[A certain set of weak rationality conditions is shown to be necessary and sufficient for a social decision function to be a cooperative game according to the formulation of von Neumann and Morgenstern. In exhibiting this broad connection between game theory and the theory of social choice, attention is focused on the critical role played by the blocking coalitions in such games.]

This paper analyzes three quarterly investment models for the detection of certain specifi- cation errors. The models are those of Anderson (1 and 2), Eisner (4), and Meyer-Glauber (10). The models are applied to thirteen manufacturing industries. A set of specification error tests developed by Ramsey (12, 13, and 14) are applied to the above models so as to detect the specification errors of omission of variables, incorrect functional form, simul- taneous equation problems, and heteroskedasticity. The models are ranked in order of the number of times they failed to be rejected by the specification error tests and the rank scheme is compared to that found in a previous study by Jorgenson, Hunter, and Nadiri (6), where more conventional criteria are used for ranking the models. industries, making use of both quarterly and annual data. Accelerator models and their variations (flexible accelerator models) as well as models considering internal and external finance are common in the estimation of the investment function. The lag structure between investment and its determinants and the manner in which replacement or the depreciation of capital is accounted for has also evoked the interest of researchers.2 From a perusal of the literature it is apparent that we face almost as many possible models for investment behavior as there are researchers. The problem at hand then is to come closer to a single general investment model from the numerous possibilities suggested. To do this we must investigate models of investment which differ both in terms of the determinants of investment as well as their lag structure so as to cover the broad range of specifications suggested. In a recent study, Jorgenson, Hunter, and Nadiri (6) (hereafter JHN) investi- gated various investment functions for several manufacturing industries using deflated, seasonally adjusted, quarterly data. JHN chose the best model based on the following criteria: (i) comparison of a given investment function with an auto- regressive scheme with regard to goodness to fit; (ii) comparison of a given invest- ment function with a model regressing investment on past anticipated investment expenditures; (iii) R2; (iv) estimates of the standard error of the fitted regression residuals corrected for degrees of freedom; and (v) Durbin-Watson ratio. The last three criteria mentioned above (and especially the third and fourth) are often the standard techniques employed by researchers in selecting a model specifica- tion.3

ITS DISAGREEABLE IMPLICATIONS about social choices have convinced many people that Arrow's impossibility theorem rests on unacceptably strong conditions. Dissatisfaction has centered on (but is not limited to) the conditions that the social ordering should be a weak ordering (WO) and that it should be independent of irrelevant alternatives (IIA). A long line of research, culminating in the results of Mas-Colell and Sonnenschein [18] and Fishburn [7], has shown, however, that the impossibility theorem is robust against reasonable relaxations of WO. (More accurately, if WO is weakened, say by waiving completeness or transitivity of the social ordering, and the remaining conditions are correspondingly strengthened to keep the problem interesting, the impossibility remains.) It seems that this line

A. D. Owen, A Proof that Both the Bias and the Mean Square Error of the Two-Stage Least Squares Estimator are Monotonically Non-Increasing Functions of Sample Size, Econometrica, Vol. 44, No. 2 (Mar., 1976), pp. 409-411

DISCUSSIONS OF IDENTIFICATION of parameters in simultaneous equation econometric models almost invariably assume that data are in the form of aggregative time series, i.e., only one measurement of each variable is available in each time period. This note shows that parameters in a model which is underidentified by the usual rank and order criteria at the aggregative level may be identified when disaggregated data aie available. The argument is presented in terms of a traditional textbook example of an underidentified model which consists of a demand and a supply function for a single commodity that are linear in price, and a market clearing equilibrium equation.

[A specialization of the Edgeworth type formulae due to Chambers [4] to approximate the marginal distribution of an econometric estimator is presented, and its application to improvement of the use of asymptotic limits in significance testing is discussed. Appendices discuss the validity of Nagar approximations to estimator moments, the exact distribution of the instrumental variable estimator, the Edgeworth approximations for 3SLS and FIML estimators, and the use of Monte Carlo procedures for assessing the appropriate probability to attach to a given significance test.]

In this paper we derive and present optimal critical points for pre-tests in regression using a minimum average relative risk criterion. We use the same type risk functions as Sawa and Hiromatsu [8] who, in a recent paper in this journal, derived pre-test critical values using a minimax regret criterion. Since James-Stein type estimators can be shown to dominate any pre-test estimator for the risk functions used here and in [8], no normative claims are made for the critical values we give. However, the use of pre-testing procedures continues in practice and the results given here, contrasted with other results, add to information about the character of costs and returns to such practices.