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Plant scale and multiplant production as determinants of industrial concentration
PLANT SCALE AND MULTIPLANT DETERMINANTS OF INDUSTRIAL David H. Ciscel and Howard
PRODUCTION AS CONCENTRATION P. Tuckman’
Over a decadeago, Stigler concluded that classicaltheory had nothing to say about relative firm size.’ A more recent survey of the literature concluded that “neoclassical theory has no full explanation of why firms grow at all nor why it is that the typical pattern of the growth rate of firms seems to lead inexorably towards persistently increasing business concentration.“3 A consequenceis that empirical researchershave tended to concentrate solely on the number and relative size of firms in an industry to measure market concentration and market power. In Stigler’s words, “the number of firms completely describes the industry structure . . . “4 The purpose of this paper is to suggestthat Stigler’s assumption is inadequate due to the importance of multiplant production (MPP), that analysis of industrial structure can be improved by the addition of a measure of plant as well as firm concentration, and that a model incorporating a measure of plant/establishment divergence and of plant scale can explain a significant amount of the concentration
in industries.
1
The authors are, respectively, Associate Professor and Distinguished Economics at Memphis State University. They would like to thank Don research assistance and Barbara Tuckman and Donald Norman for their ments.
1968),
‘George p. 33.
Invisible
3Robin Marris and Dennis Mueller, ‘The Corporation, Hand,” Journal of Economic Litmahwe, March 1980, 4
Stiglcr,
J. StigIer,
op. cit.
The Orgari~tion
of Industy
(Homewood:
Professor of Green for his helpful com-
Richard
Competition, p. 33.
D. Irwin,
and
the
2
The paper is divided into three parts. Part I reviews the work that has been done on scale economies and on multiplant production. Part II proposes a measure of divergencethat can be used to examine the impact of multiplant production (MPP) economies on concentration in an industry. Part III provides an empirical analysis of the effects of plant scale and multiplant production on concentration in the SIC 38 four-digit industries. 1.
The Economies from Plant Scale and Multiplant
Operation
Traditional price theory explains concentration within an industry largely by the presenceof scale economies. The sources of these economies differ among industries. In automobiles they result from the specialization of labor and capital, in petroleum and chemicals from the more than proportional physical gains which occur from processingliquids in large quantities, in computing and other service-intenseindustries from what Robinson calls “the economies of massed reserves,” and in aircraft production from falling unit costs due to the so-called learning curve.’ Because these economies are usually realized intra-plant, they alone are not sufficient to provide a satisfactory explanation of the development of MPP. Inter-plant scale economies result from the centralization of management services,researchand development, warehousing,distribution, and product advertising. Additional economies are attainable if specialized plants are each used to produce part of a full product line. Economic arguments other than economies of scale have been employed to explain the growth of MPP, including the advantagesof size in capital accumulation and accessto financial
‘E. University
A. G. Robinson, The of Chicago Press, 1968),
Structure
pp.26-27.
of
Competitive
Industry
(Chicago:
3
markets, pooling of risk, effects of patent laws, and the role of distributional economies. These arguments can be compelling in the analysis of individual cases,but they do not provide a general extension of price theory to the caseof MPP. On the empirical side, long run economies of scale have long been recognized as a potential source of profits.6 Moreover, the research of Saving, Weiss, Scherer et al and others provides estimates of the percentages of market share provided by the minimum optimum scale of plant (MOS). ’ Severalrecent studies of MOS have emphasized the difficulties present in its conceptual origin, its estimation, and its relationship to concentration.8 A technical link between MOS and concentration remains largely undiscovered. Bain’s classic study of the 1974 market shareof 20 industries raisesthe question of whether scaleeconomies are sufficiently important to explain the concentration existing in that year. He concludes that the existence of large scale economies relative to the whole market is “left in doubt by this investigation.“’ To date this conclusion has not been refuted. The recent massive study by Scherer et al reinforces the findings of Bain’s analysis. 6 See Matshal Hall and Leonard Weiss, “Firm Size and Profitability,” Review Economics and Statistics, August 1967, pp. 319-331 and J. M. Samuels and D. J. Smyth, “Profits. Variability of Profits, and Finn Size,” Economica, May 1968, pp. 127-139.
