Macroeconomic simulation comparison with a multivariate extension of the Markov information criterion

The paper aims to address the issue of comparing agent-based models (ABMs) with more traditional VAR and DSGE models by developing a multivariate extension of the Markov Information Criterion (MIC) of Barde (2017). The univariate MIC measures the informational distance between a simulation model and some empirical data by mapping the simulated data to a Markov transition matrix, and is proven to provide an unbiased measurement for all models reducible to a Markov process. As a result, the MIC can accurately measure distance using only simulated data, for a wide class of data generating processes. The paper first presents the multivariate extension of the MIC and its validation on VAR and DGSE models before carrying the first direct comparison between a macroeconomic ABM and a DGSE model, namely the benchmark ABM of Caiani et al. (2016) and Smets and Wouters (2007)