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Article overview
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The ABC of Simulation Estimation with Auxiliary Statistics | Jean-Jacques Forneron
; Serena Ng
; | Date: |
6 Jan 2015 | Abstract: | This paper provides a synthesis of the simulation based minimum distance
estimators used in economics with the method of ABC (Approximate Bayesian
Computation) used in other disciplines. While the two strands of work are
seemingly related, the relation between them is not well understood beyond the
fact that they all replace the likelihood by auxiliary statistics that are
informative about the data. We connect the two methods by using a reverse
sampler to engineer the ABC posterior distribution from a sequence of simulated
minimum distance estimates. Focusing on the exactly identified case, we find
that Bayesian and frequentist estimators have different bias properties for an
arbitrary choice of prior. The difference can be traced to whether we match the
sample auxiliary statistics to each or to the average of the simulated ones. In
principle, the likelihood-free Bayesian estimators can completely eliminate the
order $frac{1}{T}$ bias with suitable choice of the prior. But under a
specific relation between the structural parameters and auxiliary statistics,
the frequentist simulated distance estimators are automatically second order
unbiased. These differences are illustrated using an analytical example and a
simulation study of the dynamic panel model. | Source: | arXiv, 1501.1265 | Services: | Forum | Review | PDF | Favorites |
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