Why Finance Ministers Favor Carbon Taxes, Even If They Do Not Take Climate Change into Account

Abstract

Fiscal considerations may shift governmental priorities away from environmental concerns: finance ministers face strong demand for public expenditures such as infrastructure investments but they are constrained by international tax competition. We develop a multi-region model of tax competition and resource extraction to assess the fiscal incentive of imposing a tax on carbon rather than on capital. We explicitly model international capital and resource markets, as well as intertemporal capital accumulation and resource extraction. While fossil resources give rise to scarcity rents, capital does not. With carbon taxes, the rents can be captured and invested in infrastructure, which leads to higher welfare than under capital taxation. This result holds even without modeling environmental damages. It is robust under a variation of the behavioral assumptions of resource importers to coordinate their actions, and a resource exporter’s ability to counteract carbon policies. Further, no green paradox occurs—instead, the carbon tax constitutes a viable green policy, since it postpones extraction and reduces cumulative emissions.

Appendices

Appendix 1: Calibration and Implementation of Model

We assume that resource-importing countries are characterized by the same economic parameters. The model should apply to countries with comparable endowments and production technologies, which compete on international capital markets. These could be member states of the EU, or China and the USA. Each resource-importing country’s initial endowment of public and private capital is given by the same share of the initial global endowment. Table 5 summarizes the parameters used in the model. If not otherwise indicated, we have chosen their values in accordance with the closely related model PRIDE,²⁴ as introduced in Kalkuhl et al. (2012), and the model comparison exercise referenced therein, Edenhofer et al. (2010).

Table 5 List of model parameters

We estimate the initial global level of infrastructure $G_0$ according the ratio of public to private fixed assets from US data published by the Bureau of Economic Analysis (BEA 2013). The tax rate on consumption of 16 % is calculated as weighted average over all countries of 2013 rates taken from data of the OECD (2014), where the respective countries are weighted according to their GDP. The average payroll tax rate of 16 % is taken from the World Banks’ world development index on labor tax and contributions (World Bank 2014).

The parameters of the production function are calibrated according to the empirical literature. We insert the elasticities of substitution between the respective factors directly. The share parameters $\alpha _i$, $i=1,2,3$ are chosen such that the observed output elasticities reported in Calderón et al. (2014), Bom and Ligthart (2013), and Caselli and Feyrer (2007) are matched.

The variation of $\sigma _1$, the elasticity of substitution between the fossil resource R and general capital $\mathbf {Z}$, is a key method to generate part of our results. In particular, results are relatively sensitive to variations of $\sigma _1$. Therefore, we have calibrated the CES production function to a specific baseline point (Klump and Saam 2008). As standard value, we choose $\sigma _1 = 0.5$, which is in line with the literature on CGE models (see for example Burniaux et al. 1992; Babiker 2001; Burniaux and Truong 2002; Paltsev et al. 2005; Edenhofer et al. 2010).

As the benchmark case for the elasticity of substitution between public and private capital, $\sigma _3$, we have implemented a value of 1.1. The empirical literature gives mixed evidence about the substitutability between public and private capital and identifies both cases of relatively high and low substitutability between the two factors. It turns out that the results presented in this paper are quite robust under variation of $\sigma _3$, cf. Sect. 3.3.

1.1 Exogenously Given Growth Rates

The productivity of labor $A_L$ and fossil resources $A_R$ are assumed to increase over time due to exogenous technological change. The parameters are chosen in accordance with empirically observed output and consumption growth rates:

$$\begin{aligned} \gamma _{\zeta ,t}&= \gamma _{\zeta ,0} e^{-d_\zeta t}\\ A_{\zeta ,t+1}&= A_{\zeta ,t}\left( 1+ (\frac{\gamma _{\zeta ,t}}{1-\gamma _{\zeta ,t}})\right) , \,\, A_{\zeta ,0} \text { given, }\\ \text {where } \zeta&= L,R. \end{aligned}$$

Appendix 2: First-Order Conditions of Representative Agents

To determine the first-order conditions, we use a maximum principle for discrete time steps as given in Feichtinger and Hartl (1986). We use their concept of the discrete Hamiltonian, which is more convenient than the equivalent formulation of the optimization problems with Lagrangians. In the following we shall use the term Hamiltonian in this sense.

