# Data dictionary - Beta and Sigma Convergence Across Countries

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


Companion data for the post <https://carlos-mendez.org/post/stata_convergence/>. Each dataset ships as a labeled Stata `.dta` (v118) plus its source file. Generated by `build_data_dictionary.py`.

## Data sources

| Source | Provides | Reference / URL |
|---|---|---|
| Penn World Table 10.0 | Source income data: expenditure-side real GDP at chained PPPs, population, and 50 other macro series | Feenstra, R. C., Inklaar, R., &amp; Timmer, M. P. (2015). The Next Generation of the Penn World Table. American Economic Review, 105(10), 3150–3182. <a href="https://www.rug.nl/ggdc/productivity/pwt/" target="_blank" rel="noopener">https://www.rug.nl/ggdc/productivity/pwt/</a> |
| Patel, Sandefur &amp; Subramanian (2021) | Sample design: exclude oil producers and small countries; the post-2000 unconditional-convergence framing | Patel, D., Sandefur, J., &amp; Subramanian, A. (2021). The New Era of Unconditional Convergence. Journal of Development Economics, 152, 102687. <a href="https://doi.org/10.1016/j.jdeveco.2021.102687" target="_blank" rel="noopener">https://doi.org/10.1016/j.jdeveco.2021.102687</a> |
| Method references | Convergence estimators and concepts (beta/sigma convergence, speed, half-life) | Barro &amp; Sala-i-Martin (1992); Sala-i-Martin (1996); Young, Higgins &amp; Levy (2008). |

## Dataset links (GitHub)

| File | View on GitHub | Raw (load / download) |
|---|---|---|
| `convergence_data_prepared.dta` | [view](https://github.com/cmg777/starter-academic-v501/blob/master/content/post/stata_convergence/data/convergence_data_prepared.dta) | [raw](https://raw.githubusercontent.com/cmg777/starter-academic-v501/master/content/post/stata_convergence/data/convergence_data_prepared.dta) |
| `pwt100.dta` | [view](https://github.com/cmg777/starter-academic-v501/blob/master/content/post/stata_convergence/data/pwt100.dta) | [raw](https://raw.githubusercontent.com/cmg777/starter-academic-v501/master/content/post/stata_convergence/data/pwt100.dta) |

## Load in code

```python
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")
```

## Datasets

| File | Grain | Rows x Cols | Purpose |
|---|---|---|---|
| `convergence_data_prepared` | country-year | 5,040 x 5 | The analysis sample for all beta/sigma convergence regressions. |
| `pwt100` | country-year | 12,810 x 52 | Raw upstream source from which the analysis panel is built. |

## Cross-file variable index

| Variable | convergence_data_prepared | pwt100 |
|---|---|---|
| `avh` |  | ● |
| `ccode` | ● |  |
| `ccon` |  | ● |
| `cda` |  | ● |
| `cgdpe` |  | ● |
| `cgdpo` |  | ● |
| `ck` |  | ● |
| `cn` |  | ● |
| `cor_exp` |  | ● |
| `country` | ● | ● |
| `countrycode` |  | ● |
| `csh_c` |  | ● |
| `csh_g` |  | ● |
| `csh_i` |  | ● |
| `csh_m` |  | ● |
| `csh_r` |  | ● |
| `csh_x` |  | ● |
| `ctfp` |  | ● |
| `currency_unit` |  | ● |
| `cwtfp` |  | ● |
| `delta` |  | ● |
| `emp` |  | ● |
| `gdppc` | ● |  |
| `hc` |  | ● |
| `i_cig` |  | ● |
| `i_irr` |  | ● |
| `i_outlier` |  | ● |
| `i_xm` |  | ● |
| `i_xr` |  | ● |
| `irr` |  | ● |
| `labsh` |  | ● |
| `pl_c` |  | ● |
| `pl_con` |  | ● |
| `pl_da` |  | ● |
| `pl_g` |  | ● |
| `pl_gdpo` |  | ● |
| `pl_i` |  | ● |
| `pl_k` |  | ● |
| `pl_m` |  | ● |
| `pl_n` |  | ● |
| `pl_x` |  | ● |
| `pop` | ● | ● |
| `rconna` |  | ● |
| `rdana` |  | ● |
| `rgdpe` |  | ● |
| `rgdpna` |  | ● |
| `rgdpo` |  | ● |
| `rkna` |  | ● |
| `rnna` |  | ● |
| `rtfpna` |  | ● |
| `rwtfpna` |  | ● |
| `statcap` |  | ● |
| `xr` |  | ● |
| `year` | ● | ● |

