Sensitivity analysis using approximate moment condition models

We consider inference in models defined by approximate moment conditions. We show that near‐optimal confidence intervals (CIs) can be formed by taking a generalized method of moments (GMM) estimator, and adding and subtracting the standard error times a critical value that takes into account the potential bias from misspecification of the moment conditions. In order to optimize performance under potential misspecification, the weighting matrix for this GMM estimator takes into account this potential bias and, therefore, differs from the one that is optimal under correct specification. To formally show the near‐optimality of these CIs, we develop asymptotic efficiency bounds for inference in the locally misspecified GMM setting. These bounds may be of independent interest, due to their implications for the possibility of using moment selection procedures when conducting inference in moment condition models. We apply our methods in an empirical application to automobile demand, and show that adjusting the weighting matrix can shrink the CIs by a factor of 3 or more.

Model and Moment Selection in Factor Copula Models*

This article develops a simultaneous model and moment selection procedure for factor copula models. Since the density of the factor copula is generally not known in closed form, widely used likelihood or moment-based model selection criteria cannot be directly applied on factor copulas. The new approach is inspired by the methods for generalized methods of moments proposed by Andrews (1999) and Andrews and Lu (2001). The consistency of the procedure is proved and Monte Carlo simulations show its good performance in finite samples in different scenarios of sample sizes and dimensions. The impact of the choice of moments in selected regions of the support on model selection and value-at-risk prediction is further examined by simulation and an application to a portfolio consisting of ten stocks in the Deutscher Aktienindex (DAX30) index.