The state vector in the innovation representation is asymptotically the most efficient instrumental variable estimator for the observation matrix C. The paper compares small sample properties of IV estimators for C, the dynamic matrix A and other matrices with the system theoretic estimators described in Aoki (1987) by a small scale Monte Carlo simulations. The IV estimators appear to be about the same as the system theoretic ones as far as their small sample properties are concerned. The covariance matrix of the state vector calculated from the IV point of view are also compared with the solutions of the Riccati equations. The simulation results show that they have quite similar sample means and standard deviations. This method of calculating the state vector covariance matrices may be computationally faster than solving the Riccati equation by the Schur decomposition algorithm.