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Bureau of Economics working papers by FfC economists (other than acknowledgement by a writer that he has access to such unpublished materials) should be cleared with the author to protect the tentative character of these papers.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 originaly from experience with structure
p erformance studies. In his wathbreak ing article, Bain (1x51) employed an industryys 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 somewhat more highly signif icant r esults.^1
p. 52) •4 T wo reservations were voiced concerning this conclusion. Stigler (1968) cautioned that some such correldtions were spurious, since, for exampl e, the common eleme nts of the three- and four- firm concentration ratios (namely the top three shares) insure a high correlation. A "p r oper" formu l ation (e.g., between the three-firm ratio and the fourth share), he predicted, wo uld reveal a "vastly l ower" correlation. Sch malensee (1976) devised twelve "more or less pl ausible" concentration in dices by m a ni pula ting Census data and t es ted their corres pondence to the Herfindahl. His conclusion that importan t differences exist, h oweve r, is temp ered by his assumptio n th at the Herfi nd ahl is the "ideal" measure of industrial concentration. In any event , none of thes e stud is have expl ored t he f unda mental properties of correlation coefficients which determine why a nd when alt ernative c oncentrati on measures may m ake a differ ence. The next section of this paper develops these properties, thereby clarifying, modify ing, or ref uting some of the cl aims in the literature. Then det ailed data by f our-digit S IC industry are us ed to co ns true t al ternative cone en tr ation ra tics and provide a specific example of these properties in s tructure p erform a nce tests. We con clu de w ith some imp l ic ations of these findings for economic research and public policy.
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, x 1 ana x2. Assume we calculate the correlation coefficient between Y a nd 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 ry 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:
R = (1 )
The diagona l elements rii are of course unity, and the matrix 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 principal minors are all positive.^5 Within that constraint, howev er, a wide variety of va lu es of r12r rly, and r 2 y lS possible.
aêd performance (r 1 yl. Inferences^ that^ alternative^ concen tration ratios and/or other indices are indistinguishable aƅe simply not justified by such correla tions.
III. Properties of Concentration Ra tios In this section we shall describe a lternative 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. , m arket 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 s hares 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-
TABLE I
Descriptive Statistics of Concentration Ratios Concentration (^) Correlation Correlation
-. -. -. -. -. - Cl .175 .686 .011 .965. Ratio Mean Max. Min. With C(n+l) With S(n+1) - C2 .275 .875 .019 .991 • - C3 .345 .912 .026 • - C4 .398 .973 .032 .997. - C5 .440 .037 .998 •
- I C6 .474 .999 .041.
- ..._, I C7 .502 1.000 .045 .999. - co .526 1.000. - C -. - .546 1.000 .053. - ClO .564 1.000.
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 1n. d ustr1es..^9 DUM = zero for producer good industries, one for consumer goods industries. This variable reflects the greater importance of advertising outlays and produc t differentiation in the latter. (^) Data are from FTC, Classification and Concentration (1967}. Re gressions of equation {3} w ere 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 R^2 (.175) and
t-v a lue (2.43) of an y of the alternatives. Furthermore, the
-9-
Hé
(4. 45) (^) • (3.06) (3.74)
.16 5
'l'AULE I I M ultivariate Regressions (^) Concentrationof Industry Price-CostHatios Marg ins on Various Concentration Ha ti o KO GO GH MP'l' OUM CUN!:>'l'
l. .0906 Cl .0813 (^) -.0425 .0530 .0652 .0394. (1.93) (^) (2. 7 5) (2.91)
- .0 853 C2 .0786 (^) -.0423 .0515 .o 5 41 .o 391. (2.43) (4.30) (3.06) (2.68) (2.30) (3.72)
_,
.16y
.1 7 r)
.064 7 (2.09)
CJ. (4.30)^ -.0420(3.02)^ .0529(2.76)^ .056 8(2.35)
.OJ8 9
(3.70)
.208U.
.o 515 (l. 76)
C4 .08 0 0 ( 4.32)^ -.0419( 3.01)^ .05 38(2.80)^ .06 03(2.42)^ .038 8(3.68)^.^
.16 u
.044 5 C 5 (^) .0806 -.0420 (^) .0543 .062 5 .033 8 .2095.
