Explain instrumental variables with an example
Last updated: July 7, 2025
Quick Overview
Explain instrumental variables in simple terms and provide a concrete example.
Morgan Stanley
July 7, 20257
5
1,287 solved
Explain instrumental variables in simple terms and provide a concrete example.
Morgan Stanley values data-driven decision making. This Technical Screen question assesses whether you can design experiments, interpret results correctly, and avoid common statistical pitfalls like p-hacking or Simpson's paradox.
What the Interviewer Expects
- Derive results from first principles when needed
- Handle complex scenarios with multiple interacting variables
- Design experiments that account for real-world complications
- Discuss advanced topics: Bayesian methods, causal inference, resampling
- Connect statistical concepts to business decision-making
- Identify subtle errors in reasoning (Simpson's paradox, survivorship bias)
Key Topics to Cover
How to Approach This
- Define your hypotheses (H0 and H1) clearly before performing any test.
- Calculate required sample size BEFORE running an experiment, using power analysis.
- Remember the Central Limit Theorem: sample means become approximately normal with large n.
- Watch for Simpson's paradox. Always segment data by key dimensions.
- Distinguish between statistical significance and practical significance.
Possible Follow-up Questions
- What if the sample size is very small?
- How would you explain this result to a non-technical audience?
- How would you design a follow-up experiment based on these results?
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Browse Statistics QuestionsSample Answer
Problem Formulation
In causal inference and econometrics, we often face the challenge of estimating the effect of an independent variable (X) on a dependent variable (Y) when there is potential confounding due to omitted...
Solution Approach
To use instrumental variables, we follow these steps:
- Identify a suitable instrument Z that is correlated with X.
- Use the first stage of regression to predict X using Z:
X = π0 + π1Z + ...
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