Parameter Uncertainty in CGE Modeling of the Macroeconomic Impact

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618 tested for robustness by implementing sensitivity analyses around the elasticity mean values [9-14] . However, in practice most analyses use limited sensitivity analyses, with changes in a few key elasticities to examine the sensitivity of the results. This procedure has no way of ensuring that the chosen elasticities are the important ones, and its role is also limited by the discretionary character of the values selected. Few of the existing studies either systematically explore the parameter uncertainty propagation or examine the contribution of the various parameters to the uncertainty due to the expensive computing costs. Harrison et al. [11] and Alber et al. [13] conducted unconditional sensitivity analyses, but they focused only on some of the elasticities and failed to describe the CGE output distributional information. The purpose of this paper is to study the problem of measuring the uncertainty of CGE model simulations associated with parameter uncertainty using the macroeconomic impacts of a carbon tax in China as the policy question for the simulations. The study used Monte Carlo experiments for the parameter uncertainty propagation and employed an unconditional systematic sensitivity analysis procedure to identify critically sensitive elasticities. The analytical process adopted in this paper is extensively used in model evaluations [15] . 1 CGE Model The model developed here, integrated energyeconomy-environment dynamic CGE (TEDCGE), is a time recursive dynamic general equilibrium model, which has been presented in detail [16] . Since the dynamic mechanism has little impact on the elasticities’ influence on the CGE output and it is very time consuming compared with the static CGE model, the static version of the model was used to examine the elasticities’ uncertainties. The TEDCGE model provides a description of the China economy of 1997, the latest year for which the China input/output is available. The model identifies 10 production sectors (agriculture, heavy industry, light industry, transportation, construction, service electricity, coal, oil, and natural gas, which are numbered as 1 to 10, respectively), 10 consumption goods, and 2 household groups distinguished by rural and urban residents. The model operates by simulating the operation of markets for factors, products, and foreign Tsinghua Science and Technology, October 2006, 11(5): 617-624 exchange. The model is highly nonlinear, with equations specifying supply and demand behavior across all markets. The model pays particular attention to modeling the energy sector and its linkages to the rest of the economy. The energy use is disaggregated into coal, oil, natural gas, and electricity in the model. Along with capital, labour, and intermediate inputs, the four energy inputs are regarded as the basic inputs into the production function. The carbon tax revenue from the sectoral energy consumption is described by E 10 10 ∑∑ RC ( t) = tc ⋅ε⋅(1−fc ) ⋅θ ⋅VE ( t) ⋅ο i= 1 j= 7 h= 1 j= 7 j j j ji j (1) The carbon tax revenue from residential energy use is described by 2 10 RC C ( t) = ∑∑ tc ⋅εj ⋅θj ⋅CI hj( t) ⋅οj (2) VEji is the monetary consumption (RMB) of fuel j by sector i, CIhj is the residential consumption (RMB) of fuel j by household h, tc denotes the carbon tax rate in terms of RMB/t, εj denotes the CO2 emission coefficient of fuel j with the unit of t/TJ, fcj is the carbon fixed rate of fuel j, θj is the conversion factor of fuel j from a nominal output value to a physical term with the unit of TJ/RMB, and οj is the oxidation rate of fuel j. The CO2 emissions are calculated for each sector by means of the sectoral fuel consumption and the corresponding emission coefficient. Since the fuel consumption is in terms of the corresponding nominal output rather than directly as the physical units in the model, the sectoral real fuel consumption is first translated into physical terms, using a fuel-specific technical conversion factor, and then further converted into CO2 based on the fuel-specific emission coefficient. The fuel used by different sectors is assumed to have the same quality, implying equivalent emission factors, in terms of tons of CO2 per unit of fuel consumption, for a fuel used in production, households, or government. A carbon tax is incorporated into the model as a means of achieving an assumed carbon reduction target. The tax applies to the consumption of primary fuels only; that is, the energy sectors only pay the carbon tax on their own use of fuels. The carbon tax revenue is recycled to the economy in several alternative ways, ensuring that the total government revenue is neutral to the carbon tax.
