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In this paper are derived consistency and asymptotic normality results for the output-error method of system identification. The output-error estimator has the advantage over the prediction-error estimator of being more easily computable. However, it is shown that the output-error estimator can never be more efficient than the prediction-error estimator. The main result of the paper provides necessary and sufficient conditions for the output-error estimator and the prediction-error estimator to have the same efficiency, irrespective of the spectral density of the noise process.