Unilateral actions,
the case of international environmental problems
Urs Steiner Brandt[1]
08 February 2002
Abstract:
Hoel (1991) seriously challenges the prospect of unilateral actions to alleviate international environmental problems. By treating reductions as strategic substitutes, increased reduction in one country will inevitably decrease reductions in the other countries. It, however, remains unclear why a country tries to “set a good example” knowing that the response will be negative. The main purpose of this paper is to investigate, whether the dismissal of unilateral actions to play any part in solving international environmental problems by Hoel (1991) could withstand the reformulation of the role of unilateral actions, not as being a rather naïve attempt to set a good example, but as a transmitter of relevant information. In the case where costs ex ante are uncertain, but correlated, unilateral actions serves as a signalling devise to reveal low costs and unilateral actions have the potential to trigger positive responses abroad. However, the country engaging in unilateral actions is the one with the highest expectation about the other countries reaction, and might suffer from an effect like the winners curse in auctions theory.
JEL Classification: Q28, H4, D8
Keywords: International environmental problems, unilateral reductions, signaling costs
1. Introduction
The lack of supranational authority has as implication that policy measures at the international level must rely solely on voluntarily contributions. As exemplified by the troublesome process of regime building for the climate change issue, creation of the right set of incentives for such voluntary provision to make a significant difference for international environmental problems compared to pure non-coordinated action is not easy. This paper re-examines the prospect of unilateral actions to be a non-cooperative alternative to the cooperative actions of multinational negotiations, since the effectiveness of such negotiations have been seriously questioned. E.g. Barrett (1990 and 1994) note that an agreement will only be settled when it does not matter a much, and there might therefore be good reason for a very concerned country to initiate actions if such actions act as ‘setting a good example’. Although it cannot be expected that such actions at any point will bring around a fully cooperative solution, it nevertheless might make a difference to overcome the first, and potentially most troublesome phase in the process to build up an effective reduction regime.
Unilateral actions appear in many areas of international society. Unilateral reduction of armaments, unilateral aid to developing countries, unilateral reduction of trade sanctions or increases of trade concessions, and in the field of transboundary pollution problems, unilateral cut back of emissions. Unilateral actions to alleviate IEP have been analysed in e.g. Hoel (1991), Barrett (1990). A rather pessimistic result emerges in both. Barrett (1998) summarizes the general impression: Leadership of this kind is seldom rewarded.In the model of Hoel (1991), two countries play a non co-operative game each maximizing net-benefit from reducing environmentally harmful emissions. One country, however, also cares about the emission reduction in the other country. This is modelled by introducing a function containing non-economic variables. The argument for such unilateral actions is that they at least give a contribution in the right direction, and also that by setting a good example of this type one might affect the behaviour of other countries, and/or improve the changes of reaching international agreements of co-ordinated reductions of harmful emissions. The main findings in Hoel’s paper are that unilateral actions will at its best reduce the overall emission level (but with less than initiated by the unilateral actions itself), but at worst actually increase total emission. Hoel (1991) concludes that: ‘it might not be particularly sensible for an environmental group in a country to try to force its government to unilaterally reduce the countries emissions’ (p. 69).
Hoel (1991) mentions that ‘setting a good example’ is the reason for unilateral actions without explicitly modelling how such a setting a good example could be accomplished. In the current paper unilateral actions are re-formulated not as setting a good example, but rather as transmitting relevant information. The analysis is done in two parts. The first part serves two main purposes: To introduce private information into the model of Hoel and set-up the signalling model and to show that Hoel’s result carries over to this situation as well. This model gives a hint to what is needed in order for unilateral actions to be profitable: In order for unilateral actions to work it must somehow transmit information that directly alters the position of the reaction functions of the other countries. From this model it is possible to point to under what conditions unilateral actions are most likely to be profitable. In particular, compared to the original model of Hoel, we need the two following modifications: First, in order to more precisely understand the way environmental policy is determined in a country, it is assumed that the decision of the level of environmental regulation in a country is determined by the lobby activity of two pressure groups in a country: An industrial group lobbying for no reduction and an environmental group lobbying for high reduction. The more pressure a group exerts, the more it influences the policy outcome. The observation that the political process in a country is polymorph is analysed in e.g. Dijkstra (1999), on basis of an influential function. Secondly, we change the information-structure such that that costs are uncertain, but fully correlated between countries. Next a country can be privately informed about the costs, and can try to convince the other countries that costs are low. If it succeeds, the other countries will increase their reductions. Our signalling approach resembles the idea of 'leading by example', analysed in Hermalin (1998). Here the leader is defined on basis of being better informed, and has to undertake some costly effort to convince the others that effort is worthwhile undertaking. Huber (1998) discusses the idea of making a costly information gathering activity in order to become (privately) informed.
