Finite Sample Properties of Parameterized Expectations Algorithm Solutions; Is the Length So Determinant?

The solution of the Parameterized Expectations Algorithm (PEA) is well defined based on asymptotic properties. In practice, it depends on the specific replication of the exogenous shock(s) used for the resolution process. Typically, this problem is reduced when a sufficiently long replication is considered. In this paper, we suggest an alternative approach which consists of using several, shorter replications. A centrality measure (the median) is used then to discriminate among the different solutions using two different criteria, which differ in the information used. On the one hand, the distance to the vector composed by median values of PEA coefficients is minimized. On the other hand, distances to the median impulse response is minimized. Finally, we explore the impact of considering alternative approaches in an empirical illustration.