 = 1, . . ., n) is measured differ from the units in which bkj(j = 1, . . ., n) is measured. This means that invariant stability conditions require that each row of every stability determinant involving the sum of elements be multiplied by an arbitrary number reflecting units of measurement. Thus "unit-invariant" stability in the general case involves the sign of terms such as
For arbitrary values of ki and kj extended over the entire range of the (n+ 1) x (n+ 1)-B determinant, and given the homogeneity postulate, the general conditions then imply that all goods are gross substitutes.
15 From a historical point of view, it is somewhat amusing that although the Hicks conditions are not symmetrical with respect to the commodity chosen as numéraire, neither are the (normalized) dynamic systems used to refute the validity of the Hicks conditions as true dynamic stability conditions.
16 The proof in the general case follows by analogy to the proof of Metzler (, pp. 280-285) when his method is extended to include the augmented system.
17 I have applied this method to the problem of disentangling lags in expectational and cash balance adjustments .
18 More directly the matrix equationif k = B-1.
The usefulness of this result lies not so much in providing a policy maker with the rules of adjustment, since there is no problem if the basic matrix is known, and the rule gives insufficient information if the basic matrix is not known. The point is rather that pieces of information about the inverse may be sufficient to distract policy makers from mistakes, and that conditions like the Hicks conditions may be a sufficient guide to the relative importance to be attached to particular instruments.
19 I have discussed the implications of this condition in some detail .
20 Even the gap between the true dynamic stability and Hicksian stability may be bridged by integrating Hicksian stability conditions with the "Samuelson-Le Châtelier principle" (see, for example, Samuelson ) which can be expressed entirely in terms of the Hicksia