WANG Can (王灿) et al:Parameter Uncertainty in CGE Modeling of… 619 As with most CGE models, the substitution elasticities and the transformation elasticities are incorporated through constant elasticity of substitution (CES) and constant elasticity of transformation (CET) functions into the production and import/export decisionmaking procedure in TEDCGE. Both these functions have the same general form: ( ( ) ) 1 ρ − 1 1 2 ρ Y = φ δ ⋅ X + −δ ⋅ X ρ (3) where Y is the aggregate composite of X1 and X2, φ is the efficiency parameter, δ is the share parameter, and ρ is the substitution parameter. The substitution parameter is a function of the substitution or transformation elasticity, ε, defined as ρ = ( ε −1) ε if Eq. (3) is a CES and as ρ = ( ε + 1) ε if Eq. (3) is a CET. The full model includes, as exogenous parameters, four substitution elasticities (three in the production function and one in the import demand function) and one transformation elasticity (in the export supply function) for each of the ten sectors, for a total of 50 elasticities to be defined in the calibration process. 2 Uncertainty Analysis Method Monte Carlo simulations and unconditional systematic sensitivity analysis were used to determine the uncertainty in the CGE model results given the parameter uncertainty and to determine the importance of each individual parameter with respect to the uncertainty in the outputs. These questions are answered through quantification of the uncertainty in the screened parameters in the form of prior probability distributions, based on random parameter values and repeated model simulations. Given a large number of simulations, the probability distributions of the outcomes can be constructed as a histogram of the outcomes that approximate with arbitrarily small error the “true” probability density function of the model outcomes. Since all of the uncertain elasticities in question are theoretically constrained to be at least non-negative and non-infinite, the beta family of distributions was chosen for its finite end-points and its flexibility in representing different distribution shapes. A standard beta distribution, which is defined over the interval (0, 1), can be transformed to any desired scale through a simple linear transformation. The beta distribution function has two parameters a and b and is defined as ⎧ Γ ( a+ b) a−1 b−1 ⎪ x (1 − x) , 0 < x< 1; f( x/ a, b) = ⎨Γ( a) Γ( b) ⎪⎩ 0, o t h erwise (4) Different values for the two parameters a and b will define various shapes and variances of the distribution. For example, a and b are greater than or equal to 1 for symmetric and unimodal beta distributions. The population parameters of each elasticity’s distribution (e.g., the minimum and maximum end-points) are chosen on the basis of empirical studies. The next section presents detailed information describing uncertain elasticities examined in this paper. Once the ranges and distributions of elasticities have been established, the next step is to determine an adequate sampling intensity for the Monte Carlo experiment. The sampling intensity is chosen to limit the margins of error in the estimated means and variances of the model’s output variables of interest to a prespecified level, chosen to be 1% in this paper. This approach quantifies the variations in the model response, but the procedure cannot identify the driving uncertainties, which are the uncertain parameters that cause the most variance in the outputs of interest. An unconditional sensitivity analysis, which focuses on the output uncertainty over the entire range of values of the input parameters, is the preferable procedure for identifying the driving uncertainties. The unconditional sensitivity analysis method was described by Saltelli et al. [16] In this study, the 50 elasticities of substitution are treated as uncertain and allowed to take random values from their probability density functions. For each perturbation of the elasticities, the TEDCGE model is recalibrated and then solved for the benchmark and counterfactual equilibria. The actual data generating procedure for the calibration data set could be described as follows: For i = 1, 50 (50 elasticity parameters) Define s i points that are the mean values of s i non- overlapping intervals of equal probability, which are exhaus- tively divided in the sampling space of parameter i For j = 1, s i (fixed s i points of parameter i) For n = 1, K (sampling intensity) Select a random value from the beta distribution for each of the 49 elasticity parameters besides parameter i Calibrate the model based on the 50 parameters
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