This article presents information on socio-economic accounting. Several possible dimensions of socio-economic accounting have been suggested, including national income accounting, evaluation of social programs, the role of accounting in economic development and efforts to develop an index of social progress. This paper explores yet another dimension of socio-economic accounting-the recognition and measurement of external diseconomies, or social costs and the resulting implications for the accounting profession. The most complex and controversial, link in the assessment process is the determination of the social costs-monetizing the external diseconomies. Accountants are likely to resist involvement in such efforts because of the uncertainty involved, but such resistance is not justified. Cost determination is more the forte of accountants than of engineers and economists. Assuming that actual social cost estimation will be done by public agencies at some level of government, it then seems not unlikely that the accounting profession will be called upon to attest to such estimates.

The article discusses the use of mathematical models across a variety of disciplines and practices. Mathematical models, naturally, are represented by means of mathematical relations. The mathematical models which will be of interest in this article generally proceed via the special kinds of mathematical relations called "functions," which are used to represent some or all of the relations. Double-entry accounting has been used as a basis for planning and control at both economy-wide and individual-enterprise levels. This is to say that double-entry accounting provides a tool of great utility which can be employed in a variety of ways and contexts. Beyond the convenience of moving back and forth between accounting and interindustry analyses, the mathematics associated with this modeling has permitted a variety of other uses and extensions. The examples in this article should make it clear, however, that this is not the end. Still more may be available from further research in model equivalences and related explorations. Indeed the "models" definition we introduced in the first section of the preceding paper is designed to underscore the potential value of such continuing explorations.

The technique of partial aggregation is explored as a means of preserving the confidentiality of data while enabling research scholars to utilize the information for analytic purposes. For this purpose, two criteria are developed for evaluating the analytic consequences of partial aggregation: One measure indicates the degree of divergence or non-conformity between estimates produced by unaggregated data and partially aggregated data; and the other measure pertains to efficiency loss and expresses the fraction of the useful information in the unaggregated data which remains after the data have been grouped or partially aggregated. These measures are then applied in an experimental test using data from the Call Reports and the Income and Dividend Statements of nearly 5400 member banks of the Federal Reserve System. This experiment consists of evaluating the effect on twenty different regression models of three different levels of aggregation and seven different rules for arraying the data prior to aggregation.

Portfolio selection models based on expected value-semivariance (E-S) criteria have been suggested as offering certain advantages over the expected value-variance (E-V) approach. Although variance is more tractable mathematically, it has not always been satisfying to financial theorists ([3, pp. 278–284], [5], [6], [7, pp. 193–194], and [10, pp. 72–73]). In the pioneering work in portfolio analysis, Markowitz [7, p. 194] observed that semivariance concentrates on reducing losses as opposed to variance which considers extreme gains, as well as extreme losses, as undesirable. In the presence of nonsymmetrical probability distributions, this equal weighting of gains and losses may not adequately describe the alternative portfolios available to the decision maker.