T HE measurement of firm size plays a crucial role in applied microeconomics and industrial organization. Firm size has figured prominently in numerous studies of economies of scale in production, advertising, capital market, and cash balances, and in studies of concentration, diversification, profitability, regulation, technological change, and research and development. Even when firm size was not their main concern, many studies often found that size emerged as a robust empirical variable.' All these studies have based their findings on different alternative measures of firm size, often implying that great care in choosing between them is unnecessary since the measures are highly intercorrelated. In a note in this REVIEW, Smyth et al. (hereafter SBP) were the first to recognize that alternative measures of firm size are not interchangeable unless stricter conditions than correlation are met. They have further shown that empirical findings regarding economies of scale are not invariant with the size measure chosen, and that often different conclusions can be reached depending on the particular size measure used. The purpose of this paper is threefold: (I) to offer a general stochastic model that rigorously spells out the conditions for interchangeability among alternative measures of firm size, and of which SBP's deterministic model is a special case; (2) to conduct a statistical test of the interchangeability conditionis using a larger number of size measures, and a far larger sample than the one employed in SBP's empirical test; and (3) to empirically analyze the statistical properties of the most commonly used measures in order to help future investigators in selecting appropriate size measures suitable for their purposes. Section I reviews SBP's work, section II discusses the measurement problem, section III presents our theoretical model, and section IV concludes with some empirical evidence.

The presence of farm programs should directly affect the expectations of producers. This paper analyzes the formation of price expectations when price supports constitute an effective lower bound on the distribution of the expectations. We first investigate what the expected price would be if the usual rational expectations formula is used. This leads to a relationship that is not estimable. We suggest two alternatives -one based on a tobit approximation and the other based on a perfect prediction of when the support is going to be effective. Using a simplified model of the U.S. corn market, the methodology is demonstrated and compared to an alternative method of using futures prices as the expectation of harvest price. The analysis of supply response for the major U.S. field crops is made difficult due to government intervention in these markets. This intervention has been characterized by the use of price supports, acreage diversion, storage incentives, etc. during the last thirty years. Many studies have analyzed producer behavior in the presence of governmental involvement. Such studies have typically been concerned with modeling the effect of supports and diversions in an ex post sense rather than with how producers used the knowledge of farm programs to form their expectations. If producers are rational economic agents, their expectations of harvest prices should be conditioned both by free market forces and the type and degree of governmental intervention in the market. Of course, farm programs have varied in nature and extent during the past thirty years and it is doubtful that any structural model could capture their complexities. In this paper we attempt to introduce rational expectations in a simplified model of the U.S. corn market. In essence we focus on the formation of price expectations when price supports constitute an effective lower bound on the distribution of the expectations. We proceed by developing a theoretical model that connects the rational expectations model with a model of bounded price variation. It is shown that one representation that may characterize the corn market is a triangular structural system with endogenous switching. A full information maximum likelihood estimator is proposed for the system. Next an empirical model is specified and estimated. The model is evaluated in comparison to an augmented model that contains a futures price so that some inferences may be made concerning the rational expectations model's success in summarizing relevant market information. Expectations Under Bounded Prices Consider a market that may be represented by a simple supply and demand system Q= a,Pt* + a2W, + el, Supply Function Pt= b,Qt + b2Xt + e2t Demand Function (1) where P and Q represent market price and quantity, W and X represent supply and demand shifters, and P,* represents the rational expectation of product price at the time production decisions are made. Note that this system has a familiar recursive structure when the expected price variable is specified in terms of one or more lagged prices. When the restricted reduced form of the structural system is solved for in terms of the expected price and this expression is used to replace Pj* (Wallis (1980)) then models similar to those of Goodwin and Sheifrin (1982) and Shonkwiler and Emerson (1982)

