4. Calibration
The object of a computable general equilibrium model is to compare two states of the economy. In our case, we compare the state of the three region economies when population is aging as predicted by the demographic projections of the old-age dependency ratio to the state of the economy in the absence of such an aging shift. To accomplish the comparison we need to generate an initial equilibrium. This is what is called the calibration procedure. It consists mainly to calibrate certain parameters of the model in order to replicate what is observed in the data, given the known values of other variables or parameters. As our model is dynamic, the initial equilibrium is in fact a steady state that is, a general equilibrium that repeats every period. In our simulation experiments, we will introduce a demographic shift. The state of the economy will thus change and we will compare this new state with the original steady state, which is a state where the population structure of year 1999 remains forever.
Table 2 reports variable and parameter values that were imposed in the calibration procedure. Most values were supplied by Human Resources Development Canada as is the case for the demographic projections. We have imposed an identical intertemporal elasticity of substitution across regions that are consistent with values found in the literature. The intratemporal elasticity of substitution for is also assumed identical across the different types of demands (consumption and investment) and across regions. The value of this parameter is relative high with respect to the literature to compensate for the fact that Canada is considered in the model as a closed economy.
A matrix of interregional flows was calculated between the three regions and serve to estimate the ownership distribution of wealth (physical capital plus government bonds) across individuals and regions. It was assumed that regional physical capital was owned by regional residents first. This means that residents have a stock of wealth composed of local physical capital ownership titles plus bonds issued by local and outside regional governments. Given this interregional date and the above parameter values, regional rate of time preference was calibrated as to ensure equilibrium in the Canadian financial asset market. For simulation purposes, the general equilibrium of the economy is replicated over the 100 period horizons. The length of horizon is determined to ensure that after the demographic projected shift the economy converges to a long-run steady state. Although the model contains only 15 overlapping-generations and 3 regions, the model has more than 27,000 equations. It can thus be solved only through computations.
Table 2
| |
EAST |
CENTER |
WEST |
| GDP (when Canada GDP = 1) |
.278 |
.420 |
.302 |
| Share of capital in the production |
.280 |
.280 |
.302 |
| Wage income tax rate |
.362 |
.313 |
.308 |
| Capital income tax rate |
.458 |
.562 |
.412 |
| Consumption tax rate |
.216 |
.200 |
.177 |
| Government debt |
.264 |
.339 |
.187 |
| Intertemp. elasticity of substitution |
.275 |
.275 |
.275 |
| Elast. of subst. for consumption |
7.5 |
7.5 |
7.5 |
| Elast. of subst. for investment |
7.5 |
7.5 |
7.5 |
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