This paper considers estimation of Panel Vectors Autoregressive Models of order 1 (PVAR(1)) with possible cross-sectional heteroscedasticity in the error terms. We focus on fixed T consistent estimation methods in First differences (FD) with or without additional strictly exogenous regressors. Additional results for the Panel FD OLS estimator and the FDLS estimator of Han and Phillips (2010) are provided. In the covariance stationary case it is shown that the univariate moment conditions of the latter estimator are violated for general parameter matrices in the multivariate case. Furthermore, we simplify the analysis of Binder, Hsiao, and Pesaran (2005) by providing analytical results for the first two derivatives of the Transformed Maximum Likelihood (TML) function. We extend the original model by taking into account possible cross-sectional heteroscedasticity and presence of strictly exogenous regressors. Moreover, we show that in the three wave panel the log-likelihood function of the unrestricted TML estimator violates the global identification assumption. The finite-sample performance of the analyzed methods is investigated in a Monte Carlo study. Results indicate that under effect stationarity the TML estimator encounters problems with global identification even for moderate values of T.