Flashcards on Instrumental Variables for Causal Inference
Instrumental Variables for Causal Inference: A Student Guide
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Instrumental Variables
38 cards
Card 1
Question: What is the Wald estimator in the context of instrumental variables (IV) for binary Z and X without controls?
Answer: The Wald estimator is the ratio of the difference in means of the outcome Y by instrument Z (reduced form) and the difference in means of the exposure
Card 2
Question: What does the simulation with the scholarship lottery (Z) demonstrate, and what was the approximate IV estimate of the effect of schooling on earnings
Answer: The simulation shows that the lottery Z affects college enrollment, and the Wald / 2SLS estimate approximately recovers the true effect of ~0.05 on ea
Card 3
Question: When is it appropriate to use 2SLS instead of the Wald formula?
Answer: When the instrument or endogenous variable is not binary, or when you want to include control variables. The Wald estimator only works for binary Z an
Card 4
Question: Describe the procedure for Two-Stage Least Squares (2SLS).
Answer: 1) First Stage: Regress X on Z (and controls) to obtain predicted X̂. 2) Second Stage: Regress Y on X̂ (and the same controls). The coefficient on X̂
Card 5
Question: Why does 2SLS 'work' — why does using X̂ eliminate the endogeneity problem?
Answer: Because X̂ contains only the part of X explained by the exogenous instrument Z; this part is, by construction, uncorrelated with the error term U, so
Card 6
Question: What is an important practical warning when performing 2SLS regarding standard error estimates?
Answer: Do not run two separate regressions and report the second-stage standard errors from them — they will be incorrect. Use the proper IV command (e.g., f
Card 7
Question: What are the four types of individuals according to Imbens–Angrist (1994) for binary Z and X?
Answer: Compliers (do not take X when Z=0, take X when Z=1), always-takers (X=1 for both Z), never-takers (X=0 for both Z), and defiers (take X when Z=0 and d
Card 8
Question: What are compliers, and why are they important for interpreting the IV estimate?
Answer: Compliers are those who change their behavior X due to the instrument Z (they take X only if encouraged). The IV estimate identifies the Local Average
Card 9
Question: What does monotonicity (no defiers) mean, and why must we defend it?
Answer: Monotonicity means that the instrument pushes people in only one direction (either more towards X=1 or more towards X=0) — thus, there are no defiers.
Card 10
Question: What examples of instrument Z and exposure X are given, and what types of individuals appear there (Oregon Medicaid)?
Answer: Z = winning the Medicaid lottery, X = Medicaid enrollment. Compliers: enroll only if they win; always-takers: would enroll even without winning; never