From: Health Uninsurance in rural America: a partial equilibrium analysis
Symbol | Meaning | Symbol | Meaning |
---|---|---|---|
Principal-Agent Model | Crop diversification Index | ||
φ | Health Insurance preferred | W _{0} | Initial Wealth |
ω | Explicit characteristics | q _{ n + 1} | Terminal Wealth |
γ | Latent Characteristics | q _{ i} | Output from cropped area i |
U _{ f} | Utility of farmer (agent) | q _{ j} | Output from cropped area j |
C(z_{i}) | Administrative costs of Health insurance companies | E(y) | Expected Returns from initial wealth |
π | Utility of Health Insurance Company | r | Expected net return on the ith asset |
IC | Incentive compatibility constraints | ⋋ | Risk Attitude |
IR | Rationality constraints | σ ^{2} | Variance of Portfolio |
γ _{ a} | “Low risk” Individuals | y _{ CE} | Certainty Equivalent |
γ _{ b} | “High risk” Individuals | s _{ i} | Optimal share of crop |
τ | Health insurance loss for unknown proportions | A _{ i} | Area of available farming land used for crop i |
τ_{a}(e) | Loss prospect for γ_{a} | n | Number of crop portfolio choices |
τ_{b}(e) | Loss prospect for γ_{b} | ρ _{ τ} | Tau-Equivalent |
E(τ_{a}) | Expected loss prospect for γ_{a} | Test for IIA | |
E(τ_{b}) | Expected loss prospect for γ_{b} | B | First Regression |
R _{ a} | Risk premium for γ_{a} | b | Second Regression |
R _{ b} | Risk premium for γ_{b} | β _{ B} | Coefficient of B |
α | % of respondents in τ_{a} | β _{ b} | Coefficient of b |
1 − α | % of respondents in τ_{b} | ∂ _{ B} | Covariance of B |
m _{ p} | Alternative profile of options for health risk management | ∂ _{ b} | Covariance of b |
f _{ i} | Probability density function for consumer preference | Multinomial Logit Regression | |
Tau Equivalent Test | |||
X | Number of scale statements | δ _{ i} | Coefficient of explicit variables |
\( {\sigma}_{Y_i}^2 \) | variance of the scores of each scaled statement | β _{ i} | Coefficient of global compatibility constraints |
\( {\sigma}_X^2 \) | the total variance of scores on the respondents’ scales | ρ _{ i} | Coefficient of latent variables |
Diverse states of nature health insurance decisions by farmers | |||
p_{1}(s_{1}) | p_{2} (s_{2}) | ||
Good health | Bad health | ||
Z_{0} (no health insurance) | W + W_{0} | W + W_{0} - H | |
Z_{1} (private health insurance) | W + W_{0} - π_{p} | W + W_{0} - π_{h} - D_{h} + R_{p} | |
Z_{2} (government insurance plan) | W + W_{0} - π_{m} | W + W_{0} - π_{m} - D_{h} + R_{m} |