Historic cost, Market value, Replacement cost, Inventory

An axiomatization is presented for a Savage-type conditional subjective expected utility model. The axioms consist of extensions of the Herstein-Milnor [11] axioms for measurable utility, a generalization of an averaging condition in Bolker [4], and several structural conditions. The structural conditions are examined in some detail, and examples are given to show what happens to the numerical model when they do not hold. The numerical model expresses the utility of an act (or mixed act), given an event, as a weighted sum of the utilities of the act given events that partition the initial event, the weights being personal probabilities for the partition events conditioned on the initial event. The theory is compared to Savage's theory [18] and to a version of the theory of Luce and Krantz [14] for conditional expected utility. 1. DECISION UNDER UNCERTAINTY THE PREDICAMENT BETWEEN mathematical tractability and situational reality that is characteristic of mathematical models in the behavioral sciences is epitomized in the axiomatizations of subjective expected utility models. These axiomatizations include structural conditions that facilitate the derivation of the desired numerical representations for preference. Unfortunately, actual situations of decision making under uncertainty often fail to exhibit the structural properties that occur in the axiomatizations. Thus there is real concern about the applicability of such models to realistic decision situations. As might be expected, decision theorists have attempted to alleviate this predicament by weakening the structural conditions while maintaining the ability to derive the desired model from the axioms. An early move in this direction was made by Suppes [21] in his alternative to Savage's axiomatization [18]. The more recent axiomatizations of Bolker [3 and 4], based on Jeffrey's decision model [12], and of Pfanzagl [15 and 16] and Luce and Krantz [14], continue this line of research. The present paper is a further effort in this direction. To understand its approach we shall first review briefly some other theories. The formulation of the paper is set in the context of Savage's states-of-the-world approach to decision under uncertainty, and I shall therefore focus the discussion within this context. We suppose that the decision maker is to select an alternative, or act, from a set of acts. The consequence of his decision will depend not only on the selected act but also on which state in a set of exclusive and exhaustive states of the world obtains. The state that obtains is not known beforehand by the decision maker and does not depend on the selected act.3

THE DYMULT (dynamic multipliers) program is designed to calculate impact, interim, and total multipliers of a simple linear simultaneous equations model with lags. Builders of an aggregate econometric model have often concentrated on the validity of signs and magnitudes of the estimated regression coefficients of each structural equation and neglected to check the stability conditions of the system, which could be a symptom of specification errors in the model. The DYMULT program checks the stability conditions of the system of equations and calculates the impact, interim, and total multipliers. The matrix form of a simple lag linear simultaneous equations model can be written as follows:

[Given n observations on a system of linear stochastic difference equations with appropriate initial conditions, and given a prior density (possibly diffuse) of its parameters, this paper obtains the predictor of the time series k periods into the future with minimum mean squared error. Completely analytical solution is given for predictions from the first-order univariate system, and, in the general higher-order multivariate case, for k up to 5.]

Given n observations on a system of linear stochastic difference equations with appropriate initial conditions, and given a prior density (possibly diffuse) of its parameters, this paper obtains the predictor of the time series k periods into the future with minimum mean squared error. Completely analytical solution is given for predictions from the first-order univariate system, and, in the general higher-order multivariate case, for k up to 5. econometric equations to produce forecasts were not designed for the purpose of forecasting. In this paper, it is argued that these estimation methods may be inadequate if the resulting estimates are to be used to make ex ante predictions for more than one period ahead, and if the accuracy of the predictions is measured, as it usually is, by the mean squared errors. A formulation of the multiperiod prediction problem is presented. It will then become clear that the same set of parameter estimates cannot be optimal in making predictions for different time periods into the future, when optimality is defined by minimum mean squared errors in small samples. Recently there has been much interest in comparing different econometric models, or different versions of the same econometric model obtained by applying different estimation techniques, in terms of how well they would have forecasted the dependent variables during the sample period, given the true values of the exogenous variables and given the values of the dependent variables lagged one or more periods. It has now become clear that, as judged by ex post forecasting for the sample period, models or techniques that perform better for one-period predictions may do worse for multiperiod predictions. For example, purely auto- regressive models could do better than models based on structural equations in ex post forecasting for one quarter ahead, but were worse in forecasting three or four quarters ahead, as documented in Hickman (4). Klein (9) and Fair (3) have compared multiperiod predictions of the sample data by different estimation techniques applied to the same econometric model. A related, though different, question naturally arises as to whether different parameter estimators should be used to produce ex ante forecasts for different periods into the future. The former topic is one of fitting equations to a set of data. The latter topic is one of statistical decision, and is the subject of this paper.'

