The statistical properties of the certainty equivalence control rule and of the least squares estimates generated by this rule are examined experimentally in a linear model with two unknown parameters. It is found that the least squares certainty equivalence rule converges to its true value with probability one and is asymptotically efficient, having an asymptotic distribution with a variance as small as any other strongly consistent rule. However, while a linear combination of the parameter estimates is consistent, the evidence does not confirm that the individual estimates themselves are consistent. If these converge to their true values at all, they do so very slowly (on the order of (log t)').

T. W. Anderson, Naoto Kunitomo, Takamitsu Sawa, Evaluation of the Distribution Function of the Limited Information Maximum Likelihood Estimator, Econometrica, Vol. 50, No. 4 (Jul., 1982), pp. 1009-1027

G. H. Hillier, T. W. Kinal, V. K. Srivastava, On the Moments of Ordinary Least Squares and Instrumental Variables Estimators in a General Structural Equation, Econometrica, Vol. 52, No. 1 (Jan., 1984), pp. 185-202