Knowing that the fiscal policies matter a lot in the long run raised the ante in studying the transition, particularly the duration of the transition. If the long-run took forever to reach, then knowing the economy’s ultimate position wasn’t particularly useful. On the other hand, if the transition to the economy’s final destination was very quick, then steady-state analysis would suffice. Either way one would need to compute transition paths.
Summers (1981) and Seidman (1983), following the lead of Miller and Upton (1974), took a stab at this by computing transition paths based on the assumption of myopic expectations, specifically the assumption that agents assume that current factor prices will prevail at all future dates. This approach seems appealing on first thought, but not on second or third thought. First, one has to ask why agents would consider simply current, as opposed to past, factor prices in thinking about future factor prices. Second, if one permits agents to think about past factor prices, how many past prices should one let agents consider?
Third, what should one assume about the way agents weigh current and past factor prices in forming expectations about future factor prices? Fourth, should one value agent’s well being based on the actual time-path of factor prices that prevails or the one that agents mistakenly assume will prevail? And fifth, how do agents consider fiscal actions taken today, such as a tax cut, that necessitate future fiscal actions, like a spending cut, to satisfy the government’s intertemporal budget constraint? Ignoring general equilibrium feedback effects on factor prices is one thing. But assuming that agents think the government can borrow indefinitely to pay its bills is something else again.
In 1980 Martin Feldstein announced a major NBER conference on simulation methods in tax policy analysis to be held in 1981. Not knowing what we would write, but knowing that the conference would be held at a fancy hotel in Florida in January, Auerbach and I agreed to submit a paper. In the winter of 1980 we met to figure out what to do. We began talking about the need to compute exact transition paths in large-scale life-cycle economies under the assumption of perfect foresight and the fact that we had no idea how to do so.
Then we starting thinking about the method for solving for steady states. Since the equation for the economy’s steady-state capital-labor ratio isn’t a closed form, solving for its value involves iteration – trying a value, testing if it solves the steady state restrictions, and updating one’s guess if it doesn’t. More precisely, the procedure involves choosing a candidate value for the steady-state capital-labor ratio demanded by firms, using the marginal product equals factor price equations to determine factor prices, and then calculating whether the supplies of capital and labor provided by the household sector of the economy, given these factor prices, produces the same ratio of capital to labor as the candidate demand value. If not, one updates the candidate value by taking a weighted average of the initial demand and the new supply-side values. An alternative to this Gauss-Seidel technique is to use Newton’s method to update one’s guess of the solution.