MFIN6201 Chap.8 Instrumental Variables and Causal Evidence
Instrumental Variables and Causal Evidence
This chapter treats instrumental variables as a design for isolating exogenous movement in an endogenous regressor. Relevance links the instrument to treatment, while exogeneity and exclusion close unwanted paths to the outcome. The two-stage interpretation, just-identified ratio, weak-instrument warning and design-based defence prepare students to evaluate unfamiliar causal settings.
The first stage measures how Z changes X; the reduced form measures how Z changes Y. Their ratio gives a just-identified effect in compatible units when the IV conditions hold. A strong first stage is visible in data, but exogeneity and exclusion rely on institutional reasoning about assignment, timing and alternative pathways. A direct effect of Z on Y contaminates the ratio even when prediction is excellent.
A weak first stage divides by a noisy value near zero, creating unstable estimates and unreliable conventional approximations. IV often estimates an effect for units whose treatment responds to the instrument, so external scope may be narrower than an OLS association. The method trades breadth and precision for a potentially cleaner source of variation.
What this chapter covers
- 01
Endogeneity problem
- 02
Instrument relevance
- 03
Instrument exogeneity
- 04
Exclusion restriction
- 05
Two-stage least squares
- 06
Weak instruments
Worked example · free
A just-identified IV ratio
- +1Identify 0.12 as the first-stage effect.
- +1Identify 0.036 as the reduced-form effect.
- +1Divide 0.036 by 0.12 to obtain 0.30 outcome units per treatment unit.
Key terms
- Instrument relevance
- The requirement that an instrument changes or predicts the endogenous regressor.
- Instrument exogeneity
- The requirement that an instrument is unrelated to the structural outcome error.
- Exclusion restriction
- The claim that an instrument affects the outcome only through the endogenous regressor.
Instrumental Variables and Causal Evidence FAQ
What makes an instrument valid?
It must move the endogenous regressor, remain unrelated to omitted outcome determinants and have no direct or alternative route to the outcome. Relevance can be measured in the first stage, while exogeneity and exclusion require a credible design argument.
Why are weak instruments dangerous?
A very small first-stage effect leaves little exogenous treatment variation and makes the IV ratio unstable. Estimates can become imprecise and conventional approximations unreliable. A persuasive exclusion story cannot compensate for an instrument that barely changes treatment.
How does IV differ from adding controls?
Controls seek conditional comparability by holding measured factors fixed. IV instead isolates a particular external source of treatment variation. The gain can be stronger causal credibility, but the resulting effect may apply to a narrower population influenced by the instrument.
Can a strong first stage prove validity?
No. It shows that the instrument predicts treatment and therefore addresses relevance. It cannot rule out a direct outcome effect or correlation with omitted determinants; those conditions require design and institutional evidence.
Why can an IV estimate have narrow scope?
The estimate is learned from units whose treatment changes with the instrument. Units that always or never take treatment may not contribute the same comparison, so the responsive population should be named before generalising.
What is the reduced-form effect?
It is the effect of the instrument on the outcome before dividing by the first-stage treatment effect. In a just-identified setting, the reduced form supplies the numerator of the IV ratio and must use the same contrast and sample.
How should alternative instrument pathways be audited?
Draw every plausible route from the instrument to the outcome, including information, selection and policy channels. Exclusion is credible only when those routes are absent or convincingly blocked, not merely because the intended treatment pathway is easy to describe. Discuss the most credible rival route explicitly.
Exam move
Defend every candidate instrument in three sentences: how it changes treatment, why it is independent of omitted outcome determinants, and why it has no other route to the outcome. Compute simple IV ratios with units, then stress-test them against a weak first stage or direct channel. Connect the design back to conditional mean zero and omitted-variable bias.
Draw the allowed Z-to-X-to-Y path and cross out the direct Z-to-Y route. List any institutional mechanism that could reopen it. Keep the first-stage and reduced-form samples, signs and units aligned before dividing. Work examples with positive and negative first stages so a sign does not become a memorised rule.
Compare a strong invalid instrument with a weak plausibly exogenous one and explain why neither is automatically satisfactory. State the population whose treatment responds to Z and avoid universalising that effect. End by writing the source-of-variation sentence: the coefficient is learned from changes in X caused by the named instrument under the maintained exclusion story.
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