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Stochastic Frontier Tutorials

Learning Path

Prerequisites: Static Models tutorials, basic MLE concepts Time: 3--6 hours Level: Intermediate -- Advanced

Overview

Stochastic Frontier Analysis (SFA) separates random noise from technical inefficiency, allowing researchers to measure how close firms, hospitals, banks, or other decision-making units operate relative to the efficient frontier. This is fundamental for productivity analysis, regulatory benchmarking, and performance evaluation.

These tutorials cover the progression from basic cross-sectional SFA to advanced panel models, including the four-component model (GTRE) that separates persistent from transient inefficiency, and Total Factor Productivity (TFP) decomposition that attributes output growth to technical change, efficiency change, and scale effects.

The SFA Tutorial notebook provides additional background on the fundamentals.

Notebooks

# Tutorial Level Time Colab
1 Introduction to SFA Intermediate 45 min Open In Colab
2 Panel SFA Models Intermediate 45 min Open In Colab
3 Four-Component Model & TFP Advanced 60 min Open In Colab
4 Determinants & Heterogeneity Advanced 45 min Open In Colab
5 Testing & Model Comparison Advanced 45 min Open In Colab
6 Complete Case Study Advanced 60 min Open In Colab

Learning Paths

Basic (3 hours)

Essential SFA methods for efficiency measurement:

Notebooks: 1, 2, 5

Covers SFA fundamentals, panel extensions, and model comparison. Sufficient for basic efficiency analysis.

Complete (6 hours)

Full stochastic frontier analysis coverage:

Notebooks: 1--6

Adds the four-component model (GTRE), TFP decomposition, inefficiency determinants, and a comprehensive case study.

Key Concepts Covered

  • Stochastic frontier: Separating noise (\(v_{it}\)) from inefficiency (\(u_{it}\))
  • Production vs cost frontiers: Sign convention and interpretation
  • Panel SFA models: Battese-Coelli, Pitt-Lee, True FE/RE
  • Four-component model (GTRE): Persistent + transient inefficiency + firm heterogeneity
  • TFP decomposition: Technical change, efficiency change, scale effects
  • Inefficiency determinants: Modeling inefficiency as a function of covariates
  • Model selection: LR tests, Vuong test, information criteria

Quick Example

from panelbox.frontier import StochasticFrontier

# Estimate a panel SFA model
sfa = StochasticFrontier(
    data=data,
    formula="log_output ~ log_capital + log_labor",
    entity_col="firm",
    time_col="year",
    frontier_type="production"
).fit()

print(sfa.summary())
print(f"Mean efficiency: {sfa.efficiency.mean():.4f}")

Solutions

Tutorial Solution
01. Introduction to SFA Solution
02. Panel SFA Models Solution
03. Four-Component & TFP Solution
04. Determinants & Heterogeneity Solution
05. Testing & Comparison Solution
06. Complete Case Study Solution