Econometric identification: state what makes a coefficient causal
An estimator is a calculation; identification explains why that calculation answers a causal question under a stated model. This route separates the target effect, the source of variation, the assumptions and the numerical ratio. It uses exact hypothetical population moments so sampling uncertainty cannot conceal an identification problem.
Study route and exercise: University Reading List editorial project. How we curate · Sources checked:
On this page
Scope and responsibility
For learners with introductory economics, probability, expectations and regression vocabulary. The Effect offers a free intuitive design route; Wooldridge develops regression assumptions; Stock/Watson links applications and inference. The original binary-instrument packet is synthetic and makes no claim about an actual intervention, person or policy.
Choose your starting point
I need to understand the design before estimating
Use The Effect’s identification and causal-diagram discussion, then its instrumental-variable chapter. Name the variation you want to isolate before selecting software.
I need the regression foundations
Use the selected Wooldridge copy for assumptions, coefficient interpretation and instrumental-variable reasoning. Do not import a current edition’s page map into this 2006 entry.
I need applications plus inference
Use Stock/Watson to connect an economic question with regression, validity threats and statistical uncertainty. Keep an exact population ratio distinct from an estimated sample ratio.
Compare the three books
The Effect: An Introduction to Research Design and Causality
Nick Huntington-Klein · Edition: 2 · 2025
Free design-first spine
- Choose it when
- You need graphical intuition about what identifies an effect before technical implementation.
- Use another route when
- You need a graduate asymptotic theory text or assume a diagram alone verifies its arrows.
- Selected reading
- 2025 second-edition route: identification, causal diagrams/paths, treatment effects and the named instrumental-variable chapter.
- Limits and trade-offs
- The authorized complete web edition can receive corrections independently of the paperback ISBN 9781032580227. R/Stata/Python examples are implementation choices, not alternative identification assumptions.
Try before choosing
Draw the intended Z→D→Y path and list every other way Z could affect Y.
Check your work: Separately defend instrument independence, treatment relevance and exclusion rather than calling an instrument valid because it predicts treatment.
Introductory Econometrics: A Modern Approach
Jeffrey M. Wooldridge · 2006
Regression-assumptions spine
- Choose it when
- You want sustained cross-section regression and the logic of endogeneity/IV after statistics.
- Use another route when
- You need a modern software recipe or assume a coefficient is causal just because controls were included.
- Selected reading
- Selected 2006 copy, ISBN 9780324289787: basic regression and inference before named endogeneity/instrumental-variable material; match the copy’s own contents.
- Limits and trade-offs
- The older selected text is not silently replaced by a newer Cengage edition. Core assumptions remain useful, while software interfaces and later methods require separate reading.
Try before choosing
Write the outcome unit, treatment unit and the difference between a first stage and reduced form.
Check your work: A ratio with a nonzero denominator is numerically defined; that is not a proof of its causal interpretation.
Introduction to Econometrics
James H. Stock; Mark W. Watson · Edition: 4 · 2018
Applications-and-inference reference
- Choose it when
- You want regression theory alongside empirical questions and threats to validity.
- Use another route when
- You need a substitute for articulating the identifying source of variation or for the probability prerequisites.
- Selected reading
- Selected fourth-edition 2018 hardcover ISBN 9780134461991: regression validity/inference and instrumental-variable discussions by title.
- Limits and trade-offs
- The product page also offers later digital versions and access packages. The selected print identity remains 2018; courseware is not implied by its ISBN.
Try before choosing
Explain how a finite-sample estimate would add uncertainty to the exact population calculation below.
Check your work: Separate the sampling problem from independence, exclusion and the question of whose effect is identified.
Check your preparation
What are the variables?
Z and D are binary instrument and treatment. Y is an outcome in score points. A treatment effect compares the same unit’s potential outcomes under D=1 and D=0.
Whose effect can IV identify here?
Under the stated binary monotonic model, the average treatment effect for compliers: units whose treatment changes from 0 to 1 when Z changes. Always-takers and never-takers need not share that effect.
Why use exact moments?
They remove sampling error for the worksheet. They do not verify the structural assumptions, establish an observed study or make a population-average effect appear automatically.
A six-step study plan
Steps completed: 0 / 6
These are your own study marks, not an assessment. They are not sent to this site.
-
Define the estimand
Selected reading: The Effect treatment-effects discussion.
What to do: Write whether the target is a population effect or a complier effect, and state its unit.
Check your work: A familiar estimator name does not define the target by itself.
-
Draw the design
Selected reading: Identification and causal-path reading.
What to do: Draw Z→D→Y and mark possible alternative routes or common causes.
Check your work: Relevance and exclusion address different parts of the diagram.
-
Separate two contrasts
Selected reading: Selected IV discussion.
