Poisson Pseudo-Maximum Likelihood (PPML) Model

Model Specification

{% if n_entities %} {% endif %} {% if n_time %} {% endif %} {% if pseudo_r2 %} {% endif %} {% if iterations %} {% endif %}
Estimator: PPML with {{ fe_type }} Fixed Effects
Number of observations: {{ n_obs }}
Number of entities: {{ n_entities }}
Number of time periods: {{ n_time }}
Deviance: {{ deviance|number_format }}
Pseudo R²: {{ pseudo_r2|number_format }}
Iterations to convergence: {{ iterations }}

Parameter Estimates

{% for param in parameters %} {% endfor %}
Variable Coefficient Std. Error z-stat p-value Elasticity
{{ param.name }} {{ param.estimate|number_format }} {{ param.std_error|number_format }} {{ param.z_stat|number_format }} {{ param.p_value|pvalue_format }}{{ param.p_value|significance_stars }} {% if param.is_log %} {{ param.estimate|number_format }} {% else %} {{ (param.estimate * param.mean_value)|number_format }} {% endif %}

Interpreting PPML Coefficients

For log-transformed variables: The coefficient β represents the elasticity directly. A 1% increase in X leads to a β% change in E[y].

For level variables: The coefficient β represents the semi-elasticity. A one-unit increase in X leads to a (exp(β)-1)×100% change in E[y].

For dummy variables: The coefficient β indicates that E[y] is exp(β) times larger when the dummy equals 1 compared to 0.

{% if zeros_info %}

Zero Values in Dependent Variable

Number of zeros: {{ zeros_info.n_zeros }}
Percentage of zeros: {{ zeros_info.pct_zeros|percentage }}
Advantage over OLS-log: PPML includes {{ zeros_info.n_zeros }} observations that would be dropped in log-linear OLS
{% endif %} {% if diagnostics %}

Diagnostic Tests

{% for test in diagnostics %} {% endfor %}
Test Statistic p-value Result
{{ test.name }} {{ test.statistic|number_format }} {{ test.p_value|pvalue_format }} {{ test.interpretation }}
{% endif %} {% if fixed_effects_summary %}

Fixed Effects Summary

{% if fixed_effects_summary.entity %} {% endif %} {% if fixed_effects_summary.time %} {% endif %}
Entity fixed effects: {{ n_entities }} effects absorbed
Time fixed effects: {{ n_time }} effects absorbed
{% endif %}