Indirect Estimation of Just-Identified Models with Control Variates

Simulation estimators, such as indirect inference or simulated maximum likelihood, are successfully employed for estimating models where the likelihood function does not have a simple analytical expression. They adjust for the bias (inconsistency) produced by the estimation of an auxiliary model that can be manageable, but is essentially misspecified. The price to be paid is an increased variance of the estimated parameters. A component of the variance depends on the stochastic simulation involved in the estimation procedure. To reduce this undesirable effect, one should properly 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. This technique can be easily applied in the just-identified context, that is when the number of parameters is the same in the econometric model (the model of interest) and the auxiliary model. This is a case which often occurs in practical applications. Several models are explicitly considered and experimented with: moving average model, Arma model, stochastic differential equations, dynamic Tobit model, discrete time stochastic volatility models, logit models with random effects. Monte Carlo experiments show, in some cases, a global efficiency gain up to almost 50% over the simplest indirect estimator, obtained at about the same computational cost