### `convergence_data_prepared`

| Variable | Label | Definition | Construction | Units | Source | Coverage |
|---|---|---|---|---|---|---|
| `ccode` | Country code (3-letter ISO) | 3-letter ISO country code (PWT countrycode, renamed). | rename countrycode ccode in Section 3. | ISO-3 code | Penn World Table 10.0 | 84 countries (analysis) |
| `country` | Country name | Country name. | Carried verbatim from PWT 10.0. | string | Penn World Table 10.0 | 84 countries (analysis) |
| `year` | Calendar year | Annual time index. | Restricted to 1960 onwards for the balanced panel. | year | Penn World Table 10.0 | 1960-2019 |
| `gdppc` | Real GDP per capita (PPP, 2017 US$) | Expenditure-side real GDP at chained PPPs per person — the headline income measure. | gen gdppc = rgdpe / pop (rgdpe is in millions; pop in millions). | 2017 US$ (PPP) | Computed from PWT 10.0 | 84 countries, 1960-2019 |
| `pop` | Population (millions) | Total population. | PWT pop; the under-1-million filter drops small countries before the panel is fixed. | millions of persons | Penn World Table 10.0 | 84 countries, 1960-2019 |

| Variable | N | Miss% | Distinct | Min | Mean | Median | Max | SD |
|---|---|---|---|---|---|---|---|---|
| `ccode` | 5,040 | 0.0 | 84 | — | — | — | — | — |
| `country` | 5,040 | 0.0 | 84 | — | — | — | — | — |
| `year` | 5,040 | 0.0 | 60 | 1960 | 1989.5 | 1989 | 2019 | 17.32 |
| `gdppc` | 5,040 | 0.0 | 5,040 | 514.5 | 11,951 | 5,197.0 | 102,938 | 14,403 |
| `pop` | 5,040 | 0.0 | 5,040 | 1.14 | 52.03 | 11.71 | 1,433.8 | 160.0 |

