The revolutions underway in macroeconomics and public finance were concomitant with the revolution in the access of academic economists to high speed computers. Although PCS did not yet exist, computer programs could be punched onto computer cards and run on university mainframes. John Shoven and John Whalley were perhaps the first public finance economists to demonstrate the potential power of this new technology to study economies in general equilibrium. They showed how Harberger’s model of the corporate income tax could be expanded to include multiple industries, each facing its own effective rate of corporate income taxation, and solved, using Scarfs algorithm, on the computer.
Shoven-Whalley Model was static, but it demonstrated that one could use the computer to find market-clearing prices of multiple interconnected markets that were open at the same point in time. Although solving for the economy’s dynamic transition path involved finding a general equilibrium with respect to markets open at different points in time, this distinction didn’t necessarily seem important.
After all, Arrow’s contingent claims model showed that markets that are indexed by time can effectively be considered open in the present. On the other hand, in Arrow’s model all the agents who would ever be alive were already alive and were, therefore, available to form contracts in the present about what tb^y would do in the future. This is not the case in an ongoing life-cycle economy in which current agents are not altruistic toward future ones and will not, as a result, negotiate on their behalf. However, even this concern seemed surmountable.
After all, one could consider how the agents to be bom in the future would contract once they arrived. And given the capacity of computers, there seemed, in principal, to be no problem in simultaneously entertaining the economic behavior of those now alive as well as those yet to be bom. By limiting oneself to economies experiencing no aggregate uncertainty, one could hope to narrow all future paths of the macro economy to just one and therefore not have to entertain actions by future agents that differed depending on the state of the economy.
The real issue in immediately applying the Shoven-Whalley procedure to markets over time was that the Scarf algorithm only worked for a model with a finite number of markets and agents. There was no obvious way to solve for a general equilibrium with an infinite number of time-dated agents transacting in an infinite number of labor, consumption, and capital markets. This is a bit of an overstatement, since in certain very simple two-period life-cycle models (in which households live for just two periods), solving for the exact transition path is simple because next period’s capital-labor ratio is simply a function of this period’s capital-labor ratio — a known quantity. Once one adds three periods or makes the two period model a bit more complicated the capital-labor ratio in any given period depends on the capital-labor ratio in at least the previous two periods. Stated differently, knowing this period’s capital-labor ratio doesn’t suffice to determine next period’s ratio. One also needs to know the capital-labor ratio in one or more periods after the next one. But the equations containing the capital-labor ratios in periods after the next one involve capital-labor ratios in periods that are yet further in the future. Hence, substituting from these equations for the unknown ratios just adds different unknown ratios to the resulting expression.