Knowledge that Transforms

It has recently been shown that the utility of playing a game with side payments depends on a parameter called strategic risk posture. The Shapley value is the risk neutral utility function for games with side payments. In this paper, utility functions are derived for bargaining games without side payments, and it is shown that these functions are also determined by the strategic risk posture. The Nash solution is the risk neutral utility function for bargaining games without side payments. RECENT WORK HAS SHOWN that the Shapley value for a game with side payments is a cardinal utility function which reflects the desirability of playing different positions in a game, or in different games (cf. Shapley [14], Roth [9]). A player's utility for playing some position in a game is determined in part by his assessment of the payoff he will receive in a class of games with side payments called bargaining games. Given a player's evaluation of these bargaining games, his utility for playing a position in any game with side payments can be determined (cf. Roth [11]). It is desirable to extend these results to games without side payments, since the assumption that side payments can be made is not appropriate in many situations. In this paper we will derive a class of utility functions for playing bargaining games without side payments. Games of this sort are studied by Nash [7], who developed a solution to bargaining games which is an extension of the Shapley value for games with side payments. That is, the Nash solution coincides with the Shapley value for bargaining games with side payments. Somewhat surprisingly, the utility of playing a bargaining game without side payments is determined by the same considerations which determine the utility of playing a game with side payments. Given a player's evaluation of bargaining games with side payments, his utility for bargaining without side payments is determined.

Since dynamic regression equations are often obtained from rational distributed lag models and include several lagged values of the dependent variable as regressors, high order serial correlation in the disturbances is frequently a more plausible alternative to the assumption of serial independence than the usual first order autoregressive error model. The purpose of this paper is to examine the problem of testing against general autoregressive and moving average error processes. The Lagrange multiplier approach is adopted and it is shown that the test against the nth order autoregressive error model is exactly the same as the test against the nth order moving average alternative. Some comments are made on the treatment of serial correlation.

( N THE OCCASION of Lloyd Metzler's sixtieth birthday in 1973, the economic profession received two presents, one a collection of Metzler's papers [23, 1973], the other a volume of essays in his honor [24, 1974]. It is impossible to write a meaningful review of two volumes like these, and it would be presumptuous for me to try. I shall thus limit myself to a brief characterization of each volume and then concentrate on what is probably Metzler's most influential paper, Wealth, Saving, and the Rate of Interest [21, (1951) 1973], trying to evaluate its contribution after another quarter-century of macroeconomic theory. The Collected Papers, 24 in number, are said to include nearly all of Metzler's scientific articles. Of those listed in the Index of Economic Articles only one, a note on the effects of income redistribution published in the Review of Economics and Statistics, is missing. Three papers, all apparently written around 1962-63, were not previously published. One considers the transfer problem for the case of imported raw materials, another one discusses the significance of the tax system for the wealth effect, and the third explores the implications of partial adjustment for the stability of inventory cycles. A fourth paper, also described as previously unpublished, has, in fact, appeared before. Flexible Exchange Rates, the Transfer Problem, and the Balanced-Budget Theorem can be found in the Rivista Internazionale di Scienze Economiche e Commerciali, April 1966, and it is also listed as a contribution to the festschrift for Marco Fanno. Among the papers that remain unpublished seems to be the third chapter of Metzler's dissertation. The original texts are said to be lightly edited for consistency, which at least one reader regrets. The foreword, signed by Alice Bourneuf, Evsey Domar, Paul Samuelson, and Richard Caves, offers a concise characterization of each paper and its place both in Metzler's work and in the history of its subject matter. In earlier periods, the landmarks of scientific progress were Great Books like the Wealth of Nations, Ricardo's Principles, Marx's Capital, and Keynes's General Theory. However, as the progress of science manifests itself increasingly in journal articles, a selective library of important contributions will consist more and more of collected essays. Such a library will be deficient without Metzler's collected papers. The profession is indebted to the editors for their publication. The 22 essays in honor of Lloyd Metzler, edited by George Horwich and Paul A. Samuelson [24, 1974], range over all four fields of Metzler's own contributions, namely international trade (Ronald W. Jones, John S. Chipman, Harry G. Johnson, M. June Flanders, Joanne Salop, and Akira Takayama), mathematical economics (Kenneth J. Arrow; James P. Quirk; Murray C. Kemp and Henry Y. Wan, 84

