Knowledge that Transforms

Recent evidence shows that within an industry, smaller firms grow faster and are more likely to fail than large firms. This paper provides a theory of selection with incomplete information that is consistent with these and other findings. Firms learn about their efficiency as they operate in the industry. The efficient grow and survive; the inefficient decline and fail. A perfect foresight equilibrium is proved by means of showing that it is a unique maximum to discounted net surplus. The maximization problem is not standard, and some mathematical results might be of independent interest. 1. THEORY AND EVIDENCE ON THE GROWTH AND SURVIVAL OF FIRMS Do SMALL FIRMS grow faster than large firms? Are they less likely to survive? Early studies found no relation between the size of firms and their growth rates [8, 14, 16]. The growth of firms seemed to be proportional to their size. In later work, adjustment costs with constant returns to scale were shown to imply that firms should grow in proportion to their size [10, 11]. Recent evidence from larger samples tells a different story. Mansfield [13] finds that smaller firms have higher and more variable growth rates. Du Rietz [6], in a sample of Swedish firms, again finds that smaller firms grow faster, and that they are less likely to survive [6,8,13]. These findings conflict with the adjustment costs theory in which all firms grow at the same rate, and in which failure does not happen. To explain these deviations from the proportional growth law, I propose a theory of noisy selection. Efficient firms grow and survive; inefficient firms decline and fail. Firms differ in size not because of the fixity of capital, but because some discover that they are more efficient than others. The model gives rise to entry, growth, and exit behavior that agrees, broadly, with the evidence. The model also agrees with some more tentative findings. First, firm size and concentration seem to be positively related to rates of return.2 Second, the correlation over time of rates of return is higher for larger firms and in the concentrated industries [15, 17]. Third, the variability of rates of return at a point in time is higher in the concentrated industries [17]. Finally, higher concentration is associated with higher profits for the larger firms, but not for the smaller firms

We consider the problem of how to regulate a monopolistic firm whose costs are unknown to the regulator. The regulator's objective is to maximize a linear social welfare of the consumers' surplus and the firm's profit. In the optimal regulatory policy, prices and subsidies are designed as functions of the firm's cost report so that expected social welfare is maximized, subject to the constraints that the firm has nonnegative profit and has no incentive to misrepresent its costs. We explicitly derive the optimal policy and analyze its properties. IN THEIR CLASSIC PAPERS Dupuit [2] and Hotelling [5] considered pricing policies for a bridge that had a fixed cost of construction and zero marginal cost. They demonstrated that the pricing policy that maximizes consumer well-being is to set price equal to marginal cost and to provide a subsidy to the supplier equal to the fixed cost, so that a firm would be willing to provide the bridge. This first-best solution is based on a number of informational assumptions. First, the demand is assumed to be known to both the regulator and to the firm. While the assumption of complete information may be too strong, the assumption that information about demand is as available to the regulator as it is to the firm does not seem unnatural. A second informational assumption is that the regulator has complete information about the cost of the firm or at least has the same information about cost as does the firm. This assumption is unlikely to be met in reality, since the firm would be expected to have better information about costs than would the regulator. As Weitzman has stated, An essential feature of the regulatory environment I am trying to describe is uncertainty about the exact specification of each firm's cost function. In most cases even the managers and engineers most closely associated with production will be unable to precisely specify beforehand the cheapest way to generate various hypothetical output levels. Because they are yet removed from the production process, the regulators are likely to be vaguer still about a firm's cost function [12, p. 684]. As this observation suggests, it is natural to expect that a firm would have better information regarding its costs than would a regulator. The purpose of this paper is to develop an optimal regulatory policy for the case in which the regulator does not know the costs of the firm. One strategy that a regulator could use in the absence of full information about costs is to give the firm the title to the total social surplus and to delegate the pricing decision to the firm. In pursuing its own interests, which would then be to maximize the total social surplus, the firm would adopt the same marginal cost pricing strategy that the regulator would have imposed if the regulator had

