In the naïve model, the effect of the price increase is a 6.63% increase in the sales. In the IV model, the effect is estimated to be 18% higher. So, what is going on here, and which of the two is correct? Such an inflated effect size in the IV model compared to the naïve model is not uncommon. There are several potential reasons for this, from the most obvious to the least obvious: 1. In the naïve model, an omitted variable that is negatively correlated with the policy may cause a downward bias in the estimated effect. Our hope is to resolve such endogeneity by using [[Design Pattern I - Instrumental Variable (IV)|the IV design pattern]], so that our estimation in the IV model may provide the truer effect size. 2. The IV estimate is consistent as long as the instrument is exogenous/independent/unconfounded. This is not a testable assumption, as discussed in [[Data centricity in the IV pattern]]. If the instrument does not satisfy the assumption, then the IV estimate is in question, and the naïve effect size may be the truer. 3. The IV estimate may be larger because the IV model ends up estimating the [[Local Average Treatment Effect]] (LATE) rather than the average treatment effect as in the naïve model. Here's why. The instrumental variable, the number of registered lobbyists in the example, may influence legislation where the effect of the healthcare bill is larger than average. These may also be states where the enforcement of the bill is stricter or simply where such policies are actionable. The IV estimate is then for a subpopulation hence the LATE. If this is the case, then the IV estimate will be larger simply because of the heterogeneity in the sample. This is related to the monotonicity and homogeneity assumptions briefly discussed in [[Data centricity in the IV pattern]]. > [!info]- Last updated: January 27, 2025