Constrained Indirect Estimation

Abstract

We develop generalized indirect estimation procedures that handle equality and inequality constraints on the auxiliary model parameters by extracting information from the relevant multipliers, and compare their asymptotic efficiency to maximum likelihood. We also show that, regardless of the validity of the restrictions, the asymptotic efficiency of such estimators can never decrease by explicitly considering the multipliers associated with additional equality constraints. Furthermore, we discuss the variety of effects on efficiency that can result from imposing constraints on a previously unrestricted model. As an example, we consider a stochastic volatility process estimated through a GARCH model with Gaussian or t distributed errors. 945

Indirect estimation of large conditionally heteroskedastic factor models, with an application to the Dow 30 stocks

“…Given that the HRS auxiliary model must be estimated subject to some inequality constraints, which are sometimes binding, we must use the constrained indirect estimation procedures proposed in our earlier work (see Calzolari, Fiorentini and Sentana (2004)), which can handle a mix of equality and inequality restrictions on θ. More specifically, the Generalised Method of Moments (GMM) version of the inequality constrained indirect estimator of % is…”

“…Figures 2a-b display box-plots with the sampling distributions of the two GMM-based indirect estimators of the structural parameters φ and ρ that we have proposed, together with the 8 As explained in footnote 1 of Calzolari, Fiorentini and Sentana (2004), one should not conduct unrestricted indirect estimation in terms of the unrestricted parameters θ † because the Jacobian of the transformation is singular when θ is at the boundary of its parameter space, which violates the usual regularity conditions required for the consistency of the indirect estimators.…”

“…Therefore, we are considering the equality restricted indirect estimators studied in Calzolari, Fiorentini and Sentana (2004). In this sense, note that since the consistency of the SF estimators of b and ψ does not depend on the normality assumption, the results discussed in section 3.2 continue to apply as long as the fourth moments of the innovations remain bounded, which happens whenever η < 1 4 .…”

Indirect estimation of elliptical stable distributions

“…While it should not be a problem asymptotically, it entails important estimation difficulties with finite samples. To avoid it, we constraint the degrees of freedom to remain below an upper bound, therefore resorting to the constrained indirect estimation of Calzolari, Fiorentini and Sentana (2004).…”

Estimation methods for stochastic volatility models: a survey

“…They also state that the e ciency of the method for nite samples strongly depends on the choice of the auxiliary model, specially for small samples. Calzolari et al (2000) also develop a Monte Carlo study based on the Jacquier et al (1994) design. Their procedure is shown to be less e cient than the approach of Jacquier et al (1994), as the auxiliary model does not nest the model of interest and no prior information is used.…”