How does the design of international environmental agreements affect investment in environmentally-friendly technology?

In this paper, we investigate how the design of international environmental agreements (IEAs) affects the incentives for the private sector to invest in environmentally-friendly technology. The givens are a transboundary pollution problem involving two asymmetric countries in terms of benefits arising from global abatement. There is a single polluting firm in each country. We account for two types of IEAs: an agreement based on a uniform standard with transfers and an agreement based on differentiated standards without transfers. To carry out this study, we use a two-stage game where the private sector anticipates its irreversible investment given the expected level of abatement standards resulting from future negotiations. Our findings indicate that the implementation of the agreement based on a uniform standard with transfers may be preferable for the two countries, as it creates greater incentives for firms to invest in costly abatement technology. This result arises when this technology’s level of the sunk cost of investment is low. If this level is sufficiently high, the implementation of the same agreement is not beneficial to countries, because it takes away the incentive of each firm to invest in new abatement technology. Moreover, this agreement is not able to generate any positive gains for either country through cooperation, thus no country is motivated to cooperate.


Introduction
A study by the Organization for Economic Cooperation and Development (OECD, 2005) points out that " clear and concrete objectives and targets under multilateral environmental agreements (MEAs) create a framework within which the business sector can both align its practices with MEA goals and seize new business opportunities. Some MEAs include clear objectives, e.g., those established under the Montreal and the Kyoto Protocols. Most MEAs, however, have general objectives, which cannot always be easily translated into concrete action by the private sector..." (6). There is a need to design IEAs that incites the business sector to undertake environmentallyfriendly action. In this paper, in the context of a transboundary pollution problem out at the international level to focus on either technological change or adoption (Buchholz and Konrad (1994), Golombek and Hoel (2006), Muuls (2004)). Buchholz and Konrad (1994) have studied the choice between two abatement technologies in a two-stage game for two countries. 2 To our knowledge only Golombek and Hoel (2006) have analyzed the impact of the design of IEAs on the investment in technological change. The authors consider the case of (n) identical countries having (m) number of identical …rms each. They mainly compare two types of IEA in the presence of technology spillovers across countries: a tax agreement and a quota agreement. They show that, given the tax agreement, the outcome cannot be a …rst-best optimum because the level of the technology subsidy for investment in R&D is low. Countries 1 The Kyoto Protocol on Climate Change also includes di¤erentiated standards, however, there is a debate over whether or not it is solely a D or otherwise DT agreement. Chander et al. (2002, p.113) have pointed out that the system of marketable emission permits and the clean development mechanism may very well constitute the equivalent of monetary transfers. 2 Buchholz and Konrad (1994) show that it is individually rational for a country to choose a costly abatement technology to increase its bargaining position. This manifests via an increase in the payo¤ of the country at the threat point. This result arises from two assumptions. First, the investing …rm and the government which conducts negotiations are considered as a sole identity. Secondly, the negotiating countries are assumed to be identical. Contrary to that approach, in our model, the country and the …rm are decentralized agents in the economy, the choice of abatement technology by …rms is endogenous, and the objective of a …rm is to minimize its abatement costs. Therefore, in our case, …rms always have an incentive to select the technology which reduces its future marginal abatement costs.  (2002)). In the case of IEAs, a hold-up problem may occur if countries are willing to capture the bene…ts of their …rms-which undertake an investment in new abatement technology-by imposing more stringent international abatement standards on them. By anticipating this, the …rms could prefer not to make the initial investment. Given the assumptions made by Muuls (2004), that (i) the governments can commit to issue marketable permits and (ii) there is a single Nash bargained agreement, the hold-up problem does not appear.
In this paper, we investigate what would happen if countries were able to choose the design of their agreements and under which conditions the hold-up problem would appear. To do so, we use a two-stage game with two highly asymmetric countries in terms of their bene…ts from global abatement: one environmentally-conscious country (ENCC) and a less environmentally-conscious country (LENCC). This terminology is adopted from Petrakis and Xepapadeas (1996). For the sake of simplicity, we assume invest both in the LENCC and in the ENCC. The idea is the following: given that the …rms have invested in new abatement technology, the negotiated level of the uniform standard will be higher, which is more costly for the …rms. By anticipating this, the …rms prefer not to invest. It is the fear that the countries will create a hold-up problem that induces the …rms not to invest in costly abatement technology.
Hence, we show that, contrary to the …ndings of Muuls (2004), some Nash bargained agreements cannot solve the problems of absence of investment by the private sector. that a D agreement will be negotiated in the future, the …rm of the LENCC prefers not to invest. Then, the governments negotiate a D agreement, which is also a Pareto optimal solution. We do not deal with the question entailing the analysis of the formation of anticipations for each …rm, as it is well beyond the scope of this paper.
We just aim to highlight that the anticipation of the type of agreement leads to investment behavior by …rms, which in turn a¤ects the type of the agreement which will be e¤ectively negotiated in the future.

