks (2001) found that recommended play increases the frequency of Nash play by heterogeneous agents in a public good game with a provision point.

The experiment relies on the same design as in Spraggon (2004b) except that the size of the groups is equal to 4, and each group involves two medium capacity firms (xmax = 100) and two high capacity firms (xmax = 125). In the recommend play treatments, the following paragraph was added in the instructions :

The purpose of the Group Payoff is to insure that everyone chooses a certain Decision Number. Notice that by increasing your Decision Number by one you increase your Private Payoff by the number given in the third column of Table 1. However, by increasing your Decision Number by one you reduce the Group Payoff by 0.3. As a result you maximize your Total Payoff by increasing your decision number to the point where increasing your decision number by one more will increase your Private Payoff by less than 0.3.

With recommended play the tax instrument gets closer to the target than without, but the opposite is observed for the tax/subsidy instrument. However there is no significant effect of recommended play, neither for average emissions nor for efficiency. While there is no effect at the aggregate level, the authors observe a significant effect at the individual level. Recommended play leads to emissions below the Nash equilibrium with the tax/subsidy

instrument for large capacity firms. Providing better explanation of the instruments does not lead to more compliance as was expected 4.4 Getting closer to the field : acceptability under “extreme” conditions

A major concern with the ambient tax is that it implements a blind penalty or subsidy. Firms who made a high abatement effort might end up paying a high fine if total emissions are above the target level, while firms who did not make any abatement effort might collect a large subsidy if total emissions are below the target level. From the theoretical point of view, such an outcome is unlikely with the tax and the tax/subsidy instruments since there is a unique dominant-strategy equilibrium, which corresponds to the target level of emissions. In other words, the mechanism is purely incentive compatible : no tax is levied and no subsidy is transferred to the agents. However with the group fine such an outcome may occur if firms are imperfectly coordinated. Furthermore, when ambient pollution is subject to random shocks, taxes and subsidies may be implemented. It is therefore a concern for policy makers, whether such instrument can be applied or not. Also, in experiments subjects make errors, leading groups to under or over-abatement.

The experiment by Cochard et al. (2007) was designed to capture some of the main features of naturally occurring ambient pollution contexts : a strictly convex damage function, heterogeneous firms combined with various information imperfections : imperfect measurement of ambient pollution, unknown number of periods of interaction, limited information about the profit functions of polluting firms for the regulator, and limited information of polluting firms about other firms characteristics. Heterogeneity was taken into account by allowing for three levels of emission capacity : low, medium and high. As in Spraggon (2007) the experiment compares two information conditions. In the limited information condition subjects have no information about the endowments and private payoff tables of other group members, but are aware that endowments and private payoff tables can differ across participants. In the complete information condition subjects have complete knowledge of the endowments and private payoff tables of all participants in their group. Furthermore, a “high” and a “low” social optimum are considered. In the low social optimum each polluter’s socially optimal level of emission is between 30% and 40% of his endowment depending on his type. In the high social optimum the corresponding range is between 60% and 70% of the player’s endowment depending on his type. In the high social optimum

condition, the distance between the social optimum and the collusive outcome is larger than in the low social optimum condition. Finally, two levels of the lump-sum subsidy are considered, to account for randomness : Kinf and Ksup. In the Kinf condition polluters pay taxes although they choose optimum pollution levels, while in the Ksup condition polluters are subsided at the social optimum, although they comply.

The instrument is such that T(x) = E[D(x)] + K if x > x*, and T(x) = 0 otherwise. Note that he damage function is non-linear in emissions, ( D ( x ) = ( x + ε~ ) 2 , and ambient pollution is random. Unexpectedly, the authors found a very high acceptance rate, even if subjects are offered a high compensation for being dispensed to play the ambient tax game. The figure below summarizes one of their main findings. The horizontal axis measures the sure amount provided as a compensation to forgive the ambient tax game. This amount is measured as fractions of the socially optimum payoff (fractions ranging between 0.40% and 0.95% have been grouped into 3 categories : low, medium, high). The vertical axis measures the average acceptance rate of the ambient tax, according to the type of polluter. As can be easily seen from the diagram, acceptance rates are very high, independently of the polluter’s type and the amount of compensation to forgive playing the game.

