Choosing the Right Concentration Ratio in Industrial Organization Studies, Study notes of Literature

Download Choosing the Right Concentration Ratio in Industrial Organization Studies and more Study notes Literature in PDF only on Docsity! WORKING PAPERS DOES THE CHOICE OF CONCENTRATION RATIO REALLY MATTER? John E. Kwoka, Jr. WORKING PAPER NO. 17 October 1979 Fl'C Bureau of Economics working papers are preliminary materials circulated to stimulate discussion and critical comment. All data contained in them are in the pub6c domain. This includes information obtained by the Commission which has become part of public record. The analyses and conclusions set forth are those of the authors and do not necessarily reflect the views of other members of the Bureau of Economics, other Commission staff, or the Commission itselt Upon request, single copies of the paper will be provided. References in publications to FfC Bureau of Economics working papers by FfC economists (other than acknowledgement by a writer that he has access to such unpublished materials) should be cleared with the author to protect the tentative character of these papers. BUREAU OF ECONOMICS FEDERAL TRADE COMMISSION WASHINGTON, DC 20580 I . In troduction A common observation in industrial organiza tion literature is that the measure of "concentration" used to describe an industry or to relate its structure to performance is an issu e of at most secondary importance . Since concentration ratios and other statistics of firm size distribution are highly correlated, it is argu ed, empirical investigations will show similar results regardless of the choice of index . This paper will demonstrat e both theoretically and empirically why that conclusion is unfounded in the case where it is most likely to be valid, namely, in a comp arison of different concentration ratios. In addition, we shall suggest some economic implications of the statistical results produced by concentration ratios consisting of different numbers of firms. The belief that the choice of structur al measure is unimp or­ tant stemmed origina ly from experience with structure­ p erformance studies. In his athbreak ing article, Bain (1 51) employed an industry s eight-firm concentration ratio to explain its leading firms' profitability. The relationship ne found--a significant break at eight-firm concentration of 70 percent--has s timul ated a great deal of an alogous resear ch. Occasionally the eight-firm, but more often the four-firm, ratio (both available in the Census of Manufactures) wa s used, since the latter offered 1 somewhat more highly signif icant results. II. Properties of Correlation Coefficients Let us suppose we wish to explain some measure of perform­ ance (Y) by either of two indices of marKet structure, x1 ana x2. Assume we calculate the correlation coefficient between Y and x1 ( denoted ryl), and know fr om previous work that between X1 and X2 (denoted r12>· what can we infer about ry2, the correlatlon oetween Y and X2? In particular, if r12 is ver y large and highly significant, and ry1 is also s1gnificant (if not near ly so large) , can we conclude that ry2 must also be significant? Th e answer is mos t definitely in the neg at1ve. The neces­ sary conditions on ry2 yield very low lower bounds for typi­ cal values on ry1 and r12• To see this, consider the following matrix of correlation coefficients: (1 )R = The diagona l elements are of course unity, and the matrixrii is symmetric (i.e., rij = rji). In addition, R shares with the covariance matrix from which it is derived the pr operty of being pos iti ve de fln ite , that is, the determinants of its 5 principal minors are all positive. Within that constraint, howev er, a wide variety of va lu es of r12r rly, and r2y lS possible . -4- In order to focus on the present question, let us explore what values of r12 and r1y are consistent with r2y = 0, that is, when Y is wholly unrelated to X2• Then the matrix k can be rewritten (2 )R = 1 0 1 Positive definiteness (see footnote 5) now requires only that 2 2 1 -(r12 > -(r ly) > 0 ( 3) Possible solutions include r12 = . 7, r1y = . 7 ; also, r12 = .9, r1y = .4; or even r12 = . 95, r1y = . 