### `pwt100`

| Variable | Label | Definition | Construction | Units | Source | Coverage |
|---|---|---|---|---|---|---|
| `countrycode` | Country code (3-letter ISO) | 3-letter ISO country code. | Source PWT identifier; renamed to ccode in the prepared file. | ISO-3 code | Penn World Table 10.0 | 183 economies |
| `country` | Country name | Country name. | Carried verbatim from PWT 10.0. | string | Penn World Table 10.0 | 84 countries (analysis) |
| `currency_unit` | Currency unit | Name of the national currency. |  | string | Penn World Table 10.0 |  |
| `year` | Calendar year | Annual time index. | Restricted to 1960 onwards for the balanced panel. | year | Penn World Table 10.0 | 1960-2019 |
| `rgdpe` | Expenditure-side real GDP, chained PPPs (mil. 2017US$) | Expenditure-side real GDP at chained PPPs — used to form gdppc=rgdpe/pop. | PWT series; the post's per-capita income numerator. | millions of 2017 US$ (PPP) | Penn World Table 10.0 | 183 economies |
| `rgdpo` | Output-side real GDP at chained PPPs (in mil. 2017US$) |  |  |  | Penn World Table 10.0 |  |
| `pop` | Population (millions) | Total population. | PWT pop; the under-1-million filter drops small countries before the panel is fixed. | millions of persons | Penn World Table 10.0 | 84 countries, 1960-2019 |
| `emp` | Number of persons engaged (in millions) |  |  |  | Penn World Table 10.0 |  |
| `avh` | Average annual hours worked by persons engaged |  |  |  | Penn World Table 10.0 |  |
| `hc` | Human capital index | Human capital index based on years of schooling and returns to education (see PWT note hc). |  | index | Penn World Table 10.0 |  |
| `ccon` | Real consumption of households and government, current PPPs (mil. 2017US$) |  |  |  | Penn World Table 10.0 |  |
| `cda` | Real domestic absorption (see PWT note cda) |  |  |  | Penn World Table 10.0 |  |
| `cgdpe` | Expenditure-side real GDP at current PPPs (in mil. 2017US$) |  |  |  | Penn World Table 10.0 |  |
| `cgdpo` | Output-side real GDP at current PPPs (in mil. 2017US$) |  |  |  | Penn World Table 10.0 |  |
| `cn` | Capital stock at current PPPs (in mil. 2017US$) |  |  |  | Penn World Table 10.0 |  |
| `ck` | Capital services levels at current PPPs (USA=1) |  |  |  | Penn World Table 10.0 |  |
| `ctfp` | TFP level at current PPPs (USA=1) |  |  |  | Penn World Table 10.0 |  |
| `cwtfp` | Welfare-relevant TFP levels at current PPPs (USA=1) |  |  |  | Penn World Table 10.0 |  |
| `rgdpna` | Real GDP at constant 2017 national prices (in mil. 2017US$) |  |  |  | Penn World Table 10.0 |  |
| `rconna` | Real consumption at constant 2017 national prices (in mil. 2017US$) |  |  |  | Penn World Table 10.0 |  |
| `rdana` | Real domestic absorption at constant 2017 national prices (mil. 2017US$) |  |  |  | Penn World Table 10.0 |  |
| `rnna` | Capital stock at constant 2017 national prices (in mil. 2017US$) |  |  |  | Penn World Table 10.0 |  |
| `rkna` | Capital services at constant 2017 national prices (2017=1) |  |  |  | Penn World Table 10.0 |  |
| `rtfpna` | TFP at constant national prices (2017=1) |  |  |  | Penn World Table 10.0 |  |
| `rwtfpna` | Welfare-relevant TFP at constant national prices (2017=1) |  |  |  | Penn World Table 10.0 |  |
| `labsh` | Share of labour compensation in GDP at current national prices |  |  |  | Penn World Table 10.0 |  |
| `irr` | Real internal rate of return |  |  |  | Penn World Table 10.0 |  |
| `delta` | Average depreciation rate of the capital stock |  |  |  | Penn World Table 10.0 |  |
| `xr` | Exchange rate, national currency/USD (market+estimated) |  |  |  | Penn World Table 10.0 |  |
| `pl_con` | Price level of CCON (PPP/XR), USA GDPo in 2017=1 |  |  |  | Penn World Table 10.0 |  |
| `pl_da` | Price level of CDA (PPP/XR), USA GDPo in 2017=1 |  |  |  | Penn World Table 10.0 |  |
| `pl_gdpo` | Price level of CGDPo (PPP/XR), USA GDPo in 2017=1 |  |  |  | Penn World Table 10.0 |  |
| `i_cig` | 0/1/2/3/4 data-quality flag (see PWT note i_cig) |  |  |  | Penn World Table 10.0 |  |
| `i_xm` | 0/1/2 data-quality flag (see PWT note i_xm) |  |  |  | Penn World Table 10.0 |  |
| `i_xr` | 0/1: exchange rate market-based (0) or estimated (1) |  |  |  | Penn World Table 10.0 |  |
| `i_outlier` | 0/1 outlier flag (see PWT note i_outlier) |  |  |  | Penn World Table 10.0 |  |
| `i_irr` | 0/1/2/3 internal-rate-of-return flag (see PWT note i_irr) |  |  |  | Penn World Table 10.0 |  |
| `cor_exp` | Correlation between expenditure shares (see PWT note cor_exp) |  |  |  | Penn World Table 10.0 |  |
| `statcap` | Statistical capacity indicator (World Bank, developing countries) |  |  |  | Penn World Table 10.0 |  |
| `csh_c` | Share of household consumption at current PPPs |  |  |  | Penn World Table 10.0 |  |
| `csh_i` | Share of gross capital formation at current PPPs |  |  |  | Penn World Table 10.0 |  |
| `csh_g` | Share of government consumption at current PPPs |  |  |  | Penn World Table 10.0 |  |
| `csh_x` | Share of merchandise exports at current PPPs |  |  |  | Penn World Table 10.0 |  |
| `csh_m` | Share of merchandise imports at current PPPs |  |  |  | Penn World Table 10.0 |  |
| `csh_r` | Share of residual trade and GDP statistical discrepancy at current PPPs |  |  |  | Penn World Table 10.0 |  |
| `pl_c` | Price level of household consumption, USA GDPo in 2017=1 |  |  |  | Penn World Table 10.0 |  |
| `pl_i` | Price level of capital formation, USA GDPo in 2017=1 |  |  |  | Penn World Table 10.0 |  |
| `pl_g` | Price level of government consumption, USA GDPo in 2017=1 |  |  |  | Penn World Table 10.0 |  |
| `pl_x` | Price level of exports, USA GDPo in 2017=1 |  |  |  | Penn World Table 10.0 |  |
| `pl_m` | Price level of imports, USA GDPo in 2017=1 |  |  |  | Penn World Table 10.0 |  |
| `pl_n` | Price level of the capital stock, USA 2017=1 |  |  |  | Penn World Table 10.0 |  |
| `pl_k` | Price level of the capital services, USA=1 |  |  |  | Penn World Table 10.0 |  |

