Evaluating Policy Impacts Across Countries Over Years: Choosing the Right Model and Estimation Technique
When evaluating the impact of a policy (e.g., social spending) on an outcome variable (e.g., poverty rate) across countries over time, panel data analysis provides a robust framework. This type of data structure, which combines cross-sectional and time-series data, allows researchers to account for unobserved heterogeneity across entities (countries) and over time. Fixed effects (FE) and random effects (RE) models are commonly used for such analyses. The choice of model and estimation technique depends on theoretical considerations and the structure of the data.
Fixed Effects vs. Random Effects
1. Fixed Effects Model
The fixed effects model is appropriate when the time-invariant individual effect (\( \alpha_i \)) is correlated with the independent variables. This model controls for unobserved heterogeneity by allowing each country to have its own unique intercept, which eliminates bias from omitted variables that do not vary over time (Wooldridge, 2021).
FE is particularly suited for policy impact evaluation because it isolates the within-country variation over time, making it ideal for assessing changes in the outcome due to policy changes while holding constant all time-invariant factors.
2. Random Effects Model
The random effects model assumes that \( \alpha_i \) is uncorrelated with the independent variables. This assumption enables the inclusion of time-invariant variables in the analysis, as these variables are not absorbed into the individual-specific effect (Greene, 2020).
RE is preferred when \( \alpha_i \) is random and uncorrelated with the predictors, but this assumption is often unrealistic in policy studies, as policy determinants are frequently country-specific.
Hausman Test for Model Selection
The Hausman test compares the FE and RE models by testing whether the individual effects are correlated with the regressors. If the null hypothesis of no correlation is rejected, the FE model is appropriate; otherwise, the RE model can be used (Hausman, 1978).
Estimation Techniques
1. Ordinary Least Squares (OLS)
OLS is a foundational technique but has limitations in panel data analysis when unobserved heterogeneity is present. Pooled OLS ignores individual and time effects, leading to biased estimates if \( \alpha_i \) or time-specific effects are correlated with the regressors.
Although simple to implement, OLS is rarely appropriate for panel data without accounting for fixed or random effects.
2. Generalized Method of Moments (GMM)
GMM is a robust estimation technique for dynamic panel data models where endogeneity is a concern. Endogeneity often arises from simultaneity, measurement errors, or omitted variables. The Arellano-Bond estimator, a GMM approach, uses lagged levels and differences of endogenous variables as instruments to address this issue (Arellano & Bond, 1991).
GMM is suitable for policy studies with large \( N \) (countries) and small \( T \) (time periods). However, it can suffer from instrument proliferation, which reduces efficiency.
3. Maximum Likelihood Estimation (MLE)
MLE provides efficient estimates under certain assumptions, including normality of errors and random effects. It is particularly useful for nonlinear panel data models.
For linear models, MLE is less commonly used because FE and RE estimators often suffice and are computationally simpler. However, MLE can be advantageous in small-sample settings or when modeling heteroskedasticity.
Best Choice for Policy Impact Evaluation
The fixed effects model estimated using FE-OLS is typically the best starting point for evaluating the impact of policies like social spending on poverty rates. This approach accounts for unobserved, time-invariant heterogeneity, focusing on within-country variation. For more complex cases involving endogeneity, the GMM approach is preferred due to its ability to handle dynamic relationships. MLE may be an option if the data requires modeling beyond linear structures.
Ultimately, the choice of model and estimation technique should align with the research question, data characteristics, and theoretical framework. Sound empirical practice involves testing assumptions and ensuring robustness through specification tests, such as the Hausman test or over-identifying restriction tests for GMM models.
References
- Arellano, M., & Bond, S. (1991). Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations. The Review of Economic Studies, 58(2), 277–297. https://doi.org/10.2307/2297968
- Greene, W. H. (2020). Econometric Analysis (8th ed.). Pearson.
- Hausman, J. A. (1978). Specification Tests in Econometrics. Econometrica, 46(6), 1251–1271. https://doi.org/10.2307/1913827
- Wooldridge, J. M. (2021). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning.
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