Figure 2 : Acceptance rates according to treatment and polluter type (Cochard et al., 2007) Practically, 12 periods where implemented. Surprisingly, in all treatments except one the average group emission gets close to the socially optimal level in the last six periods. Furthermore, over time the mean group total converges towards the socially optimal level. Limited information helps to achieve the socially optimal level of emissions in the high social optimum. Efficiency of the damage tax based mechanism is higher under limited information than under complete information, and under the low social optimum than under the high social optimum. The tax mechanism does not induce individuals to emit at the socially optimal level : while small and medium capacity firms increase their emission level over time to end up slightly above the social optimum level, emissions of large capacity firms are below the social optimum.

The experiment by Cochard et al. (2007) shows that the efficiency of the ambient tax is preserved in a stochastic environment where heterogeneous firms have incomplete information and marginal damage is increasing. Therefore, as suggested by Plott (1982), the ambient tax is acceptable based on a laboratory test-bed. A further test is proposed by market experiments.

4.4 Collective incentives in market experiments

Market experiments offer a further test of the robusteness of the ambient tax instrument. Market experiments are based on the original design introduced by Plott (1983) to study traditional instruments when the regulator can observe individual emissions or abatements : a pigovian tax, optimal standards and a market for licences. A similar design was applied by Poe et al. (2004) and Vossler et al. (2006) to an ambient pollution context to evaluate the ambient tax instrument. In the baseline treatment firms interact by submitting bids for selling units of output. The demand side is simulated : units of output are bought sequentially starting with the lowest submitted bid. Subjects know the damage function which depends on the amount of units traded, and are aware that the damage does not hurt any human subject in the experiment.

The experimental design of Poe et al. (2004) and Vossler et al. (2006) is based on groups of 6 subjects assigned to the role of polluting firms. Each firm can sell up to 5 units of a good in a

competitive auction market. The demand schedule is unknown to the firms. Firms have 6

identical cost schedules with increasing marginal cost. Aggregate output y = ∑ yi generates a i =1

level of ambient pollution x = y + ε~ , where ε~ is a uniformly distributed random variable taking values between -1 and + 1. The external damage D(x) = 500x is perfectly observed by the regulator. Firms can decide to abate pollution by reducing their output level. The laissezfaire solution leads to y = 24 (each firms sells 4 units) while the socially optimal level is y* = 18 (each firm sells 3 units). The two papers focus on the effect of cheap talk on the level of ambient pollution in combination of instruments. While there are no clear predictions about possible effects of cheap-talk, tentative predictiosn are that groups will behave as a monopolist, and collusion will become more likely when the tax/subsidy instrument is implemented .

As in previously discussed experiments the first-best instrument is a linear function of total emissions :

k + t [x − x *] if x > x * T (x ) =  if x ≤ x * s[x − x *] Several variants of this mechanism are compared : the tax-subsidy mechanism ( k = 0), a fixed penalty (t = 0) and a combination of these two instruments (k > 0 and t > 0). Various combinations of parameters implementing the first best level of emissions are considered.

The experimental setup was based on 30 trading periods : 10 baseline rounds, followed by 20 rounds in which a mechanism was implemented. In cheap talk treatments subjects had the opportunity to discuss during 5 minutes before round 11 (side-payments and threats were not allowed). Results are evaluated in terms of efficiency. In the baseline treatment, the number of traded units was very close to the equilibrium level, achieving on average 98% of the potential surplus from trade. This result is in line with typical findings of auction market experiments. Efficiency was accordingly very low, between 18% and 31%.

