Reference Variables,Factor Structure,and the Approximate Multibeta Representation

The Arbitrage Pricing Theory (APT) implies that if asset returns have a factor structure, then an approximate multibeta representation holds with respect to the factors as reference variables. This paper assumes that asset returns satisfy a factor structure and derives a condition under which the approximate multibeta representation holds with respect to a set of reference variables which may not be the factors. This condition is that the regression matrix of the reference variables on the factors is nonsingular. Implications for the testability of the APT are also discussed.     

The Value of "Final Products" Counts Only Itself

Abstract . The value of final products counts only itself and not the value of so‐called intermediate products. The prevailing, contrary belief entails a twofold violation of the laws of mathematics—namely, the impermissible discarding of essential terms of equations and then the addition of the remainders of equations that are mutually exclusive and therefore not properly subject to addition. It follows that in order to count the values of the so‐called intermediate products, one must go out and count them, because they are not counted in the value of the final product. Despite prevailing belief, counting the value of intermediate products does not represent “double counting.” The implications of these findings for macroeconomic theory are major and include a radically different approach to the respective roles of saving and consumption in spending and income formation, and recognition of the fact that today's concept of gross product is actually a concept of net product.