7.3 Instrumental variables estimation

Instrumental variables estimation tackles endogeneity in impact evaluation. It uses exogenous variation to estimate causal effects when treatment variables are correlated with error terms. This method requires instruments that are relevant to the treatment but don't directly affect outcomes.

The process involves two-stage least squares, first regressing treatment on the instrument, then using predicted values to estimate causal effects. This approach helps address issues like omitted variable bias, measurement error, and reverse causality in econometric analysis.

Instrumental Variables Estimation

Concept and Purpose

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• Instrumental variables estimation addresses endogeneity issues in causal inference and impact evaluation
• Isolates exogenous variation in the treatment variable to estimate causal effects
• Used when correlation exists between treatment variable and error term in regression model
• Requires instruments satisfying relevance (correlation with treatment) and exclusion restriction (no direct effect on outcome)
• Involves two-stage least squares (2SLS) process
  • First stage regresses treatment on instrument
  • Second stage uses predicted values to estimate causal effect
• Allows consistent estimation of causal effects with omitted variable bias, measurement error, or reverse causality

Key Conditions and Process

• Instrument must correlate with treatment variable (relevance condition)
• Instrument must not directly affect outcome variable (exclusion restriction)
• Two-stage least squares (2SLS) estimation process
  • Stage 1: Regress treatment on instrument
  • Stage 2: Use predicted values to estimate causal effect
• Addresses various endogeneity issues
  • Omitted variable bias
  • Measurement error
  • Reverse causality

Valid Instruments for Impact Evaluation

Types of Valid Instruments

• Natural experiments provide valid instruments
  • Policy changes
  • Geographic variations
  • Random events (earthquakes, weather patterns)
• Randomized encouragement designs create instruments
  • Randomly assign incentives or information to encourage treatment uptake
• Regression discontinuity designs as instruments
  • Exploit discontinuities in treatment assignment based on continuous variable (age cutoffs, test score thresholds)
• Historical or institutional factors
  • Affect treatment assignment but unrelated to outcomes
  • (Colonial institutions, historical migration patterns)
• Genetic variants (Mendelian randomization)
  • Used in health and social science research
  • (Genes associated with alcohol metabolism for studying alcohol consumption effects)

Instrument Strength and Considerations

• Instrument strength crucial for efficiency and reliability
  • Strong correlation with treatment variable improves estimation precision
• Multiple instruments can improve efficiency
  • Allows for overidentification tests
• Consider trade-offs between instrument strength and validity
  • Stronger instruments may be more likely to violate exclusion restriction
• Assess plausibility of exclusion restriction
  • Theoretical arguments
  • Sensitivity analyses
• Evaluate relevance using first-stage F-statistics
  • Rule of thumb: F > 10 for strong instruments

Addressing Endogeneity with IV Estimation

Implementation of 2SLS

• Use statistical software packages (Stata, R, Python) to implement 2SLS
• First stage: Regress endogenous treatment on instrument(s) and exogenous covariates
  • Obtain predicted values of treatment
• Second stage: Use predicted values as treatment variable in outcome equation
• Account for generated regressor in second stage
  • Adjust standard errors
  • Use appropriate estimation commands in software
• Apply IV estimation in various contexts
  • Returns to education
  • Policy evaluation
  • Health interventions

Considerations and Extensions

• Local Average Treatment Effect (LATE) interpretation
  • May differ from Average Treatment Effect (ATE)
  • Represents effect for compliers (those affected by instrument)
• Multiple instruments
  • Can improve efficiency
  • Allow for overidentification tests
• Be aware of potential weak instrument problems
  • Can lead to biased estimates and incorrect inference
• Consider heterogeneous treatment effects
  • LATE may vary across subpopulations
• Assess monotonicity assumption
  • No "defiers" who always do opposite of instrument's encouragement

Interpreting IV Estimation Results

Understanding Estimates

• IV estimates represent causal effect for compliers
  • Subpopulation affected by instrument
• Compare IV estimates to OLS estimates
  • Assess direction and magnitude of bias in non-instrumented approaches
• Interpret coefficients in context of research question
  • Consider scale and units of measurement
• Analyze statistical significance and confidence intervals
  • Assess precision of results
• Consider larger standard errors in IV estimation
  • Typically larger than OLS due to two-stage process
• Discuss external validity of results
  • LATE may not generalize to entire population
• Relate results to theoretical predictions and previous empirical findings

Practical Interpretation

• Quantify magnitude of causal effects
  • (A $1000 increase in education spending leads to a 0.5 standard deviation increase in test scores)
• Assess policy implications of estimates
  • Cost-benefit analysis of interventions
• Consider heterogeneity in treatment effects
  • Effects may vary across subgroups or contexts
• Interpret results in light of instrument choice
  • Different instruments may yield different LATEs
• Discuss potential mechanisms driving causal effects
  • Direct vs indirect effects
• Address limitations and caveats of IV estimates
  • Generalizability, precision, assumptions

Instrument Strength and Validity

Assessing Instrument Strength

• Evaluate relevance using first-stage F-statistics
  • Rule of thumb: F > 10 for strong instruments
• Conduct tests for weak instruments
  • Cragg-Donald statistic
  • Kleibergen-Paap statistic
• Assess potential bias and size distortions from weak instruments
• Examine partial R-squared from first stage regression
  • Measures explanatory power of instruments
• Consider relative strength of multiple instruments
  • Some may be stronger than others

Validating Instruments

• Perform overidentification tests with multiple instruments
  • Sargan-Hansen test assesses joint validity
• Examine plausibility of exclusion restriction
  • Theoretical arguments
  • Sensitivity analyses
• Conduct falsification tests
  • Check for correlations between instrument and pre-treatment characteristics
  • Test instrument against placebo outcomes
• Assess monotonicity assumption
  • Consider potential defiers in context of heterogeneous effects
• Analyze balance of covariates across instrument values
  • Similar to balance checks in randomized experiments
• Conduct robustness checks with alternative instruments or specifications
  • Assess stability of results