Poe et al. (2004) found that cheap-talk had no significant impact on the level of output produced in the baseline laissez-faire case. 3 of the 4 implemented tax/subsidy instruments failed in reaching the socially optimal level of output. The level of output is relatively low in several experiments, indicating a tendency for firms to collude in order to enjoy a large subsidy, although collusion is imperfect. As a result efficiency was low in those treatments. In

contrast, the tax instrument produced a very high level of efficiency (94%), in line with the findings of Spraggon (2002) and Cochard et al. (2005).

There is a problematic aspect of cheap talk rounds in these experiments, which was pointed out by the authors. All groups where involved in cheap talk simultaneously. The likelihood that subjects from one group could listen to other groups’ discussion was not controlled, and therefore the suggestion to produce a collusive outcome could spread across groups.

This drawback was eliminated in Vossler et al. (2006). In their experiment, a firm’s profit function is defined by πi (yi) = pyi – C(yi) + 500, where p is output price and C(yi) is firm i’s cost schedule. A fixed capital of 500 was introduced in order to prevent bankruptcy.

They compare three instruments : a symmetric tax/subsidy instrument T(x) = 500(X – 18), which generates a tax if x> 18 and a subsidy otherwise, a group fine T(x) = 1000 if x > 8 and 0 otherwise, and a mixed instrument T(x) = 250(x -18) + 500 if x > 18 and T(x) = 500(x – 18) if x ≤ 18. As in non-market experiments the group fine and the mixed instrument generate multiple Nash equilibria where individual output decisions sum up to x = 18. Collusion among firms may render the instruments ineffective. Under perfect collusion, i.e. joint profit maximization, firms would cooperate on x = 0 in order to receive a large subsidy, while they would choose 2 for the mixed instrument and 10 in the case of a fine. Likewise, y = 14 maximizes joint profits under laissez-faire.

In half of the sessions subjects could engage in cheap talk after the baseline periods (1 – 10). In addition to the 10 baseline rounds present in all treatments, the authors run a full 30 period baseline treatment. Comparisons with other treatments, allows to test whether treatment effects are due to the instruments or additional learning effects due to more periods. The findings show that market-learning effects vanish quite quickly. It is therefore unlikely that observed output differences across treatments can be attributed to learning.

Rounds 11-20 (stage 1) and 21-30 (stage 2) are grouped separately for analyzing the data. Introducing cheap talk affects total output only marginally and not significantly, suggesting that collusion was unsuccessful under laissez-faire. When no cheap talk is allowed the tax/subsidy mechanism generates a level of output that is not significantly different from the optimum level, while other instruments fall above, although significantly below the baseline

output level. Allowing for cheap talk affects negatively and significantly output for all instruments. For the tax/subsidy groups realized (verbally) that they could reach maximal payoffs for y = 0. For the tax/subsidy average output felt from about 22 in the baseline periods to 9.0 in stage 1 and 3.9 in stage 2, a clear indication of a tendency towards full cooperation.3

Market experiments compared group fines and tax/subsidy schemes. Clearly, in accordance with findings of standard experiments, the tax/subsidy performs better than the group fine, although when cheap talk is allowed there is a tendency towards collusion, which counters the beneficial effect of the policy instrument.

5. Individual incentives A few experiments introduced individual incentives to regulate ambient pollution. Recall that individual incentives can be defined on observables, such as input use or output, or some characteristic of firms. By increasing the firm’s cost, such instruments affect the level of emissions. An input tax was studied by Cochard (2003) and Cochard et al (2005). Alternatively, firms’ characteristics may be revealed by using an auction mechanism. Such a policy instrument was studied by Cason et al. (2003), to allocate subsidies to non-point pollution abatement projects. In their experiment, tradable permits are allocated to firms though an auction. In a deliberately policy-oriented experiment, the authors try to identify the information conditions that allow the regulator to award land management contracts to maximize non-point pollution abatement for a fixed auction budget. 5.1 The input tax

Cochard (2003) compares the input tax to other instruments, under two conditions :

a

deterministic and a stochastic relation between individual emissions and the ambient concentration of pollution.

