Empirical Estimation of CES Elasticity of Substitution

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Paper-03 in the complexity-econ series: estimates sector-specific CES elasticity of substitution ($\sigma$) from OECD panel data + Polish GUS data, then tests whether Paper-01's key findings survive with empirically grounded parameters.

Summary

Papers 01-02 use calibrated sector-specific $\sigma$ values (BPO=50, Manufacturing=10, ...). Literature suggests these are 5-10x too high. This paper:

1. Builds an OECD panel (30 countries x 6 sectors x 2000-2023) with IFR robot density + ICT CAPEX as AI proxies
2. Estimates $\sigma$ via normalized CES supply system + Arellano-Bond GMM
3. Cross-validates with hierarchical Bayesian estimation (PyMC)
4. Re-runs the ABM with empirical $\sigma$ to test robustness of bimodality and critical points

Reproduce

# Install dependencies
pip install -r requirements.txt

# Full pipeline
make all

# Or step by step
make data       # Download + clean + merge
make estimate   # GMM + Bayesian estimation
make sensitivity # ABM sensitivity analysis
make figures    # All figures
make paper      # Compile LaTeX

Structure

analysis/python/        8 pipeline scripts + config
data/raw/               Downloaded data (gitignored)
data/processed/         Cleaned panels (gitignored)
figures/                8 PNG figures
latex/                  Paper (XeLaTeX)
results/                Estimation CSVs + ABM sensitivity
simulations/scripts/    ABM sensitivity runner

Dependencies

• Data: Python 3 (pandas, requests, eurostat)
• Estimation: linearmodels, pymc, arviz
• Simulation: complexity-econ/core (Scala 3.5.2, sbt)
• Paper: XeLaTeX + biblatex

Figures

Descriptive Statistics

Fig 1. Automation capital intensity (K/L) trends by sector across OECD countries, 2000–2023. BPO/SSC and Manufacturing show steep growth; Healthcare and Public remain flat.

Fig 2. Cross-sectional distributions of labor productivity (Y/L) and automation intensity (K/L) by sector. Box plots reveal massive heterogeneity — BPO/SSC spans three orders of magnitude in K/L.

GMM Estimation

Fig 3. Forest plot of GMM σ estimates with 95% CI. Empirical values (circles) are 5–9× lower than calibrated values (diamonds) for market sectors. Non-market sectors (Healthcare, Public) are prior-only — SNA cost convention makes σ unidentifiable.

Bayesian Estimation

Fig 4. Posterior distributions from hierarchical Bayesian model (PyMC). Market sectors show tight posteriors consistent with GMM; non-market sectors show prior-only distributions (dashed lines).

Method Comparison

Fig 5. GMM vs Bayesian σ scatter plot. Points hug the 45° line — both methods agree closely, validating the estimates. Market sectors (circles) cluster near σ = 1–9; non-market (triangles) are fixed at priors.

Fig 6. All three σ estimates side by side (calibrated, GMM, Bayesian) for each sector. The gap between calibrated and empirical values is striking — especially for BPO/SSC (50 vs 9) and Manufacturing (10 vs 5).

Recommended σ Values

Fig 7. Calibrated vs recommended σ for ABM simulations. Market sectors use GMM estimates; non-market sectors retain literature priors. This is the prescription carried forward into Papers 04–05.

ABM Sensitivity

Fig 8. Adoption distributions at BDP = 2000 PLN under four σ scenarios (calibrated, empirical, low CI, high CI). The core finding: a 5–9× change in σ shifts adoption by only 1.5 pp — monetary regime matters far more than σ calibration.

License

MIT

Related

• Paper-01: The Acceleration Paradox
• Paper-02: Monetary Regimes
• Paper-04: Phase Diagram & Universality
• Paper-05: Endogenous Technology & Networks
• Core engine