x̄ - > Health Insurance & Hospitalization Models

Health Insurance & Hospitalization (Survey Model)

This study uses a household survey design with a binary outcome: hospitalized = 1 if yes, 0 if no, and insurance = 1 if covered, 0 if not. This is a standard framework in health econometrics for estimating the effect of insurance on healthcare utilization.

Data Structure

Variable	Meaning
hospitalized	Admitted in last 12 months
insurance	Insured or not
age	Age in years
sex	Gender indicator
education	Education level
income	Household income
chronic_illness	Chronic condition
rural	Rural vs urban

Basic Model (Probit / Logit)

P(hospitalized = 1) = F(β₀ + β₁ insurance + β₂ X + ε)

β₁ measures how insurance affects the probability of hospitalization after controlling for covariates.

Stata Example

probit hospitalized i.insurance age c.age#c.age i.sex i.education ///
       ln_income chronic_illness i.rural, vce(robust)

margins, dydx(insurance)

Interpretation: If marginal effect = 0.08 → insurance increases hospitalization by 8 percentage points.

Why Two-Part Models Are Better

Household survey data typically contain many zeros (no hospitalization) and a skewed distribution among users. A simple logit only models whether hospitalization occurs, ignoring intensity.

Two-Part Model Structure

Part 1: P(any hospitalization > 0) → Logit/Probit

Part 2: E(admissions | hospitalization > 0) → GLM (log link, gamma/lognormal)

Advantages

• Separates access (any hospitalization) from intensity (number of visits)
• Handles zero-heavy and skewed data
• Uses full information instead of collapsing outcomes

Stata Example

* Part 1: probability of any hospitalization
logit hospitalized i.insurance age i.sex i.education ///
      ln_income chronic_illness i.rural

* Part 2: intensity (only if hospitalized)
glm n_admissions i.insurance age i.sex i.education ///
    ln_income chronic_illness i.rural if hospitalized==1, ///
    family(gamma) link(log)

Interpretation

• Part 1: Insurance increases likelihood of hospitalization
• Part 2: Insurance affects number of admissions or length of stay

Policy Insight (Kenya Context)

In Kenya and similar settings, insurance schemes often:

• Increase access to care (more people hospitalized)
• Increase intensity of care among users

Two-part models capture both effects, while simple logit only captures the first.