Abstract
Over the last decade, agent-based models in economics have reached a state of maturity that brought the tasks of statistical inference and goodness-of-fit of such models on the agenda of the research community. While most available papers have pursued a frequentist approach adopting either likelihood-based algorithms or simulated moment estimators, here we explore Bayesian estimation using a Markov chain Monte Carlo approach (MCMC). One major problem in the design of MCMC estimators is finding a parametrization that leads to a reasonable acceptance probability for new draws from the proposal density. With agent-based models the appropriate choice of the proposal density and its parameters becomes even more complex since such models often require a numerical approximation of the likelihood. This brings in additional factors affecting the acceptance rate as it will also depend on the approximation error of the likelihood. In this paper, we take advantage of a number of recent innovations in MCMC: We combine Particle Filter Markov Chain Monte Carlo as proposed by Andrieu et al. (J R Stat Soc B 72(Part 3):269–342, 2010) with adaptive choice of the proposal distribution and delayed rejection in order to identify an appropriate design of the MCMC estimator. We illustrate the methodology using two well-known behavioral asset pricing models.
Highlights
Over the last decade, agent-based models in economics have reached a state of maturity that brought the tasks of statistical inference and goodness-of-fit of such models on the agenda of the research community
In the following we provide details on explorative simulations of Adaptive Markov Chain Monte Carlo estimation using both adaptation of the proposals and delayed rejection
This paper has explored the potential use of refined Markov Chain Monte Carlo approaches for estimation of the parameters of agent-based models
Summary
Agent-based models in economics have reached a state of maturity that brought the tasks of statistical inference and goodness-of-fit of such models on the agenda of the research community. The very problem of low acceptance rates is addressed by the third entry on this topic in the recent literature by Bertschinger and Mozzhorin (2021) These authors use so-called Hamiltonian MCMC for Bayesian estimation of two agent-based models. Adopting the principle of joint preservation of volume in conservative dynamic systems, the dynamics of the parameters and their associated momentum variables is modeled as a Hamiltonian system which when used to draw new proposals of the parameters, should select these approximately along an iso-line of equal probability and, should guarantee high acceptance rates This approach requires numerical derivatives of the log probability density to implement the Hamiltonian dynamics as a conservative system of differential equations.
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