hetid: Heteroskedasticity-Based Identification

Package Overview

The hetid package provides a comprehensive R implementation of heteroskedasticity-based identification methods for econometric models with endogenous regressors. When traditional instrumental variables are unavailable, these methods exploit heteroskedasticity in the error terms to achieve identification.

Available Methods

The package implements three major identification strategies:

1. Lewbel (2012): Uses continuous heteroskedasticity drivers
2. Rigobon (2003): Exploits discrete regime changes
3. Prono (2014): Leverages time-varying conditional heteroskedasticity (GARCH)

Vignette Guide

Getting Started

• Getting Started with hetid
  • Basic introduction to the package
  • Simple examples using Lewbel’s method
  • Data generation and assumption verification
  • Read this first if you’re new to the package

Theoretical Background

• Heteroskedasticity-Based Identification: Theory and Methods
  • Mathematical foundations of all methods
  • Detailed assumptions and identification conditions
  • Klein & Vella (2010) control function approach
  • Essential reading for understanding the methods

Method-Specific Guides

• GMM Estimation for Lewbel (2012)
  • Advanced GMM implementation
  • Efficiency considerations
  • Both triangular and simultaneous systems
  • For users needing optimal estimation
• The Rigobon Method
  • Regime-based heteroskedasticity
  • Financial contagion example
  • Comparison with Lewbel approach
  • Best for discrete variance changes
• The Prono (2014) Method
  • GARCH-based identification
  • Time series applications
  • Asset pricing examples
  • Ideal for financial time series

Validation and Comparison

• Comparing Lewbel (2012) Implementations
  • Empirical verification against Stata and REndo
  • Implementation differences explained
  • Matching results across software
  • Important for replication studies

Suggested Reading Order

For Practitioners

1. Getting Started - Basic usage
2. Choose your method:
   • Cross-sectional data → Lewbel GMM
   • Regime changes → Rigobon
   • Time series → Prono
3. Package Comparison - Verify your results

For Researchers

1. Theory and Methods - Mathematical foundations
2. Getting Started - Implementation basics
3. All method-specific vignettes for comprehensive understanding
4. Package Comparison - Software validation

Quick Decision Guide

Which method should I use?
│
├─ Do you have time series data?
│  ├─ Yes → Is volatility time-varying (GARCH-like)?
│  │        ├─ Yes → Use Prono method
│  │        └─ No → Use Lewbel method
│  └─ No → Do you have discrete regime changes?
│           ├─ Yes → Use Rigobon method
│           └─ No → Use Lewbel method

Key Functions by Method

Lewbel (2012)

• generate_lewbel_data() - Generate test data
• verify_lewbel_assumptions() - Check assumptions
• run_single_lewbel_simulation() - Point estimation
• calculate_lewbel_bounds() - Set identification
• lewbel_gmm() - GMM estimation

Rigobon (2003)

• generate_rigobon_data() - Generate regime-based data
• validate_rigobon_assumptions() - Test assumptions
• run_rigobon_estimation() - Estimate model
• compare_rigobon_methods() - Compare with alternatives

Prono (2014)

• generate_prono_data() - Generate GARCH data
• run_prono_demo() - Quick demonstration
• run_single_prono_simulation() - Single estimation
• run_prono_monte_carlo() - Monte Carlo analysis

Installation

# Install from CRAN (when available)
install.packages("hetid")

# Install development version from GitHub
# install.packages("devtools")
devtools::install_github("fernando-duarte/heteroskedasticity_identification")

Getting Help

• Documentation: Use ?function_name for any function
• Examples: Each major function includes runnable examples
• Citation: Use citation("hetid") for citing the package

See Also

• Original papers: Lewbel (2012), Rigobon (2003), Prono (2014)