Replication Package

This repository reproduces all empirical results for the paper. We estimate country-specific VAR(1) models in first-differenced natural logs for k, gdp, nx, ren with an intercept. Identification is recursive (Cholesky) with the ordering k → gdp → nx → ren. Inference uses a fixed-design residual bootstrap (B = 2000) for coefficients and IRFs; confidence bands are reported as percentile and BCa (bias-corrected and accelerated). For comparison, asymptotic (delta-method) IRF bands are also provided.

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1) Repository structure

/Strave_MATLAB/

• raw_data/ # Step 0 outputs (automated EPL pipeline & transformed)
• utils/ # manifest_* helpers, sha256_file, verify_manifest
• GR_MATLAB_code/ # Greece scripts
• BEL_MATLAB_code/ # Belgium scripts
• GR_MATLAB_output/ # Greece outputs
• BEL_MATLAB_output/ # Belgium outputs
• config_paths.m # central paths & run constants
• step0_source_data.m # Step 0: fetch OWID/WB & build transforms

Scripts ("CTY" ∈ {Belgium, Greece}):

• step0_source_data.m
• step1_load__data.m
• step2_estimate_var_.m
• step2b_estimate_var_Diagnostics_.m
• step2c_var_Cointegration_.m
• step3_orthogonalized_irf_.m
• step4_bootstrap_coeff_SE_IRF_CI_.m
• step4b_IRF_asymptotic_CIS_.m
• step5_Biased_Corr_bootstrap_coeff_IRF_CI_.m

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2) Data (retrieved: Aug 2025)

• REN — Share of electricity generated by renewables (OWID): https://ourworldindata.org/grapher/share-electricity-renewables?tab=line&country=GRC~BEL&mapSelect=GRC~BEL
• GDP — GDP (constant 2015 US$) (World Bank): https://data.worldbank.org/indicator/NY.GDP.MKTP.KD
• K — Gross Fixed Capital Formation (constant 2015 US$) (World Bank): https://data.worldbank.org/indicator/NE.GDI.FTOT.KD
• X — Exports of goods and services (constant 2015 US$) (World Bank): https://data.worldbank.org/indicator/NE.EXP.GNFS.KD
• IMP — Imports of goods and services (constant 2015 US$) (World Bank): https://data.worldbank.org/indicator/NE.IMP.GNFS.KD

Step 0:

1. Fetch OWID chart CSV for renewables share and filter to target countries.
2. Fetch World Bank indicators via API (constant 2015 US$): GDP, K, X, IMP.
3. Build analysis-ready transforms per country:
   • gdp = Δ ln(GDP_2015USD)
   • k = Δ ln(K_2015USD)
   • nx = Δ ln(X_2015USD) − Δ ln(IMP_2015USD)
   • ren = Δ ln(REN_share), where REN_share = share_electricity_renewables / 100 ∈ (0,1]
4. Write outputs under /raw_data: OWID CSV (+META), WB_* CSVs (+META), merged_<CTY>_raw.csv (+META), and merged_<CTY>_transforms.csv (+TRANSFORMS.txt).

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3) Software & reproducibility

• MATLAB: R2024a (or R2020a+). No extra toolboxes required (Econometrics Toolbox optional).
• EViews: v9 used for stationarity tests.
• Random seed: 12345 (set in all bootstrap routines).
• OS: Developed on Windows.
• Provenance: Each step appends SHA-256 hashes to MANIFEST.txt via utils/manifest_*; verify with utils/verify_manifest.m.

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4) Data details

• Primary inputs are created by Step 0 and stored in /Strave_MATLAB/raw_data.
• Core file used in Step 1 (Greece example): merged_GRC_transforms.csv.
• Column order (required after Step 1 load): year, k, gdp, nx, ren.
• Units: first-differenced natural logs (Δ ln) by construction (see Step 0).
• Frequency: annual, analysis window 1990–2023.
• Missing values: rows with missing entries are dropped before differencing.
• Sources & license: OWID (renewables chart CSV) and World Bank WDI (constant 2015 US$); CC BY / CC BY 4.0.