Agents in the Economy
There are two countries and two …rms in this economy, with a single …rm in each country.

Countries
The two countries negotiate two agreements: an agreement on a uniform standard with transfers (UT) or an agreement on di¤erentiated standards without transfers (D). More speci…cally, they bargain over the levels of standards and transfers (A and A in agreement D, A and t in agreement UT).
The payo¤ functions (net bene…t) of the ENCC and the LENCC are written, respectively, as follows: where A (resp. A ) represents the negotiated level of the abatement standard of the ENCC (resp. LENCC) with A 1 (resp. A 1), x (resp. x ) is the …rm's decision to invest in the ENCC (resp. LENCC), expressed in a binary way This implies that the marginal damage constantly decreases with the level of the total pollution. The use of a quadratic bene…t function allows us to take into account the interaction between countries su¤ering from a global pollutant.

Firms
The …rms decide to invest (x = 1) or not (x = 0) in new abatement technology. technology. 5 Concerning the functional forms, we assume that the abatement cost function is increasing and convex in the case of investment in new technology, i.e., In order to capture this idea, we choose a simple speci…cation for abatement cost functions: where x = 1 (resp. x = 0) represents the decision (resp. the absence) of investment 5 The results of our model do not change if we consider di¤erent quadratic and linear abatement cost functions for both …rms. In fact, we focus on the situations "incentive uniform standard" and "disincentive uniform standard"in terms of the decisions by the private sector to invest (see Section 3.2). In this case, the only change is that the negotiated uniform standards when only the …rm of the ENCC or the LENCC invests are no longer identical. This implies that we should add an additional condition to the conditions of emergence of the two situations "incentive uniform standard" and "disincentive uniform standard."This will only change the interval of the values of F in which these two situations occur.

Timing of the Game
A two-stage game within a perfect information environment has been conceived. If this is a UT agreement, they negotiate the levels of the uniform standard ( A) and the transfer (t).
Finally, the single …rm in each country abates according to the abatement burden imposed by the agreement (i.e., according to what has been negotiated at stage 2 of the game). We implicitly assume that the …rm in each country completely complies with these regulations. 6 This requires the assumption that the governments are able to commit to the stringency of a penalty for the …rm which does not respect standards. 7 If the governments could not enforce the abatement standard, the best response of a cost minimizing …rm would be not to abate at all, and ex ante, not to invest in new abatement technology.
It is worthwhile noting that there is an interaction between stages 1 and 2. The It is also important to note that we implicitly assume that the abatement decision of a …rm is independent of its decision on production. This property holds for a speci…c class of clean-up technology called "end-of-pipe"which represents the majority of all abatement technology currently used by …rms. 8 month. 7 For instance, participating in the system of emissions trading in the European Union is mandatory for some sectors. The system charges 40 euros per tonne of CO2 for the emissions in excess of the amount stipulated in permits. 8 Skea (2000) reports that the proportion of end-of-pipe technology in pollution control investment is 80% in Belgium, 82% in Germany and 87% in France. In order to calculate the outcome of negotiations, we must …rst de…ne the payo¤ levels at the threat point. 9 In fact, this assumption does not a¤ect our results. If we posit that each country has a di¤erent negotiation power de…ned by the parameter for the ENCC and (1 ) for the LENCC, the …rstorder conditions of the programs corresponding to di¤erent negotiation situations would not di¤er. This implies that the expressions of the negotiated abatement standards would be the same as those in the initial case. The only change concerns the share of the gains of cooperation between the two countries, weighted by the value of the parameter : But, since the relative negotiation powers of the countries are the same for agreements UT and D, this does not modify the comparison of these agreements. 10 The fourth situation in which only the …rm of the LENCC invests, x = 0 and x = 1; is highly impossible. We show this impossibility for a small value of , in the neighborhood of = 0 (available on the author's website: Appendix A4 ).