In this paper we outline the computation of general equilibrium in a pure exchange economy via a fixed point decomposition procedure. For general equilibrium models of the required structure, a full equilibrium may be computed through the solution of a sequence of smaller scale 'sub-equilibrium' problems. The text contains a presentation of the methods involved along with a discussion of initial computational experience for some numerical examples. IN THIS PAPER we describe the computation of general equilibrium in a pure exchange economy via a fixed point decomposition procedure similar in spirit to the Dantzig-Wolfe decomposition algorithm for the solution of linear programming problems (Dantzig and Wolfe [2]). The method involves the generation of labels for vertices on a master simplex through the separate solution of subequilibrium problems whose parameters are determined by the coordinates of the vertex on the master simplex. For general equilibrium models of the required structure, it is possible to compute a full equilibrium through the solution of a sequence of smaller scale 'sub-equilibrium' problems. The analogues to the common constraints in the Dantzig-Wolfe procedure are common commodities with common prices, and the block diagonal structure on non-common constraints in Dantzig-Wolfe is replaced by an analogous block diagonal pattern of demands and endowments of agents over non-common goods. A natural application of the method is to international trade models with 'traded' and 'non-traded' goods. Traded goods are common to all countries, non-traded goods are traded only within the country involved. We report execution times for numerical examples using Merrill's [5] algorithm for solution of both full dimensional problems and the same problems by the decomposition procedure. We do not discuss the application of these procedures to economies with production, although it seems likely to us that a similar procedure can be applied if a comparable block diagonal structure characterizes the production set. The economic interpretation we offer for our procedure draws on the partition of the full list of commodities in a general equilibrium model into 'common' goods traded among all agents, and 'non-common' goods traded among a subset of agents. The assignment of non-common goods to agents is represented in a block diagonal pattern of demands and asset ownership by agent. Agents have

In this note the relationship between alternative concepts of noncausality is analyzed using the tool of conditional independence among a-fields. (For the reader who is unfamiliar with this technique, the Appendix sketches the proofs and the basic technical apparatus, along with some basic motivations.) Furthermore, the relationship between the concepts of noncausality and transitivity is made explicit in order to facilitate, in econometric modelling, the use of results already obtained in sequential analysis.

[This paper examines the consequences and detection of model misspecification when using maximum likelihood techniques for estimation and inference. The quasi-maximum likelihood estimator (OMLE) converges to a well defined limit, and may or may not be consistent for particular parameters of interest. Standard tests (Wald, Lagrange Multiplier, or Likelihood Ratio) are invalid in the presence of misspecification, but more general statistics are given which allow inferences to be drawn robustly. The properties of the QMLE and the information matrix are exploited to yield several useful tests for model misspecification.]

[The estimation and testing of a singular equation system in the context of a general dynamic specification is considered. In an application to factor demand equations, hypotheses suggested by economic theory are expressed in terms of the long run structure of the system under alternative dynamic specifications. Variations in the dynamic specification are found to have a significant impact upon the inferences that can be made about the long run structure.]

The paper derives and compares the local power of three different methods of testing non-nested regression models that are available in the literature. It shows that the asymptotic power of the orthodox F test against local alternatives is strictly less than that of Cox's non-nested test or the J test recently proposed by Davidson and MacKinnon [5], unless the number of non-overlapping variables of the alternative hypothesis over the null hypothesis is unity, in which case all three tests are shown to be asymptotically equivalent. The final section of the paper gives results of Monte Carlo experiments designed to check the validity of the theoretical findings of the paper and also to shed light on the small sample properties of the Cox test and the orthodox test.

We consider the market value of excess demand as a measure of disequilibrium. We show that, in a fixed exchange economy, there exist approximate equilibria whose measures of disequilibrium depend only on the endowments and not on the preferences. A related bound on the norm of excess demand, depending on the endowments and the approximate equilibrium price, is also obtained. We show the existence of allocations which are nearly competitive, as measured by the largest proportion of demand given up at the allocation by any trader. We use these results to obtain, for very general sequences of exchange economies, allocations giving all traders bundles close in norm to their demands. This result includes a 0(l1/n) rate of convergence in the case of uniformly bounded endowments.