# Impacts of Emission Reduction Policies in a Multi-Regional Multi-Sectoral Small Open Economy with Endogenous Growth

Abstract: The burden sharing of pollution abatement costs raises the issue of how to share the costs between entities (country, region or industry) and how the pollution permits should be distributed between the parties involved. This paper explores this issue in the framework of a dynamic endogenous growth 2 sectors - 2 regions - 2 inputs Heckscher-Ohlin model of a small open multi-regional economy with an international tradable permits market. Given an emission-based grand-fathering sharing rule, capital accumulation is more negatively affected by the environmental policy in the energy intensive sector. We show that such a property does not necessarily hold with a production-based grand-fathering sharing rule. We also show that the impact on capital is likely to translate into the sectoral added value level after some time, specially if the economy is submitted to an increasingly constraining environmental policy driving up the ratio price of permits to price of energy. Finally, we show that the impact of environmental policy at the regional level depends crucially on the specialization of the region along the baseline.

## Summary (3 min read)

### 1 Introduction

- The burden sharing of pollution abatement costs, e.g. in the Kyoto Protocol context, raises the issue of how to share the costs between entities (country, region or industry) and how the pollution permits should be distributed between the parties involved in the Protocol.
- One region is more specialized in the energy intensive sector.
- For a given sector, there are technological spillovers from one region to the other.
- Conditions are established under which the spread of specialization, that depends on the initial capital endowments and on the technological spillovers, might be reversed.

### 2 The model

- Given that the authors consider a small open economy, agents are price-takers and prices are determined by the Rest of the World and thus exogenous.
- Sector a produces capital goods, sector b produces consumption goods.
- National and foreign products of a certain type are supposed to be perfect substitutes.
- Emissions are linked to energy consumption, and for the sake of simplicity, e denotes simultaneously energy and emissions.

### 2.2 Endogenous growth and technical spillovers

- There is thus a interregional technological spillover at the sector level.
- The authors shall use this observation in some interpretations later on.
- Notice that ωjt is asymptotically geometric with coefficient θj 2−θj < 1, which implies that limt→+∞ ωjt = 0. ¤ This strong result follows from the fact that besides different initial sectoral dotation of capital, the two regions are identical : they face the same international prices and share the same technologies.
- In the presence of intra-sectoral spillovers, the divergence force coming from endogenous growth (namely, constant returns) is neutralized.

### 2.3 Specialization of the regions

- The authors also define the spread of specialization index at time t by the ratio of the specialization indexes of the two regions : σt = χwt χvt = kwat kwbt kvbt kvat.
- The purpose of the present subsection is to study what determines the evolution of the regions’ specialization through time.
- One observes the remarkable fact that the spread of specialization index depends only on the initial stocks of capital and on the spillovers parameters that are exogenous.
- As a consequence this index will not be affected by the environmental policies that are considered below.
- The authors have indeed the following proposition : Proposition 2.

### 3.1 Preliminaries

- The authors assume that the baseline tends in the long run to a balanced growth path characterized by the asymptotic constant growth rate g that applies to both sectors.
- As the authors aim to compare the impacts of an environmental policy (EP) between sectors and between regions, they state the two following important assumptions : 2This implies that in the long term (i.e. when the sequences are close to their limit values θj (j = a, b)) the ratio θb/θa is high enough.
- Then a remarkable fact is that the previous inequality cannot be satisfied whatever the spillover parameters (inversion of specialization is impossible).
- In a next subsection, the authors will also briefly consider a ”production-based grand-fathering” sharing rule in order to highlight how results can depend crucially on the chosen endowment rule.

### 3.2 Impact on the sectoral growth rates

- 5This could be justified if the rule applies at an aggregate level and if the firm is small and receives a fixed share of the total permits endowment.
- This is because the sectors j of both regions face the same exogenous prices and share the same technologies.
- The growth rate of the energy intensive capital sector a is more affected by the EP than the accumulation capital of the other sector if the endowment effect relative to sector a is not higher than the one relative to sector b.