Nash Equilibrium
We assume that the countries choose Nash equilibrium strategies when they do not cooperate. At the Nash equilibrium, we implicitly assume that the investment is determined prior to abatement. The objective of the ENCC is to maximize its payo¤s, taking the abatement level of the LENCC, A ; as follows:

Negotiation
We call A; A and A respectively the di¤erentiated standard of the ENCC, the differentiated standard of the LENCC, and the uniform standard.
The Nash bargaining solution is as follows: Note that the payo¤ of each country at the Nash equilibrium depends on the decisions by …rms to invest in new abatement technology. This program corresponds to the agreement on di¤erentiated standards with transfers (DT), with the largest number of negotiation variables A; A ; t. 12 The given agreements, agreements UT and D, imply the following constraints: Agreement D: t = 0:

Comparison of the Levels of Negotiated Standards
We compare the negotiated levels of di¤erentiated standards with the negotiated level of the uniform standard. 13 12 We study , in an extension, the implications of this agreement (see Section 4). 13 The …rst-order conditions indicate that the negotiated abatement levels are independent of the level of sunk cost F: Even though the level of sunk cost has a crucial role in the investment decision of the …rms, it does not a¤ect the negotiated abatement levels because, in the timing of the game, the levels of abatement standards and transfers are negotiated after the investment decision of the private sector, and the abatement cost function is additively separable.

Stage 1: Decision of investment of the …rms
The investment choice of the …rms is analyzed according to the type of IEA.

Cost condition
The threshold abatement level for which the abatement cost of the …rm in the case of investment is identical to the one in the case of non-investment is as follows: with A 1 and 1 2F 0 () F given that the …rms have invested in new abatement technology, the countries agree on higher levels of abatement standards. These high-level standards could make …rms worse o¤ compared to a situation of non-investment. Hence the …rms might decide not to invest.

Two decision-making situations: "incentive uniform standard"and
"disincentive uniform standard" We focus on two situations for which the equilibrium is unique. The …rst situation is the "incentive uniform standard"and the second one is the "disincentive uniform standard." We de…ne an incentive uniform standard (resp. a disincentive uniform standard) as the situation in which all the …rms …rst invest (resp. no …rms invest) because they correctly anticipate that an agreement based on a uniform standard with transfers will be negotiated in the future. Then, the countries negotiate the levels of the uniform The "incentive uniform standard" (resp. "disincentive uniform standard") is a situation where the implementation of the uniform agreement with transfers gives an incentive (resp. takes away the incentive of) to both countries to invest, whereas the implementation of the di¤erentiated agreement without transfers would induce only the ENCC to invest, in which case the implementation of the uniform standard has a higher (resp. lower) incentive e¤ect (x = x = 1) (resp. x = x = 0) than those of di¤erentiated standards (x = 1 and x = 0): The conditions of existence of the incentive uniform standard are the following: 1) The …rm in the LENCC does not invest in the agreement based on di¤erentiated standards without transfers. This requires a condition which ensures that it is not bene…cial for the …rm in the LENCC to deviate, i.e., that it is bene…cial for this …rm to stick to the decision of non-investment: 2) The …rm in the ENCC invests in the agreement on di¤erentiated standards without transfers. This requires a condition which ensures that it is not bene…cial for the …rm in the ENCC to deviate, i.e., that it is bene…cial for this …rm to stick to the decision of investment: C(A j x=1;x =0 ) < C(A j x=x =0 ): 3) The …rms in the ENCC and the LENCC invest in the agreement based on a uniform standard with transfers: The …rst two conditions of existence of the incentive uniform standard case also hold for the disincentive uniform standard case. The following condition allows us to distinguish between the two cases: 3bis

Welfare of Countries
The countries optimally choose the type of IEA. Optimality is de…ned according to the Pareto concept. This means that the individual welfare of a country in the optimal agreement must exceed the one in the alternative agreement, and the other country must obtain at least the same amount of individual welfare as in the alternative agreement. 17