I (^0) I
(1.57) (^) (4.34) (3.02) (2. 82) (2. 48) (3. 68)
- .04 11 C6 .08 08 -.04 (^20) .0 5 47 .0637 .0389. ( 1.49) (4.34) (3.02) (2.84) (2.51) ( 3 .6 u) .037 4 (1.37) C7 .0812 -.0420 .0550 .065 5 .038 9 .2093. (4.3 5 ) (3.01) (2. 86) (2. 51) (J. b 8 )
- (^) (.o 1.27) 348 C8 .0815(4.36) -.04 20 .0552 .06 70 .0387 .209J .1 6 4 (3.01) (2.87)^ (2.62)^ (3 .6 8) .031 5 (1.16) C9 .0820 -0.0420 .0556 .0691 .0389 .209 7. (4. 39 ) (J.Ol) (2. 88) (2. 71 ) (3.68)
- (^) (1.03).o 278 ClO .0827 -.0420 .05b0 .0716 .0389 .2104 .1 p 2 ( 4.42)^ (3.01) (2.90) (2. 82) (3.68)
--
and çechanically apèlying conventio nal tests or significance would in this case even be led to reject the hypothesis thak 1ndustr y concentration affects performance.^12 The mere fact that the correlations between ratios were very high (as most would surely characterize those just ment ioned) would be insuf ficient to draw the same conclusion regarding other--and more a pp r opri ate measures of industry structure. v. Conclusions Th i s stu dy has demo¥trated that the choice of concentration ratios can matter a great deal. The usual ar gument for di smis s ing t he choice as unimport ant has been demons trated theoretically incorr ect, or at least incomplete. Furthermore, in pract ice, the choice is show n potentially cruci al to the strength of the rela tionsh i p found and in s ome circumstances even to whether a rela t ionship is uncove red at all. Th is is n ot a trivial, dismissab le issue. The e co nomi c signif i can ce of the superi ority of the two firm concentra tion ratio is intriguing. It suggests that an i ndustr y's ability to coordinate beha vi or and raise p rice-cost margins above competitive levels may be determined not b y twenty, e ight, or even four f irms, but by the leading tw o. This could reflect the gr eater difficult y of securing and maintaining agree me nt amo ng more numerous rivals, where even the third f irm p os es some problems. such possibilities lie buried within conventional concentrati on ra tios , bu t their i mportance for pub lic p olicy demonstrates the value of more disag gregated data.
Footnotes l. Weisreveals s' r ev iew an overwhelming of 35 stud number ies of (^) whichu.s. manufacturingfocused on the ind¦stries four firm concentration ratio (Weiss 1974, pp. 204-20). More recent research maintains that patter n.
- Miller (1967) disaggregated the eight -firm concentration ratio and found that a large fifth-through-eighth firm group couldresult exert sug gests a negative that the effect four- on and industry eight-firm performance. ratios are This fundamental ly different constructs.
- T w o exceptions to this view are Miller (1972) and Kwoka (1977).
- In fairness, Scherer's comment was partially intended to contrast the "more seriou s" problems of n§rket definit ion and contaminated data due to divers ified firms.
- This implies the following conditions: (a} r 1 1 > 0 (b) (^) r 11 r 22 - (^) r21 r12 > 0 (c) r11 r22 r 33 + r12 r2y tyl + r21 ry2 r1y -(rly r22 ry1 + r2y ry2 r11 + r12 r21 ryy) > 0 For an elaboration, see Ch iang (1 972), pp. 338-40.
- (^) data,Fbr a seedesc ription Kwoka (1979}. of the nature and previous use of the
- Alsotion lowerratios, are e.g. , correlations the four, betweeneight, nonsuccessiveand twenty firm concentra versions. 8.^ encesIt^ is^ definedin percentages^ as^ the^ sumof allof^ absolutemanufacturing^ values value^ of^ the added^ differ and aregions particular of the industry's country. valueData addedare from for theall 1972 four (^) Census Census of Manufacturers (1975}.
- Thisfiftieth variable percentile is the ofmarket output share in eachof the industry, plant producingas estimated the from employment size classes of plants ln the Census of Manufactures.
Quarterly 93-324.
---o-nNJINj (^) n- (^) dnju s-Ǎ (^) t- (^) ry-ǎPǏe-rǐf-ormance, " Economics
------------ Concentration
Policy,
Rand^ McNal ly, 19 70.
O rganization Industry,
Learning,
References Bailey, D. , a nd s. E. Boyle, •The Op timal Me asure of ConceRtra tion , •December Journal ofpp. the American Statistical Association,
Bain,tion, • Jo e s. , •Re lationJournal of Profitof Economics, Rate to AugustIndustry 195 Concentra 1, p p. 2 C hiang, Alpha c., Fundamental Methods of Mathematical Economics, New York: McGraw Hil l, 1974. Kilpatrick,In dustrial R. Co ncentration, • w., "The Choice Review Among ofAlternative Economics Measureand Statistics, s of 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 Southern EconomicRa^ tios: Journal,^ A^ Comp July^ arison 1972 ,^ USif¥3 pp. Market1 07-11 2.^ Performance, • Rosenbluth,Concentration Gideon, and (^) Price"Measures of Concentrat ion, " in Business University Press, NBeR;^ Pri^ nceton:^ Prlnceton 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 197 7' pp • 18 6-93 • Stigler, George, "The Me asureme nt of Con centra tion, • in his The of Homewood: Irwin, 196 8. u.s. Bureau of (^) 19 75.the Census, 1972 Census o f Manufactures,
We iss, Antitrust, " Leo nard, in "TheGoldschrnid, Con centration-Profits H. J. , Mann, H. ke lationship M., and Weston, and J. F. , Industrial Concentration: The New Boston: Little Brown, 1974.
