The Relationship between Infant Mortality Rate and Health Expenditure in India: A Bayesian Approach

Abstract

This paper uses a Bayesian approach to fit a linear regression analysis to panel data. The dependent variable is Infant Mortality Rate and the explanatory variable is state health expenditure for the individual states in India. Various strands of previous literature are examined in order to provide a context for the relationship between state health expenditure and Infant Mortality Rate. Owing to the highly heterogeneous nature of Indian states across time, a panel data model has been considered. The time and state effects are captured in separate intercept terms and the coefficient of regression reflects only the responsiveness of Infant Mortality Rate to an increase in state health expenditure. The underlying assumption here is that the distribution of the explanatory variable affects the dependent variable only through the explanatory variable itself and the conditional distribution of the dependent variable is thus independent of the marginal distribution of the explanatory variable. Another assumption is that state and time effects are isolated from the coefficient of regression but this can be modified with an appropriate prior distribution. Proportion of state GDP allocated to healthcare is used as a proxy for state health expenditure and all calculations are performed with deviations from the mean. The underlying methodology is a Bayesian approach and all the intercept and slope coefficients are modeled with non-informative or uniform prior distributions. Further the completely pooled regression is considered, that excludes time and state heterogeneity and the pooled regression coefficient is used as a prior for the actual slope coefficient and the two coefficients of regression (i.e with a uniform prior and a normal prior with a fixed mean and uniformly distributed variance) are compared. The inference is that increasing state health expenditure has a negative effect on Infant Mortality Rate.