Parameter Uncertainty in CGE Modeling of the Macroeconomic Impact

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620 End value and the benchmark year data Run the model Calculate the mean and variance of the model output for the K runs End Calculate the importance measure of uncertain parameter i (defined as the difference between the maximum and minimum mean output value over its si points) End Rank the parameters by the value of their importance measure All beta variates were generated based on a rejection-acceptance algorithm (algorithm BS) [17] . The random data matrix can either be generated using a crude Monte Carlo algorithm or some form of stratified sampling, such as Latin hypercube sampling (LHS). LHS was used in this study to reduce the computation cost using software developed in Visual Basic to call for the execution of the general algebraic modeling system (GAMS) solution of TEDCGE. 3 Data and Results The model was calibrated to a set of data for China in 1997. The data was aggregated into three broad categories: detailed economic accounts, which are ideally maintained in the form of a social accounting matrix (SAM); structural parameters; and some subsidiary data. The National Bureau of Statistics of China (NBSC) [18] discovered the income and expenditures for each household category, the imports and exports for Tsinghua Science and Technology, October 2006, 11(5): 617-624 each sector, the labor and capital under each of the production sectors as well as their level of output, the transformation matrix between industrial output and consumer goods, the investments by sector, and government revenues and expenditures. Before calibration, a number of adjustments to the original input/output (I/O) table were necessary with the SAM used to impose a general equilibrium structure on the economy, since many inconsistencies or “residuals” may exist in the I/O table. In addition, the 50 elasticities of substitution in the model were predefined based on literature values before calibration. 3.1 Uncertainties in the input parameters Statistical information for the probability density functions for each parameter such as the mode (most likely value), the endpoints (the 0.00 and 1.00 fractiles) and the level of variance of each uncertain parameter were derived from existing literature data. All the elasticity parameters selected as uncertain in the model are summarized in Table 1 with their means, endpoints, standard deviations, and relative errors (defined as standard deviation divided by the mean). Details on how and where the information was obtained can be found in Wang [16] . Note that the distributions shown here are not meant to precisely capture accurate values of the input uncertainties, but rather to demonstrate how much variation in the outcomes can be caused by conservative estimates of the input uncertainties. Table 1 Mean and standard deviations of the uncertain parameters in the TEDCGE model Parameters Mean Lower bound Upper bound Standard deviation Relative error (%) Beta distribution parameter a b Eee 1.00 0.5 1.5 0.25 25 1.5 1.5 Eke 0.50 0.2 1.4 0.26 40 1.5 2.5 Ecl 0.55 0.2 0.9 0.18 32 1.5 1.5 Eid 1.50 0.1 4.0 0.73 42 2.5 3.5 Eed 2.50 0.1 4.0 0.73 31 3.5 2.5 Note: Eee, elasticity substitution between energies; Eke, elasticity substitution between capital and energy aggregate; Ecl, elasticity substitution between capital-energy aggregate and labor; Eid, elasticity substitution between imported goods and domestic production; Eed, elasticity transfer between export supply and domestic demand. Figures 1 and 2 give examples of the probability distributions for Eid and Eed. The TEDCGE reference runs (neglecting the uncertainties) used a nominal value of 1.5 for the elasticity of import substitution (Eid) and 2.5 for elasticity of export transfer (Eed) for all sectors. The modes of the distributions were chosen to reproduce the reference assumptions. Both of these elasticities were assumed to have the same endpoints. The lowest
WANG Can (王灿) et al:Parameter Uncertainty in CGE Modeling of… 621 endpoint was set at 0 and the highest was set at 4.0. The resulting distribution for import substitution elasticity was modeled by a beta distribution with parameters a = 2.5 and b = 3.5, while the beta parameters for export transfer elasticity were a = 3.5 and b = 2.5. Fig. 1 Probability distribution for elasticity of import substitution Fig. 2 Probability distribution for elasticity of export transfer 3.2 Uncertainty in the TEDCGE outputs Figure 3 shows the probability distributions for carbon tax rates required to achieve the carbon reduction goals of 10%, 20%, 30%, and 40% compared with the BAU scenario for 2010 in China. 5000 repetitions of the Monte Carlo experiment were first used to formulate the probability distributions. The Monte Carlo experiments were then repeated to get another probability distribution. The errors in the means and variances from these two experiments were found to be less than 1%, which means that the 5000 Monte Carlo simulations give sufficiently accurate results. The implications of the uncertainties are important when evaluating the performance of a carbon tax policy for a carbon mitigation strategy, but even in the absence of a policy the uncertainties in the carbon tax rates have implications for interpreting results. What is often called a marginal abatement cost curve for the international carbon emission trading model is in fact only one series of values from a series of distributions of possible values, given the uncertain parameters existing in the model. Policy analysis with models on carbon emission trading should be viewed in this context. Fig. 3 Probability distribution of carbon tax rate response to carbon reduction rates The mean (bold middle line), the 95% and 100% confidence intervals, and the relative error for the marginal abatement cost curve in 2010 for China calculated by TEDCGE are illustrated in Fig. 4. The results show increasing means and variances for the abatement cost as the carbon reduction goal increases. In addition, the relative error in the TEDCGE output is much smaller than the error in the input parameters (see Table 1). Fig. 4 Marginal abatement cost curve with parameter uncertainties The results show that if the input parameter statistical information is fully provided, the CGE model outputs also exhibit statistical characteristics reflecting the uncertainties transmitted from the inputs to the simulation results. Although parameter uncertainties throw doubt on the reliability of the CGE model simulation results, the input uncertainties are reduced to some extent through the CGE modeling procedure.
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