Control variates for variance reduction in indirect inference: Interest rate models in continuous time

Abstract

Simulation estimators, such as indirect inference or simulated maximum likelihood, are successfully employed for estimating stochastic differential equations. They adjust for the bias (inconsistency) caused by discretization of the underlying stochastic process, which is in continuous time. The price to be paid is an increased variance of the estimated parameters. The variance suffers from an additional component, which depends on the stochastic simulation involved in the estimation procedure. To reduce this undesirable effect, one could increase the number of simulations (or the length of each simulation) and thus the computational cost. Alternatively, this paper shows how variance reduction can be achieved, at virtually no additional computational cost, by use of control variates. The Ornstein–Uhlenbeck process, used by Vasicek to model the short‐term interest rate in continuous time, and the square‐root process, used by Cox, Ingersoll and Ross, are explicitly considered and experimented with. Monte Carlo experiments show a global efficiency gain of almost 50% over the simple indirect estimator.

Constrained Indirect Estimation

“…In particular, the recent GMM literature suggests that the continuously updated GMM-like methods suggested in Section 2.1 may improve the finite sample performance of our indirect estimators. In addition, constrained versions of the implicit bias adjustment procedures discussed by Gouriéroux, Renault and Touzi (2000), either on their own (see Arvanitis and Demos, 2003), or together with the control variates techniques developed by Calzolari, Di Iorio and Fiorentini (1998) may also prove useful in this respect. Similarly, the Laplace-type procedures recently proposed by Chernozhukov and Hong (2003) may result in estimators with better finite sample properties, particularly in dynamic latent variable models, like the SV example discussed in Section 3, in which the role of prior information on MCMC-based Bayesian estimators is non-negligible.…”

Estimating Functions in Indirect Inference

“…The correction is similar to use of the bootstrap; see Gouriéroux and Monfort (1996). Calzolari et al (1998) incorporate control variates to reduce the variance in indirect inference.…”

Constrained Indirect Estimation

“…In particular, the recent GMM literature suggests that the continuously updated GMM‐like methods suggested in may improve the finite sample performance of our indirect estimators. In addition, constrained versions of the implicit bias adjustment procedures discussed by Gouriéroux, Renault and Touzi (2000), either on their own (see Arvanitis and Demos, 2003), or together with the control variates techniques developed by Calzolari, Di Iorio and Fiorentini (1998) may also prove useful in this respect. Similarly, the Laplace‐type procedures recently proposed by Chernozhukov and Hong (2003) may result in estimators with better finite sample properties, particularly in dynamic latent variable models, like the SV example discussed in , in which the role of prior information on MCMC‐based Bayesian estimators is non‐negligible.…”