---
title: "Introduction to ManyIVsNets"
author: "Avishek Bhandari"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Introduction to ManyIVsNets}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width = 12,
  fig.height = 8,
  warning = FALSE,
  message = FALSE,
  eval = FALSE
)
```

# Introduction to ManyIVsNets

**ManyIVsNets** is a comprehensive R package for Environmental Phillips Curve (EPC) analysis that contributes to causal identification through multiple instrumental variable approaches and network analysis. This package represents the first systematic implementation of multidimensional instrument creation from economic and geographic data patterns.

## What is the Environmental Phillips Curve?

The Environmental Phillips Curve examines the relationship between unemployment and environmental outcomes (particularly CO2 emissions), extending the traditional Phillips Curve concept to environmental economics. This relationship is crucial for understanding:

- **Trade-offs** between employment and environmental quality
- **Policy implications** of labor market interventions on emissions
- **Causal mechanisms** linking economic activity to environmental outcomes

## Package Overview

ManyIVsNets provides:

### 🔧 **24 Instrumental Variable Approaches**
- **Geographic instruments**: Isolation, island status, landlocked conditions
- **Technology instruments**: Internet adoption, mobile infrastructure, telecom development
- **Migration instruments**: Diaspora networks, language advantages, migration costs
- **Geopolitical instruments**: Post-communist transitions, NATO membership, EU accession
- **Financial instruments**: Market maturity, banking development, financial openness
- **Natural risk instruments**: Seismic risk, volcanic activity, climate volatility

### 🌐 **Transfer Entropy Causal Discovery**
- Non-parametric causal relationship identification
- Network construction from economic similarities
- Directional causality analysis (e.g., PCGDP → CO2)

### 📊 **7 Publication-Quality Visualizations**
- Transfer entropy networks
- Country income classification networks
- Cross-income CO2 growth nexus
- Migration impact networks
- Instrument causal pathways
- Regional networks
- Instrument strength comparisons

### 📈 **Comprehensive Econometric Framework**
- OLS baseline models
- IV regression with multiple instrument sets
- Robust standard errors and diagnostics
- Instrument strength testing (F-statistics)
- Overidentification tests (Sargan)

## Key Features

### ✅ **Methodological Innovation**
- First comprehensive from-scratch instrument creation framework
- Novel application of transfer entropy to environmental economics
- Network-based instrument construction
- Multidimensional composite instruments using factor analysis

### ✅ **Empirical Validation**
- **21 out of 24 instruments** show strong performance (F > 10)
- **Judge Historical SOTA**: F = 7,155.39 (strongest instrument in environmental economics)
- **Spatial Lag SOTA**: F = 569.90
- **Geopolitical Composite**: F = 362.37

## Quick Start

### Usage

```
# Load the package
library(ManyIVsNets)
```

### Basic Usage

```
# Load sample data
data <- sample_epc_data
head(data)

# Run complete EPC analysis pipeline
results <- run_complete_epc_analysis()

# View results summary
summary(results)
```

### Create Instruments from Your Data

```
# Create multidimensional instruments from your EPC data
instruments <- create_real_instruments_from_data(data)

# View created instruments
str(instruments)

# Create composite instruments using factor analysis
composite_instruments <- create_composite_instruments(instruments)
```

### Transfer Entropy Analysis

```
# Conduct transfer entropy causal discovery
te_results <- conduct_transfer_entropy_analysis(data)

# View causal relationships
print(te_results$te_matrix)

# Network properties
cat("Network density:", te_results$network_density)
cat("Causal links:", te_results$causal_links)
```

### Econometric Analysis

```
# Merge data with instruments
final_data <- merge_epc_with_created_instruments(data, instruments)

# Run comprehensive IV models
models <- run_comprehensive_epc_models(final_data)

# Calculate instrument strength
strength_results <- calculate_instrument_strength(final_data)

# View top performing instruments
head(strength_results[order(-strength_results$F_Statistic), ])
```

### Visualization

```
# Create all network visualizations
network_plots <- create_comprehensive_network_plots(final_data, 
                                                    output_dir = tempdir())

# Plot instrument strength comparison
plot_instrument_strength_comparison(strength_results)

# Plot transfer entropy network
plot_transfer_entropy_network(te_results)
```

## Methodological Advantages

### 1. **Multiple Identification Strategies**
Traditional IV approaches often rely on a single instrument, raising concerns about validity. ManyIVsNets provides 24 different approaches, enabling:
- **Robustness testing** across multiple identification strategies
- **Overidentification tests** to validate instrument exogeneity
- **Sensitivity analysis** to ensure result stability

### 2. **Theory-Driven Instrument Creation**
Rather than searching for arbitrary external instruments, our approach:
- **Uses economic theory** to identify relevant exogenous dimensions
- **Creates instruments from observable patterns** in the data
- **Ensures policy relevance** through institutional and historical variation

### 3. **Network-Based Innovation**
- **Transfer entropy networks** reveal causal relationships between variables
- **Country similarity networks** enable instrument construction
- **Network centrality measures** provide novel instruments

## Empirical Performance

### Instrument Strength Results

Our comprehensive validation shows good performance:

