Journal Article Algorithms for Social Choice Functions Get access Donald E. Campbell Donald E. Campbell Ontario Economic Council and University of Toronto Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 47, Issue 3, April 1980, Pages 617–627, https://doi.org/10.2307/2297312 Published: 01 April 1980 Article history Received: 01 June 1977 Accepted: 01 April 1979 Published: 01 April 1980

where b = (X'X)Y'X'y is the least squares estimator of fl. It is easily shown that z is N(6, o_2 V) where V = R (X'X) 'R'. The usual unbiased estimator of o.2 is s2= (y -Xb)'(y -Xb)/(Tk). In situations in which we wish only to decide whether H is true or not we can use a direct test of H such as an F test. It is perhaps more common that when H is rejected we want to know which components of 6 are different from zero and of the non-zero components which are positive and which negative. In this situation we have a multiple decision problem and a natural solution is to use an induced test. As an example suppose in the case q = 2 that we wish to test the hypothesis H: 01 =02 = 0. Since H is true if and only if the separate hypotheses H1: 01 = 0 and H2: 02= 0 are both true, this suggests a sequence of separate tests which will induce a test of H. Testing the two hypotheses H1 and H2 where we are interested in whether 01 or 62 or both are different from zero induces a multiple decision problem in which the four possible decisions are

Journal Article Symmetry Conditions for Market Demand Functions Get access W. E. Diewert W. E. Diewert University of British Columbia Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 47, Issue 3, April 1980, Pages 595–601, https://doi.org/10.2307/2297310 Published: 01 April 1980 Article history Received: 01 January 1977 Accepted: 01 August 1979 Published: 01 April 1980

Mayers and Rice conjecture that an investor with better information will on average plot above the security market line as drawn by uninformed investors. This paper demonstrates that this conjecture is false in general, by constructing a counterexample. However, the Mayers-Rice conjecture is really part of a much broader hypothesis concerning whether increases in expected returns correspond to increases in expected utilities. It is shown that this latter hypothesis is true when the investor has an exponential or logarithmic utility function.

This paper uses a simple difference equation model to investigate the dynamic characteristics of the foreign exchange market under a regime of flexible exchange rates. It is shown that unhedged trade transactions can produce a dynamically unstable market, particularly if contracts are denominated in the seller's currency. We then examine the influence of trade hedging, using either the forward market or an artificial currency unit, and find that it considerably enhances the overall likelihood of stability.

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Where rates of return are perfectly correlated, risk reduction through diversification cannot be achieved. Where rates of return are less than perfectly correlated, however, then, to the extent that these interrelationships can be known, modern portfolio theory provides a framework in which risk reduction through diversification can be achieved. Markowitz was the first to give rigorous content to the concept of portfolio diversification [14], and to introduce a formulation for treating portfolio selection as a mathematical optimization problem. In order to facilitate application of his own covariance approach, Markowitz first suggested [15, pp. 96–101], and Sharpe later developed a market model formulation according to which it is assumed that the rates of return on various securities “are related only through common relationships with some basic underlying factor” [18, p. 281]. More than 25 years have passed since Markowitz introduced his original formulation, and the literature dealing with the portfolio selection problem that he identified has grown considerably since then. Unfortunately, many problems remain which prevent full and effective implementation of this framework for investment analysis.