THE PITT MODEL AND SIMULATION RESULTS
6.6 SENSITIVITY ANALYSIS
In CGE simulations it is essential to examine the sensitivity of modelling results to key parameter values. The results of shocks (1a) and (1b) illustrate that the form of production has a significant impact on the change in the skill premium due to
10 For technical reasons, it is not possible to simultaneously model endogenous factor endowment multipliers and endogenous technical change using MPSGE. Consequently, the regional-generic factor endowment multipliers estimated in the previous simulation enter as exogenous variables in Shock 3.
11 Tyers and Yang (2000) also discover that negative skill-augmenting technical change is required to induce an increase in wage inequality when there is capital skill complementarity (see Tyers and Yang 2000, Table 8, p. 35).
changes in factor endowments. The production nest in shock (1b) allowed the elasticity of substitution between skilled labour and equipment to differ from that between unskilled and equipment, whereas that in shock (1a) did not. Also, the results of Chapter 2 illustrate that the effect of changes in the stock of equipment on the skill premium is determined by the elasticity of substitution between skilled labour and equipment relative to the branch elasticity of substitution between the composite of the two and unskilled labour. It is, therefore, sensible to examine the sensitivity of the results to substitution possibilities between skilled labour, capital, and unskilled labour.12 As mentioned above, the choice of the branch elasticity of substitution between the skill-equipment composite and unskilled labour was directed by the results of a large body of empirical literature, while the corresponding elasticity parameter for skilled labour and equipment was more arbitrarily assigned. Sensitivity analysis, therefore, focuses on the latter.
Figure 6.3 plots estimated changes in the skill premium for different values of the elasticity of substitution between skilled labour and equipment in shock (1b). The chart shows that the change in the skill premium is larger the greater the complementarity (the less the branch elasticity of substitution) between skilled labour and equipment. It is also evident that small changes in the branch elasticity of substitution can induce large changes in the estimated change in the skill premium. For example, a decrease in the branch elasticity parameter by five percent, to 0.38, results in the predicted change in the skill premium increasing to
12 Unreported simulations revealed that the results are relatively insensitive to changes in the branch elasticity of substitution in the top level of the value added nest.
20.6 percent, a 29.6 percent increase. This represents an elasticity of sensitivity of –5.92.
Figure 6.3
Sensitivity of the skill premium to the branch elasticity of substitution between equipment and skilled labour in shock (1b)
0 10 20 30 40 50
0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 Branch elasticity between equipment and skilled labour
Change in skill premium (%)
Figure 6.4
Sensitivity of the skill premium to the annual decrease in the price of high-tech equipment in shock (1b)
0 5 10 15 20 25 30 35
16.6 16.8 17.0 17.2 17.4 17.6 17.8
Annual decrease in the price of high-tech equipment (%)
Change in skill premium (%)
The estimated change in the skill premium is less sensitive to increases in the branch elasticity of substitution than to decreases. Therefore, shock (1b) is still able to explain a large component of the observed increase in the skill premium when complementarity between skilled labour and equipment is reduced. As a result, the predicted change in the skilled to unskilled wage is still positive when the relevant branch elasticity parameter is 0.5, which represents a large increase in the skill premium relative to the estimate in shock (1a).
In addition to the degree of complementarity in the model, the size of the increase in the endowment of equipment, measured in efficiency units, is also an important determinant of the outcome of shock (1b). In Chapter 4, the estimated change in the stock of equipment increased dramatically when improvements in quality were accounted for. Consequently, the sensitivity of the change in the skill premium to the quality-adjusted price index used in Chapter 4 is also examined. Figure 6.4 plots the results of the analysis when the branch elasticity of substitution between skilled labour and equipment is fixed at 0.4. The illustration shows that the change in the skill premium is extremely sensitive to estimated improvements in the efficiency of high-tech equipment. Also, the relationship between the change in the skilled to unskilled wage ratio and the annual percentage decrease in the price of high-tech equipment is approximately linear in the neighbourhood of the estimated value of this variable (17.2 percent). Using the two extreme points in Figure 6.4 to measure the gradient of the line, the change in the skill premium increases by 21.9 percentage points for each 1.0 percentage point increase in the annual price of high-tech equipment. This indicates that if the annual percentage decrease in the price of
high-tech equipment was 2.2 percentage points less than that estimated, the introduction of capital-skill complementarity would result in a decrease in the skill premium relative to the case when the two factors are substitutes (i.e. the predicted decrease in shock (1b) would be greater than that in shock (1a)).13 It is therefore, possible to conclude that the price of high-tech equipment must decline by at least 15 percent annually for the presence of capital-skill complementarity to have a positive impact on the skill premium.
Additional simulations (not reported) show that the gradient of the line characterising the relationship between the change in skill premium and annual decrease in the price of high-tech equipment is steeper the smaller the branch elasticity of substitution between skilled labour and equipment. For example, the gradient is 13.1 when the relevant elasticity parameter is 0.5 and 43.7 when the branch elasticity of substitution is 0.3. This indicates that the change in the skill premium is more sensitive to the measurement of the stock of equipment the greater the complementarity between skilled labour and equipment.
6.7 CONCLUSIONS
This chapter has outlined the construction of a global, small-scale CGE model and implemented several simulations in order to determine the cause(s) of increased wage inequality in the UK. The first simulation demonstrated that the large increase in the relative supply of skilled labour should, ceteris paribus, have resulted in a large decrease in the skill premium, which means that the observed
13 This possibility was discussed in Chapter 2. When there is an increase in the supply of both skilled labour and equipment, the skill premium will only increase if the expansion of the stock of equipment is sufficiently large.
increase in wage inequality is a result of a large increase in the relative demand for skilled labour. Remaining simulations examined the two usual suspects behind the increase in relative demand, namely technical change and trade. The results exonerate trade and single out technical change as the culprit behind the increase in the skill premium. Specifically, if elasticity parameters in the production specification and the average annual decrease in the quality-adjusted price index of high-tech equipment are accurately estimated, the increase in UK wage inequality can be attributed to changes in the composition of the capital stock brought about by improved technology embodied in high-tech equipment assets. This finding is in agreement with the majority verdict of a large body of empirical literature.
However, unlike other CGE studies, that infer changes in technology from changes in factor costs shares (Tyers and Yang, 1997; Jean and Bontout, 2000) or choose the amount of technical change to generate observed changes in relative wages (Tyers and Yang, 2000), a direct measure of technical change is employed by the PITT model. Specifically, observing changes in the efficiency-unit share of equipment in the total capital stock simulates technical change in the PITT model.
Sensitivity analysis revealed that small changes in key parameter values result in large changes in the estimated impact of skill-biased technical change, as modelled in this chapter, on wage inequality. Two crucial components include the degree of complementarity between skilled labour and equipment and the rate of improvements in the efficiency of high-tech equipment assets. The less the complementarity between skilled labour and equipment, the smaller the simulated increase in the skill premium. The estimated increase in the skill premium is also smaller the smaller the improvement in the efficiency of new high-tech equipment
assets, as measured by the average annual decrease in the quality-adjusted price index for these assets.
Overall, providing that the branch elasticity of substitution between skilled labour and equipment and the average annual decrease in the quality-adjusted price of high-tech equipment are accurately estimated, the results suggest that the PITT model is able to explicitly explain the increase in UK wage inequality.