Explain instrumental variables with an example

Question

Explain instrumental variables in simple terms and provide a concrete example.

Codemia · Accepted Answer

The analytical question at hand involves understanding the impact of a new security feature on user retention rates at CrowdStrike. However, there may be confounding factors such as customer engagement levels or previous security incidents that influence retention independently of the new feature. To isolate the effect of the new feature, we would need data on user retention rates, the timing of feature adoption, and potential confounding variables like user engagement metrics and prior incidents.

To address the confounding variables and establish a causal relationship between the introduction of the new feature and user retention, we can deploy instrumental variables (IV). An effective IV must be correlated with the independent variable (the new feature) but not directly affect the dependent variable (user retention) other than through the independent variable. For this scenario, we could use the 'time of feature rollout' in different geographical regions as an instrumental variable, assuming that the rollout timing impacts the adoption of the feature but does not directly influence user retention.

Suppose we have two cohorts: one that adopted the new security feature in Q1 and another in Q2. The retention rates for Q1 are 80% (with the new feature) and for Q2 (without) are 70%. The instrumental variable (rollout timing) shows that Q1 customers had access to the feature due to an earlier rollout. To calculate the IV effect, we use a two-stage least squares (2SLS) approach. First, we regress the adoption of the new feature on the instrumental variable (time of rollout) and get the predicted values of feature adoption. Then, we regress user retention on these predicted values to obtain the causal effect of the feature on retention.

If our analysis shows that users who adopted the new feature (as predicted by the IV) have a retention rate of 85%, compared to the unadopted group at 70%, we can conclude that the new security feature has a positive impact on user retention. This interpretation is conditional on the validity of our instrumental variable, meaning we assume that the rollout timing truly does not affect retention directly, thus providing a clearer view of the feature's effect.

Common mistakes in using instrumental variables include selecting a weak instrument that does not adequately correlate with the independent variable, leading to biased estimates. Additionally, failing to validate the exclusion restriction (the assumption that the instrument affects the dependent variable only through the independent variable) can lead to flawed conclusions. It's crucial to ensure that the chosen instrument meets these criteria to maintain the integrity of the causal inference.

Explain instrumental variables with an example

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