This paper is interested in the small sample properties of the indirect inference procedure which has been previously studied only from an asymptotic point of view. First, we highlight the fact that the Andrews (1993) median-bias correction procedure for the autoregressive parameter of an AR(1) process is closely related to indirect inference; we prove that the counterpart of the median-bias correction for indirect inference estimator is an exact bias correction in the sense of a generalized mean. Next, assuming that the auxiliary estimator admits an Edgeworth expansion, we prove that indirect inference operates automatically a second order bias correction. The latter is a well known property of the Bootstrap estimator; we therefore provide a precise comparison between these two simulation based estimators.
The possibility of exact maximum likelihood estimation of many observation-driven models remains an open question. Often only approximate maximum likelihood estimation is attempted, because the unconditional density needed for exact estimation is not known in closed form. Using simulation and nonparametric density estimation techniques that facilitate empirical likelihood evaluation, we develop an exact maximum likelihood procedure. We provide an illustrative application to the estimation of ARCH models, in which we compare the sampling properties of the exact estimator to those of several competitors. We find that, especially in situations of small samples and high persistence, efficiency gains are obtained.
Procedures for computing the parameters of a broad class of multifactor continuous time models of the term structure based on indirect estimation methods are proposed. The approach consists of simulating the unknown factors from a set of stochastic differential equations which are used to compute synthetic bond yields. The bond yields are calibrated with actual bond yields via an auxiliary model. The approach circumvents many of the difficulties associated with direct estimation of this class of models using maximum likelihood. In particular, the paper addresses the identification issues arising from singularities in the yields and spreads which tend not to be recognised in existing estimation procedures and thereby overcome potential misspecification problems inherrent in direct methods. Indirect estimates of single and multifactor models are computed and compared with the estimates based on existing estimation procedures.