Run Complete Lewbel (2012) Monte Carlo Simulation

Executes a comprehensive Monte Carlo simulation to evaluate the performance of Lewbel's (2012) heteroscedasticity-based identification strategy. This is the main function that orchestrates all simulation components.

Usage

run_lewbel_monte_carlo(
  config = NULL,
  run_verification = TRUE,
  run_bootstrap_demo = TRUE,
  run_sample_analysis = TRUE,
  run_sensitivity = TRUE,
  generate_plots = TRUE,
  verbose = TRUE
)

Arguments

config: If NULL, uses default configuration.
run_verification: Logical. Whether to run assumption verification (default: TRUE).
run_bootstrap_demo: Logical. Whether to run bootstrap demonstration (default: TRUE).
run_sample_analysis: Logical. Whether to run sample size analysis (default: TRUE).
run_sensitivity: Logical. Whether to run sensitivity analysis (default: TRUE).
generate_plots: Logical. Whether to generate visualization plots (default: TRUE).
verbose: Logical. Whether to print progress messages (default: TRUE).

Value

A list containing:

config: Configuration used
results_main: Main simulation results
results_by_n: Sample size analysis results (if run)
results_by_delta: Sensitivity analysis results (if run)
bootstrap_demo: Bootstrap demonstration results (if run)
analysis: Summary analysis
plots: Visualization plots (if generated)

Details

This function runs a complete Monte Carlo evaluation including:

Verification of Lewbel's identifying assumptions
Main simulation comparing OLS vs 2SLS (Lewbel) estimators
Bootstrap demonstration for set identification bounds
Sample size consistency analysis
Sensitivity analysis to heteroscedasticity strength
Comprehensive result analysis and visualization

The simulation uses parallel processing for efficiency and includes proper seed management for reproducibility.

References

Lewbel, A. (2012). Using heteroscedasticity to identify and estimate mismeasured and endogenous regressor models. Journal of Business & Economic Statistics, 30(1), 67-80. doi:10.1080/07350015.2012.643126

Examples

if (FALSE) { # \dontrun{
# Run with default settings
results <- run_lewbel_monte_carlo()

# Run with custom configuration
custom_config <- create_default_config(
  num_simulations = 500,
  gamma1 = -0.5,
  delta_het = 1.5
)
results <- run_lewbel_monte_carlo(custom_config)

# Run only main simulation without extras
results <- run_lewbel_monte_carlo(
  run_bootstrap_demo = FALSE,
  run_sample_analysis = FALSE,
  run_sensitivity = FALSE
)
} # }