The results are that unilateral actions are more likely the larger the response and the higher the correlation, in both cases implying that the actual level of unilateral action is smaller. Equally important, though, the more likely that unilateral actions will be initiate, the lower the estimated costs of getting informed, the larger the expected response, the higher the expected correlation. The curse of the country that initiates the unilateral action is that since the country with the highest estimate will initiate the unilateral action, this country is likely to over-estimate the actual response. Without putting too much emphasize in unilateral actions should not from the outset be disregarded as a policy options as one gets the impression from Hoel (1991).
2. Model
First, a model of an international environmental problem that resamples the original specification of Hoel will be presented. This will enable us to use Hoel’s model as a benchmark and his results as a point of departure for further analysis. The set of countries is . Each country emits ei, which causes environmental degradation both domestically and abroad. For simplicity, assume a global emission problem. Hence, each country is affected by the total emission level . Let the emission level in case of no environmental concern at all be . Hence, and define , the set of emission levels. Compared to , a country might undertake certain reduction effort. Let be the actual reduction level of country i. Due to the global pollutant assumption, it is the total reduction level is relavant for a country’s reduced level of environmental degradation .
measures the benefit to country i from total reduction, q. The benefit is derived from reduced damages from controling emission. On the other hand, costs from controlling emissions only depend on own reductionss, qi, and is measured by . We make the standard assumptions: on the functions that and while and . Hence, the net-benefit to country i from own and total reduction efforts amounts to:
/ (1)If each country behaves non co-operatively, it maximises its own net-benefit function with respect to its own reductions, qi, considering only damages in its own country but not those abroad, or alternatively, not considering the public good character of its own reduction effort on the other countries’ well being. Formally, the definitions of the non co-operative levels of reductions are: , where .[2]As done throughout the literature, assume that in case: of no coordination, these levels will result.[3]
The first order condition (for country i) is obtained by differentiating (1) with respect to own reduction and taking the other countries reduction, q-i for given:
.
Define the best reply function, or the reaction function of country i, as the function that relates the optimal choice of country i to the choice of reduction of the other countries . The slope of this function is determined as .[4]
Since we have that . Moreover given the assumptions on the benefit and cost functions, there exists a unique (and interior) Nash-equilibrium given by at the intersection of the reaction curves.[5]
One immediate question arises, how to define a unilateral action, since movements away from Nash are not a self-enforcing move. In Hoel (1991), this is done by introducing a function in which case a unilateral action by country i is defined as a situation in which country i plays the game as if it has the payoff function where h>0 although its true net-benefit function is . Hoel stresses that h is not a choice variable. Let us generalize Hoel’s definitions. Consider the following situation. Two countries play non-cooperatively, i.e. . Then at some point in time country 1 deviates by playing , since choices are simultaneously, country 2 continues to play . In the next period country 1 again chooses , while country 2 chooses its best reply to , namely . From this point on, the two countries play (, ). However, in order to simplify, we make the assumption that a unilateral action is immediately meet by optimal response of country 2. A Nash equilibrium consists of two requirements, the first being the best reply property, and secondly the consistency of beliefs. Define as the expectation of country i about choice of the other countries.
Definition:Unilateral action:
/ (2a)(2b)
(2c)
In this way, we have that (,) is a self-enforcing (equilibrium) point, since the country that makes the unilateral action anticipates the response of its opponents. 2c says that country i is fully aware of the consequences of its move. Since it does correctly anticipate the reaction of the other countries, and still chooses , it has no reasons to deviate.
Given the definition given above, it is easily determined what happens in Hoel’s case. Since reductions are strategic substitutes, i.e. , any unilateral increase in reduction by one country will be replied by a decrease in reduction by all other countries. This is illustrated, in a two-country version, in figure 1.
Figure 1: An unilateral increase in reduction by one country will be replied by a decrease in reduction by the other country.
Although total reduction might be increased by a unilateral move, it does not seems to be a good idea for country i to engage in unilateral actions, as long as its aim of setting a good example will be strategically exploited by its opponents. No rational country will ever find it worthwhile undertaking unilateral actions given this model set-up.
Now, it is time to look at the way the costs influence the Nash-equilibrium. First of all, in appendix 1, it is shown that
and / (3)The intuition behind (3) is that increased costs of country 1 leads to less reduction by country 1, which increases the marginal benefit of country 2 of the same level of reduction, and, hence, this country will reply by increased reduction effort.
