The role of speculative short term capital movements in balance of payments adjustment and in exchange market stability is examined. A theory of speculative behavior with a distributed lag model of expectation formation at its core is developed and empirically tested using the Canadian data for the period 1952-1960. Tests of an alternative but generically similar specification of the model are also presented and discussed.

THIS PAPER is a sequel to [5] in which a generalized correlation coefficient (the trace correlation) for multi-equation models was presented. This paper is concerned with the development of partial trace correlations. The relation between partial trace correlations and the trace correlation is analogous to the relation between partial correlation coefficients and the multiple correlation coefficient in a single-equation model.2 In the latter the multiple correlation coefficient measures the extent to which the regression relationship on all of the independent variables accounts for the observed variation in the dependent variable. In addition there are partial correlation coefficients which measure the extent to which the regression on a particular independent variable explains the observed variation in the dependent variable, holding the influence of the other independent variables constant. Similarly in multi-equation models there is the trace correlation3 which is a measure of the extent to which the regression relationship explains the variation in the set of jointly dependent variables. The purpose of this paper is to develop the analogue of partial correlation coefficients for multiequation models, i.e., to develop a measure of the degree to which the regression relationship on a subset of the independent variables accounts for the variation in the jointly dependent variables, while holding the influence of the other independent variables constant. As in the case of the trace correlation the basic concepts are developed through the use of canonical correlation theory. This is done in Section 2, and in Section 3 partial trace correlations are defined. In Section 4 the asymptotic sampling variances are given.

THE MULTI-PRODUCT firm occupies a prominent place among important but neglected topics in economic theory. Barring the programming approaches, a search of the literature reveals no comprehensive theoretical treatment of the subject. Indeed the brief development by Hicks in the mathematical appendix to Value and Capital [6] is probably the most thorough treatment in the sense of considering both the production and sales activities of the firm. Since Hicks allots only four pages to this topic, this is a remarkable state of affairs. While the literature on all phases of the multi-product firm is scanty, a few writers have considered the selling side of such a firm; the works of Bailey [1], Clemens [3], and Weldon [10] may be cited in this connection. On the cost and production side the literature is virtually non-existent. Even the work of Carlson [2], a standard reference for twenty years, deals only with the special case of joint cost but not with any other aspect of the multi-product firm. The purpose of this paper is to present a theory of cost and production for the multi-product firm. In developing this theory, the traditional concept of the firm as a social mechanism that connects the markets for factors of production with the markets for finished products will be retained. This is in contrast to the usual inward looking view of the firm that appears in the programming literature. But once the problem is clearly stated in traditional terms, it becomes apparent that the Kuhn-Tucker theorem, which can be thought of as the logical basis of the optimization techniques of activity analysis, can be used in a straightforward way to solve the problems of cost and production in the multi-product firm. The solution of the problem will show that the optimum conditions for the multi-product firm are different from those of the single-product firm. These differences are discussed briefly in the final section of the paper.