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5) How to run (example: Greece)

a) Source data & transforms (automated)
Run step0_source_data.m
Outputs (under raw_data): OWID & WB CSVs (+META), merged_GRC_raw.csv (+META), merged_GRC_transforms.csv (+TRANSFORMS.txt)

b) Load prepared Δln data
Run step1_load_GREECE_data.m
Output: GR_prepared.mat

c) Estimate VAR(1)
Run step2_estimate_var_GREECE.m
Output: GR_VAR_estimates.mat

d) Diagnostics
Run step2b_estimate_var_Diagnostics_GREECE.m
Outputs: GR_VAR_diagnostics.mat, GR_DIAGNOSTICS.txt

e) Orthogonalized IRFs (point)
Run step3_orthogonalized_irf_GREECE.m
Outputs: GR_IRFs_point.mat, GR_IRFs_point_tidy.csv, GR_IRFs_point_H10.(png|pdf|emf)

f) Bootstrap (coefficients & IRFs)
Run step4_bootstrap_coeff_SE_IRF_CI_GREECE.m
Outputs: GR_bootstrap_results.mat, GR_coefficients_bootstrap_(csv|xlsx), GR_IRFs_Bands_95.(png|pdf|emf)

g) Asymptotic benchmark (delta method)
Run step4b_IRF_asymptotic_CIS_GREECE.m
Outputs: GR_asymptotic_results.mat, GR_IRFs_Asymptotic_(Normal|Percentile)_95.(png|pdf|emf)

h) BCa IRF bands
Run step5_Biased_Corr_bootstrap_coeff_IRF_CI_GREECE.m
Outputs: GR_BCa_IRF_bands.mat, GR_IRF_BCa_tidy_95.csv, GR_IRFs_BCa_95.(png|pdf|emf)

For Belgium, run the corresponding BEL scripts. Outputs are saved in BEL_MATLAB_output/.

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6) Paths & configuration

Default paths (configurable in config_paths.m):

• Base (repo): ...\OneDrive\Υπολογιστής\Strave\Strave_MATLAB
• Data (Step 0 output): ...\Strave_MATLAB\raw_data
• Output (Greece): ...\Strave_MATLAB\GR_MATLAB_output
• Output (Belgium): ...\Strave_MATLAB\BEL_MATLAB_output
• config_paths.m also centralizes IRF horizon H, bootstrap draws B, and the RNG seed.

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7) Methods summary

• Model: VAR(1) in Δ ln with intercept; variable order (k, gdp, nx, ren).
• Identification: recursive (Cholesky, lower-triangular Σ_u).
• IRFs: Ψ(h) = A^h * P, with P = chol(Σ_u), horizons h = 0…10.
• Diagnostics: LM tests (lags 1–2), White heteroskedasticity (cross-terms), Jarque–Bera per equation and joint, stability via companion eigenvalues.
• Cointegration (reference): system-wide Johansen trace/max-eig (focus on r = 0) for no-const and unrestricted-const cases; reported for context only.
• Bootstrap: fixed-design residual bootstrap; resample centered residuals, simulate with observed initial condition, re-estimate, recompute IRFs; report percentile CIs.
• BCa: jackknife to compute z0 and acceleration a; apply BCa adjustment to bootstrap IRFs.
• Asymptotic benchmark: simulate vec(B̂) ~ N(vec(B̂), Σ_u ⊗ (X’X)^{-1}); report normal ± z*sd and percentile bands.
• Reproducibility: IRF(0) equals the Cholesky column; unstable draws skipped; fixed seed.

