Although Alan and I have never formally described our methods of double checking the code, after each modification of the model we subject it to a set of tests to make sure there are no misspecifications (bugs). One of these tests is checking that national saving is precisely zero in the long-run if there is neither population nor productivity growth. Another is to check that the economy sits in its initial steady state when one a) runs a transition, but b) specifies no policy change.
A third test is to check that each agent exactly exhausts her budget constraint at the end of her life and never violates her non negativity constraint with respect to labor supply. More info A fourth is to check that the government is satisfying its intertemporal budget constraint. And a fifth test is to confirm that alternative ways of running the exact same fiscal policy, such as taxing consumption via a retail sales tax or via a proportional income tax with 100 percent expensing, produce precisely the same economic results. Many of these checks are redundant; i.e., if any agent was off her budget constraint or if the government was off its budget constraint, the economy’s steady-state saving rate would not be zero when zero rates of population and productivity growth are assumed.
The final concern – that our economy might feature multiple equilibria- was something Alan and I never worried about. The reason is that after doing hundreds of simulations with a range of different initial conditions, we knew instinctively that, for the parameter values we were using, the model was finding unique equilibria. Why were we so sure? The answer is that if the model featured multiple equilibria the transition path would be a) either very hard to compute, b) highly sensitive to initial conditions, or c) highly sensitive to the year after which we assumed the economy was in a steady state. Again, for our assumed preference and technology parameters we didn’t find any of these things to be the case. Moreover, when we set particular parameter values to the extremes levels that foster multiple equilibria, such as very small values for the intertemporal elasticity of substitution or the elasticity of substitution in production between capital and labor, we found we were no longer able to compute transition paths or even steady states.
If our intuition and simulation experience told us that our transition paths were unique, we were still very relieved when Laitner (1984) took on the task of examining this issue formally by linearizing our model. He found that, for at least the linearized version of our model, there was a unique transition path for the range of parameter values we were using.