Household Choice for Health and Life Insurance

Motivation and Gaps

• Financial Risk Hedging: Households face continuous financial risk in their lifecycle (e.g., unexpected loss in earnings) and hedge these risks by choosing multiple insurance policies.
• The Policy Relevance:
  • Health care reform (e.g., Affordable Care Act / Obamacare) is an ongoing policy debate in the US.
  • Designing effective policy requires understanding how the demand for health insurance interacts with other major risk-hedging products (e.g., life insurance).
• The Research Questions:
  1. Are household choices for health and life insurance independent, substitutes, or complements?
  2. Does the choice of health insurance directly spill over to stimulate life insurance adoption?

Research Methodology & Model

• Data Source: rotating US Consumer Expenditure (CE) Survey panel (nationally representative US household sample), using 2008–2009 data.
• Sample Selection: Restricts to active households with a single main decision-making unit paying positive net premium, yielding N = 20,551 households (excluding Medicare/Medicaid).
• Joint Bivariate Probit Model Specification:
  • Latent utility equations for Health Insurance (\(y^*_{HIh}\)) and Life Insurance (\(y^*_{LIh}\)):

\[y^*_{HIh} = x'_h \beta_{HI} + z'_{HIh} \gamma_{HI} + \epsilon_{HIh}\] \[y^*_{LIh} = x'_h \beta_{LI} + z'_{LIh} \gamma_{LI} + \lambda_{LI} y_{HIh} + \epsilon_{LIh}\]

• Joint Error Structure: (\(\epsilon_{HIh}, \epsilon_{LIh}\)) follow a Bivariate Normal distribution:

\[\begin{pmatrix} \epsilon_{HIh} \\ \epsilon_{LIh} \end{pmatrix} \sim N \left( \begin{pmatrix} 0 \\ 0 \end{pmatrix}, \begin{pmatrix} 1 & \rho \\ \rho & 1 \end{pmatrix} \right)\] (where \(\rho\) captures the unobserved utility correlation. Sign of \(\rho\) indicates complements (\(\rho > 0\)) or substitutes (\(\rho < 0\)))

Key Results: Complementarity & Spillovers

• Empirically estimated parameters (Table 3) reveal highly significant joint correlation and direct spillovers:

1. Significant Positive Correlation (\(\rho\))

• Correlation Coefficient (\(\rho\)): 0.2372*** (se 0.0004)
• Interpretation: The choices are strongly positively correlated. Health and life insurance are highly complementary risk-minimizing goods in the basket of households.

2. Significant Direct Spillover Effect (\(\lambda_{LI}\))

• Health Insurance Effect on Life Insurance: 0.5142*** (se 0.0006)
• Interpretation: Holding health insurance directly increases the likelihood of a household choosing to purchase life insurance by a massive baseline.

3. Risk Averseness & Shocks

• Premium Self-Payment (Risk Averseness): Massive positive effects on both health (5.6265***) and life (6.7620***) choices.
• Health Shocks & Disability: Disability (0.4518*** / 0.3400***) and Severe Unhealthy status (0.2802*** / 0.2708***) strongly lift both choices.

Life-Cycle Dynamics: Asymmetric Age Effects

• Contrasts the highly distinct, non-linear effects of age across the two insurance types:

Health Insurance: U-Shape

• Age Coefficient: -0.0606*** | Age-Squared Coefficient: 0.0709***
• Interpretation: Young households possess a high initial stock of health, requiring lower insurance. As age increases, health depletion occurs, leading to substantial hedging through health insurance investments.

Life Insurance: Inverted U-Shape

• Age Coefficient: 0.0280*** | Age-Squared Coefficient: -0.0215***
• Interpretation: Concern for dependents’ financial security peaks during family formation and peak earning years (middle age). In older ages, concern declines as household assets accrue and children exit dependency.

Socio-Economic & Demographics

• Education (Divergence at College Level):
  • High school graduation or lower reduces insurance purchasing (e.g., Non-high school graduate -0.4484*** for health, -0.2091*** for life).
  • College Graduates strongly prefer health insurance (0.1827***) but exhibit a negative association with life insurance (-0.0500***).
• Income and Financial Wealth:
  • Regular post-tax income positively drives both health (0.0041***) and life (0.0004***) choices.
  • Active retirement/pension deductions (acting as planning indicator) positively drive both (0.0190*** / 0.0235***).
• Gender:
  • Females are positively associated with health insurance (0.0891***) but negatively with life insurance (-0.0627***) compared to males.

Policy & Strategic Implications

1. Health Policy and Healthcare Reform

• Since health and life insurance are strong complements, healthcare reforms (e.g., ACA mandates, health insurance tax credits, or subsidies) will have significant positive spillovers in stimulating private life insurance markets.
• Policy evaluation must not analyze health insurance markets in isolation; shocks in life insurance markets directly filter through to health coverage choices.

2. Strategic Naming & Pricing

• Insurance companies should coordinate cross-insurance marketing and bundling strategies (health + life policies).
• Leverage households’ risk-averse triggers (such as self-payment incentives) to cross-sell.

Citation: Kumar, Ashish (2019). “Investigating household choice for health and life insurance.” Applied Economics Letters, 26(4), 267-273. DOI: 10.1080/13504851.2018.1467543