A LTHOUGH econometric models have been constructed for a wide variety of macro-economic systems, there have been few reports, if any, of econometric models which have attempted to examine a firm in its entirety. This paper presents some results of a study intended to develop a relatively comprehensive simultaneous-equations model of a firm. The model consists of ten relational equations and five definitional equations. Endogenous variables in the model include sales, prices, output, inventories, various cost and expense items, and investments. The effects of exogenous variables such as wage rates, raw material prices, and external demand determinants are also estimated. Other variables which would make the model more complete are considered but not included in the final version because of limitations of the available data. The data used to estimate the parameters of this quarterly model refer to a firm that is a wholly-owned division of a larger, parent corporation.' The subject firm manufactures and sells a variety of models of what is essentially one product used primarily in the manufacture of home laundry appliances such as clothes washers and dryers. The firm is in an oligopolistic market, being one of a few suppliers of this product to the home laundry equipment industry. Comparison of ordinary least squares estimates and two-stage least squares estimates of the parameters of the model indicates that for this particular sample there was not a great deal of difference in the results of these alternative estimating procedures. The two sets of estimates are generally within a few percentage points of each other and in only one case is the difference as large as 15 per cent. The inclusion of various detailed cost and expense variables in the model offers an opportunity to analyze the internal operations of this firm in some depth. However, many of the conclusions which may be drawn from this model should be considered as being extremely tentative at this time. For the firm under study, the elasticity of demand with respect to price and the elasticity of price with respect to cost are both highly inelastic. These low elasticities might be explained by the competitive nature of this particular component parts industry in which total demand is determined by factors beyond its control and where price reductions by one firm may be met by similar actions of other firms in order to eliminate any great price advantage. The fact that partial elasticity of demand is larger with respect to sales effort than to product engineering effort indicates that expenditures for sales effort are, on the average, relatively more efficient at increasing sales than expenditures for product engineering. This does not seem unreasonable, particularly in an industry where there may not be much product differentiation among firms. Also, the estimated model indicates that expenditures for product engineering, capital equipment, and administration do result in some reductions in this firm's manufacturing costs, as expected. In the original functions explaining expenditures for sales effort, capital equipment, product engineering, and manufacturing engineering, the estimates of the coefficients of certain explanatory variables such as profits, sales minus inventory, and the firm's share of the total industry sales are all negative. Although it is by no means conclusive, these negative coefficients may be interpreted as an indication that the firm is operating with satisficing [9] criteria rather than maximizing criteria with respect to sales and profits. Further analysis of these same functions explaining the expenditures for investment and expense items indicates that expenditures for capital investment and manufacturing engineering are more sensitive to changes in sales than are expendi* The author is an Assistant Professor in the Department of Industrial Engineering and Operations Research at Cornell University. He is indebted to Professor T. C. Liu for many valuable suggestions during the course of this study. The interpretation of results and any shortcomings are the author's own responsibility. 1For security reasons, the corporation will be namel ss.

This paper investigates whether breastfeeding affects 5- to 6-year old children's cognitive development using three U.S. longitudinal data sets. The results for the full samples roughly point to a dose-response effect of breastfeeding on children's cognitive outcomes, with breastfeeding six months or more associated with about one-tenth of a standard deviation increase in cognitive test scores. The breastfeeding effects do not appear to be due to differences in maternal employment, cognitive ability, or parenting skills. In contrast, within-sibling results show no statistically significant breastfeeding effect.

The random assignment of cadets to social groups at West Point provides a rare opportunity to highlight potentially misleading estimates of social group effects found in many studies. Estimates of contemporaneous group effects in human capital production are typically positive and significant; however, evidence in this study suggests that occurrences common to a group may account for much of this correlation. Models that address these biases provide little evidence of group effects in academic performance, although there is evidence of group influences in choice outcomes such as the selection of academic major and the decision to remain in the Army.

This paper analyzes both theoretically and empirically how an absolute grading standard that allows only a small number of distinct grades affects student course performance outcomes. The clearest prediction of the model is that course performance of “grade-motivated” students will tend to be clustered slightly above the boundaries that separate grades, as long as the variance of the random component of performance is not too large. A more tenuous prediction is that the proximity of a grade-motivated student to a grade boundary going into the final exam should influence final exam performance, after controlling for prefinal exam performance. An empirical investigation of the course performance of university students who were enrolled in introductory economics classes that used an absolute grading standard finds evidence in favor of both of these predictions. The results suggest that student effort decisions respond to the incentives created by the grading system.

A model in which women search for husbands characterized by their wages predicts increasing within-group male wage inequality, raises the expected value of continued marital search, and so lowers female marriage propensities. Using 1970, 1980, and 1990 census data, I test this hypothesis within geographically, racially, and educationally defined marriage markets. The estimates suggest rising male wage inequality accounted for 7% to 18% of the decline in the propensity to marry between 1970 and 1990 for white women and more-educated black women. Growing wage inequality appears to have had little effect on the marriage behavior of less-educated black women.