Beta-Convergence Analysis of Country Growth with Python and R

This project analyzes β-convergence in economic growth between emerging and developed countries using GDP per capita data from 2004 to 2024. β-convergence examines whether poorer economies tend to grow faster than richer ones, potentially reducing income disparities over time.

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Project Overview

β-convergence is estimated using cross-sectional regressions of average GDP per capita growth rates across four periods:

• Pre-Crisis (2004–2008)
• Recuperation (2009–2013)
• Stability (2014–2018)
• Recent (2019–2024)

The workflow combines Python for visualization and data handling with R for econometric inference.

Interpretation of β Coefficients:

• β < 0: Indicates convergence <=> Poorer economies growing faster
• β > 0: Indicates divergence <=> Richer economies maintaining growth advantage

Methodology

• Data source: World Development Indicators (WDI)
• Sample: 58 countries (Emerging vs Developed)
• Approach:
  • Period-average GDP per capita growth
  • OLS β-convergence regressions
  • Robust standard errors (HC1)
  • Linear Probability Model for development status

Dataset Description

Source

World Development Indicators (WDI) - 2004-2024

Official Data Source

Structure

• Country Code: Unique identifier (e.g., USA, CHL, IND)

• Group: Economic classification ('Emerging' or 'Developed')

• Period Growth Rates:

  • Pre-Crisis (2004-2008)
  • Recuperation (2009-2013)
  • Stability (2014-2018)
  • Recent (2019-2024)

File Structure

.
├── data/
│   ├── clean_data.csv        
│   └── gdp_data.csv         
├── visualizations/
│   ├── R_outputs/           
│   └── python_outputs/      
├── .gitignore
├── ETL.ipynb               
├── install_r_packages.R
├── LICENSE
├── main.ipynb               
├── README.md
├── regressions.R
├── requirements.txt
└── utils.py

Methodology

Analytical Tools

Python Libraries:

import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn.linear_model import LinearRegression

R Libraries:

library(sandwich)
library(lmtest)

Data Processing

1. Import and clean WDI dataset
2. Calculate average growth rates for each period
3. Classify countries into Emerging/Developed groups
4. Remove empty rows and standardize column names

Visualizations

1. Correlation Matrix Heatmap

• Tool: Python/Seaborn
• Purpose: Explore relationships between growth periods
• Output: Inter-period correlation overview

2. Beta-Convergence Analysis Plots

Tool: Python/Matplotlib

Three Key Comparisons:

1. Stability (2014-2018) vs. Recuperation (2009-2013)
2. Recent (2019-2024) vs. Pre-Crisis (2004-2008)
3. Recuperation (2009-2013) vs. Pre-Crisis (2004-2008)

Each visualization includes regression lines and β coefficients

Regression Analysis

Single-Variable Models

Regression 1: Stability vs. Recuperation

sreg1 <- lm(Stability..2014.2018. ~ Recuperation..2009.2013., data=df_wdi)
summary(sreg1)
coeftest(sreg1, vcov = vcovHC(sreg1, type="HC1"))

Regression 2: Recent vs. Pre-Crisis

sreg2 <- lm(Recent..2019.2024. ~ Pre_Crisis..2004.2008., data=df_wdi)
summary(sreg2)
coeftest(sreg2, vcov = vcovHC(sreg2, type="HC1"))

Regression 3: Recuperation vs. Pre-Crisis

sreg3 <- lm(Recuperation..2009.2013. ~ Pre_Crisis..2004.2008., data=df_wdi)
summary(sreg3)
coeftest(sreg3, vcov = vcovHC(sreg3, type="HC1"))

Multivariate Regression Model

Theoretical Specification

The model is specified as:

$$Developed_i = β_0 + β_1 * PreCrisisGrowth_i + β_2 * RecuperationGrowth_i + u_i$$

R Implementation

mreg <- glm(developed ~ Pre_Crisis..2004.2008. + 
                    Recuperation..2009.2013.,
                  data=df_wdi)
summary(mreg)
vif(mreg)
coeftest(mreg, vcov = vcovHC(mreg, type="HC1")) 

Model Parameters

• Sample: 58 countries
• Dependent Variable: Developedᵢ ∈ {1, 0} where:
  • 1 = Developed economy
  • 0 = Emerging economy
• Independent Variables:
  • PreCrisisGrowthᵢ: Average GDP growth (2004-2008)
  • RecuperationGrowthᵢ: Average GDP growth (2009-2013)
• Error Term: uᵢ, ∀ 𝔼[uᵢ|Xᵢ] = 0

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Key Findings

Emerging Economies

• Persistent divergence
• Positive β coefficients across all periods
• Faster-growing economies maintain their advantage

Developed Economies

• Weak convergence in early periods
• Shift toward divergence in recent years
• No evidence of long-run income equalization

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Limitations

• Small cross-sectional sample (58 countries)
• No panel structure → potential omitted heterogeneity
• Linear Probability Model constraints
• σ-convergence not tested

Conclusion

The analysis reveals distinct growth patterns between emerging and developed economies, with emerging markets showing persistent divergence while developed economies transition from weak convergence to divergence in recent years. These findings provide valuable insights for economic policy formulation and international development strategies.