Review of Partial and Point Identification Results Using Instrumental Variable Type Assumptions

INTRODUCTION: Studies using instrumental variable (IV) methods rely on strong assumptions to present a point estimate for the average treatment effect (ATE), yet epidemiologists may be unaware of how combinations of IV-type assumptions lead to partial or point identification.

METHODS: We reviewed the identification results under IV-type assumptions presented in the statistical, epidemiological, and econometric identification literature, and synthesized the results into a common notation and description of underlying assumptions. We primarily considered identification of the ATE for dichotomous treatments and outcomes. 

RESULTS: Without data or assumptions, we know nothing about the ATE (bounds: [-1, 1]). With no assumptions, observed data cuts the width of these bounds in half. Under the exclusion restriction and independence assumptions (i.e., the IV-type assumptions), the identification region may be smaller. Assuming marginal versus joint independence results in different expressions for the bounds, although in practice the bounds may often be equal. Bounds under the IV-type assumptions may be quite wide; combining these with further assumptions will be discussed. In particular, further assuming additive or multiplicative effect homogeneity leads to point identification, although the point estimates will differ when the effect is non-null. Examples of bounds and point estimates for the ATE under these various sets of assumptions will be presented, with discussion of when these assumptions may be more or less reasonable in practice.

CONCLUSIONS: Causal inference relies on a trade-off between making strong, untestable assumptions, and making more conservative assumptions that may not readily inform public health practice. Estimating the ATE under several sets of IV-type assumptions makes clear how much our conclusions rest upon the assumptions being made.