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Censored & Selection Tutorials

Learning Path

Prerequisites: Basic MLE concepts, understanding of sample selection bias Time: 3--7 hours Level: Beginner -- Advanced

Overview

Censored and selection models address two distinct but related data problems. Censoring occurs when the dependent variable is observed only within a certain range (e.g., income capped at zero, expenditure truncated above a threshold). Sample selection arises when the decision to observe the outcome is correlated with the outcome itself (e.g., wages observed only for those who choose to work).

These tutorials cover Tobit models for censored panel data, the Honore bias-corrected estimator for fixed effects Tobit, and the Panel Heckman selection model in both two-step and FIML variants. You will learn to test for selection bias, construct valid exclusion restrictions, and interpret the inverse Mills ratio (IMR).

Notebooks

# Tutorial Level Time Colab
1 Censoring Fundamentals Beginner 45 min Open In Colab
2 Tobit Panel Models Intermediate 45 min Open In Colab
3 Honore Bias-Corrected Estimator Advanced 60 min Open In Colab
4 Panel Heckman (Two-Step) Advanced 60 min Open In Colab
5 Heckman MLE (FIML) Advanced 60 min Open In Colab
6 Identification & Exclusion Restrictions Advanced 45 min Open In Colab
7 Marginal Effects Advanced 45 min Open In Colab
8 Complete Case Study Advanced 60 min Open In Colab

Learning Paths

Tobit (3 hours)

Censored data models:

Notebooks: 1, 2, 3

Covers censoring fundamentals, panel Tobit, and the Honore bias-corrected estimator.

Selection (5 hours)

Add sample selection correction:

Notebooks: 1, 2, 3, 4, 5, 6

Covers Tobit, Panel Heckman (two-step and FIML), and identification strategies.

Complete (7 hours)

Full censored and selection model coverage:

Notebooks: 1--8

Adds marginal effects for censored models and a comprehensive case study.

Key Concepts Covered

  • Censoring vs truncation: Different data problems requiring different models
  • Tobit model: MLE for censored outcomes (Type I, Type II)
  • Honore estimator: Bias-corrected FE Tobit using pairwise trimming
  • Panel Heckman (two-step): Selection equation + outcome equation
  • Heckman FIML: Full Information Maximum Likelihood joint estimation
  • Exclusion restrictions: Variables in selection but not outcome equation
  • Inverse Mills Ratio (IMR): Correction term for selection bias
  • Marginal effects: Unconditional, conditional on being uncensored
  • Selection bias testing: Significance of the IMR / correlation parameter

Quick Example

from panelbox.models.censored import PanelHeckman

# Panel Heckman selection model
heckman = PanelHeckman(
    data=data,
    outcome_formula="wage ~ education + experience",
    selection_formula="employed ~ education + experience + children",
    entity_col="id",
    time_col="year"
).fit()

print(heckman.summary())
print(f"Selection correlation (rho): {heckman.rho:.4f}")
print(f"IMR significant: {heckman.imr_pvalue < 0.05}")

Solutions

Tutorial Solution
01. Censoring Fundamentals Solution
02. Tobit Panel Solution
03. Honore Estimator Solution
04. Heckman Selection Solution
05. Heckman MLE Solution
06. Identification Solution
07. Marginal Effects Solution
08. Case Study Solution