Ten years ago Harvey Averch and I developed a model of the firm's behavior under the constraint that the return on capital investment not exceed a given level, specified by a governmental regulatory body. Major assumptions of the model are that (a) the firm seeks to maximize profit, (b) the market cost of capital is constant, (c) the allowable or fair rate of return exceeds the cost of capital, and (d) no regulatory lag exists. Under these assumptions the model leads to conclusions that the capital-labor ratio is greater than that which would minimize cost at the level of output selected by the firm, and that the firm may have an incentive to serve competitive markets even if revenues fall below incremental cost in those markets, with the difference more than compensated by increased net revenues permitted through price increases in its monopoly services. This formulation has attracted numerous comments, critiques, and replies. However, virtually all the discussion has remained on theoretical grounds. Unfortunately, little empirical analysis has appeared to suggest the importance of these distortions in the real world. The purpose here is briefly to note major developments in the theory, to examine bits of evidence that have come to light, and to address possibilities for further empirical work.

In a recent issue of this Review, Philip Coelho and Moheb Ghali have argued that various studies purporting to show a persistent differential between wages in northern and states have used data unadjusted for regional differences in price level; that the differential has been proved for nominal wages, not real wages. Using data for 1963 they show that the average nominal wage rate for a sample of five northern metropolitan areas is significantly greater than such an average for five southern metropolitan areas. However, after the nominal wage figures are adjusted for differences in the cost of living in each of the ten areas, this differential disappears. This result survives the introduction of dummy variables to account for differences in industry composition, sex, color, and capital-labor ratio. It seems almost unbelievable that earlier studies of the wage differential have ignored regional differences in price levels, and Coelho and Ghali must be commended for calling attention to this anomaly. However, they have not proved the end of the NorthSouth wage differential; at least not to the satisfaction of this writer. The reason is that of the five cities used in their sample, only one, Atlanta, would be accepted by many as southern, the classification of Baltimore, Dallas, Houston, and Washington, D.C. as by the Departments of Labor and Commerce notwithstanding.' The purpose of this note is to repeat Coelho and Ghali's comparisons for another sample of cities, half of whose members would be recognized as by any reasonable observer.2 Required data for each metropolitan area are number of production workers, total man-hours, and total wages for production workers, classified by industry, and cost of living indices. The first three items are provided in the Census of Manufactures 1967 and the latter can be obtained for the year 1967 from the Handbook of Labor Statistics 1970. Table 1 shows that our sample seems to give roughly the same results as that of Coelho and Ghali. Average hourly nominal wages for the five northern areas are 14.4 percent higher than for the areas. This differential drops to 4 percent when real hourly wages are considered. The same phenomenon occurs for annual wages. Looking at the figures for the individual cities however, it is clear that Baton Rouge is an extreme outlier. If we compare average hourly wages between the five northern areas and the four areas excluding Baton Rouge, we find that when we shift from nominal to real wages the percentage difference drops from 25.6 to 15.1, still a sizeable difference. It would be preferable to establish the continued existence of the North-South wage differential without excluding Baton Rouge from the sample. This might be accomplished by showing that the high average wages in Baton Rouge are a result of the industrial composition of that region. Our method of distinguishing between regional effects and industry effects is identical to that of Coelho and Ghali. We calculate wage rates and annual wages for every industry (two digit classification) and for every metropolitan area.3 The model takes the form: * Assistant professor of economics, Michigan State University. I The title of one of the sessions at the December 1971 meeting of the American Economic Association, at which two papers were presented, was Is the South Still Backward? M. I. Foster included only Atlanta in his definition of the South. F. Ray Marshall omitted Baltimore and Washington, D.C. from his definition. 2 We do not repeat the last part of their analysis involving regional differences in sex, color, and capitallabor ratio. 3 No observations were available for the following industries in: Boston, SIC 21; Buffalo, SIC 21, 31; Pitts-

