Sensitivity Analysis

A number of assumptions are made in the model calibration to determine the values of some important parameters, such as substitution elasticity between varieties σ^s , shape of parameter firms firms γ ^s_i fixed trade costs F^s_ij and variable trade costs τ^s_ij. In this section, I check the robustness of the simulation results in the above section to alternative assumptions about these parameters.

(1) Substitution elasticity between varieties

Empirical estimates of industrial markup ratios usually range from 10%-20%,¹⁷ implying a much higher substitution elasticity σ^s of 6-11 than that chosen in Section 3. However, some direct estimates of substitution elasticity between product varieties suggest lower values. For example, Broda and Weinstein (2006) estimate the elasticity between (10-digit Harmonized System) varieties for the US, and find an average of 6.6 for the 2,715 5-digit SITC sectors and 4.0 for the 256 3-digit SITC sectors. The more aggregated the sectors, the less substitutability there is between varieties. In view of the mixed empirical evidence about the substitution elasticities, I conduct sensitivity analysis simulations for both higher and lower values. In the higher (lower) elasticity simulation, markup ratios are 0.05 smaller (higher) than their benchmark values in Table 1, with the elasticity values ranging from 5-7.7 (3.9- 5.0). In the sensitivity analysis simulations, the shape parameter γ^s_i are kept same with that used in the benchmark simulations.

Table 6 [ PDF 72.9KB | 1 page ] shows the welfare and trade effects of the three trade liberalization simulations under alternative substitution elasticity values. It finds that the trade expansion and welfare gains of a trade cost reduction are smaller when there is higher elasticity between varieties and larger when there are lower elasticity between varieties. The results also show that the effects of fixed trade cost reductions are very sensitive to the elasticity values. Under low (high) elasticity assumptions, the gain in global trade and welfare from fixed trade cost reduction is 70% higher (60% lower) than that obtained from benchmark assumptions of substitution elasticity. The impact of elasticity values on the effects of a tariff reduction is less significant, generally ranging from 4% to 9% for trade expansion and from 10% to 20% for welfare gains. The choice of different substitution elasticity values has only a modest impact on the effects of reducing variable trade costs.

These findings are consistent with the theoretical prediction that the substitution elasticity between varieties has a negative effect on the elasticity of trade flows with respect to tariff and fixed trade costs (see equation (27)), as a higher substitution elasticity makes the extensive margin less sensitive to changes in trade barriers, damping the impacts of a trade cost reduction on trade flows (Chaney, 2006). This property makes the firm heterogeneity CGE model distinctly different from the Armington CGE model, in which an increase in Armington elasticity roughly leads to the same magnitude of increase in the trade expansion and welfare.

(2) Shape Parameter in the Pareto Productivity Distribution

In the firm heterogeneity model, the dispersion of firm productivity plays an important role in determining the impact of trade barriers on trade flows. Table 7 [ PDF 83.8KB | 1 page ] presents the simulation results of a 50% cut in global manufacturing tariffs obtained under the assumption that the shape parameters γ^s_i are one-third higher than their benchmark values in Table 1. The results are sensitive to the choice of productivity dispersion parameter. A one-third increase in shape parameters leads to 40-50% higher global welfare gains and trade expansion under the simulation of tariff reduction. This sensitivity analysis simulation confirms that the shape parameter γ^s_i, rather than the substitution elasticity between varieties, is the key parameter governing the effects of trade liberalization in the Melitz-type firm heterogeneity model.

(3) Fixed Trade Costs

The base year variable and fixed trade costs are calibrated based on the assumption that 60% of firms sell in the domestic market, and that the elasticity of the extensive margin with respect to trade flow is 0.6. To explore the sensitivity of the model results to the size of fixed trade costs, I conduct two sets of sensitivity analysis. The first set reduces the base year share of firms selling in the domestic market from 60% to 45%. This raises the base year fixed trading costs by one-third. As both the fixed domestic trading costs and fixed exporting costs are raised proportionally, the calibrated base year variable trade costs are not affected by the increase of fixed trade costs. The second set of simulations raises the elasticity of the extensive margin with respect to trade flow from 0.6 to 0.8, assuming that changes in the extensive margin account for 80% of the difference in export values across regions. Under this simulation set, the base year fixed domestic trading costs are the same as in the benchmark simulations, but both variable trade and fixed exporting costs are changed in calibration. Table 8 [ PDF 43.5KB | 1 page ] reports the welfare effects of the three trade liberalization simulations under the two alternative assumptions about fixed costs. The results are essentially unchanged for the three simulations. This is not surprising, because the policy shocks imposed in the three simulations are all expressed as percentage changes relative to their baseline levels. Despite the differences in calibrated base year fixed trading costs, the firstround effects of a tariff cut and trade cost reduction on trade are the same between the benchmark simulations and the sensitivity analysis. The slight differences reported in Table 8 are mainly due to the second-round effects on income distribution and expenditure pattern.

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