Understanding the Price Dynamics in the Jiangsu SO₂ Emissions Trading Program in China: A Multiple Periods Analysis

Abstract

Because emissions permits can be considered to be a pseudo-commodity, the permit price in the emissions trading markets has already attracted great interest from the economic literature. This research took the Jiangsu sulfur dioxide (SO₂) emissions trading program in China as a case study to examine the price dynamics over the next 10 years (2011–2020) based on Jiangsu’s new SO₂ emissions trading policy design. An adaptive agent-based simulation model was developed to estimate the price dynamics as well as the impact of energy price, policy design, and new environmental regulation on the permit price. The results showed that the equilibrium price of the Jiangsu SO₂ emissions trading market is approximately 4.20 CNY/kg, and the permit price will fluctuate around this price if the other conditions are not changed. If the coal price increases during 2011–2016, the permit price will decline to 2.79 CNY/kg by 2020 under China’s current coal–electricity price mechanism. In addition, the banking mechanism will smooth the price fluctuations and the average permit price will be generally higher when banking is not allowed. Finally, the stricter environmental regulation will reduce the market supply of permits and will raise the permit price. According to China’s potential new SO₂ discharge standard, the permit price will jump to 11 CNY/kg. The quantification of the permit price dynamics can help power plants to make decisions on emissions trading.

Appendices

Appendix 1: Marginal Profits

The representative firms’ optimization problem is:

$$ \max \pi = G{q^k}{p_e} - {p_c}q - \phi \alpha q\theta {\kappa^{{\frac{1}{{1 - {\theta^{*}}}}}}} - {p_d}\alpha q(1 - \theta ) $$

(14)

$$ {\mathrm{subject} \mathrm{to}\text{:}}\quad A - \alpha q(1 - \theta ) = 0 $$

(15)

We define the Lagrangian expression as:

$$ L = G{q^k}{p_e} - {p_c}q - \phi \alpha q\theta {\kappa^{{\frac{1}{{1 - \theta }}}}} - {p_d}\alpha q(1 - \theta ) + \lambda (A - \alpha q(1 - \theta )) $$

(16)

The necessary first-order conditions determining a maximum at (q ^*, θ ^*, λ ^*, x ^*) are:

$$ Gk{q^{*}}^{{^{{k - 1}}}}{p_e} - {p_c} - \phi \alpha \theta {\kappa^{{\frac{1}{{1 - {\theta^{*}}}}}}} - {p_d}\alpha (1 - {\theta^{*}}) - {\lambda^{*}}\alpha (1 - {\theta^{*}}) = 0 $$

(17)

$$ - \phi \alpha {q^{*}}{\kappa^{{\frac{1}{{1 - \theta }}}}}\left( {1 + \frac{{\theta \ln \kappa }}{{{{(1 - \theta )}^2}}}} \right) + {p_d}\alpha {q^{*}} + {\lambda^{*}}\alpha {q^{*}} = 0 $$

(18)

Solving Eq. 18, we have:

$$ {\lambda^{*}} = \phi {\kappa^{{\frac{1}{{1 - \theta }}}}}\left( {1 + \frac{{\theta \ln \kappa }}{{{{(1 - \theta )}^2}}}} \right) - {p_d} $$

(19)

Here, λ ^* is the Lagrangian multiplier and represents the marginal profits of a unit permit.

Appendix 2: Estimation of Future Price (p ₂)

The shadow price of the emissions permit is influenced by the price of electricity and coal. Thus, we assume that all firms estimate the future price based on the status of current emission discharge (E ₂ = E ₁). Thus, we have:

$$ \max \pi = Gq_2^k{p_{{e2}}} - {p_{{c2}}}{q_2} - \phi \alpha {q_2}{\theta_2}{\kappa^{{\frac{1}{{1 - {\theta_2}}}}}} - {p_d}\alpha {q_2}(1 - {\theta_2}) - {p_2}{x_2} - a - b\left| {{x_2}} \right| $$

(20)

$$ {\mathrm{subject} \mathrm{to}\text{:}}\quad A + {x_2} - \alpha {q_2}(1 - {\theta_2}) = 0 $$

(21)

The solution is described by the following first-order equations:

$$ Gkq_2^{{k - 1}}{p_{{e2}}} - \phi \alpha {\kappa^{{\frac{1}{{1 - {\theta_2}}}}}}\left( {1 + \frac{{{\theta_2}\ln \kappa }}{{1 - {\theta_2}}}} \right) - {p_{{c2}}} = 0 $$

(22)

$$ \lambda = \phi {\kappa^{{\frac{1}{{1 - {\theta_2}}}}}}\left( {1 + \frac{{{\theta_2}\ln \kappa }}{{{{(1 - {\theta_2})}^2}}}} \right) - {p_d} $$

(23)

$$ - {p_2}\pm b + \lambda = 0 $$

(24)

where p _c2 and p _e2 are, respectively, the estimated coal price and electricity price for the next period. As E ₁ = E ₂ = αq ₂(1 − θ ₂), we have:

$$ Gk{q_2}^{{k - 1}}{p_{{e2}}} - \phi \alpha {\kappa^{{\frac{{\alpha {q_2}}}{{{E_1}}}}}}\left( {1 + \frac{{(\alpha {q_2} - {E_1})\ln \kappa }}{{{E_1}}}} \right) - {p_{{c2}}} = 0 $$

(25)

where q ^*₂ is the solution of Eq. 22 and λ ^* is the Lagrangian multiplier, which represents the shadow price of one unit permit. Thus, firms estimate the future price as p ₂ = λ ^* + b for sellers and p ₂ = λ ^* − b for buyers. According to Eq. 25, p ₂ is mainly affected by the estimated p _c2 and p _e2. Herein, we assume that the estimated percentage increase of p _c is o. Thus, we have:

$$ {o_i} = \frac{{{p_{{ci2}}}}}{{{p_{{ci}}}}} $$

(26)

