Those who have better ability tend to have
Those who have better ``ability’’ tend to have higher edu. and earn more! College Graduates No College Unmeasured Confounders (Ability) Exposure (Edu) No Unmeasured Confounders: More edu increases income (p: 10^-16!) $30 K income With Unmeasured Confounder (i. e. abilitiy) More edu does not increase income(p: 0. 32!) $50 K income $60 K income Outcome (Earning) Directed Acyclic Graph (DAG) Representation Goal: How do you determine causality in the presence of unmeasured confounders?
College Graduates No College $30 K income $50 K income $60 K income Unmeasured Confounders (Ability) Exposure (Edu) Outcome (Earning) Directed Acyclic Graph (DAG) Representation
Unmeasured Confounders (e. g. Ability) Assumption 3 No Unmeasured Confounders Instrument (Z) (e. g. proximity to college) Exposure (D) (e. g. Edu) Assumption 1 Relevance The random instrument (by (A 3)) ``injects’’ some randomness into the exposure via (A 1) and only into the exposure (A 2). Assumption 2 Exclusion Restriction Outcome (Y) (e. g. Earnings) If all the assumptions are satisfied, instrument is valid and the causal effect can be estimated!
Steps for IV Analysis 1) Find IVs related to exposure. 2) Assume they meet other IV assumptions 3) Run two stage least squares (TSLS) (regress D on Zs, then Y on predicted D) Instrument (Z 1) (proximity to 4 yr college) Assumption 3 No Unmeasured Confounders Instrument (Z 2) (proximity to 2 yr college) (Z) Instrument … Instrument (ZL) (quarter of birth) # Dhat = predict(lm(D ~ Z)); coef(lm(Y ~ Dhat)) Unmeasured Confounders (Ability) Exposure (D) (Edu) Assumption 1 Relevance Assumption 2 Exclusion Restriction Outcome (Y) (Earnings)
Choice to live near college towns may not be completely random! Steps for IV Analysis 1) Find IVs related to exposure. 2) Assume they meet other IV assumptions 3) Run two stage least squares (TSLS) (regress D on Zs, then Y on predicted D) Takeaway Point: Instrument (Z 1) (proximity to 4 yr college) Assumption 3 No Unmeasured Confounders # Dhat = predict(lm(D ~ Z)); coef(lm(Y ~ Dhat)) Unmeasured Confounders (Ability) In practice, some IVs are not likely to completely satisfy all (A 1)-(A 3) Instrument (Z ) (proximity to 2 yr assumptions. Exposure (D) Outcome (Y) college) Instrument (Z) 2 (Edu) … Instrument (ZL) (quarter of birth) Assumption 1 Relevance Assumption 2 Exclusion Restriction (Earnings) Living close to colleges may provide indiv. with more opportunity besides edu. (Barter et al. 2006 for survey) Association may be weak, especially quarter of birth (Bound et al. 1995)
Summary statistics Standard IV methods Methods for violations of IV assumptions (A 1)-(A 3)
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