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Performance of the Ambient Tax: Does the Nature of the Damage Matter?

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Abstract

The ambient tax is often considered as an efficient instrument to achieve a first best outcome of ambient pollution when the regulator cannot observe individual emissions, or when monitoring costs are prohibitive. While this view is supported to a large extent by experimental findings, there remains several hurdles that hinder the implementation of the ambient tax in the field. One of these hurdles is the nature of the damage. Experimental findings suggest that the efficiency of the ambient tax is higher under external damage, i.e. if ambient pollution affects non-polluters (Spraggon in J Public Econ 84:427–456, 2002) than under internal damage, i.e. if ambient pollution affects polluters themselves (Cochard et al. in Environ Resour Econ 30:393–422, 2005). But this result rests on very different experimental settings. Therefore, we designed a new experiment that allows to compare external and internal damage within a common setting. Our main finding is that the ambient tax is equally efficient under internal and external damage.

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Notes

  1. In a broader sense one could consider boycotts of environmentally damaging products as a type of collective penalty. By adopting such a perspective, Millock and Zilberman (2006) report several other examples (e.g., during 1990–1991 the US boycotted Mexican tuna to stop the use off fishing nets that threatened dolphins).

  2. Note that since we assume \(x_{i\text { }}=e_{i}\) it is equivalent to say that firm \(i\) chooses directly its level of emission. However, for ease of exposition and interpretation we shall assume that the firm chooses its level of input.

  3. Note that with these parameters each player’s profit function is increasing and concave in \(x_{i}\). In the absence of regulation, the profit function is increasing for \(x<30\) and decreasing for \(x>30\).

  4. Results are available from the authors upon request. We used a robust specification for the errors because emission variability is highly group-dependent.

    Table 2 Average and median emission per group in each treatment
  5. Available from the authors upon request.

  6. The inter-periodic variability of average group emission is measured by \( \frac{\left( \sum _{t=1}^{t=10}\frac{(X_{t}-\overline{X}_{t})^{2}}{10} \right) ^{1/2}}{\overline{X}_{t}}\).

  7. The inter-group variability of average group emissions is measured by \(\frac{ \left( \sum _{i=1}^{i=6}\frac{(x_{i}-\overline{x}_{i})^{2}}{6}\right) ^{1/2}}{\overline{x}_{i}}\).

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Acknowledgments

We like to thank Charles Figuières and Klarizze Puzon for their valuable comments on an earlier draft of the paper. The remarks of two anonymous referees helped to improve substantially the quality of the paper. Finally we wish also to thank Timo Goeschl and Etienne Montaigne for their support.

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Correspondence to Marc Willinger.

Appendix: Instructions

Appendix: Instructions

We provide the instructions of the external damage treatment, for sequences 1 and 2. The instructions for the internal damage treatment are identical to those of the external damage treatment with one difference: the payoff of each group member in both sequences is reduced by an amount that depends on the other group members’ investment level. Precisely each token invested by group member \(j\) reduces the payoff of group member \(i\) by 12 ecus. (N.B. the original instructions referred to screen shots: for the sake of space, they are omitted in this presentation).

1.1 Instructions

The experiment in which you are about to participate is intended to study decision-making. The instructions are simple. If you follow them scrupulously and if you take appropriate decisions, you can earn a significant amount of money.

All your answers will be treated in an anonymous way and will be collected through a computer network. Please enter your choices into the computer system which will indicate to you your gains as the experiment proceeds. The total amount of money than you will earn during the experiment will be paid out to you, in cash, at the end of the session.

1.1.1 General Framework of the Experiment

There are 18 participants in the room. At the beginning of the experiment the host computer will be composing randomly 3 groups of 6 persons. The composition of the groups will remain identical for the whole duration of the experiment. You will not be able to identify the other members of your group and the other members of your group cannot identify you.

The gains that you will achieve depend both on your own decisions and on the decisions taken by the other members of your group. Each of your decisions entails a gain or a loss, expressed in ecus. The total amount of ecus that you will accumulate throughout the experiment will be converted into euros and paid out for real at the end of the session. The conversion rule of ecus into euros will be outlined at the end of these instructions.

The experiment is divided into 20 periods each of which consists of two sequences of 10 periods. The remainder of this document details the instructions for the first sequence of 10 periods (periods 1–10). The instructions for the second sequence will be distributed to you after the first sequence will be ended.

1.1.2 Decisions

At the beginning of each period, each member of your group, including yourself, will have an endowment of 32 tokens. In each period, you will have to decide how many tokens you invest. You are free to invest any amount between 0 and 32: \(0, 1, 2,\ldots , 30, 31\) or 32 tokens.