| Variable | N | Miss% | Distinct | Min | Mean | Median | Max | SD |
|---|---|---|---|---|---|---|---|---|
| `countrycode` | 12,810 | 0.0 | 183 | — | — | — | — | — |
| `country` | 12,810 | 0.0 | 183 | — | — | — | — | — |
| `currency_unit` | 12,810 | 0.0 | 136 | — | — | — | — | — |
| `year` | 12,810 | 0.0 | 70 | 1950 | 1984.5 | 1984 | 2019 | 20.21 |
| `rgdpe` | 10,399 | 18.8 | 10,399 | 20.24 | 304,425 | 30,250 | 20,856,496 | 1,200,024 |
| `rgdpo` | 10,399 | 18.8 | 10,397 | 36.53 | 306,730 | 30,838 | 20,596,346 | 1,203,818 |
| `pop` | 10,399 | 18.8 | 10,388 | 0.004 | 30.96 | 6.15 | 1,433.8 | 116.2 |
| `emp` | 9,529 | 25.6 | 9,505 | 0.001 | 14.17 | 2.86 | 799.3 | 58.06 |
| `avh` | 3,492 | 72.7 | 3,397 | 1,380.6 | 1,986.9 | 1,972.4 | 3,039.8 | 284.0 |
| `hc` | 8,637 | 32.6 | 8,615 | 1.01 | 2.09 | 1.99 | 4.35 | 0.727 |
| `ccon` | 10,399 | 18.8 | 10,397 | 16.06 | 224,900 | 24,630 | 16,704,312 | 884,170 |
| `cda` | 10,399 | 18.8 | 10,399 | 21.76 | 304,727 | 31,295 | 21,390,006 | 1,223,429 |
| `cgdpe` | 10,399 | 18.8 | 10,397 | 20.26 | 305,907 | 30,320 | 20,797,638 | 1,212,956 |
| `cgdpo` | 10,395 | 18.9 | 10,394 | 18.45 | 305,928 | 30,479 | 20,566,036 | 1,211,077 |
| `cn` | 10,314 | 19.5 | 10,313 | 21.16 | 1,210,992 | 84,026 | 81,598,688 | 4,738,848 |
| `ck` | 7,409 | 42.2 | 7,344 | 5.87e-06 | 0.035 | 0.003 | 1.00 | 0.112 |
| `ctfp` | 6,412 | 49.9 | 6,345 | 0.046 | 0.712 | 0.710 | 3.35 | 0.281 |
| `cwtfp` | 6,412 | 49.9 | 6,344 | 0.073 | 0.703 | 0.704 | 2.04 | 0.265 |
| `rgdpna` | 10,399 | 18.8 | 10,386 | 13.88 | 320,659 | 33,838 | 20,563,592 | 1,182,815 |
| `rconna` | 10,399 | 18.8 | 10,397 | 19.18 | 236,845 | 27,727 | 16,801,878 | 890,550 |
| `rdana` | 10,399 | 18.8 | 10,397 | 24.42 | 313,761 | 33,593 | 21,431,476 | 1,182,355 |
| `rnna` | 10,314 | 19.5 | 10,313 | 28.19 | 1,453,456 | 126,277 | 81,726,344 | 4,878,384 |
| `rkna` | 7,409 | 42.2 | 7,273 | 0.005 | 0.477 | 0.435 | 1.97 | 0.318 |
| `rtfpna` | 6,412 | 49.9 | 6,290 | 0.200 | 0.959 | 0.951 | 8.12 | 0.366 |
| `rwtfpna` | 6,412 | 49.9 | 6,294 | 0.093 | 0.944 | 0.943 | 3.57 | 0.309 |
| `labsh` | 7,970 | 37.8 | 3,155 | 0.090 | 0.533 | 0.537 | 0.903 | 0.125 |
| `irr` | 7,952 | 37.9 | 7,655 | 0.010 | 0.128 | 0.104 | 1.10 | 0.096 |
| `delta` | 10,314 | 19.5 | 10,311 | 0.013 | 0.042 | 0.039 | 0.100 | 0.013 |
| `xr` | 10,399 | 18.8 | 6,197 | 7.89e-15 | 7,647.5 | 3.07 | 76,369,942 | 748,913 |
