  This paper introduces a new model for panel data with Markov-switching GARCH
effects. The model incorporates a series-specific hidden Markov chain process
that drives the GARCH parameters. To cope with the high-dimensionality of the
parameter space, the paper exploits the cross-sectional clustering of the
series by first assuming a soft parameter pooling through a hierarchical prior
distribution with two-step procedure, and then introducing clustering effects
in the parameter space through a nonparametric prior distribution. The model
and the proposed inference are evaluated through a simulation experiment. The
results suggest that the inference is able to recover the true value of the
parameters and the number of groups in each regime. An empirical application to
78 assets of the SP\&100 index from $6^{th}$ January 2000 to $3^{rd}$ October
2020 is also carried out by using a two-regime Markov switching GARCH model.
The findings shows the presence of 2 and 3 clusters among the constituents in
the first and second regime, respectively.