Proposition
In the case of very asymmetric countries (small ), the implementation of the agreement on a uniform standard with transfers is either: A) optimal for each country if the level of sunk cost is su¢ ciently low ( F low) and if the marginal bene…ts from global abatement are su¢ ciently high ( b high), in which case it is the incentive uniform standard; or B) not optimal for a higher level of sunk cost ( F high), in which case it is the disincentive uniform standard. 16 When the countries are identical ( = 1), in fact, the type of IEA does not a¤ect the decisions of the …rms to invest, because the levels of di¤erentiated standards are the same, thus the standard is uniform. Furthermore, we know that the national …rms have, by de…nition, the same set of possible abatement technology. Under these givens, the implementation of standards (no matter whether di¤erentiated or uniform) leads either to the absence of investment or to full investment by all the …rms, according to the level of sunk cost of investment. 17 Proof is available on the author's website: Appendix D. As regards Proposition B, our …ndings indicate that the implementation of a UT agreement is no longer bene…cial for the countries if the level of sunk cost is su¢ ciently high. In this case, the implementation of the uniform agreement takes away the incentives of the two …rms to invest. The idea is the following: given that the …rms have invested in new abatement technology, the negotiated level of the uniform standard will be higher, which is more costly for the …rms. By anticipating this, the …rms prefer not to invest. It is the fear that the countries will create a hold-up problem that induces the …rms not to invest in costly abatement technology. Moreover, the implementation of this agreement is not able to generate positive gains for each country through cooperation. However, if the sunk of investment in new abatement technology is low, to give incentives to get its …rm to invest in this technology, it is better for the less environmentally-conscious country to negotiate a future agreement based on a uniform standard with a side payment scheme.
In this model, the …rms are the driving force behind the investment in environmentallyfriendly technology, pushing governments to design agreements accordingly. 18 Luken and Grof (2006, p.4) report that "production and consumption of CFC's, halons and other ozone depleting chemicals has been almost completely phased out in industrialized countries." 19 As reported by Barrett (2003, p 20 We have also veri…ed the renegotiation-proofness of the di¤erent negotiations that take place in stage 1 of the game. Thus, individual countries do not have an incentive to deviate from a UT agreement, when both …rms invest in new abatement technology (incentive uniform standard). are the driving force behind the investment in environmentally-friendly technology, pushing …rms to invest according to ex ante negotiated agreement, given that the sunk cost of investment in abatement is su¢ ciently low.
(2) Agreements based on di¤erentiated standards with transfers are not frequently observed in reality and there is even a lack of consensus when an agreement is labeled as such, as in the case of the Kyoto Protocol (see footnote 1). However, for the sake of thoroughness, a DT agreement should not be overlooked. How would the implementation of the agreement based on di¤erentiated standards with transfers a¤ect the decisions of the …rms to invest?
We again focus on the case of very asymmetric countries. 21 Our …ndings imply that this agreement could give incentives to both …rms to invest, contrary to the agreement based on di¤erentiated standards without transfers. Transfers compensate the abatement e¤orts of the LENCC, therefore its negotiated abatement standard is

Conclusion
We have shown that the type of IEA may incite …rms to invest in new environmentallyfriendly technology. This has been achieved through a two-stage game in which …rms …rst anticipate their irreversible investment before two-government negotiations on the environment take place. We have focused on two situations for which equilibrium is unique: the incentive uniform standard and the disincentive uniform standard.
Each of these situations correspond to a set of values of the parameters of the model.
If …rms anticipate that the D agreement will be negotiated in the future, then only the …rm in the environmentally conscious country invests in new abatement technology. If …rms anticipate that the UT agreement will be negotiated in the future, then both (resp. no) …rms invest, provided that the level of the sunk cost of investment is su¢ ciently low (resp. high) (incentive uniform standard resp. disincentive uniform standard). In this model, the …rms are the driving force behind the investment in environmentally-friendly technology, pushing governments to design agreements accordingly. Their actions can lead to either the negotiation of the uniform or the di¤erentiated agreement. Therefore, countries should …rst give …rms enough time to invest in new technology, and then negotiate the levels of the uniform standard and the transfer, given that the sunk cost of investment is su¢ ciently low.
In this paper, in the case of highly asymmetric countries, we have focused on two situations in terms of decision to invest. A next step would be to investigate all the outcomes for less heterogenous countries.