We estimate a dynamic system of simultaneous equations using country-level panel data from developing countries to identify the dynamic causal structural relationships between Poverty, GDP per capita and Health. For this, we develop innovative econometric methods for incomplete panel data to correct for endogeneity and the selectivity issues coming from missing data of poverty, and which have never been considered before. First, we find that the data generation of poverty indicators through household surveys depends positively on democracy and the level of wealth in the country. Furthermore, the probability to conduct a household survey in a given period is higher when a household survey has been conducted in the previous period. Moreover, we find that higher GDP per capita causes lower infant and child mortality rates but not necessarily poverty reduction. Our results highlight also the impact of health on GDP per capita and on the alleviation of poverty. Finally, we find no evidence about a significant influence of poverty on GDP per capita and health.