| `pl_con` | 10,399 | 18.8 | 10,394 | 0.018 | 0.357 | 0.286 | 22.37 | 0.417 |
| `pl_da` | 10,399 | 18.8 | 10,396 | 0.015 | 0.360 | 0.300 | 22.12 | 0.418 |
| `pl_gdpo` | 10,399 | 18.8 | 10,397 | -31.22 | 0.369 | 0.293 | 19.41 | 0.617 |
| `i_cig` | 10,399 | 18.8 | 5 | — | — | — | — | — |
| `i_xm` | 10,399 | 18.8 | 3 | — | — | — | — | — |
| `i_xr` | 10,399 | 18.8 | 2 | — | — | — | — | — |
| `i_outlier` | 10,399 | 18.8 | 2 | — | — | — | — | — |
| `i_irr` | 7,952 | 37.9 | 4 | — | — | — | — | — |
| `cor_exp` | 1,653 | 87.1 | 1,641 | -0.058 | 0.558 | 0.572 | 1.00 | 0.196 |
| `statcap` | 2,117 | 83.5 | 254 | 14.44 | 67.37 | 67.78 | 98.89 | 15.20 |
| `csh_c` | 10,399 | 18.8 | 10,394 | -14.92 | 0.643 | 0.638 | 9.17 | 0.289 |
| `csh_i` | 10,399 | 18.8 | 10,396 | -3.73 | 0.218 | 0.207 | 5.31 | 0.138 |
| `csh_g` | 10,399 | 18.8 | 10,399 | -3.30 | 0.190 | 0.168 | 2.79 | 0.119 |
| `csh_x` | 10,399 | 18.8 | 10,397 | -2.44 | 0.226 | 0.138 | 3.47 | 0.265 |
| `csh_m` | 10,399 | 18.8 | 10,397 | -15.44 | -0.295 | -0.198 | 41.25 | 0.647 |
| `csh_r` | 10,399 | 18.8 | 10,106 | -15.88 | 0.017 | 4.24e-04 | 7.47 | 0.240 |
| `pl_c` | 10,399 | 18.8 | 10,397 | 0.016 | 0.371 | 0.306 | 23.10 | 0.425 |
| `pl_i` | 10,399 | 18.8 | 10,397 | 0.006 | 0.425 | 0.379 | 33.50 | 0.628 |
| `pl_g` | 10,399 | 18.8 | 10,399 | 0.009 | 0.348 | 0.246 | 18.52 | 0.410 |
| `pl_x` | 10,399 | 18.8 | 10,389 | 0.008 | 0.415 | 0.455 | 2.10 | 0.197 |
| `pl_m` | 10,399 | 18.8 | 10,386 | 0.021 | 0.408 | 0.461 | 5.07 | 0.204 |
| `pl_n` | 10,314 | 19.5 | 10,312 | 0.013 | 0.359 | 0.296 | 20.65 | 0.436 |
| `pl_k` | 7,409 | 42.2 | 7,344 | 0.064 | 1.38 | 0.976 | 31.99 | 2.00 |

## Known limitations & caveats

- <strong>Real data.</strong> 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.
- <strong>Balanced-panel selection.</strong> 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.
- <strong>Sample exclusions.</strong> Oil producers (IMF classification) and countries under 1 million population are dropped, following Patel et al. (2021); convergence results are sensitive to these choices.
- <strong>Low explanatory power.</strong> 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.
- <strong>Beta ≠ sigma.</strong> 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).

---

*Generated by `build_data_dictionary.py`. Stata format: .dta v118.*