The experimental setting follows the design of Cochard et al. (2005) already exposed previously. The damage generated by excessive polluting input use affects only polluting firms (internal damage). Under laissez-faire firm i chooses the level of input use xi to

3 The authors note that one group succeeded in sustained full cooperation. In the other groups individual deviations where observed, which is comparable to free-riding in voluntary contribution experiments.

maximise its profit taking into account strategic interaction generated by the internal damage :

πi (xi, x-i) = -3xi2 + 108xi –10x-i , i = 1, .., 4. Note that xi can either be interpreted as the level of emission or the level of input use. The unique dominant strategy equilibrium is xi = 18, while the socially optimum level of input use is xi* = 13, obtained by maximizing social welfare 4

W = ∑ π i . The optimal input tax T ( xi ) = 30 xi implement the socially optimum level of i =1

ambient pollution as a dominant strategy equilibrium where each firm chooses the level of input use xi* = 13. However, players might cooperate by choosing xi = 8 to maximize joint profits. These predictions carry over to the stochastic case, a zero mean random shock on the ambient pollution..

Recall that under laissez-faire the observed level of emissions gets very close to the predicted Nash equilibrium level, and accordingly efficiency is close to zero.Introducing the input tax, leads to average and asymptotic group input use roughly equal to52 units, while individual input use is close to the sub-game perfect equilibrium of the repeated game (13 units per subject per period). Letting ambient pollution be affected by a random shock, does not significantly modify these result. Therefore, both settings, deterministic and stochastic, achieve very high average efficiency rates (96.51% and 93.48% respectively) and approach 100% in some periods. Moreover, the asymptotic efficiency is 98.18% in the deterministic case and 96.34% in the stochastic case. Additionally, the input tax was shown to be significantly more efficient than the ambient tax/subsidy and a “small” group fine. On the other hand, the input tax’s efficiency is not significantly different from the ambient tax and a “large” group fine.

These results indicate that under both certainty and uncertainty the input tax is highly efficient in meeting the target. Notice however, that since input use is observed without error, perfect enforcement of the tax is feasible. As seen from the field, such a setting might be realistic in some cases (e.g. taxation of leaded fuel) but not in others (e.g. taxation on pesticides loads). When input use is not perfectly observable, the regulator might rely on a self-reporting mechanism with probabilistic monitoring of declarations. In such a context the input tax might be less effective (see Alm et al (1992) for experimental results on tax evasion). Actually, one of the advantages of collective incentives policies relies on the avoidance of costly individual decision monitoring. On the other hand, assuming perfect compliance allows

comparing the relative efficiency of individual and collective incentives without any perturbations from misreporting behaviour.

5.2 Using auctions to allocate subsidies for abatement projects

In previously discussed experiments, we assumed that the regulator knows perfectly the firms’ technologies and firms know perfectly the damage function. In “real life” however, one has often to deal with situations where firms’ abatement costs are not directly observable by the regulator and firms do not know the social benefit of their abatement effort. In other words, there if often “dual information asymmetry”. Starting from an empirical case where the regulator knows better the environmental benefits of various abatement projects, while landholders know better the cost of these projets, Cason et al (2003) investigate the allocative efficiency of a multi-unit discriminatory auction mechanism. The aim of the regulator is to allocate subsidies from a limited budget to the most environmentally efficient abatement project per unit of public currency spent. The aim of the experiment was to investigate whether a one-sided reduction of information asymmetry would lead to a better selection of abatement projects to be subsidized. More precisely, if firms are privately informed about the environmental benefits (called “quality” hereafter) of their abatement projects, are they more likely to reveal their costs ?

