sw2023 0.3.0

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

sw2023

Nonparametric Multiple-Output Stochastic Frontier Analysis

Python implementation of Simar & Wilson (2023):

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

Extended with a 4-component panel decomposition (transient + persistent inefficiency).

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Features

Feature	Status
Multiple inputs & outputs (distance function)	✅
Local Linear Least Squares (LLLS) frontier	✅
SVKZ / HMS σ_η estimator	✅
JLMS individual efficiency	✅
4-component panel (transient + persistent)	✅
Pairs / Cluster bootstrap CI	✅
Asymptotic CI (CLT + delta method)	✅
Wild bootstrap significance test (PSVKZ 2024)	✅
Cross-validation bandwidth selection (LOO-CV)	✅
Stata 16.1+ integration	✅
Visualization	✅

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Installation

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

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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')
m.fit()

print(m.efficiency_.mean())          # mean efficiency
m.summary()

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

Bootstrap confidence intervals

from sw2023 import bootstrap_sw

result = bootstrap_sw(X, Y, B=200, alpha=0.05)
print(result['eff_mean_ci'])          # [lower, upper]
print(result['phi_hat_ci'])           # (n, 2) frontier CI
print(result['eff_individual_ci'])    # (n, 2) individual efficiency CI

Asymptotic CI (CLT-based, 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 (PSVKZ 2024)

from sw2023 import test_r3_significance

res = test_r3_significance(X, Y, B=499)
print(res['p_value'])                 # H₀: E(ε³|Z) = const

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Stata Integration (16.1+)

* Set Python path (once)
python set exec "/usr/local/bin/python3"

* Cross-sectional
local sw_args "x1 x2 x3 | y1 y2 y3 y4 | method=HMS"
python script "sw2023_stata.py"

* Panel (4-component)
local sw_args "x1 x2 x3 | y1 y2 y3 y4 | method=HMS firm=farmid time=year"
python script "sw2023_stata.py", args("panel")

Results are stored as new Stata variables: sw_efficiency, swp_te, swp_pe, etc.

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Methodology

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

1. Direction vector d ∈ R^(p+q): defines the efficiency direction in joint (input, output) space
2. Rotation (X, Y) → (Z, U): projects onto frontier coordinates
3. LLLS: nonparametric kernel regression of U on Z → conditional moments r̂₁, r̂₂, r̂₃
4. σ_η estimation: σ̂_η = max(0, (-r̂₃/a₃)^(1/3)) (SVKZ) or HMS for wrong-skewness
5. JLMS: E[η | ξ̂] → individual efficiency 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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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.
• 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.

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License

MIT License