The Critical Level of Concentration: An Empirical Analysis

Abstract

* The authors would like to thank H. Michael Mann, Robert W. Kilpatrick and John A. Henning for their helpful comments on an earlier draft and Harland Hasey for his assistance with the computer program. We would especially like to thank James Delaney for making a substantial contribution to Part II of this paper. The authors, of course, remain solely responsible for any errors. I A fairly detailed summary of eight of these studies can be found in Norman R. Collins and Lee E. Preston, Concentration and Price-Cost Margins In Manufacturin,g Industries (Berkeley: University of California Press, I968), pp. I8-50. To our knowledge, there are approximately thirty such studies. Leonard Weiss in a recent paper, presented to a joint meeting of the American Economic Association and the Econometric Society, entitled 'Quantitative Studies of Industrial Organization' in Frontiers of Quantitative Economics, ed. by M. D. Intriligator (Amsterdam: North-Holland Publishing Co., 1971) pp. 362-403, provides an excellent critical analysis of these studies. 2 To our knowledge, there have been only two published studies, George Stigler's Capital and Rates of Return in Manufacturing Industries (Princeton: Princeton University Press, I963) and Yale Brozen's, 'Bain's Concentration and Rates of Return Revisited', The Jouirnal of Law and Economics (October 1971), pp. 35I-6I, that have found little or no statistical relationship between concentration and profitability. Robert Kilpatrick reports that Stigler's method of correcting for excessive salary withdrawal contains a statistical bias. When the bias is corrected for, a positive and significant relationship between concentration levels and profitability is uncovered. See Robert Kilpatrick, 'Stigler on the Relationship Between Industry Profit Rates and Market Concentration', The Journal of Political Economy (May/June I968), pp. 479-88. Brozen argues that the positive and significant statistical relationship reported in previous studies is the result of using small samples to test the hypothesis, i.e., small samples bias the findings. He found that when Bain's sample [Joe S. Bain, 'Relation of Profit Rate to Industry Concentration: American Manufacturing, 1936-I940', The Quarterly journal of Economics (August I}95I, pp. 293-324] is expanded from 42 to 78 industries for 1939 (75 for 1940) there is no relationship between concentration levels and profitability. Obviously, a larger sample is preferred to a smaller sample if other things are equal. However, it is not correct to state, as a general proposition, that '[t]he smaller the sample, the greater the sample bias'. See Yale Brozen, op. cit., p. 36I. As one commentator concluded: 'A larger sample is better than a small sample of data of equal quality, but a small sample of carefully compiled information is better than a large sample of inaccurate material.' See Daniel B. Suits, Statistics: An Introduction to Quantitative Econonmic Research (Chicago: Rand McNally & Co., 1963), p. 76. Casual observation indicates that Brozen may not have found a positive relationship because his larger sample contains a number of industries which do not correspond closely to theoretical definition of an industry, e.g., food preparation, not elsewhere classified. as was pointed out elsewhere: 'It seems obvious to us that adding more and more poorly corresponding industries to the sample is more and more akin to adding, as bona fide observations, numbers drawn from a table of random digits, making the null hypothesis more and more difficult to reject,' H. M. Mann, J. A. Henning, and J. W. Meehan, Jr., 'Statistical Testing in Industrial Economics: A Reply on Measurement Error and Sampling Procedure', The Journal of Industrial Economics (November i 969), p. I00.