The HI and DI programs are modeled very simply. The Ш and DI levels of lump-sum transfers are picked to generate payroll tax rates of 2.9 percent and 1.9 percent, respectively, corresponding to their 1996 statutory rates. Like the OASI tax, DI contributions apply only to wages below $62,700. The HI tax, in contrast, is not subject to an earnings ceiling. Lump-sum HI and DI benefits are provided on an equal basis to agents above and below age 65, respectively.
Given our parameter choices, the model generates a pre-tax interest rate of 9.3 percent, a net national saving rate of 5.3 percent, and a capital/national-income ratio of 2.6. Consumption accounts for 73.4 percent of national income, net investment for 5.2 percent, and government purchases of goods and services for 21.4 percent. These figures are close to their respective 1996 NIPA values. The post-tax interest rate equals 0.08 and is calculated following Auerbach (1996).
Solving the Model
The model solves for the full rational-expectations dynamic (Nash) equilibrium with a Gauss-Seidel algorithm. The calculation starts with a guess for certain key variables and then iterates on those variables until a convergence criterion is met. The identifying restrictions of the model are used to compute the remaining economic variables as well as the updates for the iterations. The solution involves several steps and inner loops that solve for household-level variables before moving to an outer loop which solves for the time-paths of aggregate variables and factor prices.
Since the decision to opt out by any agent will be affected by the exact time path of factor prices—which, in turn, is affected by the opting out decisions of other agents—the opting out choice is determined endogenously for each agent. The solution algorithm iterates until each agent, given the prevailing path of factor prices, prefers his/her intertemporal allocation of consumption and leisure and his/her decision whether to opt out. 24 hour payday loans