3 . Such values of r12 are consistent with the evidence cited in the previous s ect io n, and th ese r1y's ar e ver:y muc h on tne orde r of those found in structure-performance studies (see Weiss, 1974, and r efe rences the rein) . Thus, one conclusion of this exercise is that a high c orrelation betwe en two measures of market structure (r12> and substantial correlation between one measure and industry perform- ance (r1y> need not imply any relationship wh atsoev er betwe en the other measure and performance (r2y) . Certainly they do not imply a rela tionship of simi la r size and/or significance. Alternatively, these correlations can be interpreted to mean that the weakn ess or absence of one relationship (r2y} and a high correlation between two structural measures (r12> does not preclud e a relations hip between the sec ond structural statistic -s- a d performance (r1yl. Inferences that alternative concen­ tration ratios and/or other indices are indistinguishable a e simply not justified by such correla tions. III. Properties of Concentration Ra tios In this section we shall describe alternative concentration ratios for u.s. manufacturing and explore their relationships to industry performance. There are, of course, as many concentra­ tion ratios as firms (i.e. , market shares) in any industry. The data required for their calculation, however, have not gener­ a lly been available, and this study will use estimates generated by a private mar keting research firm. Their reliability has been . . 6 checked and found satisfactory, and the data have performed well 1n prev1ous uses. The top 10 ma rke t shares for each of 314 four-di git SIC industries in 1972 constitute the basic new data. These have been summed into the corresponding succession of concentration ratios, labeled C l, • • • ,ClO and described i n Tabl e I. Thus Cl (the large st share itself) averages .175 for all industries, and ranges from a high of .686 to a low of .011. Since at least one industry has only seven firms id entified in the data base,_ the maximum C7 = 1. 00 0. The pattern of increasing means in these data is qui te reg ul ar, though it obscures huge ra nges. The las t two columns of Tabl e I speak to Stigler's comment and the argument of the preceding section. Co rrela tions among successive concentration ratios are extremely large, in part -6- par. Industry GD = geographical dispersion variable, to reflect local , regional, or national extent of market and thereby correc.t Census data for scope of true econom1c markets. Its definition imp lies a ne gative sign against PCM.8 GR = a growth variable defined as the percenta ge change in industry shipments between 19 67 and 1972 . Theory predicts more rapidly growing industries will have higher margins, · MPT = the market share of the midpoint plant size in the indu stry, to capture scale economies which require different m inimum market shares in different . 9 . d1n ustr1es. DUM = zero for producer good industries, one for consumer goods industries. This variable reflects the greater importance of advertising outlays and product differentiation in the latter. Data are from FTC, Classification and Concentration (1967}. Re gressions of equation {3} were performed on all ten con­ centration ratios, as reported in Table II. Although Cl, the leading firm share, has considerable strength and significance by itself in explaining industry price-cost margins, substantial impr oveme nt occurs from using the two-firm concentration ratio.10 That statistic yields the highest R2 (.175) and t-value (2.43) of an y of the alternatives. Furthermore, the -9- H (4. 45) • (3.06) (3.74) 3. 4. .1 6 5 7. 9. 'l'AULE I I M ultivariate Regressions of Industry Price-Cost Marg ins on Various Concentration Hatios Concentration Ha ti o KO GO GH MP'l' OUM CUN!:>'l' l. .0906 Cl .0813 -.0425 .0530 .0652 .0394 .2128 (1.93) (2. 7 5) (2.91) 2. .0 853 C2 .0786 -.0423 .0515 .o 5 41 .o 391 .2088 (2.43) (4.30) (3.06) (2.68) (2.30) (3.72) _, .16y .1 7 r) .064 7 (2.09) CJ .0791 (4.30) -.0420 (3.02) .0529 (2.76) .056 8 (2.35) .OJ8 9 (3.70) .208U .1 71 .o 515 ( l. 76) C4 .0800 (4.32) -.0419 (3.01) .05 38 (2.80) .06 03 (2.42) .0388 (3.68) .2094 .16 u .0445 C 5 .0806 -.0420 .0543 .062 5 .033 8 .2095 .166 I 0I 5. (1.57) (4.34) (3.02) (2. 82) (2. 48) (3. 68) 6. .0411 C6 .0808 -.04 20 .0 5 47 .0637 .0389 .2092 ( 1.49) (4.34) (3.02) (2.84) (2.51) ( 3 .6 u) .037 4 C7 .0812 -.0420 .0550 .065 5 .038 9 .2093 .164 (1.37) (4.3 5) (3.01) (2. 86) (2. 51) (J.b8) 8. .o 348 C8 .0815 -.0420 .0552 .06 70 .038 .209J .1 6 4 (1.27) (4.36) (3.01) (2.87) (2.62) ( 3 .6 8) .163.031 5 C9 .0820 -0.0420 .0556 .0691 .0389 .209 7 (1.16) (4. 