of
‘T. R. Saving, “Estimation of Optimum Size of Plant by Survivor Technique,” Quarsady Journal of Economics~ November 1961, pp. 569407. Leonatd Weiss, “The SutvivaI Technique and the Extent of Suboptimal Capacity,” Journal of Political Economy, June 1964, pp. 246-261. F. M. Scbetet, Alan Bechenstein, Erich Kaufet, and R. D. Murphy, Tbe Economics of Multi-Hant Operation: An IntemationcJ Comparisons Study (Cambridge: Hatvatd University Rest., 1975). 8 Peter
F. Coty, “A Technique for Obtaining Improved Estimates of Scale, ” Rev&w of Economics and Statistics, Febtuaty 1981. pp. “Minimum Efficient Size and Seller Concenttation: An Empirical Journal of Industrial Economkx, Match 1980, pp. 287-307. Bela Gold, Perspectives on Size, Scale, and Returns,” Tbe Journal of Economic Litemturr, 1981, pp. 5-33. Optimal Davies,
Twenty 38-39.
9Joe S. Bain, ManufacNting
” Economies Industties,”
of ScaIe,
Concentration,
Am&can
Economic
and Condition
Review, Match
Minimum 96-106. S. Problem,” “Changing Match
of Entty in 1954. pp.
4
The role of MPP in facilitating concentration has also been explored. Nelson, for example, examines concentration in the manufacturing industries and finds that several industries have substantial numbers of multiproduct firms.’ ’ Similarly, Blair finds a substantial number of industries in which a divergence exists between the number of firms and the number of plans.’ ’ More recently Scherer et al and Miller have examined the effects of minimum efficient scale on multiplant operation.’ 2 Scherer also deals briefly with the effects of MPP on concentration in his textbook. These studies provide an interesting insight into the importance of MPP in industry; they do not consider the direct relationship between MPP, MOS, and industrial concentration. The evidence suggeststhat MPP is related to concentration. For example, Nelson’s study of 83 four-digit industries finds that the leading four firms own more than one plant in 79 of these industries; they own more than three plants in half.’ 3 Nelson also reports a negative correlation between the ratio of the average plant size of the top four firms to the industry averageand the four firm concentration ratio. His work supports the view that MPP, rather than large plant size, is responsiblefor market concentration .
Statar
10 Ralph L. (New Haven:
vitch,
“John 1972),
Nelson, Concentration Yzlc University Press,
M. BIG, Economic pp. 102-113.
in Manufacturing 1963).
Concenmtion
(New
York:
12P. M. Schcrcr, et zl., op. cit. See also Edwzrd hl. Miller, of Plant,” Sovtbem Econmic Journal, April 1978, pp. 861-872. 13N&on,
op.
cit.,
pp. 62-77.
Indurtties
of
tbe
Hzrcourt,
Brzce,
“Size
of Finn
United
Jovzno-
znd Size
5
Further support is found in Blair’s work which uses 1967 Census data to analyze plant size and finds the highest productivity levels in plants in the middle size range.’ 4 Blair also finds that large plants (measured by number of employees) are declining in importance through time, a conclusion also reached by Shepherd in an independent study.’ ’ If MPP is a major source of market concentration, then Stigler’s belief that the number of firms “describes” the industry is an oversimplification; students of market concentration must also consider the divergence between the number of plants and the number of firms in explaining industrial concentration. Moreover, if MPP is a major source of concentration, industry studies should reveal a large number of plants owned by a limited number of firms in concentrated industries. Alternatively, if scale economies are the sole source of concentration, the industry should be characterized by a few large firms and the number of plants should not diverge sharply from the number of firms. It is important to distinguish the sources of concentration in industry. If scale economies are responsible for concentration, the implication is that technology, rather than collusion, is responsible. In this context anti-trust or other “corrective” actions may not be optimal from society’s point of view since the break-up of large firms will result in higher average costs of production. This increases product prices and in the face of foreign competition puts domestic industry at a competitive disadvantage. Alternatively, if ownership economies are the source of MPP, existing theory provides little guidance concerning the effects of successful anti-trust actions.
14 15
Blair,
op. cit.,
pg. 98.
William C. Shepherd, “What Does mies of Scale?” Soutbem Economic Journal,
the Survivor July 1967,
Technique pp. 113-122.