A summation social choice function is a social choice function whose choice sets are determinable from maximum sums of utilities that preserve individual preference. Assuming the set of alternatives is finite and individual preferences are irreflexive and transitive, a unanimity-type condition is shown to be necessary and sufficient for a social choice function to be a summation social choice function. The effects of conditions of voter independence, anonymity, and neutrality are noted.

An intertemporal model for the capital market is deduced from the portfolio selection behavior by an arbitrary number of investors who aot so to maximize the expected utility of lifetime consumption and who can trade continuously in time. Explicit demand functions for assets are derived, and it is shown that, unlike the one-period model, current demands are affected by the possibility of uncertain changes in future investment opportunities. After aggregating demands and requiring market clearing, the equilibrium relationships among expected returns are derived, and contrary to the classical capital asset pricing model, expected returns on risky assets may differ from the riskless rate even when they have no systematic or market risk. ONE OF THE MORE important developments in modern capital market theory is the Sharpe-Lintner-Mossin mean-variance equilibrium model of exchange, commonly called the capital asset pricing model.2 Although the model has been the basis for more than one hundred academic papers and has had significant impact on the non-academic financial community,' it is still subject to theoretical and empirical criticism. Because the model assumes that investors choose their portfolios according to the Markowitz [21] mean-variance criterion, it is subject to all the theoretical objections to this criterion, of which there are many.4 It has also been criticized for the additional assumptions required,5 especially homogeneous expectations and the single-period nature of the model. The proponents of the model who agree with the theoretical objections, but who argue that the capital market operates as if these assumptions were satisfied, are themselves not beyond criticism. While the model predicts that the expected excess return from holding an asset is proportional to the covariance of its return with the market

[Transitivity-like properties for binary social choices on a triple of alternatives are shown to follow from simple conditions that apply within each voter preference profile, coupled with structural profile restrictions such as those used in single-peakedness. These results are compared to results obtained under the simple majority rule. The special intraprofile conditions used in the main theorem are related to interprofile conditions such as independence, neutrality, and monotonicity.]

Robert C. Blattberg, Evaluation of the Power of the Durbin-Watson Statistic for Non-First Order Serial Correlation Alternatives, The Review of Economics and Statistics, Vol. 55, No. 4 (Nov., 1973), pp. 508-515

N this paper, I will generalize the modified Newton method previously applied in Chow (1968) to the computation of full-information maximum likelihood estimates of parameters of a system of linear structural equations to the case of a system of nonlinear structural equations. The success of that method for linear systems 1 has stimulated my present attempt to generalize it for nonlinear systems. The subject of maximum likelihood estimation of nonlinear simultaneous equation systems has been studied by Eisenpress and Greenstadt (1966). There are three main differences between their approach and ours. First, their basic formulation is more general, assuming that all parameters in the system may appear in every equation,2 whereas we assume as the basic setup that there is a distinct set of parameters belonging to each equation. Second, partly because of the first, we are able to obtain simpler and more explicit expressions for the derivatives of likelihood function required in the calculations. Third, and also partly because of the first, we can conveniently deal with the important problem of linear restrictions on the parameters in the same equation or in different equations. A fourth feature of this paper, and a feature which has partly motivated it, is the contrast of the linear with the nonlinear case. As it will be shown, there are many similarities in the computations of both. This demonstration can enhance our understanding of the nature of the estimation equations. Two additional features of this paper are the treatments of identities in the system and of residuals which may follow an autoregressive scheme. We will derive in section II the estimation equations for nonlinear systems, under the assumptions that each structural equation contains a distinct set of parameters, that the parameters are not subject to any linear restrictions, and that the (additive) residuals are serially uncorrelated. Section III treats the special case when some equations are linear, and contrasts this case with the nonlinear case. Section IV deals with identities and linear restrictions on the parameters. Section V is concerned with the problem of autoregressive residuals.