Generalized covariance‐based inference for models set‐identified from independence restrictions

This article develops statistical inference methods for a class of set‐identified models, where the errors are known functions of observations and the parameters satisfy either serial or/and cross‐sectional independence conditions. This class of models includes the independent component analysis (ICA), Structural Vector Autoregressive (SVAR), and multi‐variate mixed causal–non‐causal models. We use the Generalized Covariance (GCov) estimator to compute the residual‐based portmanteau statistic for testing the error independence hypothesis. Next, we build the confidence sets for the identified sets of parameters by inverting the test statistic. We also discuss the choice (design) of these statistics. The approach is illustrated by simulations examining the under‐identification condition in an ICA model and an application to financial return series.