MODEL AVERAGING IN TWO-STAGE LEAST SQUARES

Abstract

Causal inference using observational data is common since randomised controlled trials might not be available. However, producing reliable causal inferences from observational studies is challenging due to possible confounding with unobserved variables. The instrumental variable (IV) methods are attractive since they can lead to a consistent answer to the main question in causal modelling. However, it is acknowledged in the literature that using weak IVs might not suit the inference goal satisfactorily. We consider the problem of estimating causal effects in an observational study, allowing some IVs to be weak. To incorporate them in a 2-stage least squares (2SLS) estimation procedure, we consider a model averaging technique. Theoretical properties are established, including the consistency and asymptotic normality of the estimated causal parameter. Numerical studies are conducted to assess the performance in low- and high-dimensional settings. A real data example on home price is analysed to illustrate our methodology.