### 3.4 The dynamic production-based grand-fathering rule

- To highlight how results depends crucially on the chosen endowment rule, let us consider briefly the dynamic production-based grand-fathering rule, where a firm’s current permits endowment depends on its previous period production6.
- The authors assume that this dependance is identical across sectors and regions and that it is internalized by firms when they maximise their profits.
- Because of assumption (33), the second term between brackets of the RHS is lower for sector a.
- But if pbt is increasing (as is observed empirically), then the first term between brackets of the RHS is lower for sector b, and the overall effect is undecidable without more information on the parameters.
- Configurations of parameters are possible where one obtains the opposite effect as the one obtained with the emission-based grandfathering rules analyzed above, i.e. with equality (39) is reversed (for example if the consumption good price increases sufficiently quickly because of a low exogenous technical progress ρt).

### 3.5 Impact on the sectoral added value

- In the remaining of the paper the authors return exclusively to the emission-based grand-fathering rules because they lead to more clear-cut conclusions.
- The second one measures the impact on the regional sectoral capital stock analyzed in the previous subsection.
- Indeed, because of the increase of total cost of energy, its share arises in the value of production.
- And this effect is stronger the higher βj.
- The above proposition is likely to be verified 14 in the case of a more and more constraining EP.

### 3.6 Impact on the sectoral revenues with transfers

- Let us first consider the non anticipated emission-based grand-fathering sharing rule.
- In this last equality appears sector j’s growth rate characterising the EP scenario.
- The inequality (49) necessarily holds after some time.
- Then the above proposition follows again by a similar reasoning.

### 3.7 Impact on the regional product

- In subsection 3.5, the authors have checked that vaijt vaBijt does not depend on i and that the inequality vaiat vaBiat < vaibt vaBibt is likely to be verified.
- There should not be any inversion of specialization at date t w.r.t. date 0. Now Proposition 2 states the conditions for a specialization inversion.
- This implies that in the long term, i.e. when the sequences are close to their limit values θj (j = a, b), the above inequality implies that the ratio θb/θa is low enough.
- This implies that in the long term, i.e. when the sequences are close to their limit values θj (j = a, b), the above inequality implies that the ratio θb/θa is high enough.
- If kwa0 − kva0 > 0, the regions have opposite specializations (i.e. kwa0 > kva0 and kwb0 < kvb0), then a remarkable fact is that the above inequality is necessarily satisfied whatever the spillover parameters.

### 3.8 Impact on the regional revenues with transfers

- 7Remember that the spread of specialization index is not modified by the environmental policy.
- In the previous subsection, the authors have checked the conditions ensuring that the inequality riat rBiat < ribt rBibt is verified.

### 4 Conclusion

- The model presented in this paper has been designed to study the burden sharing of pollution sharing in the context of a Kyoto-like protocol in a multi-regional multi-sectoral economy.
- In order to get the dynamic picture, the authors have considered time-dependent intrasectoral spillovers across regions and learning-by-investing in each sector.
- In such a context, the authors have shown progressively how the typical wisdom gathered for the static case can be altered.
- In particular, the authors have disentangled the main price-based and quantitybased mechanisms which determine the impact of environmental policy at different levels (sectoral value-added and regional notably).
- Nonetheless, a much more serious quantitative assessment is needed, and this would require a rigorous calibration of the model, including the exogenous price processes involved.

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##### Frequently Asked Questions (2)

###### Q2. What are the future works mentioned in the paper "Impacts of emission reduction policies in a multi-regional multi-sectoral small open economy with endogenous growth∗" ?

The model presented in this paper has been designed to study the burden sharing of pollution sharing in the context of a Kyoto-like protocol in a multi-regional multi-sectoral economy. In such a context, the authors have shown progressively how the typical wisdom gathered for the static case can be altered.