7.1 Panel data analysis

Panel data analysis combines cross-sectional and time-series data, offering powerful insights for impact evaluation. It increases sample size, controls for unobserved factors, and captures dynamic relationships, making it a valuable tool for estimating causal effects.

However, panel data comes with challenges like attrition bias and complex statistical techniques. Fixed effects models control for time-invariant factors, while random effects models assume uncorrelated individual effects. Proper interpretation and assumption testing are crucial for reliable results.

Panel Data for Impact Evaluation

Characteristics and Advantages

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• Panel data combines cross-sectional and time-series data allows analysis of individual units over multiple time periods
• Increases sample size enhances statistical power and precision of estimates
• Controls for unobserved heterogeneity reduces omitted variable bias
• Studies dynamic relationships captures changes and trends over time
• Analyzes between-unit and within-unit variations provides more robust estimates of causal effects
• Addresses selection bias and omitted variable bias common challenges in impact evaluation
• Estimates fixed effects models controls for time-invariant unobserved factors
• Requires careful consideration of temporal aspects includes lag structures and potential serial correlation

Limitations and Challenges

• Potential attrition bias occurs when participants drop out of the study over time
• Increased complexity in data collection and management requires specialized software and skills
• Needs specialized statistical techniques demands advanced econometric knowledge
• Temporal aspects consideration involves complex lag structures (1 month, 6 months, 1 year)
• Potential serial correlation violates assumption of independent observations

Fixed vs Random Effects Models

Fixed Effects Models

• Control for time-invariant unobserved heterogeneity allows each unit to have its own intercept
• Use within-unit variation estimates effect of time-varying covariates on outcome of interest
• Particularly useful when unobserved heterogeneity correlates with explanatory variables
• Can be extended to include time fixed effects controls for common shocks across units (economic recessions, policy changes)
• Focuses on within-unit changes over time interprets coefficients as average effect within units

Random Effects Models

• Assume individual-specific effects uncorrelated with independent variables models as part of error term
• More efficient when assumptions hold can estimate effects of time-invariant variables
• Combines within and between-unit variations interprets coefficients using both sources of variation
• Can be extended to include time random effects accounts for time-specific variations
• Useful when interest lies in making inferences about the larger population from which the sample is drawn

Model Selection and Extensions

• Hausman test guides choice between fixed and random effects assesses consistency of random effects estimator
• Both models can include time effects controls for common shocks (economic cycles, policy changes)
• Dynamic panel models incorporate lagged dependent variables captures persistence and adjustment processes
• Interaction terms assess heterogeneous treatment effects across subgroups or time periods

Interpreting Panel Data Results

Coefficient Interpretation

• Represent average effect of one-unit change in independent variable on dependent variable holds other factors constant
• Fixed effects coefficients focus on within-unit changes over time
• Random effects coefficients combine within and between-unit variations
• Marginal effects calculate impact of interventions in non-linear panel models (logit, probit)
• Lagged effects in dynamic panel models require consideration of short-term and long-term impacts
• Interaction terms assess heterogeneous treatment effects across subgroups or time periods

Statistical Inference and Model Fit

• Standard errors account for potential clustering at unit level avoids understating uncertainty of estimates
• ###r-squared_0### in fixed effects models represents proportion of within-unit variance explained
• F-tests assess joint significance of fixed effects determines if individual-specific effects are needed
• Likelihood ratio tests compare nested models evaluates improvement in model fit
• Information criteria (AIC, BIC) guide model selection balances model fit and complexity

Assumptions of Panel Data Analysis

Key Assumptions

• Parallel trends assumption crucial for difference-in-differences analysis requires similar trends in treatment and control groups absent intervention
• Strict exogeneity in fixed effects models requires error term uncorrelated with explanatory variables across all time periods
• Random effects orthogonality assumption individual-specific effects uncorrelated with explanatory variables
• Homoskedasticity and no serial correlation in idiosyncratic error term for both fixed and random effects models
• Sufficiency of sample size large number of units (N) relative to time periods (T) ensures consistency of estimators

Data Requirements and Diagnostics

• Balanced panel data preferred all units observed in all time periods
• Unbalanced panels require careful treatment of missing data (imputation, weighting)
• Tests for unit root processes essential for long time series avoids spurious regression results
• Hausman test assesses appropriateness of random effects versus fixed effects models
• Breusch-Pagan Lagrange Multiplier test determines presence of individual-specific effects
• Wooldridge test checks for autocorrelation in panel data models
• Modified Wald test examines group-wise heteroskedasticity in fixed effect models