A spatial AR(1) model could be a good start, BUT ... one has to be very cautious due to potential reverse causality: the composition of the indices has to be known. E.g., the HDI index involves literacy, life expectancy and income - naturally, if you take is as a proxy for human capital and explain economic growth the model will be biased because you already have "income" in the index. Moreover, life expectancy is also endogenous.
I am a bit sceptical of the HDI because literacy rates are quite homogeneous among developed countries, but it will not be the case for developing ones.