This paper proposes two new panel unit root tests based on Zaykin et al. (2002)’s truncated product method. The first one assumes constant correlation between P-values and the second one uses sieve bootstrap to allow for general forms of cross-section dependence in the panel units. Monte Carlo simulation shows that both tests have reasonably good size and are powerful in cases of some very large P-values. The proposed tests are applied to a panel of real GDP and inflation density forecasts, resulting in evidence that professional forecasters may not update their forecast precision in an optimal Bayesian way.