sw2023 0.3.2

Nonparametric Multiple-Output Stochastic Frontier Analysis (Simar & Wilson 2023)

sw2023

Nonparametric Multiple-Output Stochastic Frontier Analysis in Python

A Python implementation of the nonparametric stochastic frontier estimator of Simar & Wilson (2023, Journal of Business & Economic Statistics) for production technologies with multiple inputs and multiple outputs.

Simar, L., Wilson, P.W. (2023). Nonparametric, Stochastic Frontier Models with Multiple Inputs and Outputs. Journal of Business & Economic Statistics, 41(4), 1391–1403. https://doi.org/10.1080/07350015.2022.2110882

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Features

Feature	Status
Multiple inputs & outputs (directional distance function)	✅
Local Linear Least Squares (LLLS) frontier estimation	✅
SVKZ and HMS σ_η estimators	✅
JLMS individual efficiency recovery	✅
LOO-CV and Silverman bandwidth selection	✅
Pairs bootstrap confidence intervals	✅
Asymptotic CI (CLT + delta method)	✅
Wild bootstrap significance test (Parmeter et al. 2024)	✅
4-component panel (transient + persistent inefficiency)	✅
Stata 16.1+ integration (pure Mata, no Python dependency)	✅

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Installation

pip install sw2023                  # core (numpy, scipy, pandas)
pip install sw2023[viz]             # + matplotlib
pip install sw2023[dev]             # + jupyter, pytest

Requirements: Python >= 3.8, numpy >= 1.21, scipy >= 1.7, pandas >= 1.3

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Quick Start

Cross-sectional model

import numpy as np
from sw2023 import SW2023Model

X = np.random.lognormal(0, 0.5, size=(200, 2))   # 2 inputs
Y = np.random.lognormal(0, 0.5, size=(200, 3))   # 3 outputs

m = SW2023Model(X, Y, method='HMS', bandwidth_method='loocv')
m.fit()
m.summary()

print(m.efficiency_.mean())         # mean efficiency
print(m.sigma_eta_.mean())          # mean sigma_eta

Bootstrap confidence intervals

from sw2023 import bootstrap_sw

result = bootstrap_sw(X, Y, B=199, alpha=0.05)
print(result['eff_mean_ci'])        # [lower, upper]
print(result['phi_hat_ci'])         # (n, 2) frontier CI

Asymptotic CI (fast)

m = SW2023Model(X, Y, method='HMS')
m.fit()
ci = m.confint_asymptotic(alpha=0.05)
print(ci['phi_hat_ci'])             # (n, 2)
print(ci['se_phi'])                 # (n,) standard errors

Significance test for inefficiency heterogeneity

from sw2023 import test_r3_significance

res = test_r3_significance(X, Y, B=299)
print(res['p_value'])               # H0: E(eps^3 | Z) = const

Panel model (4-component)

from sw2023 import PanelSW2023

m = PanelSW2023(X, Y, firm_id, time_id, method='HMS')
m.fit()
print(m.eff_transient_.mean())      # transient efficiency
print(m.eff_persistent_.mean())     # persistent efficiency

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Stata Integration (16.1+)

* Cross-sectional
local sw_args "x1 x2 | y1 y2 | method=HMS"
python script "sw2023_stata.py"

* Panel (4-component)
local sw_args "x1 x2 | y1 y2 | method=HMS firm=firmid time=year"
python script "sw2023_stata.py", args("panel")

* Wild bootstrap significance test (pure Mata, no Python needed)
sw2023test y1 y2, inputs(x1 x2) reps(299)

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Replication

All numerical results in the accompanying manuscript can be reproduced with:

# Quick verification (< 5 minutes)
python replication.py

# Exact replication of Table 1 (n_sims=100, ~30 minutes)
python replication.py --full

Pre-computed Monte Carlo results (100 replications per cell) are provided in mc_imse_results.csv. IMSE ratios relative to Simar & Wilson (2023) Table F.1 range from 0.94 to 1.29 with median 1.04.

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Methodology

The SW(2023) estimator handles multiple outputs without imposing a parametric form on the frontier. Key steps:

1. Direction vector d ∈ R^(p+q): defines the efficiency direction
2. Rotation (X, Y) → (Z, U): projects onto frontier coordinates
3. LLLS: kernel regression of U on Z → conditional moments r̂₁, r̂₂, r̂₃
4. σ_η estimation: σ̂_η = (-r̂₃/a₃⁺)^(1/3) (SVKZ) or HMS for wrong-skewness
5. JLMS: E[η | ξ̂] → individual efficiency score exp(-η̂)

The 4-component panel extension decomposes:

U_it = φ(Z_it) + ||d||·v_it - ||d||·u_it + ||d||·α_i - ||d||·μ_i

• v_it: transient noise
• u_it ~ N⁺(0, σ_u²): transient inefficiency
• α_i ~ N(0, σ_α²): individual heterogeneity
• μ_i ~ N⁺(0, σ_μ²): persistent inefficiency

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Citation

If you use this package, please cite:

@misc{Lee2025sw2023,
  author = {Lee, Choonjoo},
  title  = {{sw2023}: Nonparametric Multiple-Output Stochastic Frontier
            Analysis in {Python}},
  year   = {2025},
  note   = {Manuscript submitted for publication}
}

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References

• Simar, L. & Wilson, P.W. (2023). Nonparametric, Stochastic Frontier Models with Multiple Inputs and Outputs. Journal of Business & Economic Statistics, 41(4), 1391–1403.
• Parmeter, C.F., Simar, L., Van Keilegom, I. & Zelenyuk, V. (2024). Inference in the nonparametric stochastic frontier model. Econometric Reviews, 43(7), 518–539. https://doi.org/10.1080/07474938.2024.2339193
• Hafner, C.M., Manner, H. & Simar, L. (2018). The "wrong skewness" problem in stochastic frontier models: A new approach. Econometric Reviews, 37(4), 380–400. https://doi.org/10.1080/07474938.2016.1140284
• Jondrow, J., Lovell, C.A.K., Materov, I.S. & Schmidt, P. (1982). On the estimation of technical inefficiency in the stochastic frontier production function model. Journal of Econometrics, 19(2–3), 233–238.

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License

GNU General Public License v3 or later (GPL-3.0-or-later). See LICENSE for details.