Collaborative optimal carbon tax rate under economic and energy price shocks: A dynamic stochastic general equilibrium model approach

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Abstract

Existing literature on climate policy analysis in an international environmental agreement does not condition the optimal policy on the economic conditions of the countries. This paper constructs a two-country environmental dynamic stochastic general equilibrium (E-DSGE) model to compare the optimal carbon tax rates between countries in noncooperative and cooperative scenarios in the presence of different economic shocks. Compared to those in the cooperative scenario, countries without cooperation would have an optimal carbon tax rate that increases less in response to a positive home-country total factor productivity (TFP) shock and decreases more in response to a positive energy price shock. Further, in the noncooperative scenario, the carbon tax rate decreases in response to the foreign-country TFP shock, but to a lesser extent than that in the cooperative scenario. Countries’ cooperation does not necessarily lead to a lower emissions stock. It decreases only in response to positive home- and foreign-country TFP shocks, and it increases in response to a positive energy price shock.

Introduction

As pointed out by Hoel (1991), transboundary pollution problems can be characterized as the environmental impacts on each country from a worldwide pollutant requiring countries’ collective efforts to mitigate. There is extensive literature studying how international environmental agreements should be formulated so that the free-riding problem can be avoided. As will be reviewed below, most of the existing literature studies the international environmental agreement formation and supranational climate policy independent of the economic conditions of the countries. Indeed, recent studies find that the optimal environmental policy should be specific to the economic conditions. For example, Annicchiarico and Di Dio (2015) and Heutel (2012) show that the optimal carbon tax rate should be procyclical: it should increase during the booms and decrease during the busts. Hence, it is expected that the optimal climate policy that is jointly decided by the countries should depend on the economic environments of each country, especially for the countries whose business cycles are less synchronized. In this regard, this paper determines the optimal carbon tax rates in an international environmental agreement for countries that have different economic conditions. We construct a two-country environmental dynamic stochastic general equilibrium (E-DSGE) model that incorporates countries’ economic conditions. Our model is mainly based on the E-DSGE model by Annicchiarico and Di Dio (2015), who include environmental components in the standard DSGE model. Unlike that in Annicchiarico and Di Dio (2015) and most of the existing E-DSGE models, we focus on the policy interaction between two countries instead of studying the climate policy in a closed economy setting. The different economic conditions in the two countries can be characterized by realizations of different types of economic shocks. In particular, the total factor productivity (TFP) shocks from both countries and the energy price shock are considered in the model. The main feature of our model is that it assumes that the global emissions stock, which could hurt firms’ productivity as in Annicchiarico and Di Dio (2015) and Heutel (2012), is accumulated by the CO2 emissions from both countries. Since the social planner without cooperation would choose a carbon tax rate that maximizes the interests of its own country, the optimal tax rates in the scenarios with and without cooperation are expected to be largely different.

Our research objectives are twofold. First, we compare the optimal carbon tax rates between the noncooperative and cooperative settings in the presence of different economic shocks. Second, we examine whether an international environmental agreement could mitigate global environmental degradation under different economic shocks. Comparing the situation in which the optimal carbon tax rates are set in an international environmental agreement, we find that countries without an international environmental agreement would choose a carbon tax rate that is less procyclical in response to positive home-country TFP and positive energy price shock. Put differently, the carbon tax rate increases less and decreases more in response to the positive home-country TFP and energy price shocks, respectively. Moreover, the carbon tax rate decreases in response to a positive foreign-country TFP shock, and it decreases even more in the international environmental agreement scenario.

The reasons for the policy differences are as follows. First, with a positive home-country TFP shock, more CO2 is emitted, which would hurt firms’ productivity in both countries. Meanwhile, in the noncooperative setting, the Ramsey planner is only concerned about the social welfare of its home country, and neglects the externalities that are created for another country. The carbon tax rate would increase only to the level that is the best for the home-country’s welfare, and it should increase more for the benefits of the foreign-country firms. Likewise, when facing a positive energy price shock, the Ramsey planners in the two countries would reduce the carbon tax rate in order to maintain the firms’ profits. However, the reduction in the carbon tax rates would increase the CO2 emissions and, therefore, deteriorate the firms’ productivity. Since in the noncooperative setting the planner would neglect the negative externalities that are created for another country, it would reduce the tax rate to a larger extent. Finally, when there is a positive foreign-country TFP shock, the noncooperative Ramsey planner would choose to decrease the carbon tax rate. This is because the shock stimulates the foreign economy, which increases the global emissions stock, reducing the firms’ productivity in the home country. Hence, the positive foreign-country TFP shock induces the same effect as a negative home-country TFP shock. In this regard, the carbon tax rate would respond negatively to the shock. Put differently, the home-country carbon tax rate is countercyclical to the foreign-country business cycles. Moreover, the global (or supranational) Ramsey social planner reduces the optimal carbon tax rate even more, in order to reduce the difference of the household utilities in the two countries.

Concerning the difference in the environmental consequences between the noncooperative and cooperative scenarios, it is shown that the emissions stock is not necessarily lower under the cooperative scenario. It is found that international cooperation results in a lower emissions stock only under positive TFP shocks from both countries, while it would increase the emissions stock with a positive energy price shock. However, the difference in the household utilities of both countries would decrease when countries cooperate. The fact that international cooperation could lead to a higher emissions stock has been documented in the literature (e.g., Hoel (1991) and Hoel (1992)).

The remainder of the paper is organized as follows. Section 2 reviews the related literature. Section 3 presents the settings of the E-DSGE model. Then, the numerical analysis is performed in Section 4; our main findings will also be explained in the section. Finally, Section 5 concludes.

Section snippets

Literature review

One of the originalities of this paper is that it studies how international cooperation affects the optimal carbon tax rate using a two-country E-DSGE model in the presence of transboundary pollution. The E-DSGE model, which is an extension of the DSGE model that is a standard tool in the macroeconomic literature, was first proposed by Heutel (2012) and Fischer and Springborn (2011). The terminology ’E-DSGE’ model was first introduced in Khan et al. (2019) to refer to the emerging literature.

Model

This section presents a two-country environmental dynamics stochastic general equilibrium (E-DSGE) model. On the household side, each country is populated by a continuum of identical households. Each of whom derives its utility from consumption and leisure, and makes dynamic consumption and saving decisions. On the production side, the final output is made of capital, labor, and energy. Capital and labor are supplied by household, while energy is imported, with the energy price that is

Choice of parameters

In this section, we discuss how the values of the model parameters are chosen. Since our model setting is extended from Annicchiarico and Di Dio (2015), we thus heavily based our parameter choices on their works. Table 1 summarizes the parameter values that are used for calibration. In the model, it is assumed that each period is a quarter.

On the household side, we set the discount factor β to be 0.99, which implies that the (quarterly) discount rate is approximately 1% (1/(1+1%)0.99). As in

Conclusion

This paper solves the optimal carbon tax rates for countries that are with and without an international environmental agreement and under different economic conditions. There are two objectives of the paper. First, we study whether and in what situations international cooperation could reduce the global emissions stock. Second, we investigate how different the carbon tax rate would be in scenarios where countries cooperate and do not cooperate.

To answer the above questions, we extend the E-DSGE

CRediT authorship contribution statement

Ying Tung Chan: Writing - original draft.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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