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High Model Uncertainty and Approximating Combined Distributions

Some frameworks of model uncertainty combine a large number of densities. Computing the quantiles of the combined distribution might be practically infeasible when the number of densities is large. We introduce a numerical procedure that can reduce the computational burden. This consists of proving a sequential update formula that estimates different moments of the combined distribution and a finite moment problem that reconstructs the distribution from the moments. Based on an example on the determinants of long-run economic growth, we show that tracking the first four moments of the combined distribution along with generalized lambda distribution fit, provides a good approximation for the overall shape of the distributions.