Green and Blue Dividends and Environmental Tax Reform: Dynamic CGE Model

Abstract

The challenge of climate change needs to be tackled with environmental policies carefully designed to achieve environmental benefits and avoid negative economic effects. The introduction of an environmental tax in the economic system can generate a double benefit represented by the attainment of the environmental target (first or green dividend) and other additional benefits (second/third or blue dividends) represented by gains in welfare, employment, consumption etc. In this perspective, the general equilibrium analysis is able to quantify the environmental and welfare direct and indirect effects that an environmental policy generates within the economic system. Since international environmental agreements set clear target deadlines on the reduction of GHG emissions, in this chapter a dynamic CGE model based on a bi-regional SAM framework for Italy is developed.

Appendices

Appendix 1

Dynamic CGE model specification

The dynamic CGE model developed in this paper is calibrated on the SAM integrated with environmental data. It is solved using the GAMS (General Algebraic Modeling System) software to find the equilibrium prices, quantities and incomes over the time.

Given the structure of the economy described by the SAM, to determine prices and quantities which maximize producers’ profits and consumers’ utility, we solve the Arrow-Debreu (1954) problem as an optimization problem of the consumer subject to income, technology and feasibility constraints. When programming on GAMS usually, this maximization problem is turned into a Mixed Complimentary Problem (MCP) and solved (solver used MILES) as a system of non-linear equation. In our model, the optimization problem for all the consumers (Böhringer et al. 1997) has been settled as:

$$ \hbox{max} \sum\limits_{t = 0}^{T} {\left( {\frac{1}{1 + \rho }} \right)^{t} } u\left[ {C_{t} } \right] $$

(4)

subject to:

$$ C_{t} = x\left( {K_{t} ,L_{t} ,M_{t} ,Ta_{t} } \right) - I_{t} - E_{t} $$

(5)

$$ K_{t + 1} = (1 - \delta )K_{t} + I_{t} $$

(6)

The first order conditions deriving from this maximization problem are:

$$ P_{t} = \left( {\frac{1}{1 + \rho }} \right)^{t} \frac{{\delta u \left( {C_{t} } \right)}}{{\delta C_{t} }} $$

(7)

$$ PK_{t} = (1 - \delta )PK_{t + 1} + P_{t} \frac{{\delta x\left( {K_{t} ,L_{t} ,M_{t} ,Ta_{t} } \right)}}{{\delta K_{t} }} $$

(8)

$$ P_{t} = PK_{t + 1} $$

(9)

Than the corresponding mixed complimentary problem can be formulated as a sequence of market clearing, zero profit and budget constraint conditions.

Market clearing conditions holds for all commodities and primary factors markets. Analytically, we can summarize the conditions as follow:

$$ X_{t} \ge B_{t} ,d\left( {P_{t} , RA} \right) + I_{t} + E_{t} ,P_{t} \ge 0,\;P_{t} \left( {X_{t} - B_{t} ,d\left( {P_{t} ,RA} \right) - I_{t} - E_{t} } \right) = 0 $$

(10)

$$ \begin{aligned} L_{t} & \ge X_{t} \frac{{\delta C\left( {RK_{t} ,PL_{t} ,PM_{t} ,Ta_{t} } \right)}}{{\delta PL_{t} }}, \\ PL_{t} & \ge 0,PL_{t} \left( {L_{t} - X_{t} \frac{{\delta C\left( {RK_{t} ,PL_{t} ,PM_{t} ,Ta_{t} } \right)}}{{\delta PL_{t} }}} \right) = 0 \\ \end{aligned} $$

(11)

$$ \begin{aligned} K_{t} & \ge X_{t} \frac{{\delta C\left( {RK_{t} ,PL_{t} ,PM_{t} ,Ta_{t} } \right)}}{{\delta RK_{t} }}, \\ RK_{t} & \ge 0,\;RK_{t} \left( {K_{t} - X_{t} \frac{{\delta C\left( {RK_{t} ,PL_{t} ,PM_{t} ,Ta_{t} } \right)}}{{\delta RK_{t} }}} \right) = 0 \\ \end{aligned} $$

(12)

$$ \begin{aligned} M_{t} & \ge X_{t} \frac{{\delta C\left( {RK_{t} ,PL_{t} ,PM_{t} ,Ta_{t} } \right)}}{{\delta PM_{t} }}, \\ PM_{t} & \ge 0,PM_{t} \left( {K_{t} - X_{t} \frac{{\delta C\left( {RK_{t} ,PL_{t} ,PM_{t} ,Ta_{t} } \right)}}{{\delta PM_{t} }}} \right) = 0 \\ \end{aligned} $$

(13)

Zero profit conditions posits that total supply in each commodity market is determined by the perfect competitive market condition, that is to say, price equals average total cost (profit are zero). In a general equilibrium model, the price that clears the market (demand equals to supply) also equals average total costs for each commodity. Analytically, we can summarize the conditions as follow:

$$ P_{t} \ge PK_{t + 1} ,I_{t} \ge 0,\quad I_{t} \left( {P_{t} - PK_{t + 1} } \right) = 0 $$

(14)

$$ PK_{t} \ge RK_{t} + \left( {1 - \delta } \right) PK_{t + 1} , K_{t} \ge 0, K_{t} (PK_{t} - RK_{t} - \left( {1 - \delta } \right) PK_{t + 1} )= 0 $$

(15)

$$ C\left( {RK_{t} , PL_{t} , PM_{t} , Ta_{t} } \right) \ge P_{t} , X_{t} \ge 0, X_{t} \left( {C\left( {RK_{t} , PL_{t} , PM_{t} , Ta_{t} } \right) - P_{t} } \right) = 0 $$

(16)

Income balance conditions derive from the budget constraint:

$$ RA \ge PK_{0} K_{0} + \sum\limits_{t = 0}^{T} {\left( {PL_{t} L_{t} + PM_{t} M_{t} - Ta_{t} } \right)} - PK_{t + 1} K_{t + 1} , RA \ge 0 $$

(17)

The variables are:

t :

Time periods

T :

Terminal period

ρ :

Individual time-preference parameter

u :

Utility

C _t :

Consumption in period t

x :

Production function

X _t :

Total output in period t

K _t :

Capital in period t

L _t :

Labour in period t

M _t :

Imports in period t

Ta _t :

All taxes payed by sectors in period t

I _t :

Investment in period t

E _t :

Exports in period t

δ :

Capital depreciation rate

γ :

interest rate

P _t :

Price of output in period t

d :

Demand function

PK _t :

Price of capital in period t

RK _t :

Rental of capital in period t

PL _t :

Wage in period t

PM _t :

Price of imports in period t

RA :

Consumer’s disposable income

Appendix 2

Results from sensitivity analysis

See Tables 3 and 4.