Recently in this Review, Charles Goetz and James Buchanan advanced the proposition that output-generated external diseconomies may be associated with a production possibilities curve internal to an attainable curve and that under competition it would be the former on which equilibrium would occur. This in turn they take to imply that the conventional tax-bounty analysis offers, in general, an incorrect remedy in that it applies to the wrong production possibilities curve. The present discussion does not deny that the results indicated by Goetz and Buchanan occur, as they too note, in the context of input-generated external diseconomies nor that their results may be conceivable in the context of output generated external diseconomies.' We do however denv that the analytical structure they offer in support of their conclusion is admissible. The analytical case Goetz and Buchanan make is, in terms of Dean Worcester's classification, that of Externalities which are internal to a specific (p. 884). They employ the crucial specification, on which their results turn, that the costs of each firm (where firms are identical) depend on a function which includes the output of other firms, as distinct from total industry output, as an argument. Where ci, qi, Qi are, respectively, firm total cost, firm total output, and output of all other firms corresponding to any particular firm, i, we have

[The exact finite sample properties of an asymptotically unbiased but nonconsistent estimator of a structural variance are examined briefly.]

IN recent years several research studies have used a data base consisting of a time series of cross-section samples. A primary reason is that panel data of this type are potentially richer in information than a single cross-section sample. To date, however, the question of how to best analyze data bases of this type has not been fully explored in any of the research. To illustrate, a number of prior research projects which have utilized this type of data base are briefly reviewed. Hoch (1962) used moving cross-section samples as the data base for estimating the parameters of a CobbDouglas production function by analysis of covariance. Specifically the data were collected on 63 Minnesota farms for the years 1946 to 1951. Hoch reported an observed difference between the least squares parameter estimates and covariance estimates and the elasticities developed from these estimates. In terms of method, the major conclusion was that the covariance model might produce less biased elasticities and marginal return estimates. Massy and Frank (1965) investigated the relationship between price changes and dealing activities on a -firm's market share for frequently purchased household and food products. Panel data covering a 101-week time period of family purchase history provided the data base for the study. However, the data were aggregated so no methodological insight could be inferred concerning the question of analyzing time series of cross-section data. Laughhunn and Lyon (1971) applied Bayesian regression in analyzing a time series of cross-section cigarette consumption data using the Tiao and Zellner (1964) approximation method. The primary methodological issue in this research was to observe differences that might exist between classical pooling and the Bayesian regression technique. Comparison of the two techniques revealed very little difference between either parameter estimates or standard errors. Schipper (1964) used covariance regression to analyze a series of cross-section samples (19541957) collected by the Survey Research Center, University of Michigan. The central focus of this study was to analyze consumer discretionary behavior particularly with respect to durable expenditures, short term debt, and discretionary saving. The major methodological finding was that several differences between the covariance regression model and individual cross-section regressions existed. Schipper suggested the individual cross-section analyses might be biased but could not prove this point since he did not use experimental data. Palda and Blair (1970) conducted an analysis of toothpaste demand by using multiple cross sections of data collected by MRCA during the period 1958-1962. One focus of their research was to investigate the potential cross-section specification bias, based on the rationale presented by Simon and Aigner (1970), that can exist because of omitted variables. An interpretation of the results led them to think that the covariance model may reduce the specification bias. This interpretation cannot be considered conclusive since the analysis was not conducted in an experimental framework. Since there is an interest on the part of economic and business researchers to use multiple cross-section sample data, this would appear to be a sufficient reason for evaluating the different methods available for combining and analyzing the samples. Earlier work in this area includes studies by Nerlove (1967, 1968). He assumed models of the form Yit = aYit-l + Uit and Yit = aYit-l + 1-Xit + Uit respectively with Uit = yi + Vit with yi and Vit uncorrelated where =o-2 = 2 +or2. The estimation methods used were OLS, generalized least squares utilizing known p (p = o-A2/o-X2) analysis-of-covariance estimates with cross-sectional effects only, two-round estimates based on an estimated value of p, and maximum likelihood estimates. Generally, Nerlove's findings indicated that generalized least squares (if p is known) produces good esti-

Peter L. Bernstein, What Rate of Return Can You "Reasonably" Expect?, The Journal of Finance, Vol. 28, No. 2, Papers and Proceedings of the Thirty-First Annual Meeting of the American Finance Association Toronto, Canada, December 28-30, 1972 (May, 1973), pp. 273-282