The computerized auction experiment involved groups of eight seller subjects. Since a discriminative price rule was applied, successful sellers received their offer price for their sold item4. In order to restrict the likelihood of collusion among sellers, they received only little feedback after each round. Furthemore, each project’s cost was private information. However, sellers were ‘‘free to discuss all aspects of the market fully for up to two minutes but they could not show each other any information on [their] record sheets.’’ These communication rules were implemented because they better reflect the field characteristics. For the same reason, sellers were not allowed to show each other their record sheets. For the auction to be efficient, projects with the lowest cost and with the highest environmental benefits should be selected. In order to evaluate the performance of the auction mechanism, three performance indicators are used : i) the percentage of maximum abatement realized (P-MAR), defined as the amount of pollution abatement realized by the auction mechanism, as a percentage of the highest amount of abatement that could be achieved with 4

Sellers could offer several items, but they were restricted to a single transaction.

the government’s auction budget; ii) the percentage of optimal cost–effectiveness realized (POCER), defined as the actual abatement per dollar spent in the auction as a percentage of the abatement per dollar spent in the ‘‘maximal abatement’’ solution5, iii) seller profits. Since seller profits represent money that the government ‘‘overspends’’, lower seller profits are better from the government’s perspective. Seller profits are zero at the offer = cost benchmark.

The main result of the experiment is that market performance is higher when sellers are uninformed about the environmental benefits of their abatement projects. The reason is that if sellers are aware of the quality (environmental benefits) of their projects, high quality project owners tend to increase their offer because such projects receive priority for being subsidized. This leads to adverse selection of projects, whereby efficient high-quality projects are not subsidized because sellers make prohibitive offers. Therefore, less abatement is undertaken per dollar spent when firms are aware of the quality of their projects. Since not all efficient projects are excluded from subsidies, profits tend however to be higher when information is made available. Furthermore, for both informed and uninformed firms, there is clear tendency for performance to decreases over time, as subjects acquire more experience. As a consequence their profits increase, which means that subsidies do not meet the target to increase abatement effort. The authors propose various means that could be applied in practive to mitigate the adverse effects of information and learning. For example if environmental quality is multidimensional, the regulator can conceal the weights that he puts on the various dimensions, and change these weights from time to time to avoid that they become public information.

6. Collective instruments for monitoring stock externalities In this section we report experimental findings about the efficiency of collective incentives with respecto to dynamic externalities, called stock-externalities hereafter. In these experiments (Giordana and Willinger (2007), Giordana (2008)) collective incentive instruments where designed to regulate the exploitation of a common-pool resource. The regulator cannot observe individual withdrawals from the common pool, and therefore policy

5

P-OCER can differ from P-MAR because part of the government’s budget may be left unspent.

instruments are based on the level of the stock. Therefore, management of a common poolresource, is subject to the same type of information-asymetry as non-point source pollution.

Designing policies aimed at reducing groundwater or air pollution requires taking into account stock externalities. Once the natural capacity to absorb pollutants elements by the ecosystems is exceeded, pollution accumulates, in groundwater bodies or the atmosphere, generating persistent effects. Empirical and experimental findings showed that in a dynamic environment, resource exploitation can lead to dramatic inefficiencies, enhancing the need for effective policies to cope with them (Clark, 1974, Herr et al, 1997).

In a dynamic setting the moral hazard problem persists, but the design of policies is complicated by the continuously changing environment. With a finite horizon, policy parameters must be adjusted from one period to the next to adapt incentives to the remaining time and to the evolution of economic damages in response to pollution accumulation. Efficient internalization of stock externalities can therefore be achieved by adjusting the tax rate, the penalty, and the targets after each period (Xepapadeas, 1992, 1994). However, if the regulator faces budget or technical constraints, the implementation of an optimal dynamic policy instrument might not be feasible. The regulator’s policy choice set may be restricted to second best policies, if periodical modifications of tax rates are difficult to implement, or not acceptable by agents. Such situation may lead to the implementation of fixed instead of flexible policy instruments.

