Question

1. Describe each of the five assumptions (or more, since it's better!) required for an instrumental variable's analysis. 2. Label the three assumptions represented in the diagram below. 3. Why is the effect measured from an instrumental variables approach referred to as the local average treatment effect?

Answer 1

(i) the five assumptions of instrumental variable analysis are as follows:

1. The instrument must be associated with the exposure. This can be checked by verifying if there is an association between the two. the relationship is such that the instrument must be predictive of exposure. this assumption is called assumption of relevance.

2. the instrument can only effect the outcome through having an effect on exposure. the instrument cannot directly effect the outcome. This assumption is called exclusion restriction. There are certain test available to test this, however, the knowledge of relationship between the three- instrument, outcome and exposure must be known as an verifiable factor.

3. The instrument do not share common causes with the outcome. This assumption ma be called exchangeabilty or independence assumption. This also means that the instrument does not have any confounding effect on outcome.

4. Forth assumption is effect of homogeneity. it states the instrument should change the effect of of the exposure on the outcome among the exposed and unexposed on the additive scale.

5. Assumption of monotonicity. this is an alternative assumption to effect of homogeneity assumption.

(ii) there is relationship between instrument (Z) and treatment (D)

instrument only affect outcome (Y) via treatment (D)

instrument(Z) is not affected by the unmeasured confounders (X)

(iii)  Population average causal effects are estimable under an important assumption on the effect of the instrument on the endogenous regressor and without this assumptions only average effects for subpopulations are identifiable that are induced by the instrument to change the value of the endogenous regressors. Such subpopulations as compliers, and to the average treatment effect that is point identifed as the local average treatment effect. This terminology stems from the canonical example of a randomized experiment with noncompliance.