Capital stock in each simulation period equals last period's capital stock plus gross investment minus depreciation. No optimal behavior is assumed for investment and capital accumulation. All net investments in the previous period are assumed to become new production capital in the next period.

Accumulation patterns for capital stock depend upon the depreciation rate and gross investment rate, which is set exogenously as a percentage of GDP. However, household and corporate savings, government surplus (deficit), and foreign capital inflow (foreign savings) are assumed to be perfect substitutes and collectively constitute the sources of gross investment.

Household saving decisions are endogenous in the model. It represents future consumption goods for the household with zero subsistence quantity (by assuming intertemporal separable preferences, ELES demand system). Government saving (deficit) is fixed and growth is at the same rate as real GDP.

In calibrating the baseline scenario, two economy wide, ownership-specific (one for SOEs, and one for IPEs and NSEs) Hicks-neutral efficiency factors are determined endogenously to obtain a prespecified growth path of real GDP and total employment in SOEs. When alternative scenarios are simulated, the two TFP growth rates are set exogenously, while the growth rate of real GDP and the total employment in SOEs are solved endogenously.

# _Population projection and labor force dynamics_

The sustainability of a pension system is closely related to the demographic structure of the labor force, which depends largely on the dynamics of population growth. Correctly modeling the structure and trend of population and labor force growth is a necessary condition for any successful pension reform design and analysis. Therefore, a population dynamics and labor supply submodel is an indispensable component of the CGE model for China's pension reform.

Our population projection model is based on the deterministic difference equation model developed by Leslie (1945), which has been used widely in mathematical demography and population dynamics studies. In such a model, China's population is taken as a whole, all factors that influence population growth, such as fertility and motility rate, are defined in terms of statistical means. We assume that changes of time, birth, and death are the three major determinants of population growth. The influence of other social and economic factors is implicitly included in those three determinants. Economic growth is assumed to affect fertility rate and motility rate through exogenously specified total fertility rate and life expectancy changes. We do not consider migration as a determinant because the number of immigrants is very small compared with China's huge population.

Newborn population equals the number of women at their fertility age (age 15 to 49) multiplied by the corresponding fertility rate. The population in each age group equals previous year's population at the next younger age group multiplied by the corresponding motility rate. There will no people live longer than 100 years. Fertility and motility rates, proportion of each gender in the newborn population, and base year population demographic distribution can be obtained from population survey data.

Labor supply at each age (15-70) for a given year equals the population in that age group for that year multiplied by a labor participation rate, which is gender and age specific. These specified labor forces are then aggregated into the 22 groups of labor inputs specified earlier in the cost and labor demand functions. We assume that workers start to retire at age 40. The total new retirees in a given year is the sum of all surviving workers age 40 and over multiplied by a retirement rate that is gender and age-specific. The total retiree in a year is the sum of the surviving retirees from all previous 18