In Giordana and Willinger (2007) and Giordana (2008), 5 firms extract units from a stock of a common resource. In each period t = 1,…,10, firm i extract yit units. The evolution of the 5

resource stock S t is described by S t +1 = S t − ∑ yit + r , where r is a constant natural recharge i =1

known

by

all

agents.

Extracted

units

generate

a

profit

equal

to

π i ( yit ) = 5.3 ⋅ yit − 0.09 ⋅ (yit ) − yit ⋅ (7.6 − 0.01 ⋅ S t ) . The externality affecting firms is the 2

evolution of the resource stock : present withdrawals reduce future stock diminishing future profits. Two behavioral assumptions are considered to solve the dynamic game: myopic agents or farsighted but selfish agents (called rational agents hereafter). The predictions of these assumptions are compared to the optimum extraction path which corresponds to maximizing the sum of discounted profits of all firms over the temporal horizon. Figure 3

shows the the extraction trajectories calculated, under laissez-faire, with a closed-loop solution (agents observe S t at the beginning of each period) and assuming that the discount factor is equal to one for rational and optimum strategies, and zero for the myopic one. The difference with the optimum extraction trajectory highlights the inefficiency of the myopic and rational strategies. Taking the optimum strategy as an efficiency benchmark6, the myopic and rational strategies achieve, respectively, 74% and 52% of efficiency with respect to the benchmark. Results from 6 groups of 5 subjects repeating 4 times the 10 period dynamic game, indicate that the myopic strategy is the best fitting one. The observed extraction trajectory achieves 50% of efficiency.

16 14 12

Withdrawals

10 8 6 4 Rational Myopic Optimum

2 0

1

2

3

4

5

6

7

8

9

10

Period

Figure 3 : Predicted extraction path under altenative behavioural hypotheses (Giordana & Willinger, 2007)

In order to cope with stock externalities Giordana (2008) tested in the laboratory a first best flexible ambient tax. The tax rate and the threshold are adjusted after each period to reflect the evolution of the stock (and the internal damage) inducing the optimal extraction trajectory. Given the specification of the profit, the internal damage function is non linear. In order to simplify the implementation in the laboratory, the tax rate was calculated assuming that all agents are perfectly myopic. The tax rate at each period t is therefore just a function of the available stock S t . The tax thresholds are defined on the basis of the remaining stock after the

6

Efficiency is defined as the wealth accumulated until the end of period T under a particular strategy with respect to the optimum strategy.

( )

extractions of the period. This leads to S t * = S t − 5⋅ y t * (S t ), where y t* S t is the optimum feedback strategy.

The performance of the instrument was evaluated according to effectiveness and efficiency. Effectiveness measures the instrument’s capacity to curb the extractions path towards the optimum with respect to the unregulated benchmark. Efficiency measures total welfare, defined as aggregate profits in percentage to optimum profits. Efficiency is measured either by taking into account tax and penalty payments (net efficiency) or not (gross efficiency). Effectiveness is measured in absolute or relative terms (considering the actual evolution of the stock that may differ between groups). Absolute effectiveness is calculated by the mean squared deviation of the observed extractions with respect to the optimal path. For relative effectiveness observed deviations from the optimum path are normalized by the distance between the prediction and the optimum benchmark.

The flexible ambient tax increases significantly efficiency achieving 78% of efficiency However, as coordination failed, the tax was frequently charged affecting net efficiency which became negative (-141%). Relative effectiveness indicates that the instrument curbed the extraction trajectory towards the optimum only 25.16% of its capacity.

Giordana and Willinger (2007) experimented a second best fixed ambient tax. This policy is characterized by a fixed tax rate equal to 0.2 (equal share of the common tax) and fixed tax thresholds for each period (announced at the beginning of the game) which correspond to the optimal stock trajectory. Given that it is a second best policy, theoretical predictions for myopic firms assumed that the target would not be met in every period. Thus, the predicted gross and net efficiencies were, respectively, 82% and -20%. The fixed ambient tax performed poorly. The observed gross efficiency is 63%, but relative effectiveness indicates that the extraction trajectory was curbed towards the optimum only 0.61% of its capacity. An econometric analysis indicates that the main reason of the coordination failure was not relatively low taxes but the stickiness of the targets.

