Knowledge that Transforms

This paper is a sequel to On the Stability of the Competitive Equilibrium, I, by K. J. Arrow and L. Hurwicz. It extends the results of I in several directions. In particular, it provides a proof of stability in the large (and not merely locally) when all goods are gross substitutes; this result is found to be valid for processes where the price adjustment rate is a continuous sign-preserving, but not necessarily proportionate, function of excess demand. The paper deals both with systems where one of the commodities plays the role of numeraire and with systems where all commodities are treated symmetrically.

which the relationships are not exact, so that a set of ideal economic variables is assumed to be generated by a set of dynamic stochastic relationships, as in Koopmans [12], and the actual economic time series are assumed to differ from the ideal economic variables because of random disturbances or measurement errors. The asymptotic error variance matrix for the coefficients of one of the relationships is obtained in the case in which these relationships are estimated using instrumental variables. With this variance matrix we are able to discuss the problem of choice that arises when there are more instrumental variables available than the minimum number required to enable the method to be used. A method of estimation is derived which involves a characteristic equation already considered by Hotelling in defining the canonical correlation [10]. This method was previously suggested by Durbin [7]. The same estimates would be obtained by the maximum-likelihood limited