Taming Model Uncertainty in the Environmental Kuznets Curve

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_bma_dsl/data/"
use "${BASE}synthetic_ekc_panel.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_bma_dsl/data/"
df = pd.read_stata(BASE + "synthetic_ekc_panel.dta")

# load every dataset at once
files = ["synthetic_ekc_panel"]
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 + "synthetic_ekc_panel.dta", "synthetic_ekc_panel.dta")
df, meta = pyreadstat.read_dta("synthetic_ekc_panel.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_bma_dsl/data/"
df <- read_dta(paste0(BASE, "synthetic_ekc_panel.dta"))

Overview & sources

Companion data for a Stata tutorial that confronts the model-uncertainty problem in testing the Environmental Kuznets Curve (EKC). With 12 candidate control variables there are 2⁹² = 4,096 possible regressions on log CO₂ per capita, and choosing one is a hidden assumption. The tutorial applies two principled solutions — Bayesian Model Averaging (BMA, via Stata’s bmaregress) and Post-Double-Selection LASSO (DSL, via dsregress) — to estimate the inverted-N cubic relationship between log CO₂ and log GDP. The data is fully synthetic, built from a known data-generating process in which 5 controls truly affect emissions and 7 are pure noise, so each method can be graded against ground truth. With country and year fixed effects, BMA recovers the GDP cubic almost exactly and flags 6 of 8 true predictors at PIP ≥ 0.80 with zero false positives; DSL produces fast cluster-robust estimates. Stripping the fixed effects inflates the GDP coefficient and generates false positives.

Data sources

Cite this data

Please cite this dataset as follows.

APA

Mendez, C. (2026). Taming Model Uncertainty in the Environmental Kuznets Curve: BMA and Double-Selection LASSO with Panel Data [Data set]. https://carlos-mendez.org/post/stata_bma_dsl/

Belloni, A., Chernozhukov, V., & Hansen, C. (2014). Inference on treatment effects after selection among high-dimensional controls. Review of Economic Studies, 81(2), 608–650. Raftery, A. E. (1995). Bayesian model selection in social research. Sociological Methodology, 25, 111–163. Grossman, G. M., & Krueger, A. B. (1995). Economic growth and the environment. Quarterly Journal of Economics, 110(2), 353–377.

BibTeX

@misc{mendez2026statabmadsl,
  author       = {Mendez, Carlos},
  title        = {Taming Model Uncertainty in the Environmental Kuznets Curve: BMA and Double-Selection LASSO with Panel Data},
  year         = {2026},
  howpublished = {\url{https://carlos-mendez.org/post/stata_bma_dsl/}},
  note         = {Data set}
}

@article{belloni2014inference,
  author  = {Belloni, Alexandre and Chernozhukov, Victor and Hansen, Christian},
  title   = {Inference on Treatment Effects after Selection among High-Dimensional Controls},
  journal = {Review of Economic Studies},
  volume  = {81}, number = {2}, pages = {608--650}, year = {2014}
}
@article{raftery1995bayesian,
  author  = {Raftery, Adrian E.},
  title   = {Bayesian Model Selection in Social Research},
  journal = {Sociological Methodology},
  volume  = {25}, pages = {111--163}, year = {1995}
}
@article{grossman1995economic,
  author  = {Grossman, Gene M. and Krueger, Alan B.},
  title   = {Economic Growth and the Environment},
  journal = {Quarterly Journal of Economics},
  volume  = {110}, number = {2}, pages = {353--377}, year = {1995}
}

Variable explorer search & filter all 18 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

The synthetic outcome — log CO₂ per capita — is generated from a cubic EKC with country and year fixed effects (the inverted-N shape):

ln(CO2)_it = β₁·ln(GDP)_it + β₂·ln(GDP)²_it + β₃·ln(GDP)³_it + Xᵗᵘᵘᵉ·γ + α_i + δ_t + ε_it

with the true coefficients written into the DGP: β₁ = -7.10, β₂ = +0.81, β₃ = -0.03 (designed turning points near \$1,895 and \$34,647), five true control slopes — fossil_fuel +0.015, renewable -0.010, urban +0.007, democracy -0.005, industry +0.010 — and seven noise controls with a true coefficient of exactly 0 (globalization, pop_density, corruption, services, trade, fdi, credit). Country fixed effects are N(0, 0.50) draws, the year effect is a downward decarbonization trend, and observation noise is N(0, 0.15).

• GDP polynomial: ln_gdp_sq = ln_gdp², ln_gdp_cb = ln_gdp³ — the linear/squared/cubic terms that trace the inverted-N.
• Turning points (income where emissions change direction): x* = [-β₂ ± √(β₂² - 3β₁β₃)] / (3β₃), GDP* = exp(x*).
• BMA: averages over the 2⁹² = 4,096 model space; each variable’s posterior inclusion probability (PIP) is PIP_j = Σ_{k: x_j ∈ M_k} P(M_k | data), the posterior weight on models containing it (robustness threshold PIP ≥ 0.80). The posterior mean is β̂_j = Σ_k P(M_k | data)·β̂_{j,k}.
• Double-Selection LASSO: LASSO-select controls for the outcome, then for each variable of interest, take the union, then run OLS on that union (cluster-robust SE) — "select, then regress" protection against omitted-variable bias.

The true predictors and several noise variables are deliberately correlated with GDP in the DGP (e.g. globalization, services strongly), so a naive regression would flag the noise as "significant"; the task for BMA and DSL is to see through that correlation.

The datasets

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Known limitations & caveats

• Synthetic data. There is no real data behind this tutorial. Every value is simulated from a known data-generating process; results are internally consistent with the calibration but are NOT empirical evidence about real-world CO₂ emissions or the EKC.
• Inspired by, not identical to. The panel is inspired by Gravina & Lanzafame (2025) but the values are fully synthetic and do not reproduce that study's data.
• Known answer key. Exactly 5 controls (fossil_fuel, renewable, urban, democracy, industry) have a true non-zero effect; the other 7 are pure noise with a true coefficient of zero. Use this only to grade method accuracy, not to draw substantive conclusions.
• Weak signals are hard. Two true controls (urban +0.007, democracy -0.005) have small coefficients and fall below the PIP ≥ 0.80 threshold even though they belong — a realistic limitation, not a data error.
• Fixed effects matter. The cubic-EKC recovery and zero-false-positive selection hold only with country and year fixed effects; pooled (no-FE) estimates inflate the GDP coefficient 2–3× and generate false positives.
• Country IDs are arbitrary. country_id 1–80 are synthetic identifiers with no real-country mapping; the CSV rows are not sorted by id.