For a given period your gain will depend only on your investment decision the current period. This gain is indicated in Table 13. It depends only on the number of tokens that you decide to invest. The first column of the table indicates the token invested, the second column the gain of the corresponding invested token and the third column the total earning of your investment decision.

Table 13 Gain corresponding to your investment decision

Reading the table is easy:

  • If you invest 0 token your total gain will be equal to 0 ecu.

  • If you invest 3 tokens, your gain will be 177 ecus for the first token, 171 ecus for the second token and 165 ecus for the third token. The total earning for an investment of 3 tokens is therefore equal to: 177 + 171 + 165 = 513 ecus.

  • If you invest 20 tokens, your gain will be 177 ecus for the first token, 171 ecus for the second token, ..., 69 ecus for the 19th token and 63 ecus for the 20th token. The total earning for an investment of 20 tokens is therefore equal to: \(177 + 171 + \cdots + 69 + 63 = 2400\) ecus.

1.1.3 Course of a Period

In the first sequence there will be 10 periods that will follow the same course. At the beginning of a period you will have an endowment of 32 tokens. You have to decide how many tokens to invest (see figure 1.1). Once all participants have chosen their investment level, the screen shown in figure 2.1 will be displayed. This screen will inform you about the following data for the current period: the number of tokens invested by you, the total number of tokens invested by your group and your gain for the period.

At any time, by clicking the “history” button you can see the data of previous periods (see figure 3.1). The history screen displays, for every past period, the number of tokens invested by yourself, the total number of tokens invested by your group, your earning for the period, and your cumulated earning since the beginning of the experiment.

1.1.4 Final Detail

When the 10th period will be over, you will receive the instructions for the second sequence.

At the end of the second sequence, your total gain accumulated over the 20 periods (sequence 1 + sequence 2) will be converted into euro. The rate of conversion of ecus into euro is: 6250 ecus = 1 euro (or, equivalently 1 ecu = 0.00016 euro). In addition to your eventual gain or loss you will receive 10 extra euros to guarantee that you will not be losing your own money for this experiment. If for instance your total amount of ecus is 15000 you will receive 12.40 euro in cash (10 euro + (15000/6250) = 10 + 2.40 = 12.40 euro).

1.2 Instructions for Sequence 2

The composition of the groups remains the same as in sequence 1: in other words you will still interact with the same 5 participants than in sequence 1.

1.2.1 Decisions

As in sequence 1 in the beginning of each period you will receive an endowment of 32 tokens, and you must decide about the number of tokens to invest. In this sequence your gains for each period depend both on your own investment decision and on the investment decisions of the other members of your group.

The gain on your investment (called individual gain in this sequence) is indicated in Table 13 of the first sequence instructions. The novelty for this sequence is the addition of a second component of your gain of a period: the collective loss.

Calculation of the Collective Loss

  • If the total number of tokens invested by your group is less than or equal to 120 tokens then the collective loss is zero and no member of the group will suffer any loss.

  • If the total number of tokens invested by your group is strictly larger than 120 tokens then each group member undergoes a loss equal to 60 ecus \(\times \) (total number of tokens invested by the group \(-\) 120).

In other words, if the total number of tokens invested by the group exceeds 120, every member of the group will suffer a loss of 60 ecus for each token invested beyond 120. Table 14 shows the various possibilities of collective loss according to the total number of tokens invested by the group.

Table 14 Losses due to the group investment

Your payoff for a period consists of two parts:

  1. (i)

    Your individual gain which depends only on your investment

  2. (ii)

    The collective loss which depends on the total number of tokens invested by your group

Examples:

  1. (1)

    You invest 12 token. Your group invests a total of 100 tokens. Given that 100 \(\le \) 120 there is no collective loss, your gain for the period is 1728 ecus.

  2. (2)

    You invest 12 token. Your group invests a total of 140 tokens. Since \(140> 120\), each member of your group suffers a loss which amounts to 60 \(\times \) (140 \(-\) 120) = 1200 ecus. Your gain for the period is 1728 \(-\) 1200 = 528 ecus.

1.2.2 Summary of a Period and History

After all the participants have decided about their investment (figure 1.2), the screen of figure 2.2 will appear. This screen will inform you about the following data for the current period: the number of tokens invested by you, the total number of tokens invested by your group, your individual gain, the collective loss for this period and your gain for the period.

At any time by clicking the “history” button you can access the history of previous periods (see figure 3.2). This screen displays, for each past period, the number of tokens you have invested, the total number of tokens invested by your group, your individual gain, the collective loss, your payoff for the period and the cumulative gain since the first period.

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Willinger, M., Ammar, N. & Ennasri, A. Performance of the Ambient Tax: Does the Nature of the Damage Matter?. Environ Resource Econ 59, 479–502 (2014). https://doi.org/10.1007/s10640-013-9743-y

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