Table 2 Summary of symbols used for variables in equations
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(zi) | 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 |
τa(e) | Loss prospect for γa | n | Number of crop portfolio choices |
τb(e) | Loss prospect for γb | ρ τ | Tau-Equivalent |
E(τa) | Expected loss prospect for γa | Test for IIA | |
E(τb) | Expected loss prospect for γb | B | First Regression |
R a | Risk premium for γa | b | Second Regression |
R b | Risk premium for γb | β B | Coefficient of B |
α | % of respondents in τa | β b | Coefficient of b |
1 − α | % of respondents in τb | ∂ 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 | |||
p1(s1) | p2 (s2) | ||
Good health | Bad health | ||
Z0 (no health insurance) | W + W0 | W + W0 - H | |
Z1 (private health insurance) | W + W0 - πp | W + W0 - πh - Dh + Rp | |
Z2 (government insurance plan) | W + W0 - πm | W + W0 - πm - Dh + Rm | |