PanelSFA

Parametric Stochastic Frontier Analysis with a scikit-learn compatible API. This library implements foundational and state-of-the-art frontier models, enabling the estimation of technical efficiency in both cross-sectional and panel data settings.

Installation

pip install -e .

Dependencies: numpy>=1.23, scipy>=1.9, scikit-learn>=1.2

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Models

Class	Paper	Inefficiency Distribution	Key Extra Parameters
CrossSectionalSFA	ALS 1977	Half-Normal	—
TimeDecayPanelSFA	BC 1992	Truncated-Normal + time decay	groups, time
EffectsPanelSFA	BC 1995	Truncated-Normal (effects)	groups, Z
TrueFixedEffectsSFA	Greene 2005	Half-Normal (Intercepts profiled)	groups
TrueRandomEffectsSFA	Greene 2005	MSL with Halton Draws	groups, n_simulations
FourComponentSFA	Kumbhakar et al. 2014	Transient & Persistent Inefficiency	groups

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Quick-start

ALS 1977 – Cross-Sectional

The foundational stochastic frontier model using a half-normal distribution for inefficiency.

from panelsfa import CrossSectionalSFA

model = CrossSectionalSFA(model_type="production")
model.fit(X, y)

print(model.coef_)      # Frontier coefficients (β)
print(model.gamma_)     # Signal-to-noise ratio (γ)
te = model.score_efficiency(X, y)  # Technical Efficiency ∈ (0, 1]

BC92 – Time-Varying Decay Panel

Extends ALS to panel data, allowing inefficiency to evolve deterministically over time via the $\eta$ parameter.

from panelsfa import TimeDecayPanelSFA

model = TimeDecayPanelSFA(model_type="production")
model.fit(X, y, groups=entity_ids, time=time_index)

print(model.eta_)  # η > 0 implies inefficiency decreases over time
te = model.score_efficiency(X, y, groups=entity_ids, time=time_index)

BC95 – Inefficiency Effects Panel

Allows environmental covariates ($Z$) to directly explain the mean of the inefficiency distribution in a single-step estimation.

from panelsfa import EffectsPanelSFA

# Z contains covariates like farmer age or education level
model = EffectsPanelSFA(model_type="production")
model.fit(X, y, groups=entity_ids, Z=Z_covariates)

print(model.delta_)  # Coefficients quantifying inefficiency drivers
te = model.score_efficiency(X, y, Z=Z_covariates)

Greene (2005) – True Fixed Effects (TFE)

Handles unobserved, time-invariant heterogeneity by profiling out firm-specific intercepts $\alpha_i$, preventing them from being captured as inefficiency.

from panelsfa import TrueFixedEffectsSFA

model = TrueFixedEffectsSFA(model_type="production")
model.fit(X, y, groups=entity_ids)

print(model.alphas_)  # Recovered firm-specific intercepts
te = model.score_efficiency(X, y)

Greene (2005) – True Random Effects (TRE)

Uses Maximum Simulated Likelihood with Halton draws to integrate out a randomly distributed firm effect $w_i$.

from panelsfa import TrueRandomEffectsSFA

model = TrueRandomEffectsSFA(n_simulations=500)
model.fit(X, y, groups=entity_ids)

print(model.sigma_w_sq_) # Variance of the random effect (heterogeneity)
te = model.score_efficiency(X, y)

Kumbhakar et al. (2014) – Four-Component Model

Disentangles four distinct components: firm heterogeneity, random noise, persistent inefficiency, and transient inefficiency.

from panelsfa import FourComponentSFA

model = FourComponentSFA(model_type="production")
model.fit(X, y, groups=entity_ids)

# Multi-dimensional efficiency scoring
eff = model.score_efficiency(X, y, groups=entity_ids)
print(eff['transient'])   # Short-term deviations
print(eff['persistent'])  # Structural failures
print(eff['overall'])     # Unified efficiency score

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Numerical Engine & Parameterization

To ensure convergence on non-convex likelihood surfaces, PanelSFA utilizes an OLS Warm-Start with an intercept shift and reparameterizes constrained variables to an unconstrained space.

Natural Parameter	Optimizer Parameter	Transform Back
$\sigma^2 > 0$	$\ln(\sigma^2)$	exp(·)
$\gamma \in (0, 1)$	$\text{logit}(\gamma)$	sigmoid(·)
$\beta, \mu, \eta, \delta, \alpha$	identity	—

Optimizer: L-BFGS-B (Limited-memory BFGS) for high-dimensional stability.

• Efficiency Scoring: Jondrow-Lovell-Materov-Schmidt (JLMS) conditional expectation $E[u|\varepsilon]$.

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