Beta and Sigma Convergence Across Countries

Downloads

Each dataset is available as a labeled Stata .dta and its source file.

⇩ Download all data (ZIP)stata_codebook.do

Run stata_codebook.do in Stata once to attach long-form per-variable notes to the .dta files.

Load directly in code

Every file loads straight from GitHub (raw URLs). Swap the file name to load any dataset.

Stata

* Stata 14+ : `use` reads an https URL directly
global BASE "https://raw.githubusercontent.com/cmg777/starter-academic-v501/master/content/post/stata_convergence/data/"
use "${BASE}convergence_data_prepared.dta", clear
describe
notes

Python

!pip install -q pyreadstat
import pandas as pd
BASE = "https://raw.githubusercontent.com/cmg777/starter-academic-v501/master/content/post/stata_convergence/data/"
df = pd.read_stata(BASE + "convergence_data_prepared.dta")

# load every dataset at once
files = ["convergence_data_prepared", "pwt100"]
data = {f: pd.read_stata(BASE + f + ".dta") for f in files}

# pyreadstat (richest metadata) reads LOCAL files -> download first
import pyreadstat, urllib.request
urllib.request.urlretrieve(BASE + "convergence_data_prepared.dta", "convergence_data_prepared.dta")
df, meta = pyreadstat.read_dta("convergence_data_prepared.dta")

Copy and paste this snippet in Google Colab app. https://colab.research.google.com/notebooks/empty.ipynb

R

# R : haven::read_dta auto-downloads an https URL
library(haven)
BASE <- "https://raw.githubusercontent.com/cmg777/starter-academic-v501/master/content/post/stata_convergence/data/"
df <- read_dta(paste0(BASE, "convergence_data_prepared.dta"))

Overview & sources

Companion data for a hands-on Stata tutorial that tests whether poorer countries are catching up to richer ones. The analysis uses Penn World Table 10.0 (Feenstra, Inklaar & Timmer, 2015) expenditure-side real GDP in purchasing-power-parity terms and builds the complete convergence toolkit — OLS beta-convergence regressions of annualized growth on log initial income, an algebraic conversion of the OLS slope λ to the structural speed β = −ln(1+λs)/s (Barro & Sala-i-Martin, 1992), direct Nonlinear Least Squares, rolling windows, and sigma convergence measured by the variance of log GDP per capita. Over 1960–2019 the OLS slope is essentially zero, but splitting at 2000 reveals a structural break: divergence during 1960–2000 flips to convergence during 2000–2019 (β = 0.36% per year, half-life 190 years), even as the variance of log income rose 90.8% — beta convergence without sigma convergence.

Data sources

Cite this data

Please cite this dataset as follows.

APA

Mendez, C. (2026). Beta and Sigma Convergence Across Countries: A Stata Tutorial [Data set]. https://carlos-mendez.org/post/stata_convergence/

Feenstra, R. C., Inklaar, R., & Timmer, M. P. (2015). The Next Generation of the Penn World Table. American Economic Review, 105(10), 3150–3182. Barro, R. J., & Sala-i-Martin, X. (1992). Convergence. Journal of Political Economy, 100(2), 223–251.

BibTeX

@misc{mendez2026stataconvergence,
  author       = {Mendez, Carlos},
  title        = {Beta and Sigma Convergence Across Countries: A Stata Tutorial},
  year         = {2026},
  howpublished = {\url{https://carlos-mendez.org/post/stata_convergence/}},
  note         = {Data set}
}

@article{feenstra2015pwt,
  author  = {Feenstra, Robert C. and Inklaar, Robert and Timmer, Marcel P.},
  title   = {The Next Generation of the Penn World Table},
  journal = {American Economic Review},
  volume  = {105}, number = {10}, pages = {3150--3182}, year = {2015}
}
@article{barro1992convergence,
  author  = {Barro, Robert J. and Sala-i-Martin, Xavier},
  title   = {Convergence},
  journal = {Journal of Political Economy},
  volume  = {100}, number = {2}, pages = {223--251}, year = {1992}
}

Variable explorer search & filter all 54 variables

Type to filter by name or label, or use the chips to filter by type. Each row shows a mini distribution. Click a header to sort.

Cross-file variable index

Which file each variable appears in (● = present).

Construction & formulas

Convergence is measured on annualized growth and log initial income across the 84-country cross-section, with per-capita income gdppc = rgdpe / pop.

• Annualized growth (g_i): g_i = (1/s)·ln(y_{i,t+s} / y_{i,t}) over a window of s years.
• Beta convergence (OLS) (λ): g_i = α + λ·ln(y_{i,0}) + ε_i — a negative slope λ means poorer countries grow faster (convergence).
• OLS → structural speed (β): β = −ln(1 + λs) / s (Barro & Sala-i-Martin 1992); note the sign convention flips — positive β means convergence.
• NLS direct estimate: g_i = α − (1 − e^{−βs})/s · ln(y_{i,0}) + ε_i, fit with Stata nl; matches the OLS conversion to ~10⁻¹⁷.
• Half-life (τ): τ = ln(2) / β — years to close half the income gap.
• Sigma convergence (σ²_t): variance of ln(gdppc) across countries at year t; falling σ²_t means the income spread is narrowing.
• Rolling window: re-estimate λ (then β) for every start year 1960–2010 with the end year fixed at 2019.

The datasets

Switch datasets with the tabs. Each shows the full variable dictionary plus a sortable statistics table with mini distributions and data coverage.

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Known limitations & caveats

• Real data. Income comes from Penn World Table 10.0 (Feenstra, Inklaar & Timmer, 2015) — expenditure-side real GDP at chained PPPs in 2017 US$. Results depend on this income measure and the chosen sample restrictions.
• Balanced-panel selection. The analysis subset keeps only the 84 countries with GDP data since 1960, excluding ~40 economies (disproportionately African and small-island) that entered PWT coverage later; results may not generalize to the full set of developing countries.
• Sample exclusions. Oil producers (IMF classification) and countries under 1 million population are dropped, following Patel et al. (2021); convergence results are sensitive to these choices.
• Low explanatory power. The convergence regressions have R² between 0.001 and 0.069 — the research question is about the sign and significance of the slope, not prediction.
• Beta ≠ sigma. Beta convergence (poorer countries growing faster) is necessary but not sufficient for sigma convergence (a narrowing distribution); the two diverge in this sample (Young, Higgins & Levy, 2008).