The continuation of low rates of fertility and reductions in mortality rates of the elderly have revived the interest of economists in the examination of the economic impacts of aging populations. These concerns combined with the analysis of the income status of the elderly and their activities from the broad framework of the economics of aging. The rapid growth of support programs for the aged also has been the focus of considerable economic analysis. This review highlights the most important areas of research in the literature on aging. The first section discusses the determinants of population age structure changes and their impact on the size and composition of the dependent groups. The following section provides a review of the economic status of the elderly and the sources of income in old age. Section III incorporates the economic characteristics of the elderly into a life-cycle context while Section IV examines the empirical evidence concerning labor supply decisions of the aged. Social Security and private pensions and their influence on the economy are analyzed in Section V. The final section of this article reviews evidence on the interaction between aging and macroeconomic variables. (excerpt)

In his comment on our paper (1976) McCulloch makes two main points. First, he argues that we have set up our spline function in the wrong way. Second, he argues that our computations are seriously in error. McCulloch also makes one minor point about the placing of knot points. In this reply, we will show that none of these comments in way affect our findings. The first point concerns the way in which we set up our spline As McCulloch correctly points out, we treat M/ Y as spline function of r. The reason for this particular setup, of course, is that we do indeed regard M/ Y as being causally function of r. McCulloch argues, however, that to detect trap one should treat r as spline function of M/ Y. The reasonableness of this argument depends in part on the definition of liquidity According to McCulloch, a trap consists of horizontal section of the demand for money function, or at least horizontal asymptote under the demand for money function, when the interest rate r is placed on the vertical axis and money (or money divided by income, M/ Y) on the horizontal axis. Clearly, by treating M/ Y as spline function of r, we were able to test whether or not the interest elasticity of the money demand function approached infinity at some low interest rate. Furthermore, we were able to test this definition of trap without entailing bias in the coefficients. McCulloch's point, then, concerns only the other definition of trap. More specifically, he argues that our setup did not permit us to determine whether the interest elasticity of the money demand function was infinite at some low interest rate. The reason, according to McCulloch, is that while spline can fit horizontal segment, it cannot fit vertical segment, since it is piecewise polynomial. Apparently, McCulloch is arguing that spline can estimate zero slope coefficient but not an infinite slope coefficient. We have no quarrel with this argument. However, if one were to obtain zero slope coefficient by treating r as spline function of M/ Y, it seems reasonable to assume that one would obtain very large slope coefficient (if the spline program generated output at all) by treating M/ Y as spline function of r. Since we obtained relatively small slope coefficient, we felt justified in concluding that our empirical results did not provide any evidence of horizontal segment to the money demand function. In event, we have re-run our equations treating r as spline function of M/ Y as McCulloch suggests. As we suspected, the results indicate that our finding that there is no evidence of horizontal segment to the money demand function remains intact. Moreover, these results are consistent with our finding that the interest elasticity of the demand for money tended to decline as the interest rate became small, finding that is not unique to our study, as we reported in our paper. The second point concerns the relationship between the estimated parameters and continuity. McCulloch calculates the functional value at the second knot forj= 0 using our estimated parameters for the 1920-1970 period. He finds that for j=0 the value is 2.482, whereas the value for j =1 is + 0.322. McCulloch considers this to be discontinuity and therefore questions the elasticities calculated from these parameters. We agree with McCulloch that this is considerable discontinuity. However, the computations are not seriously in error. The problem is that the decimal point was misplaced. Unfortunately, when our figures were copied from the printouts, the symbol D and the accompanying numbers were completely ignored. The D and the numbers, however, indicate the correct placement of the decimal point. After correctly placing the decimal point, one finds that using the parameters for j=0 for the 1920-1970 period to calculate the functional value for the second knot (XI = 2.286) gives SJ(2.286 -) = .391 -.0477h