In our paper, we assume that coal price (p _c ) increases 10 % annually from 2006 to 2010 and 5 % annually from 2011 to 2020. Thus, we set o _i to be uniformly distributed over the range [0.05, 0.15] from 2006 to 2009 and [0.0, 0.1] from 2010 to 2009. p _e2 is calculated based on Eq. 27. o _i is generated at the beginning of every trading period.

$$ \Delta {p_{e}} = \frac{{\left( {1 - 30\% } \right)\Delta {p_{c}}q}}{{G{q^{k}}}} $$

(27)

Appendix 3: Learning Strategies

At a given time t, an individual ZIP agent (denoted by subscript i) calculates the shout price p _i (t) from price λ _i,j using the agent’s real valued profit margin μ _i (t) according to:

$$ {p_i}(t) = {\lambda_{{i,j}}}\left( {1 + {\mu_i}(t)} \right) $$

(28)

This implies that a seller’s margin is raised by increasing μ _i and lowered by decreasing μ _i with the constraint that μ _i (t) ∊ [−1, 0]:∀t. The aim is that the value of μ _i for each trader should alter dynamically in response to the actions of other traders in the market, increasing or decreasing to maintain a competitive match between that trader’s shout price and the shouts of the other traders. According to the Widrow–Hoff “delta rule” [51], we have:

$$ Y\left( {t + 1} \right) = Y(t) + \varDelta (t) $$

(29)

where Y(t) is the actual output at time t, Y(t + 1) is the actual output in the next time step, and $\varDelta (t)$ is the change in output, determined by the product of the learning rate coefficient v and the difference between Y(t) and the desired output at time t, denoted by D(t):

$$ \varDelta (t) = v\left( {D(t) - Y(t)} \right) $$

(30)

The following adaptation method is employed by the ZIP traders. When a trader is required to increase or decrease its profit margin, a “target price” (denoted τ _i (t)) will be calculated for each trader and the Widrow–Hoff rule will then be applied to make the trader’s shout price in the next time step (p _i (t + 1)) closer to the target price τ _i (t). Because the shout price is calculated using the (fixed) limit price λ _i,j and (variable) profit margin μ _i , it is necessary to rearrange Eq. 27 to give an updated rule for the profit margin μ _i in the transition from time t to t + 1:

$$ {\mu_i}\left( {t + 1} \right) = {{{\left( {{p_i}(t) + {\Delta_i}(t)} \right)}} \left/ {{{\lambda_{{i,j}}} - 1}} \right.} $$

(31)

where Δ _i (t) is the Widrow–Hoff delta value calculated using the individual trader’s learning rate β _i :

$$ {\Delta_i}(t) = {v_i}\left( {{\tau_i}(t) - {p_i}(t)} \right) $$

(32)

All that remains is to determine how to set the target price τ _i (t). While a simple method would be to set the target price equal to the price of the last shout (i.e., τ _i (t) = q(t)), this presents a significant problem. When the last shout price is very close to or equal to the trader’s current shout price (i.e., p(t) ≈ q(t)), the value of Δ _i (t) given by Eq. 31 will be very small or 0. Thus, traders who would have shouted prices close to q(t) are likely to make negligible alterations to their profit margins, and so will shout very similar prices when next given the opportunity.

There are many ways in which the target price τ _i (t) could be determined. In the our model, the target price is generated using a stochastic function of the shout price q(t):

$$ {\tau_i}(t) = {H_i}(t)q(t) + {Y_i}(t) $$

(33)

where H _i is a randomly generated coefficient that sets the target price relative to the price q(t) of the last shout price and Y _i (t) is a (small) random absolute price alteration (or perturbation). When the intention is to increase the dealer’s shout price, H _i  > 1.0 and Y _i  > 0.0; when the intention is to decrease it, 0.0 < H _i  < 1.0 and Y _i  < 0.0. In our model, we set H _i to be uniformly distributed over the range [1.0, 1.05] for price increases and over [0.95, 1.0] for price decreases, giving relative rises or falls of up to 5 % and Y _i is uniformly distributed over [0.0, 0.1] for increases and [−0.1, 0.0] for decreases. The value of each trader’s learning rate v _i is randomly generated when the trader is initialized, using values uniformly distributed over [0.1, 0.5].

Appendix 4: Parameters Initialization

We assume that all power plants have the same value of k; therefore, we have the regression equation:

$$ \ln \left( {{g_i}} \right) = k\ln \left( {{q_i}} \right) + \ln {G_i} + \varepsilon $$

(34)

Here, ɛ is the error. Using the real data of 45 power plants, the regression results are presented in Table 3. The coefficient of ln q is the value k in Eq. 34. Therefore, we have k = 0.92011 (see Table 3).

Table 3 Regression results of Eq. 34

In addition, we assume that all the power plants have the same value of κ and distinct ϕ _i . α _i q _i θ _i is the emission reduction for power plant i. Thus, we have the regression equation:

$$ \ln {c_i} = \ln {\phi_i} + \ln {R_i} + {x_i}\ln \kappa + {\varepsilon_i} $$

(35)

Here, ${x_i} = \frac{1}{{1 - {\theta_i}}}$ and ɛ is the error. Using the database of 45 power plants, the regression coefficient of x _i is the value ln κ. Therefore, we have ln κ = 0.0565 and κ = 1.0581363(see Table 4).

Table 4 Regression results of Eq. 35