Accuracy in Recursive Minimal State Space Methods

The constructive existence of a recursive minimal state space (MSS) representation is not always guaranteed. However, because of its numerical efficiency, this type of equilibrium is frequently used. What are the consequences of computing and simulating a model without a constructive proof? To answer this question, we identify a condition which is associated with a convergent and computable MSS representation in a RBC model with state contingent taxes. This condition ensures the existence of a benchmark equilibrium that can be used to test frequently used algorithms. To verify the accuracy of simulations even if this condition does not hold, we derive a closed form recursive equilibrium which contains the MSS representation. Both benchmark representations are accurate and ergodic. We show that state of the art algorithms, even if they are numerically convergent, may underestimate capital (and thus overestimate the benefits of capital taxes) by at least $$65\%$$ 65 % , a figure which is in line with recent findings using accurate benchmarks. When an existence proof is not available, we found 2 sources of inaccuracy: the lack of a convergent operator and the absence of a well-defined (stochastic) steady state. Moreover, we identify a connection between lack of convergence and the equilibrium budget constraint which implies that simulated paths may be distorted not only in the long run but also in any period. When we have a constructive proof, inaccuracy is generated by the lack of qualitative properties in the computed policy functions.