Background
In economics and statistics, model selection is crucial for ensuring that the models accurately reflect the underlying data without overfitting. The Information Criterion (IC) is a method used for this purpose, combining a measure of goodness-of-fit with a penalty for the complexity of the model.
Historical Context
Credits for the development of the popular information criteria often go to Hirotugu Akaike, who introduced the Akaike Information Criterion (AIC) in 1974. The Bayes-Schwarz Information Criterion (BIC), also known as Schwarz Criterion, was independently created by Gideon Schwarz in 1978, building on prior contributions in Bayesian statistics.
Definitions and Concepts
The Information Criterion balances the trade-off between model complexity and goodness-of-fit:
- Akaike Information Criterion (AIC) measures the relative quality of statistical models for a given dataset.
- Bayes Information Criterion (BIC) is similar to AIC but includes a more substantial penalty for models with more parameters, promoting simpler models.
The core formulae reveal this balance:
- \( \text{AIC} = 2k - 2\ln(L) \)
- \( \text{BIC} = k \ln(n) - 2\ln(L) \)
Where \( k \) is the number of estimated parameters, \( L \) is the likelihood function, and \( n \) is the number of observations.
Major Analytical Frameworks
Classical Economics
In classical economic analysis, model selection usually depends more on theoretical fit rather than statistical validation, rendering information criteria less commonly used.
Neoclassical Economics
Neoclassical economics often relies on empirical data. Information criteria aid in selecting models that provide a trade-off between accuracy and simplicity, ensuring robust theoretical constructs.
Keynesian Economic
Macroeconomic models in Keynesian economics may benefit from information criteria to avoid overly complex interpretations, aiding policymakers in decision-making.
Marxian Economics
The focus on critique in Marxian economics diminishes the direct requirement for statistical models, thus reducing the application and necessity for information criteria.
Institutional Economics
Given its divergence into historical and sociological contexts, fewer rigid theoretical models necessitate an elaborate use of criteria, though explanatory models can occasionally employ such techniques.
Behavioral Economics
Behavioral economics often employs empirical studies where model selection criteria help embody the less predictable human behaviors accurately within robust frameworks.
Post-Keynesian Economics
In post-Keynesian analysis, which deals more with structural and long-run economic policies, information criteria help in selecting more accurate models without over-representing variability.
Austrian Economics
The Austrian School, emphasizing qualitative methodologies, saw limited direct application of information criteria until recent empirical modeling trends emerged.
Development Economics
Here, model complexity and fitness are balanced to avoid factions or systems bias, making information criteria an important tool in policy development and impact analysis.
Monetarism
Monetarism’s reliance on quantitative details for money supply and inflation models benefits from applying informational criteria to prevent over-complicated interpretations.
Comparative Analysis
Comparing AIC and BIC often involves noting the stronger penalty for additional parameters in BIC, making it more stringent relative to AIC, encouraging simpler models where possible.
Case Studies
Empirical studies in econometrics often show applications where:
- AIC and BIC similarly retain the most critical parameters.
- BIC precludes unnecessary parameters more rigidly, promoting principled economic interpretations.
Suggested Books for Further Studies
- “Model Selection and Model Averaging” by Yuhong Yang
- “Econometric Theory and Methods” by Russell Davidson and James G. MacKinnon
- “Information Criteria and Statistical Modeling” by Sadanori Konishi and Genshiro Kitagawa
Related Terms with Definitions
- Likelihood Function: A function that represents the probability of observed data under various parameter assumptions.
- Goodness of Fit: Measures the degree of fit between model predictions and actual data observations.
- Overfitting: Creating a model that captures noise rather than the underlying process, often alleviated by using information criteria.