AbstractA first order autoregressive non‐Gaussian model for analysing panel data is proposed. The main feature is that the model is able to accommodate fat tails and also skewness, thus allowing for outliers and asymmetries. The modelling approach is designed to gain sufficient flexibility, without sacrificing interpretability and computational ease. The model incorporates individual effects and covariates and we pay specific attention to the elicitation of the prior. As the prior structure chosen is not proper, we derive conditions for the existence of the posterior. By considering a model with individual dynamic parameters we are also able to formally test whether the dynamic behaviour is common to all units in the panel. The methodology is illustrated with two applications involving earnings data and one on growth of countries. Copyright © 2009 John Wiley & Sons, Ltd.