EMET8002 Chap.11 Instrumental Variables and Two-Stage Least Squares
Instrumental Variables and Two-Stage Least Squares
What an instrument does
Instrumental variables recover causal effects when a regressor is endogenous. A valid instrument must be relevant, correlated with the regressor, and exogenous, affecting the outcome only through the regressor.
The chapter explains why weak instruments mislead and why the exclusion restriction must be argued rather than tested.
Estimation and examples
Two-stage least squares, its first and second stages and the Stata commands are set out, followed by the lecture's candidate instruments for returns to education and its examples from military service, family firms and corporate finance.
Schooling and wages in the Week 11 lab
The Week 11 lab estimates the effect of schooling on hourly wages.
It asks why wages are logged, what sources of endogeneity threaten OLS, which controls to add and how the education coefficient moves, which variables in the dataset could serve as instruments, and how the 2SLS estimate compares with OLS. Credit follows from arguing each instrument's relevance and exclusion restriction in words and from reporting the first stage beside the result.
What this chapter covers
- 01
Why instrumental variables
- 02
The two parts of an endogenous regressor
- 03
Relevance and the first-stage F-test
- 04
Exogeneity and the exclusion restriction
- 05
Weak instruments
- 06
First and second stages
- 07
Returns to education
- 08
Candidate instruments and their critiques
Worked example · free
An instrumental variables return to schooling
- 1First stage: the schooling gap is 12.6 − 12.1 = 0.50 years.
- 1Reduced form: the log wage gap is 2.95 − 2.90 = 0.05.
- 1IV estimate: 0.05 divided by 0.50 is 0.10, about 10% higher wages per extra year.
Key terms
- Instrumental Variable
- A variable correlated with an endogenous regressor but not with the error term.
- Weak Instrument
- An instrument that explains little of the endogenous regressor, making inference unreliable.
- Two-Stage Least Squares
- An estimator that regresses the outcome on first-stage fitted values of the regressor.
- First Stage
- The regression of the endogenous regressor on the instrument and any controls.
Instrumental Variables and Two-Stage Least Squares FAQ
What makes an instrument valid?
It must be relevant, meaning correlated with the endogenous regressor, which a first-stage F-test can check, and exogenous, meaning uncorrelated with the error so that it affects the outcome only through the regressor. The second condition cannot be tested and must be argued.
Why might two valid instruments give different IV estimates?
Each instrument shifts the regressor for a different group of people, so each identifies the effect for that group. The lecture stresses that different instruments identify different parameters and answer different questions.
Is father's education a good instrument for schooling?
It is likely relevant, since it correlates with a child's schooling, but its exogeneity is doubtful. It may affect wages directly, through family networks or inherited ability, which would place it in the error term and violate the exclusion restriction.
What happens with a weak instrument?
If the instrument explains little of the variation in the endogenous regressor, statistical inference becomes unreliable and the IV estimator is biased. A small first-stage F-statistic is the warning sign, and the remedy is a stronger instrument rather than a more confident reading of the estimate.
Which problems can instrumental variables solve?
They address endogeneity from omitted variables, measurement error in the regressor, and simultaneous or reverse causality, provided a valid instrument exists. The lecture stresses that good instruments are hard to find, so most of the work lies in defending the one you use.
Assessment move
For every instrument you meet, write two sentences: one for why it shifts the regressor and one for the most plausible way it could affect the outcome directly. Then decide whether the second sentence defeats the design. Then compare your IV and OLS estimates and explain which source of bias best accounts for the gap between them.
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