1.1 Household

The household maximizes its intertemporal welfare (6) taking into account the budget constraint (7) and the equation of motion for his assets (8). Since the economic impact of a single household on the total of all profits is small, the representative household takes $\Pi ^F$ and governmental transfers $\Gamma$ as given. The Hamiltonian is given by

$$\begin{aligned} \mathcal {H}^{{\textit{HH}}}_t = U(C_t/L_t) + \lambda _t \left[ \left( 1 + (r_t - \delta )\right) K^s_t + w_tL_t + \Pi ^F_t + \Gamma _t - C_t (1 + \tau _{C,t}) \right] , \end{aligned}$$

and thus the first order and terminal conditions for the control and costate variables C and $\lambda$ are

$$\begin{aligned}&\displaystyle \frac{L_t^{\eta -1}}{C_t^{\eta }} = \lambda _t (1+\tau _{C,t}) , \end{aligned}$$

(19)

$$\begin{aligned}&\displaystyle \lambda _{t-1} ( 1 + \rho ) = \lambda _t \left( 1 + r_t - \delta \right) , \end{aligned}$$

(20)

$$\begin{aligned}&\displaystyle \left( I_T - (1-\delta ) K^s_T\right) \lambda _T = 0. \end{aligned}$$

(21)

1.2 Resource Extraction Sector

The resource owner maximizes her intertemporal stream of profits (16) taking into account the resource constraint (17), the equation of motion for the stock (13), and possibly a unit tax $\tau _{RO}$ on exports. We assume that the government of the resource-exporting country recycles the tax revenue $\tau _{RO,t}R_t =: \Psi _t$ as lump-sum transfer to the resource owner. The resource owner does not anticipate its influence on $\Psi$, but takes it as given. The Hamiltonian then reads

$$\begin{aligned} \mathcal {H}^{RO}_t = \left( p_t - \frac{r_t}{\kappa _t(S_t)} - \tau _{RO,t}\right) R_t + \lambda ^R_t (S_t - R_t) + \Psi _t, \end{aligned}$$

and thus the first-order and terminal conditions for the control and costate variables R and $\lambda ^R$ are

$$\begin{aligned}&\displaystyle \lambda ^R_t = p_t(1-\tau _{RO,t}) - \frac{r_t}{\kappa _t} , \end{aligned}$$

(22)

$$\begin{aligned}&\displaystyle \lambda ^R_t - \lambda ^R_{t-1} ( 1 + r_t - \delta ) = - \frac{r_t R_t \chi _2\chi _3}{\chi _1 S_0} \left( \frac{S_0-S_t}{S_0}\right) ^{\chi _3-1}, \end{aligned}$$

(23)

$$\begin{aligned}&\displaystyle \lambda ^R_{T-1}S_T = 0. \end{aligned}$$

(24)

Appendix 3: Solution Algorithm

We solve the model in four phases:

• Phase 1 Find good initial values.

• Phase 2 Find symmetric policy variables with Nash algorithm.

• Phase 3 Solve model with fixed policy variables to find good lower bound for investment in last period.

• Phase 4 Find symmetric policy variables with Nash algorithm and fixed lower bound for last-period investment.

To find a Nash equilibrium, we use the following algorithm:

Appendix 4: Additional Data

1.1 Extension of Table 1

Table 6 Extended version of Table 1

1.2 Data Table Corresponding to Fig. 1

Table 7 Underlying data for Fig. 1

1.3 Data Tables Corresponding to Figs. 3, 4 and 5

Table 8 Amount of fossil resources left underground at the end of the time horizon in gigatons of carbon, GtC (corresponds to Fig. 3)

Table 9 Net present value of of resource owner’s profits in trillion US$ (corresponds to Fig. 4)

Table 10 Social welfare in an importing country measured as balanced growth equivalent (corresponds to Fig. 5)

Appendix 5: Time Consistency

To check whether governments have an incentive to deviate from the tax paths they have announced at the beginning of the first period, we have performed the following experiments. First, we calculate the tax paths of two standard benchmark cases in which the governments may only use the carbon tax or only the capital to finance the infrastructure investments, $\{\tau _R\}_t$ and $\{\tau _K\}_t$, respectively. Then, we run the model again, but fixate the respective tax rate in the first n time periods to the value we have found in the benchmark case. Now, we compare the benchmark tax paths with the newly found ones $\{\widetilde{\tau _R}\}_t$ and $\{\widetilde{\tau _K}\}_t$, respectively.

Fig. 6

Governments have no incentive to deviate from the initially announced carbon tax path

For the carbon tax it turns out that governments do not deviate at all from the announced tax path (Fig. 6). For the capital tax we observe minor unsystematic deviations (Fig. 7). Measured in tax revenues, we find that on average this difference is less than 0.01 % points if $n=5$ and less than 0.26 % points if $n=10$. Here, we express the relative difference in fractions of GDP. More precisely, for each period t we calculate the difference as

$$\begin{aligned} \Delta = \frac{\tau _K r K^d}{{\textit{GDP}}} - \frac{\widetilde{\tau _K} \widetilde{r} \widetilde{K^d}}{\widetilde{{\textit{GDP}}}}. \end{aligned}$$

Fig. 7

Governments deviate only to an insignificant extent from the initially announced capital tax path