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Two-Stage Least Squares (2SLS) Estimator
Estimation method where the first stage predicts the endogenous variable from the instrument, and the second stage uses these predictions to estimate the causal effect.
Weak Instrument
Instrumental variable with weak correlation to the endogenous variable, leading to biased estimators and invalid confidence intervals.
Sargan Over-identification Test
Statistical test verifying the validity of multiple instruments by examining whether the residuals are correlated with the instruments.
Wu-Hausman Test
Statistical test comparing OLS and IV estimators to determine if the variable is truly endogenous and justifies the use of instruments.
First Stage F-statistic
Statistic measuring the strength of the relationship between instruments and the endogenous variable in the first stage of 2SLS.
Local Average Treatment Effect (LATE)
Causal effect identified by an instrumental variable that applies specifically to 'compliers', those whose treatment changes due to the instrument.
Monotonicity
Assumption that no individual responds to the instrument in the opposite direction of the expected effect on treatment.
Stock-Yogo Critical Value
Critical threshold used to detect weak instruments based on the potential bias of the 2SLS estimator compared to OLS.
Anderson-Rubin Test
Robust inference method in the presence of weak instruments that maintains correct coverage even with weak instruments.
Optimal Instrument
Linear combination of instruments that minimizes the variance of the IV estimator under the assumption of homoscedasticity.
Intention to Treat (ITT)
Effect of random assignment to treatment rather than the treatment itself, often used as an instrument in randomized trials with non-compliance.
Compliers
Subpopulation of individuals whose treatment status changes according to the value of the instrument, defining the LATE population.