Glossary

Bayesian Information Criterion (BIC)

BIC is a model selection criterion similar to AIC that trades off goodness of fit against complexity. BIC's penalty for each additional parameter is larger than AIC's because it grows with the log of the sample size, so BIC tends to favour simpler models, especially in large s...

Definition

BIC is a model selection criterion similar to AIC that trades off goodness of fit against complexity. BIC's penalty for each additional parameter is larger than AIC's because it grows with the log of the sample size, so BIC tends to favour simpler models, especially in large samples. Like AIC, the model with the smallest BIC is preferred.

Why It Matters

When researchers must choose among competing models, BIC offers a more conservative standard than AIC. Because its penalty increases with sample size, BIC penalises over-parameterisation more heavily and is more likely to identify the true data-generating process in large samples. This makes BIC particularly useful in macroeconomic and financial applications where parsimony is valued and overfitting is a real concern.

Example

A researcher comparing three models for predicting Turkish household consumption has sample size n = 500. Model 1 (2 parameters) has BIC = 210.5, Model 2 (5 parameters) has BIC = 208.3, and Model 3 (8 parameters) has BIC = 215.7. Despite Model 3 having the best in-sample fit, BIC selects Model 2 because its penalty-adjusted performance is superior.

Related Terms

Software Notes

  • SPSS: Analyze > Regression > Linear; BIC is reported alongside AIC in the model summary. Use the STATS FIT extension for detailed comparison tables.
  • R: Use BIC(model) after fitting with lm(), arima(), or VAR(). Compare models with BIC(model1, model2).
  • Stata: After estimation, run estat ic to display BIC alongside AIC. For stepwise selection with BIC, use stepwise, bic.