What to do: Compute E[D|Z=1]−E[D|Z=0] and E[Y|Z=1]−E[Y|Z=0].
Check your work: Label the first stage in treatment-probability units and the reduced form in outcome points.
-
Explain the ratio
Selected reading: The original population packet.
What to do: Derive the complier share and interpret the Wald ratio under all assumptions.
Check your work: The interpretation is local to compliers; report no unsupported effect for every unit.
-
Change one structural restriction
Selected reading: The solved direct-effect follow-up.
What to do: Remove a known additive direct instrument effect before dividing, then allow its stated range.
Check your work: Do not keep the old exclusion interpretation after permitting a direct path.
-
Write a bounded report
Selected reading: Stock/Watson inference or Wooldridge assumptions.
What to do: Report the calculation, assumptions, target group and what actual data would still need to establish.
Check your work: A sensitivity range is not a confidence interval, and a precise ratio does not validate a design.
Worked exercise
Original IV population: a ratio is local to a response type
In a wholly hypothetical population, exact moments are E[D|Z=0]=0.20, E[D|Z=1]=0.60, E[Y|Z=0]=10, E[Y|Z=1]=14. D and Z are binary and Y is measured in points. Find the first stage, reduced form, complier share and the effect identified by their ratio.
Assumptions
Z is independent of both potential outcomes and potential treatment-uptake types. Treatment and outcomes are well defined and consistent, with no interference. Exclusion means Z affects Y only through D. Monotonicity is D(1)≥D(0) for every unit, and the first stage is nonzero. Moments are exact population quantities, not sample estimates or human data.
- The first stage is 0.60−0.20=0.40 in treatment probability. The reduced form is 14−10=4 outcome points. The Wald ratio is 4/0.40=10 points per treatment switch.
- With binary monotonic uptake,0.20 are always-takers,0.40 are compliers and 0.40 never-takers. There are no defiers under the stated assumption.
- Independence and exclusion make the outcome contrast attributable to treatment changes among the 0.40 compliers. Dividing by that share identifies their mean effect 10.
- No corresponding treatment change reveals the missing counterfactual effects for always- or never-takers. Their effects, and therefore the overall population average, are not determined by these four moments.
Answer and interpretation
First stage 0.40, reduced form 4, complier share 0.40 and complier average effect 10 points under the complete model. This is not automatically an average effect for everyone.
Test the result
Check type shares sum to 1 and 0.40×10=4. If exclusion or independence is withdrawn, the numerical ratio still exists but its stated causal meaning need not survive.
Change an assumption
Changed exclusion: the instrument also adds to the outcome
Keep the same exact moments and uptake assumptions, but replace exclusion by Y=Y_base(D)+δZ. The same additive direct effect δ applies to every unit, with no D interaction; Z remains independent of baseline potential outcomes and uptake types. First set δ=1.5 points, then suppose only 0≤δ≤2 is known.
- The observed reduced form 4 now includes both the direct δ and the complier-treatment contribution 0.40×LATE_base. Thus 4=δ+0.40×LATE_base.
- At δ=1.5, the baseline complier effect is (4−1.5)/0.40=6.25 points. The unchanged naive ratio 10 combines the two channels.
- For δ∈[0,2], the corrected effect ranges from (4−2)/0.40=5 to 4/0.40=10. This is a structural sensitivity range under a uniform additive path, not a confidence interval or a result for unrestricted violations.
Answer and interpretation
Known direct effect 1.5 gives corrected complier effect 6.25; a direct effect restricted to [0,2] gives [5,10]. The original exclusion claim has been replaced, not somehow verified.
Test the result
Multiply each endpoint by 0.40 and restore its corresponding δ to recover 4. A heterogeneous direct effect or D interaction would require a different model.
Common mistakes
Relevance called validity
An instrument can move treatment and also affect outcomes through another path.
Local effect called everyone’s effect
Complier responses do not identify effects for units whose treatment never changes.
Sensitivity called precision
Exact moments remove sampling noise, not uncertainty about structural restrictions.
Before moving on
- I can state the target and each separate identification assumption.
- I can reproduce the ratio, response-type shares and direct-path correction.
- I can distinguish a local causal effect, a structural sensitivity range and sample uncertainty.
Sources and edition checks
Sources checked:
- Author: complete free research-design text
The free design/toolbox structure supports identification before implementation.
- Routledge: selected 2025 second edition
The selected 2025 second edition and independently updated web pagination are distinguished.
- KRIHS library: held 2006 third edition and contents
The selected older copy’s regression/IV scope is retained rather than replaced by a newer edition.
- Pearson: selected 2018 fourth-edition hardcover and later formats
The selected 2018 hardcover is distinguished from later digital products. The population moments and solutions are original.
These are proposed study activities, not official course assignments or a claim that every book has been read cover to cover.