ECMT3120 Chap.3 Endogeneity and Instrument Validity
Endogeneity and Instrument Validity
Endogeneity links a regressor to the structural error and makes the OLS slope combine a target effect with omitted influences. This chapter traces omitted variables, simultaneous determination, measurement error and proxy strategies before introducing instrumental variables.
It keeps relevance separate from exogeneity, derives the simple covariance ratio, shows why first stage evidence cannot establish exclusion, and explains why weak instruments magnify even modest validity failures.
What this chapter covers
- 01
Endogenous and exogenous regressors
- 02
OLS bias decomposition
- 03
Omitted variables and proxy strategies
- 04
Instrument relevance and first stage evidence
- 05
Instrument exogeneity and exclusion reasoning
- 06
Simple instrumental variable covariance ratio
- 07
Weak and invalid instrument interaction
Worked example · free
Compute a simple IV ratio
- +1Label the 1.2 session change as the first stage and the 4.8 point change as the reduced form.
- +1Divide 4.8 by 1.2 to obtain 4 productivity points per additional completed session.
- +1Use random assignment to support independence of the reminder from baseline omitted determinants.
- +1Defend exclusion by ruling out direct morale, monitoring and information effects on productivity.
- +1State that the effect applies to behaviour changed by the reminder under the maintained assumptions.
- +1Do not describe random assignment of the reminder as random assignment of completed training.
Key terms
- Endogeneity
- Correlation between an included regressor and the structural error that contaminates the OLS comparison.
- Proxy variable
- An observed measure intended to stand in for an omitted determinant under additional measurement assumptions.
- Instrument relevance
- The condition that an excluded instrument changes or predicts the endogenous regressor after controls.
- Instrument exogeneity
- The condition that an instrument is unrelated to the structural error and has no forbidden path to the outcome.
- Reduced form
- The relationship between an exogenous instrument and the outcome before scaling by the first stage.
- Weak instrument
- An instrument that supplies little predictive variation in the endogenous regressor, creating imprecision and poor finite sample behaviour.
Endogeneity and Instrument Validity FAQ
Why does endogeneity break ordinary least squares?
When a regressor covaries with the structural error, the OLS slope combines the target effect with the influence of omitted factors associated with the regressor. The problem is identification, so a smaller standard error or larger sample does not remove the contaminated comparison.
What is the difference between a proxy and an instrument?
A proxy tries to measure the omitted factor itself, while an instrument seeks a source of regressor movement that avoids correlation with omitted structural determinants. A variable can predict the regressor strongly yet fail as an instrument because it also affects the outcome directly.
Can instrument exogeneity be tested in a first stage?
No. The first stage concerns whether an instrument predicts the endogenous regressor after controls. Exogeneity concerns an unobserved structural error and usually requires economic or institutional reasoning about direct effects, omitted common causes and behavioural responses.
Exam move
For every candidate instrument, draw the intended path from instrument to endogenous regressor to outcome and then search for one forbidden path into the structural error. Write statistical evidence under relevance and design reasoning under exogeneity. Practise the simple covariance ratio with units so the numerator and denominator remain distinct.
For omitted variable bias, state the sign of the omitted factor's outcome effect and its covariance with the regressor. When an instrument is weak, explain both the loss of precision and the magnification of small validity failures. End by naming the population or behaviour whose variation the instrument actually changes rather than claiming a universal effect. Make relevance and validity physically separate on the page.
Under relevance, record the first-stage sign, size and uncertainty after controls. Under validity, list direct effects, shared causes, behavioural responses and timing channels that could connect the instrument to the outcome outside the intended route. Practise distinguishing a proxy, which measures an omitted determinant, from an instrument, which supplies an alternative source of regressor movement.
For a binary instrument, label the reduced form and first stage before dividing, attach units to both differences, and check that the resulting ratio has outcome units per regressor unit. If the denominator is small, explain why the ratio becomes unstable and why a slight exclusion violation matters more.
Finish with a scoped sentence that identifies the people or decisions whose exposure responds to the instrument and avoids presenting a local comparison as a universal causal law.
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