README

Reduced-Form Estimators Documentation Framework

Overview

This directory contains comprehensive documentation for all reduced-form estimators in the BEAR toolbox. Each estimator has its own markdown file with detailed settings and hyperparameter descriptions.

Completed Estimators

• ordinary.md - Ordinary Least Squares
• minnesota.md - VAR with Minnesota Prior
• flat.md - VAR with Flat Prior
• cogley_sargent_sv.md - Cogley-Sargent Stochastic-Volatility VAR
• hierarchical_panel.md - Hierarchical Panel
• minnesota_favar_twostep.md - Two-Step FAVAR with Minnesota Prior

Remaining Estimators by Category

Plain Estimators (3 remaining)

• normal_wishart.md - VAR with Normal-Wishart Prior
• ind_normal_wishart.md - VAR with Independent Normal-Wishart Priors
• normal_diffuse.md - VAR with Normal-Diffuse Prior

Time-Varying Estimators (9 remaining)

• beta_tv.md - Time-Varying VAR
• general_tv.md - VAR with Time-Varying Parameters and Stochastic Volatility
• carriero_sv.md - Carriero Stochastic Volatility VAR
• ccmm_sv.md - CCMM Stochastic Volatility VAR with Random Walk Heteroscedasticity
• ccmm_svo.md - CCMM Stochastic Volatility VAR with Outliers
• ccmm_svot.md - CCMM Stochastic Volatility with Jumps and Large Shocks
• large_shock_sv.md - Stochastic Volatility VAR for Large Shocks
• gen_large_shock_sv.md - General Stochastic Volatility VAR for Large Shocks
• random_inertia_sv.md - Stochastic Volatility with Random Inertia

Panel Estimators with Separable Units (3 remaining)

• mean_ols_panel.md - Mean OLS Panel
• normal_wishart_panel.md - Normal-Wishart Panel
• zellner_hong_panel.md - Zellner-Hong Panel

Panel Estimators with Cross-Unit Dependence (2 remaining)

• static_cross_panel.md - Static Cross-Unit Panel
• dynamic_cross_panel.md - Dynamic Cross-Unit Panel

One-Step Factor-Augmented Estimators (5 remaining)

• flat_favar_onestep.md - One-Step FAVAR with Flat Prior
• minnesota_favar_onestep.md - One-Step FAVAR with Minnesota Prior
• normal_wishart_favar_onestep.md - One-Step FAVAR with Normal-Wishart Prior
• ind_normal_wishart_favar_onestep.md - One-Step FAVAR with Independent Normal-Wishart Prior
• normal_diffuse_favar_onestep.md - One-Step FAVAR with Normal-Diffuse Prior

Two-Step Factor-Augmented Estimators (4 remaining)

• flat_favar_twostep.md - Two-Step FAVAR with Flat Prior
• normal_wishart_favar_twostep.md - Two-Step FAVAR with Normal-Wishart Prior
• ind_normal_wishart_favar_twostep.md - Two-Step FAVAR with Individual Normal-Wishart Prior
• normal_diffuse_favar_twostep.md - Two-Step FAVAR with Normal-Diffuse Prior

Time-Varying Factor-Augmented Estimators (5 remaining)

• beta_tv_favar.md - Two-Step FAVAR with Time-Varying Coefficients
• general_tv_favar.md - Two-Step FAVAR with Time-Varying Parameters and Stochastic Volatility
• cogley_sargent_sv_favar.md - Two-Step FAVAR with Cogley-Sargent Stochastic Volatility
• carriero_sv_favar.md - Two-Step FAVAR with Carriero Stochastic Volatility
• random_inertia_sv_favar.md - Two-Step FAVAR with Random-Inertia Stochastic Volatility

Specialized Estimators (2 remaining)

• threshold.md - VAR with Threshold-Based Regime Switching
• mixed_frequency.md - Mixed-Frequency VAR

Documentation Template Structure

Each estimator file should follow this structure:

# Estimator Name (`ClassNameEstimator`)

## Description
Brief description of the estimator and its purpose.

## Technical Details  
- Key technical characteristics
- Mathematical formulation (high level)
- Relationship to other estimators

## User Settings (Hyperparameters)

### Estimator-Specific Settings
[Unique parameters for this estimator]

### Inherited Base Settings  
[Standard parameters inherited from base classes]

### Used Hyperparameters
[Only parameters actually accessed by the estimator implementation]

## Implementation Details
- Key algorithmic details
- Prior specifications  
- Sampling procedures

## Usage Recommendations
- When to use this estimator
- Typical parameter values
- Tuning guidelines

## Limitations
- Known restrictions
- Computational considerations
- Methodological limitations

## Comparison to Other Estimators
- Relationships to similar methods
- Trade-offs and advantages

Key Information Sources

Code Locations

1. Settings Classes: /tbx/bearing/+[category]/+estimator/+settings/[EstimatorName].m
2. Estimator Classes: /tbx/bearing/+[category]/+estimator/[EstimatorName].m
3. BEAR5 Implementations: /tbx/bear/+bear/[relevant functions].m
4. BEAR5 Settings: /tbx/bear/+bear/+settings/[VARType]settings.m

Settings Inheritance Hierarchy

1. Base Settings: base.estimator.Settings (Lambda1-5, Autoregression, etc.)
2. Category Settings: May add category-specific parameters
3. Estimator Settings: Final estimator-specific parameters
4. Mixins: Special cases like SVMixin for stochastic volatility parameters

Parameter Mapping (BEAR5 → BEARING)

• lambda1 → Lambda1 (overall tightness)
• lambda2 → Lambda2 (cross-variable weighting)
• lambda3 → Lambda3 (lag decay)
• lambda4 → Lambda4 (exogenous tightness)
• lambda5 → Lambda5 (block exogeneity)
• ar → Autoregression (AR prior mean)
• gamma → HeteroskedasticityAutoRegression (SV models)
• alpha0 → HeteroskedasticityShape (SV models)
• delta0 → HeteroskedasticityScale (SV models)

Uncertainty Annotation System

• No annotation: High confidence in description
• ?: Some uncertainty, parameter role reasonably inferred
• ???: High uncertainty, significant speculation involved

Priority Recommendations

1. High Priority: Minnesota, NormalWishart, CogleySargentSV, BetaTV (most commonly used)
2. Medium Priority: FAVAR estimators, Panel estimators
3. Lower Priority: Specialized estimators with narrow use cases

Quality Assurance Checklist

For each completed estimator:

• Only used parameters documented with defaults
• Parameter usage verified by examining implementation code
• Usage recommendations provided
• Uncertainty levels appropriately marked (?, ???)
• Cross-references to related estimators
• Technical implementation details included