What is Instrumental Variables?
Instrumental Variables are variables that shift treatment uptake, are independent of causes of the outcome under the design, and affect the outcome only through treatment, allowing a causal effect to be identified under additional assumptions.
Quick Facts
| Specification | Official Specification |
|---|
How It Works
Validity requires more than a strong first stage
Relevance requires the instrument to change treatment probability and can be assessed empirically. Exchangeability requires no common causes of instrument and outcome under the adjustment strategy. Exclusion requires the instrument to affect the outcome only through the treatment. The latter assumptions are principally defended by design and subject knowledge, not certified by a large first-stage statistic. Naimi and Whitcomb derive the IV estimand and make these assumptions explicit.
The causal target is often local to compliers
With binary instrument and treatment, monotonicity rules out units whose treatment moves opposite to the instrument. The Wald estimand then averages effects among units whose treatment would change with the instrument. Complier status is latent and instrument-specific, so LATE cannot be relabeled as ATE, ATT, or the effect for every observed treated unit without stronger assumptions.
Weak instruments and invalid instruments fail differently
A weak first stage creates unstable ratios, finite-sample bias, and misleading conventional confidence intervals; use weak-instrument-robust inference and report first-stage evidence. A strong but invalid instrument can produce a precise wrong answer when exclusion or exchangeability fails. Predeclare the causal graph, inspect reduced forms and compliance, test available implications, and perform sensitivity analyses instead of treating overidentification tests as proof.
Key Characteristics
- Uses externally induced variation in treatment rather than all observed variation
- Requires relevance, exchangeability, exclusion, and treatment consistency
- Often needs monotonicity for a complier-average interpretation
- Targets LATE rather than population ATE under heterogeneous effects
- Can be estimated with a Wald ratio or two-stage procedures
- Needs weak-instrument and assumption-sensitivity analysis
Common Use Cases
- Estimating treatment received when randomized assignment has noncompliance
- Using eligibility lotteries to evaluate program participation
- Studying an endogenous exposure when a defensible encouragement exists
- Estimating local effects in a fuzzy Regression Discontinuity Design
- Auditing whether a proposed instrument supports the intended policy estimand
Example
Loading code...Frequently Asked Questions
What makes an Instrumental Variable valid?
A valid instrument must move treatment, be independent of causes of the outcome under the design, and affect the outcome only through treatment. Consistency and no interference are also needed, while monotonicity supports a LATE interpretation. Relevance alone is testable; the other assumptions require substantive justification.
Can the exclusion restriction be tested from observed data?
Usually not directly because it concerns an absent causal path from instrument to outcome. Multiple instruments can create overidentifying restrictions, but passing those tests does not prove every instrument valid. Design knowledge, negative controls, mechanism analysis, and sensitivity checks remain necessary.
What is a weak instrument?
A weak instrument changes treatment only slightly, making the first-stage denominator small. Wald and 2SLS estimates can then be unstable and conventional normal approximations unreliable. Report the first stage and use weak-instrument-robust intervals rather than relying on a universal F-statistic cutoff.
Do Instrumental Variables estimate the Average Treatment Effect?
Not generally. Under binary treatment, binary instrument, and monotonicity, the standard IV estimand identifies LATE for compliers whose treatment responds to that instrument. It equals a broader ATE only under stronger effect-homogeneity or structural assumptions.
Is Two-Stage Least Squares sufficient for causal interpretation?
No. 2SLS is an estimator, not an identification argument. Its coefficient is causal only for a clearly defined estimand under valid instruments, appropriate functional assumptions, support, and correct uncertainty calculations. Robust standard errors do not repair exclusion or exchangeability violations.