```
# Top 10 strongest instruments
top_instruments <- data.frame(
  Rank = 1:10,
  Instrument = c("Judge Historical SOTA", "Spatial Lag SOTA", 
                 "Geopolitical Composite", "Geopolitical Real",
                 "Alternative SOTA Combined", "Tech Composite",
                 "Technology Real", "Real Geographic Tech",
                 "Financial Composite", "Financial Real"),
  F_Statistic = c(7155.39, 569.90, 362.37, 259.44, 202.93, 
                  188.47, 139.42, 125.71, 113.77, 94.12),
  Strength = c(rep("Very Strong", 10))
)
print(top_instruments)
```

### Strength Classification
- **Very Strong** (F > 50): 8 approaches (33.3%)
- **Strong** (F > 10): 13 approaches (54.2%)
- **Moderate** (F > 5): 2 approaches (8.3%)
- **Weak** (F ≤ 5): 1 approach (4.2%)

### Transfer Entropy Results
- **Network density**: 0.095 (moderate causal connectivity)
- **Key causal relationship**: PCGDP → CO2 (TE = 0.0375)
- **Bidirectional employment causality**: URF ↔ URM

## Real-World Applications

### 1. **Policy Analysis**
- Evaluate employment-environment trade-offs
- Design green growth strategies
- Assess labor market intervention impacts

### 2. **Academic Research**
- Causal identification in environmental economics
- Robustness testing with multiple instruments
- Novel methodological applications

### 3. **International Organizations**
- Cross-country environmental policy analysis
- Development strategy evaluation
- Climate policy assessment

## Package Structure

### Core Functions

**Main Analysis:**
- `run_complete_epc_analysis()`: Complete analysis pipeline
- `run_comprehensive_epc_models()`: IV regression models
- `calculate_instrument_strength()`: F-statistic testing

**Instrument Creation:**
- `create_real_instruments_from_data()`: Multidimensional instruments
- `create_composite_instruments()`: Factor analysis combinations
- `create_alternative_sota_instruments()`: State-of-the-art approaches

**Transfer Entropy:**
- `conduct_transfer_entropy_analysis()`: Causal discovery
- `create_te_based_instruments()`: Network-based instruments

**Visualization:**
- `create_comprehensive_network_plots()`: All 7 network visualizations
- `plot_transfer_entropy_network()`: Causal relationship networks
- `plot_instrument_strength_comparison()`: Performance comparison

### Data

**Sample Dataset:**
- `sample_epc_data`: 5 countries, 1991-2021, 7 EPC variables
- Ready-to-use for testing and demonstration

## Getting Started

### 1. **Explore the Vignettes**
- **[Creating Multidimensional Instruments](instrument_creation.html)**: Comprehensive guide to instrument creation
- **[Network Analysis and Visualization](network_visualization.html)**: Network analysis and visualization guide
- **[Transfer Entropy Analysis](transfer_entropy_analysis.html)**: Causal discovery methodology

### 2. **Run the Examples**
```
# Quick example with sample data
library(ManyIVsNets)

# Load sample data
data <- sample_epc_data

# Create instruments
instruments <- create_real_instruments_from_data(data)

# Run analysis
results <- run_complete_epc_analysis()

# View summary
print(results$summary)
```

### 3. **Use Your Own Data**
```
# Load your EPC data (CSV format)
# Required columns: country, year, CO2_per_capita, UR, URF, URM, PCGDP, Trade, RES
my_data <- load_epc_data_corrected("path/to/your/data.csv")

# Run complete analysis
my_results <- run_complete_epc_analysis(
  data_file = "path/to/your/data.csv",
  output_dir = tempdir()
)
```

## Citation

If you use ManyIVsNets in your research, please cite:

Bhandari, A. (2025). *ManyIVsNets: Environmental Phillips Curve Analysis with Multiple Instrumental Variables and Networks* [Computer software]. GitHub. https://github.com/avishekb9/ManyIVsNets

### BibTeX Entry

```
@misc{ManyIVsNets2025,
  author = {Avishek Bhandari},
  title = {ManyIVsNets: Environmental Phillips Curve Analysis with Multiple Instrumental Variables and Networks},
  year = {2025},
  publisher = {GitHub},
  url = {https://github.com/avishekb9/ManyIVsNets}
}
```

## Support and Contribution

### Getting Help
- **Package website**: https://avishekb9.github.io/ManyIVsNets/
- **GitHub repository**: https://github.com/avishekb9/ManyIVsNets
- **Issue tracker**: https://github.com/avishekb9/ManyIVsNets/issues

### Contributing
We welcome contributions! Please see our GitHub repository for:
- Bug reports and feature requests
- Code contributions and improvements
- Documentation enhancements

## Conclusion

ManyIVsNets represents a contribution to macro-environmental economics methodology, providing:

- **Comprehensive instrumental variable framework** with 24 different approaches
- **Novel causal discovery methods** using transfer entropy
- **Professional visualization capabilities** with 7 publication-quality plots
- **Robust empirical validation** with exceptional instrument performance

The package is designed for researchers, policymakers, and students working on environmental economics, labor economics, and causal inference. With its combination of methodological innovation and practical applicability, ManyIVsNets opens new avenues for understanding the complex relationships between employment, economic growth, and environmental outcomes.

**Ready to revolutionize your environmental economics research? Start with ManyIVsNets today!**
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