[The exact finite sample properties of an asymptotically unbiased but nonconsistent estimator of a structural variance are examined briefly.]

R. L. Basmann, D. H. Richardson, R. J. Rohr, An Experimental Study of Structural Estimators and Test Statistics Associated with Dynamical Econometric Models, Econometrica, Vol. 42, No. 4 (Jul., 1974), pp. 717-730

R. L. Basmann, D. H. Richardson, R. J. Rohr, Finite Sample Distributions Associated with Stochastic Difference Equations--Some Experimental Evidence, Econometrica, Vol. 42, No. 5 (Sep., 1974), pp. 825-839

Let V(X) be any direct utility function characterizing consumer preferences that are reflexive, transitive, and complete, and whose parameters are fixed relative to the usual linear budget constraint p X = M. Here X designates the vector (X1,.. ., X,) and is confined to the positive n-orthant; Xi designates quantity of the ith commodity; p is the vector (P,, ...,pn) of positive commodity prices; and M designates total expenditure. Let X(p, M) designate the system of demand functions derived from V(X) subject to pX = M, which possess the properties of zero degree homogeneity, symmetry, and semidefinite negativity. Let W( X; 0) designate a direct utility function with (a) parameter vector 0 dependent on the price vector p that appears in the budget constraint and (b) that rationalizes the same system of demand functions as V(X), namely, X(p, M). Probably, many economists who have considered price-dependent preferences' would conjecture that every such price-dependent utility function W(X; p) satisfying (a) and (b) is of the rather restricted form