Naïve OLS specification:

\[\ln(Y_i) = \alpha + \gamma \cdot \text{Institutions}_i + X_i' \theta + \eta_i\]

      U
     ↙ ↘
Institutions → Y

• Arrow \(U \to \text{Institutions}\) and \(U \to Y\) open a back‑door path: OLS conflates both.

Class check (1–2′):

• What observable proxy for \(U\) might you add to \(X\)? Why won’t that fully solve the problem?

3. Quick Review: Identification Strategies

Definitions:
“An identification strategy is your full blueprint for causal inference: - Data/design (IV, DiD, RDD…)
- Core assumptions (unconfoundedness, parallel trends, valid instruments)
- Estimator (2SLS, OLS, local‑linear…)
- Diagnostics (balance tests, placebo, over‑id)”

Two pillars for Identtification using IV’s:

• Relevance: \(\text{Cov}(Z,D) \neq 0\)
  
• Exclusion: \(Z\) affects \(Y\) only through \(D\)

4. IV as a Special Identification Strategy

Research question:
> “Do colonial institutions causally determine today’s GDP per capita?”

Endogeneity recap:
“Better places might have attracted settlers in the first place, so institutions aren’t randomly assigned.”

Instrument: Settler mortality \(Z\)
- High mortality → extractive institutions
- Low mortality → European‑style institutions

2SLS equations on slide:

First stage:
\[D_i = \pi_0 + \pi_1 Z_i + X_i'\gamma + u_i\]

Second stage:
\[\ln(Y_i) = \beta_0 + \beta_1\,\widehat{D}_i + X_i'\delta + \varepsilon_i\]

1. Check Understanding:
   

• Explain how \(\widehat{D}_i\) is the “predicted institutions” from mortality, purged of endogeneity.

5. DAG of the OLS vs. IV Designs

Recap OLS DAG

Introduce IV DAG:

     U
    ↙ ↘
   Z → D
    ↘ ↓
      Y

1. Explain arrows:

• \(Z \to D\): instrument relevance
  
• \(D \to Y\): causal pathway we want
  
• \(U \to D\) & \(U \to Y\): confounders we wish to block
  
• No direct \(Z \to Y\) allowed under exclusion.

1. Student exercise (5′):
   

• On paper or whiteboard, have students add arrows representing each potential back‑door (disease, human capital, measurement noise).

6. Threats to Exclusion & “Back‑Door” Paths (55–65′)

A. Disease channel:
- \(Z\) proxies historical disease environment → persistent health burdens → \(Y\).

B. Human‑capital channel:
- Low mortality → settlers invest in schooling/health → higher modern human capital → \(Y\).

C. Measurement error & omitted colonial factors:
- Noisy \(Z\) correlated with other unobserved colonial intensity factors → direct impact on \(Y\).

Mini‑poll or show of hands:
- “Which threat seems most plausible? A, B, or C?”
- Use this to decide which robustness check to emphasize next.

7. Robustness Checks in AJR (65–72′)

For each check, state which back‑door it targets:

Geography & disease controls (latitude, percentage of tropical land)
- Targets Disease channel (A)

Alternative instrument (European life expectancy)
- Checks Measurement error/noise (C)

Sample restrictions (drop small or atypical colonies)
- Mitigates extreme outliers and colonial–frontier confounding (C)

Placebo tests (predict pre‑colonial outcomes)
- Validates conditional independence: if \(Z\) affects something pre‑colonially, exclusion is suspect.

Over‑identification tests (J‑test with multiple IVs)
- Provides statistical check against multiple direct channels.

8. Wrap‑up, Discussion & Further Reading (72–75′)

Recap key points: - OLS is biased by unobserved \(U\).
- IV hinges on relevance and exclusion.
- DAGs make hidden back‑doors visible.
- Robustness checks are our toolbox for defending exclusion.

Discussion and References

Discussion questions: - “What additional data (e.g. historic schooling rates) could help close the human‑capital channel?”
- “Could a regression discontinuity design ever apply in this context?”

Further reading: - Albouy (2008), “Re‑examining mortality data in ‘Colonial Origins’.”
- Glaeser et al. (2004) comment & AJR reply.