{% extends 'common/base_v2.html' %} {% block summary %}

Stochastic Frontier Analysis

{% if model_info %}

{{ model_info.frontier_type|default('Production') }} Frontier {% if model_info.distribution %} — {{ model_info.distribution }} distribution {% endif %}

{% endif %}
Log-Likelihood
{{ fit_statistics.loglikelihood|default('--')|round(2) }}
σu (Inefficiency)
{{ variance_components.sigma_u|default('--')|round(4) }}
σv (Noise)
{{ variance_components.sigma_v|default('--')|round(4) }}
λ = σuv
{{ variance_components.lambda_param|default('--')|round(4) }}
{% if model_info and model_info.converged is defined %}
{% if model_info.converged %}Optimization converged{% else %}Warning: Optimization did not converge{% endif %}
{% endif %}
{% endblock %} {% block content %}
{% if efficiency %} {% endif %} {% if charts %} {% endif %}

Parameter Estimates

{% if coefficients %} {% for coef in coefficients %} {% endfor %}
Variable Coefficient Std. Error t-stat p-value
{{ coef.name }} {{ coef.coef|round(4) }} {{ coef.se|round(4) }} {{ coef.tstat|round(3) }} {{ coef.pvalue|pvalue_format }} {{ coef.stars }}

Significance: * p<0.1, ** p<0.05, *** p<0.01

{% else %}

No coefficient data available.

{% endif %}

Variance Decomposition

{% if variance_components.sigma_sq is defined and variance_components.sigma_sq != '—' %} {% endif %}
σv (Noise) {{ variance_components.sigma_v|default('--')|round(4) }} Standard deviation of symmetric noise
σu (Inefficiency) {{ variance_components.sigma_u|default('--')|round(4) }} Standard deviation of inefficiency
σ (Composite) {{ variance_components.sigma|default('--')|round(4) }} √(σ²v + σ²u)
σ² (Total Variance) {{ variance_components.sigma_sq|round(4) }} σ²v + σ²u
λ = σuv {{ variance_components.lambda_param|default('--')|round(4) }} Signal-to-noise ratio of inefficiency
γ = σ²u/σ² {{ variance_components.gamma|default('--')|round(4) }} Share of variance due to inefficiency

Interpretation

  • λ > 1: Inefficiency dominates noise
  • γ close to 1: Most variance is due to inefficiency
  • γ close to 0: Most variance is noise (OLS may be adequate)
{% if efficiency %}

Efficiency Summary

Mean Efficiency
{{ efficiency.mean|percentage }}
Median Efficiency
{{ efficiency.median|percentage }}
Min Efficiency
{{ efficiency.min|percentage }}
Max Efficiency
{{ efficiency.max|percentage }}
Observations{{ efficiency.count|number_format }}
Std. Deviation{{ efficiency.std|round(4) }}
{% if charts and charts.efficiency_distribution %}
{{ charts.efficiency_distribution|safe }}
{% elif efficiency_chart %}
{{ efficiency_chart|safe }}
{% endif %} {% if charts and charts.efficiency_summary %}
{{ charts.efficiency_summary|safe }}
{% elif ranking_chart %}
{{ ranking_chart|safe }}
{% endif %}
{% endif %} {% if charts %}
{% if charts.coefficient_plot %}

Coefficient Estimates

{{ charts.coefficient_plot|safe }}
{% endif %} {% if charts.variance_chart %}

Variance Decomposition

{{ charts.variance_chart|safe }}
{% endif %}
{% endif %}

Model Specification

{% if model_info and model_info.n_entities %} {% endif %} {% if model_info and model_info.n_periods %} {% endif %}
Frontier type {% if model_info and model_info.frontier_type %} {{ model_info.frontier_type }} {% else %} -- {% endif %}
Distribution{{ model_info.distribution|default('--') if model_info else '--' }}
Observations{{ model_info.nobs|default('--')|number_format if model_info else '--' }}
Entities{{ model_info.n_entities|number_format }}
Time periods{{ model_info.n_periods }}
Parameters{{ model_info.nparams|default('--') if model_info else '--' }}
Log-Likelihood{{ fit_statistics.loglikelihood|default('--')|round(4) }}
AIC{{ fit_statistics.aic|default('--')|round(2) }}
BIC{{ fit_statistics.bic|default('--')|round(2) }}
Converged {% if model_info and model_info.converged is defined %} {{ 'Yes' if model_info.converged else 'No' }} {% else %} -- {% endif %}
{% endblock %} {% block extra_js %} {% endblock %}