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8) Expected outputs

• Prepared data: *_prepared.mat
• VAR estimates: *_VAR_estimates.mat
• Diagnostics: *_VAR_diagnostics.mat, *_DIAGNOSTICS.txt
• IRFs: *_IRFs_point.mat, *_IRFs_point_tidy.csv, figures (PNG/PDF/EMF)
• Bootstrap results: *_bootstrap_results.mat, coefficients tables (CSV/XLSX)
• IRF bands: percentile and BCa (MAT, CSV, PNG, PDF, EMF)
• Asymptotic results: *_asymptotic_results.mat and figures
• MANIFEST: per-step MANIFEST.txt with SHA-256 hashes of key artifacts

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9) Troubleshooting

• Ensure Step 0 completed and raw_data contains merged_<CTY>_transforms.csv.
• Ensure column order after Step 1 is (year, k, gdp, nx, ren).
• Cholesky errors: covariance is stabilized with a ridge; persistent issues may indicate outliers.
• Update baseDir/rawDir/outBase in config_paths.m if using different paths.
• EMF export is Windows-specific; PNG and PDF are cross-platform.

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10) Citation & references

If using this package, please cite the paper.

References

• Efron & Tibshirani (1993) — An Introduction to the Bootstrap
• Efron & Hastie (2016) — Computer Age Statistical Inference
• Kilian (1998) — Small-sample confidence intervals for IRFs
• Lütkepohl (2005) — New Introduction to Multiple Time Series Analysis
• Lütkepohl & Kilian (2017) — Structural Vector Autoregressive Analysis
• Runkle (1987) — Vector Autoregressions and Reality

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11) License & contact

• License: MIT
• Contact: Aeneas Vafiadakis — aineias.edu@gmail.com
• Issues may be reported via the GitHub issue tracker.

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Aggregate process (table)

Paper artifact	Script (section)	Inputs	Output filenames (canonical)
Step 0: EPL & transforms	step0_source_data.m	OWID CSV, WB API	merged_<CTY>_raw.csv (+META); merged_<CTY>_transforms.csv (+TRANSFORMS.txt); OWID/WB CSVs (+META)
Step 1: load Δln data	step1_load_<CTY>_data.m	merged_<CTY>_transforms.csv	<CTY>_prepared.mat; <CTY>_TRANSFORMS.txt; <CTY>_tidy.csv
VAR estimates	step2_estimate_var_<CTY>.m	<CTY>_prepared.mat	<CTY>_VAR_estimates.mat
Diagnostics TXT & MAT	step2b_estimate_var_Diagnostics_<CTY>.m	prepared + estimates	<CTY>_VAR_diagnostics.mat; <CTY>_DIAGNOSTICS.txt; GR_regression_diagnostics*.{csv,xlsx}
Johansen summary	step2c_var_Cointegration_<CTY>.m	prepared	<CTY>_JOHANSEN_SYSTEM.txt; <CTY>_Johansen_system.mat
Point IRFs (grid)	step3_orthogonalized_irf_<CTY>.m	estimates	<CTY>_IRFs_point.mat; <CTY>_IRFs_point_tidy.csv; <CTY>_IRFs_point_H10.{pdf,png,emf}
Percentile IRFs	step4_bootstrap_coeff_SE_IRF_CI_<CTY>.m	prepared + estimates	<CTY>_bootstrap_results.mat; <CTY>_IRFs_Bands_95.{pdf,png,emf}; <CTY>_coefficients_bootstrap*.{csv,xlsx}
Asymptotic benchmarks	step4b_IRF_asymptotic_CIS_<CTY>.m	prepared + estimates	GR_IRFs_Asymptotic_Normal_95.*; GR_IRFs_Asymptotic_Percentile_95.*
BCa IRFs (main)	step5_Biased_Corr_bootstrap_coeff_IRF_CI_<CTY>.m	prepared + boot draws	<CTY>_BCa_IRF_bands.mat; <CTY>_IRF_BCa_tidy_95.csv; <CTY>_IRFs_BCa_95.{pdf,png,emf}