When applied to stock externalities collective instruments perform poorly. This might be due to the complex environment, since subjects need to take into account the dynamic effect of their current decision, a cognitively difficult task. Simplifying instruments to provide clearer

incentives does not improve efficiency. The implementation of time inconsistent instruments deteriorates performance, since early deviations from the predicted path alter the incentives introduced by each policy, encouraging thereby non optimal behavior or just confusing agents with distorted signals.

6. Conclusion In this paper we rewieved various experiments designed to evaluate the performance of corrective policies for an ambient pollution externality. Under ambient pollution policy options are restricted to observables (total emissions) or proxies of emissions (input use, …) or some characteristic of polluters (size, location, …). A large set of instruments is based on aggregate emissions and take the general form : T(x) = D(x) + k if x > x* and T(x) = S(x) otherwise, where D(x) corresponds to total (expected) damage, S(x) to a subsidy for abatement below the target and k to a lump sum transfer. The interpretation is that each polluter is liable to pay the total damage generated by the pollution activity if emissions are above some external target x*, and will be subsidized if aggregate abatement effort bring total emissions below the target. Most of the experiments reviewed in this survey tested a linear form : T(x) = t(x – x*) + k if x > x* and T(x) = s(x – x*) otherwise

The main finding of the experimental literature on ambient pollution is that the tax/subsidy instrument (t = s > 0) and the tax instrument (t > 0, s = k = 0) perform remarkably well in achieving the target emission level x*. These findings contrast with Nalbatian & Schotter’s (1997) findings about group performance under exogenous targeting. Furthermore, these instruments proved to be robust to various treatment effects, including heterogeneity of emission capacity, incomplete information, random shocks on the level of ambient pollution, and varying the damage function. Even when these various effects are intertwined as in real life situations, the ambient tax instrument still exhibits a high level of efficiency in meeting the target. Finally plunging these instruments into a market environment, does not disrupt their performance. Therefore, with respect to experimental testbedding, the ambient tax and the ambient tax/subsidy could be recommended as acceptable policy instruments to be implemented in the field, at least as a field experiment (see Plott, 1994). However, there is a serious limitation for the tax/subsidy instrument which was highlighted in almost all

experiments : the tendency towards collusion among polluting firms, which may increasingly reduce its efficiency over time.

For exactly the same reason as for the tax and the tax/subsidy instruments, group fines (s = t = 0, k > 0) and random fining should not be recommended to policy makers, although further testing is required, in particular in the field. Experimental findings show that these instruments perform poorly under various conditions, in contrast to the ambient tax and ambient tax/subsidy. The difficulty to coordinate individual actions because of multiplicity of nash equilibria seems to be the main reason of their low efficiency. There is however one important exception : when damage is internal and no random shocks affect ambient pollution, the group fine is significantly more efficient than the ambient tax/subsidy, which has almost no effect on emissions. However, more research is required to understand clearly why, i.e. how do the environmental externality (internal damage) and the policy externality (group incentive) interact.

An important limitation of collective incentives appeared under stock externalities. When ambient pollution accumulates over time, a dynamic externality might be created among agents, like in the case of a common pool depletion. Experimental findings show that collective incentives, first-best and second-best, perform rather poorly in such an environment, probably because of task-complexity.

Finally we presented a few results about individual incentives and available policies to deal with dual information asymmetries. This literature is still in it’s infancy, but from an empirical point of view, individual incentives policies are still the most likely policies to be acceptable in many cases. Their limitation of course is the availability of a reliable estimate of input use. Taking into account dual asymmetries moves one closer to the field, and might prevent the implementation both of individual and collective penalties, since optimal targets are unknown. This opens up the question of designing new instruments adapted to such a context.

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