Testing the validity of instrumental variables in just-identified linear non-Gaussian models.

Abstract

Instrumental variable (IV) estimation constitutes a powerful quasi-experimental tool to estimate causal effects in observational data. The IV approach, however, rests on two crucial assumptions-the instrument relevance assumption and the exclusion restriction assumption. The latter requirement (stating that the IV is not allowed to be related to the outcome via any path other than the one going through the predictor), cannot be empirically tested in just-identified models (i.e. models with as many IVs as predictors). The present study introduces properties of non-Gaussian IV models which enable one to test whether hidden confounding between an IV and the outcome is present. Detecting exclusion restriction violations due to a direct path between the IV and the outcome, however, is restricted to the over-identified case. Based on these insights, a two-step approach is presented to test IV validity against hidden confounding in just-identified models. The performance of the approach was evaluated using Monte-Carlo simulation experiments. An empirical example from psychological research is given to illustrate the approach in practice. Recommendations for best-practice applications and future research directions are discussed. Although the current study presents important insights for developing diagnostic procedures for IV models, sound universal IV validation in the just-identified case remains a challenging task.