7.3 Instrumental variables estimation
4 min read•august 16, 2024
Instrumental variables estimation tackles 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 , first regressing treatment on the instrument, then using predicted values to estimate causal effects. This approach helps address issues like , 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 ()
- 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
- 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
- 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 ()
- 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
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
- (LATE) interpretation
- May differ from (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 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
- 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
Key Terms to Review (21)
Average Treatment Effect: The average treatment effect (ATE) is a key concept in causal inference that measures the difference in outcomes between units that receive a treatment and those that do not. It provides a summary of the overall impact of an intervention across a population, helping to understand how effective a treatment is on average. By estimating the ATE, researchers can assess the effectiveness of various interventions and inform policy decisions.
Effects of health interventions: The effects of health interventions refer to the outcomes resulting from specific health-related programs or treatments aimed at improving health conditions in a population. These effects can be measured in terms of changes in health status, quality of life, and healthcare utilization, among other indicators. Understanding these effects is crucial for evaluating the effectiveness of different health interventions and for making informed decisions about resource allocation in healthcare systems.
Endogeneity: Endogeneity refers to a situation in econometrics where an explanatory variable is correlated with the error term in a regression model, leading to biased and inconsistent estimates. This can occur due to omitted variable bias, measurement error, or simultaneous causality, which complicates the interpretation of causal relationships. To address endogeneity, researchers often turn to instrumental variables as a method to obtain unbiased estimates.
Exogeneity: Exogeneity refers to the condition in which an explanatory variable is not correlated with the error term in a regression model, implying that the variable is determined outside the model. This concept is crucial for ensuring unbiased and consistent estimates in causal inference, as it indicates that any variations in the explanatory variable do not arise from omitted variables or simultaneous causality. Understanding exogeneity helps to distinguish between different estimation strategies used to address issues like endogeneity in various econometric methods.
External validity: External validity refers to the extent to which the findings from a study can be generalized to settings, populations, and times beyond the specific context in which the study was conducted. It plays a crucial role in determining how applicable the results of an evaluation are in real-world scenarios, influencing decisions about policies and programs based on those findings.
Impact of education on earnings: The impact of education on earnings refers to the relationship between an individual's level of education and their potential income, where higher levels of education typically lead to increased earnings over a lifetime. This concept highlights the economic benefits of education, suggesting that investments in education can lead to better job opportunities, higher wages, and improved career advancement prospects, ultimately contributing to economic growth and reducing income inequality.
Internal Validity: Internal validity refers to the degree to which a study accurately establishes a causal relationship between an intervention and its effects within the context of the research design. It assesses whether the observed changes in outcomes can be confidently attributed to the intervention rather than other confounding factors or biases.
James Heckman: James Heckman is a prominent economist known for his work in microeconomics, particularly in the areas of labor economics and the development of econometric techniques like instrumental variables. He is recognized for his contributions to understanding the importance of early childhood education and the evaluation of policy interventions, emphasizing how selection bias can affect causal inference in economic studies. His work has laid the groundwork for more accurate estimations of treatment effects and has influenced practices related to instrumental variables in econometrics.
Limited Information Maximum Likelihood: Limited Information Maximum Likelihood (LIML) is a statistical method used for estimating the parameters of a model when there is endogeneity present, specifically in the context of instrumental variables estimation. It provides a way to deal with situations where traditional methods, like ordinary least squares, may yield biased or inconsistent estimates due to correlated errors or omitted variable bias. LIML is particularly useful when the instruments are weak or when a full information approach is infeasible.
Local Average Treatment Effect: Local Average Treatment Effect (LATE) refers to the average effect of a treatment or intervention on individuals who are influenced by an instrumental variable to receive the treatment. This concept is crucial when traditional methods of estimation may not yield unbiased results due to selection bias, particularly in settings where not all individuals receive the treatment. LATE captures the causal impact specifically for the subgroup of individuals whose treatment status is altered by the instrumental variable, making it a key consideration in both instrumental variables estimation and regression discontinuity analysis.
Mendelian Randomization: Mendelian randomization is a method used in epidemiology that leverages genetic variants as instruments to estimate causal relationships between risk factors and health outcomes. This technique helps to mitigate confounding factors and reverse causation by using the random assortment of genes during meiosis, which mimics a randomized controlled trial. By assessing the association between genetic variants and outcomes, researchers can infer the potential causal impact of modifiable exposures.
Natural Experiments: Natural experiments are observational studies where researchers take advantage of a naturally occurring event or situation that resembles a controlled experiment. These experiments often occur when an external factor, such as a policy change or natural disaster, creates a scenario where individuals or groups are exposed to different conditions, allowing for causal inference without random assignment. They are particularly valuable in evaluating the impact of interventions or changes in policy in real-world settings.
Omitted Variable Bias: Omitted variable bias occurs when a model leaves out one or more relevant variables that influence both the dependent and independent variables, leading to incorrect or misleading estimates of causal relationships. This bias can distort the perceived effects of included variables, making it essential to identify and account for all relevant factors to ensure accurate analysis.
Over-identification: Over-identification occurs when the number of instrumental variables exceeds the number of endogenous variables in a model. This situation can create challenges in estimating parameters accurately, as it may lead to an excess of instruments that can introduce bias and complicate interpretation. In the context of instrumental variables estimation, over-identification tests help determine whether the additional instruments are valid and relevant.
Paul Rosenbaum: Paul Rosenbaum is a prominent statistician known for his work on causal inference, particularly in the context of observational studies. His contributions have been instrumental in developing methods like propensity score matching and instrumental variables estimation, which help researchers address issues related to confounding and selection bias when estimating treatment effects.
Randomized controlled trials: Randomized controlled trials (RCTs) are experimental studies that randomly assign participants to either a treatment group or a control group to measure the effect of an intervention. This design helps to minimize bias and confounding variables, allowing for more reliable conclusions about the causal impact of the intervention on outcomes of interest.
Regression Discontinuity Designs: Regression discontinuity designs (RDD) are a quasi-experimental design used to estimate the causal effects of interventions by exploiting a predetermined cutoff point in a continuous variable. These designs allow researchers to compare outcomes just above and below the cutoff, effectively controlling for selection bias and confounding factors that could skew results. By focusing on individuals near the cutoff, RDD aims to mimic random assignment, making it a powerful tool for causal inference.
Relevance Condition: The relevance condition is a critical requirement in instrumental variable analysis, which states that the instrument must be correlated with the endogenous explanatory variable. This correlation ensures that the instrument can effectively help isolate the causal effect of the independent variable on the dependent variable by providing valid variation. The importance of this condition lies in its ability to ensure that any estimation derived from the model is not biased due to omitted variable bias or measurement error.
Strong instruments: Strong instruments are variables used in instrumental variables estimation that are highly correlated with the endogenous explanatory variable but uncorrelated with the error term in the regression model. They play a critical role in addressing issues of endogeneity and ensuring that the estimates of causal relationships are valid. The strength of an instrument affects the efficiency and consistency of the estimation process.
Two-stage least squares: Two-stage least squares (2SLS) is an estimation technique used in statistical models, particularly when dealing with endogenous variables that may be correlated with the error term. This method helps to provide consistent estimators by using instrumental variables in two steps: the first step predicts the endogenous variable using instruments, and the second step estimates the main model using these predicted values. By addressing issues of endogeneity, 2SLS allows for more accurate inference in causal relationships.
Weak instruments: Weak instruments refer to instrumental variables that have a weak correlation with the endogenous explanatory variable in a regression model. This weakness can lead to biased and inconsistent estimates of the causal effect being studied, making it challenging to draw reliable conclusions from the analysis.