Next, private information about reduction costs is introduced. The main purpose of this section is to show how to determine an expected (or Bayesian) Nash equilibrium and how revelation of information can result in changes in reductions of the other country. This model serves as a (benchmark) framework for the following, focussing exclusively on the effect stemming from information transmission.
Since this point of the analysis mainly is used for expositional purposes, assume for simplicity two countries, denoted country i and country j, with net benefit functions described by (1). Both countries have private information about a cost parameter (a shift parameter). Assume a two cost situation; with probability i and with probability (1-j), where iis country i’s belief about the other countries cost, i=1,2. Each country knows its own cost-parameter, and on basis of the beliefs, each country can calculate the expected value of its opponent’s cost-parameter, denoted . Therefore the derivation of the reaction functions is straightforward.[6] The reaction functions are given by where is country i’s expectation about the choice of its opponent’s output choice. For convenience, the reaction functions are rewritten as , where is a vector of beliefs. The Nash equilibrium is given by .
Most importantly, it follows from (3)[7], that
and / (4)These two derivatives form the basic incentives in this paper. If country i can reveal its costs as high, then this will trigger a higher reduction of country i in return as illustrated in figure 2A. It follows, however, from (2) and (3) that although revelation of costs can increase the response of the other country, we cannot in this set-up have that both non-coordinated increase their reduction. To see this, suppose that country i can report verifiable information about ci costlessly to country j. If its costs are high, then due to (3), it is optimal for country i to reveal its costs. Given this, if it does not reveal that it has high costs, it will certainly perceived as having low costs, and a low cost type can as well verify truthfully.
Figure 2a / Figure 2bIf country i’s costs are revealed ad high, then the new Nash equilibrium is given by point A in figure 2A (in figure 2, country i=country 1). Now look at figure 2B, where it is shown that country 1 prefers A to . But this is not the end of the story, though. The low cost country has the same incentives as the high cost country to try to persuade the uninformed party that costs are high. So in order for the high cost type to be perceived as having truly high costs, must engage in an action that perfectly distinguishes it from the shadow of the low cost country. The appropriate way to analyse this is by use of a signaling game model.
Next we assume that although it becomes common knowledge that this country is now completely informed about costs, there exists no verification technology, the reason being that no matter the true state of costs, the informed country always has a strong incentive to announce that costs are low. The only way a country can convince the relevant parties that it has high costs, is by engaging in a unilateral deviation from non-cooperative optimum by such an amount that only a country with high costs will find worthwhile undertaking.
Define as the net benefit for country i from playing qi, and the optimal response from country j, given country i’s type. Since country j’s response is solely determined by its estimate of country i’s type, it is more convenient to write . Moreover, let and be the full information maximizer of NBi for the low costs and the high cost type, respectively. Note that , see figure 3 for an example.
As usual for dynamic games, the timing of the events is all-important, and in the analysis here the order of events is as follows: Nature draws a (common) type from the set {L, H}, according to a probability distribution (, 1-) where =prob (=H). Then the informed country, denoted country i, chooses a reduction level qiQi. The other country, country j, observes qj, but not , and chooses its reduction level qjQj. Payoffs are given by and .
Sequential equilibrium
Throughout this paper we restrict attention to pure strategy equilibria. In this case there are two different kinds of equilibria; separating equilibria, where each type sent different signals, and pooling equilibria where the two types sent the same signal. Since our analysis focuses on the prospects of unilateral actions, we will focus exclusively on sequential separating equilibrium, or more precisely, we are interested in the condition for a separating equilibrium to exist and especially, the conditions for a low cost country to successfully reveal itself.[8] In a separating equilibrium, the receiver can perfectly infer the type of the sender. Formally, a collection of reduction levels and beliefs forms a sequential equilibrium if the following conditions are satisfied:
i) Optimality for the country with costs :
ii) Beliefs are Bayes-consistent:
a)
b)
c)
After observing qi, the receiver must form a belief about which types could have sent qi. These posterior beliefs are denoted (qi) with (Lqi)+(Hqi)=1. The first requirement of strategies that form a sequential equilibrium is sequentially rationality, which amount to say that for each qi, qj must maximise expected payoff, given the beliefs. Regarding the optimality of beliefs, if and the receiver e.g. observes , then it most be that costs are high, and the only consistent belief is and given this belief, it is optimal for the high cost type to play . In this particular signaling game the requirement of consistency of beliefs does not place any restrictions on beliefs following out-of-equilibrium signals, i.e. any beliefs are admissible if an out-of-equilibrium outcome is observed.