In this note we establish the existence of the first two moments of the asymptotic trace statistic, which appears as weak limit of the likelihood ratio statistic for testing the cointegration rank in a vector autoregressive model and whose moments may be used to develop panel cointegration tests. Moreover, we justify the common practice to approximate these moments by simulating a certain statistic, which converges weakly to the asymptotic trace statistic. To accomplish this we show that the moments of the mentioned statistic converge to those of the asymptotic trace statistic as the time dimension tends to infinity.