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.

[The choice of development period and consequent introduction time for a single innovation by an expected profit maximizing firm operating under conditions of rivalrous competition is studied. Factors taken into account by the firm are the increasing cost with compression of the development period, the reduction of profit opportunities with prolongation of the development period, and the probability of rival innovation and imitation which affect the potential rewards available to the firm. Comparisons is made with the timing that would be selected in the absence of rivalry. The effects of intense rivalry are also examined.]

The situation in which a seller is aware that his pricing policy will affect the probability of entry of competing suppliers is studied. The seller's optimal policy is developed under the assumption that the entry probability is a non-decreasing function of product and that the objective is present value maximization. It is shown that the optimal pre-entry tends to fall as the discount rate drops, the market growth rate rises, the post-entry profit possibilities decline, or certain non-price barriers to entry fall. ECONOMISTS HAVE LONG known that maximizing immediate profits is often not the optimal strategy for a firm to pursue if its planning horizon extends beyond the present. A policy for achieving the highest overall reward may dictate the sacrifice of some current gain. This point has played a central role in the development of the theory of a The theory deals with determination of the entrypreventing by a supplier of a market when potential entrants exist. The supplier in question may be a firm or a group of (tacitly) cooperating firms. The high short term profits associated with the pursuit of monopoly pricing must be balanced against the loss of long term profits upon entry of additional suppliers attracted by the high price. In an early paper formalizing the problem, Bain [2] defined the price as the highest that the established sellers can set without inducing entry. Modigliani [9] developed a graphical derivation of the limit and analyzed a number of its determinants. Fisher [6] related these results to Cournot's duopoly model. Recent contributors include Pashigian [10] and Dewey [5]. On the other side of the Atlantic, Harrod [7], in an attack on the doctrine of excess capacity, argued that a long-run profit maximizing firm would set to preclude entry. According to Hicks' [8] formalization of Harrod's argument, the firm seeks maximization of a weighted sum of short-run and long-run profits, with the relative weights reflecting the firm's attitudes regarding these periods. It follows from this that the firm may not set at its entry preventing level. Explicit criticism of the limit concept has not been lacking. Williamson [13], while extending the concept of a limit to a limit price-selling cost frontier, suggested that the deterministic framework be modified to a probabilistic one. In proposing a stochastic approach, he noted that the limit theory is highly rigid, with a single point or curve dividing certain entry from no entry. Williamson also observed that the assumed optimality of the limit implied that the firm would be willing to prevent entry at any cost. Stigler [12, p. 227] has pointed out that the attractiveness of entry will depend not only upon the current rate of return to the industry, but also upon the anticipated rate of growth of industry demand. If the latter is large, then the present value of future profits may be sufficiently large

A. L. Nagar, Y. P. Gupta, The Moment Matrix of the Two-Stage Least-Squares Estimator of Coefficients in Different Equations of a Complete System of Simultaneous Equations, Econometrica, Vol. 38, No. 1 (Jan., 1970), pp. 39-49