39 ) (J.Ol) (2. 88) (2.71 ) (3.68) 10. .o 278 ClO .0827 -.0420 .05b0 .0716 .0389 .2104 .1 p 2 (1.03) (4.42) (3.01) (2.90) (2. 82) (3.68) pattecn of cesults w ith the moce inclusive concentcat ion catio is pecfectly cegular, w ith R2 decl ining fcom .175 w ith C2 co . 1 62 w ith ClO. Th e pecfocmance of the cead ily available concen­ tcat ion cat ios foe four and eight ficms is distinctly infecioc to that usin g C2, with C8 the wocst for being the largest aggcegat e. In deed, wh ile C2 is significant at ovec .99, C4 is signif icant at only .95 in a one-tail test, an d C8 actual ly falls below .9 0 . Th is occurs despite the fact that the pactial corcelation between 11C2 and C4 is .96, and that between C2 and ca is .as. It is also wocth noting that all the control variables ace stable, s ignif icant, and have the expected signs throughout. In dustcy macgins ace higher with lacger cap ital-output ratios, less geo gcaphical dispecsion, faster orientation growth, lacger scale economies, and a consumer goods to the industry. Thus, the fact that C2's relationship to pric e-cost mar gins is highly sign if icant and all these concentcat ion ratios are highly correlated does not insure the emergence of a clear rela­ t ionship between these alternativ es and margins. The more inclus ive concentration ratios s imply ace too inclusive. Adding shaces not causally cela ted to performance adds random noise which in suff icient amounts can drive even a significant under­ ly ing variable (C2) to statistical insignificance (a s in C8). Reseacch conf ined to the moce aggregated concentration rat ios -11­ 10. Th ese resul s do not fully reflect the de ree of added R2explanatory power due to C2 vs. Cl. The of the regres sion witnout either concentration ratio is .162.· _ While the addition of Cl raises this by . 007 , C2 causes R 2 to increase by .013, a near doubli ng of the importance of the concentration itself. 11. Although it is the partial correlations (holding the other independent variables constant) that are relevant to these multivariate relationships, another common error in the literature is to note only the simp le correlation coefficients among structural measures. In the present examp le, they are larger yet. The simp le correlation between C2 and C4 is .98; and between C2 and CS, .93. 12. Indeed, the use of inappropriate concentration ratios might be a factor contributi ng to some findings of no such relationship. See Weiss (1974) , pp. 203 ff. -14­ 1971, 702-6. Quarterly 93-324. --- o -n In- du -st- r-y Pe-rf-ormance, " Economics -- -------- --Concentration Policy, 1955. Rand McNal ly, 19 70. Organization Industry, Learning, References Bailey, D . , and s. E. Boyle, •The Op timal Me asure of ConceRtra­ tion, • Journal of the American Statistical Association, December pp . Bain, Jo e s. , •Re lation of Profit Rate to Industry Concentra­ tion, • Journal of Economics, August 195 1, pp. 2 Chiang, Alpha c., Fundamental Methods of Mathematical Economics, New York: McGraw Hil l, 1974. Kilpatrick, R . w., "The Choice Among Alternative Measure s of In dustrial Co ncentration, • Review of Economics and Statistics, May 1967, pp. 258-60. Kwoka, John E. , Jr. , •Large Firm Dominance and Price Cost Journal, July 197 7, , pp. 183-89. , •The Effect of Market Share Distribution Review of and Statistics, Margins in Manufacturing Industries,• Southern Economic February 1979, pp . 101-109. Miller, Richard, "Marginal Concentration Ratios and Industry Profit Rates , • Southern Economic Journal, Oct ober 1967, Wa shingt on, pp. 259-68. , "Number-Equivalents, Relative Entropy, and Ra tios: A Comp arison USif¥3 Market Performance, • Southern Economic Journal, July 1972, pp. 107-11 2. Rosenbluth, Gideon, "Measures of Concentrat ion, " in Business Concentration and Price NBeR; Pri nceton: Prlnceton University Press, Scnerer, F. M., Industrial Market Structure and Economic Performance, Ch 1c ag o: Schmalensee , Ri chard, "Using the H-Index of Concen tr ation wi th Published Data , " Review of Economics and Statistics, May 19 7 7' pp • 18 6-9 3 • Stigler, George, "The Me asureme nt of Con centra tion, • in his The of Homewood: Irwin, 196 8 . u.s. Bureau of the Census, 1972 Census o f Manufactures, 19 75. We iss, Leo nard, "The Con centration-Profits ke lationship and Antitrust, " in Goldschrnid, H. J. , Mann, H. M., and Weston, J. F . , Industrial Concentration: The New Boston: Little Brown, 1974. -15­