Show
about
Econo-
6
ZZ. Divergence Measures, MPP, and Concentration
Ratios
A number of indices are currently used to measure concentration; measures of divergence are usually based on some variant of these. Most frequently employed is the concentration ratio which measures the market share of the top firms in an industry (usually the leading 4, 8, or 12). Blair uses the percentage point difference between the shares held by the eight largest plants and those held by the eight largest companies to capture divergence.r 6 A problem with his measure is that it limits analysis of concentration in an industry to the top firms and ignores what is happening among smaller firms.’ 7 Likewise, Nelson uses the ratio of the difference in the number of firms and establishments to the number of firms in an industry. This measure works best if firms and plants are assumed to have equal sized market shares since it assigns equal importance to each firm.’ ’ The Herfindahl index, a second measure of concentration is computed from the sum of the squared market shares of each firm in an industry. ’ 9 Since the market share of a firm must always be equal to or exceed the market share of a plant, the ratio of the Herfindahl index for the firms in an industry to the Herfindahl index for plants must be equal to one (if the number and size of firms and plants is equal) or exceed one. This measure of divergence, referred to as DM, is more complete than Blair’s and more accurate than Nelson’s.
16Blair’s by an analysis
choice of the
of measure was apparently determined by data availability, not type of concentration measure best able to capture divergence.
17William Boyes and David Smyth, Economics, September 1979, pp. 289-302. 18 Nelson,
op. cit.,
p. 62.
19Stigler,
op. cit.,
p. 33.
I1The Optimal
Concentration
Ratio,”
Applied
7
The Data. In framing our analysis toward the future rather than the past, we have chosen to analyze a high technology industry group which has exhibited growth and change in the last decade. The SIC 38 industry group (Scientific Instruments) provides a good example of the market situation in a high-technology industry. This group has 13 four-digit industries, including Engineering and Scientific Instruments (ESI), Automatic Temperature Controls (ATC), Process Control Instruments (PCI), Fluid Meters and Counting Devices (FMCD), Electrical Measuring Instruments (EMI), Measuring and Control Instruments Not Elsewhere Classified (MCI), Optical Instruments and Lenses (OIL), Surgical and Medical Instruments (SMI), Surgical Appliances and Supplies (SAS), Dental Equipment and Supplies (DES), Opthalmic Goods (OG), Photographic Equipment and Supplies (PES), and Watches, Clocks, Devices and Parts (WCDP). Our analysis utilizes data from the population of firms and establishments maintained by Economic Information Systems, a New York firm, as of December 1978. This source includes all firms and plants in the U.S. with more than 25 employees.*’ In the SIC 38 industry group are 3,550 plants and 2,932 firms. The use of population rather than sample data eliminates problems of sample bias and permits more accurate Herfindahl calculations. Blair’s measure of divergence is calculated in Table 1 which also shows the four and twelve firm and plant concentration ratios for each industry. The figures suggest substantial variation in the degree of measured concentration among the industries.
20 Since the it is a comprehensive group.
EIS
data bank provides relatively complete population coverage, data base for measuring concentration in the SIC 38 industry
For example, the Photographic Equipment and Supplies industry is heavily concentrated (55.9), while the Engineering and Scientific Instruments industry is relatively unconcentrated (16.0) at the four-firm level. Note, too, that divergence exists in virtually all of the industries with the largest measuredlevel in the most concentrated industries. The weakness of Blair’s divergence measure is evidenced in Table 1, its susceptibility to variation based on the number of firms and plants used in the calculation. For example, in two industries (PES and WCDP) divergence narrows when the top twelve firms/establishments, rather than the top four, are examined. Our divergence measure, DM, is shown in Table 2, together with the Herfindahl indexes for the firms and plants in each industry. Like Blair’s measure, it suggestssubstantial variation in the degreeof concentration among industries. However, rank ordering the numbers produced by each measure shows that they differ in their ordering of the industries according to divergence.*’ The Spearman rank-order correlation between our measure and the Blair four-firm/plant ratio is 0.91; between our measure and the Blair twelve-firm/plant ratio the correlation is 0.80. Note that the correlation is extremely sensitive to the number of firms included in the Blair measure.We favor elimination of this problem by the use of the Herfindahl ratio. In no industry does our divergence measure equal one. Virtually all of the high technology industries have more than one plant per firm, and in severalthe number of plants owned by the firms with the largest market sharesis considerable.For example,
with
*‘Note that in our measure the greatest divergence occurs in the WCDP ATC a close second, while the least occurs in the PC1 industry.
industry
9
at the end of 1978 the ES1 industry had 13 plants owned by the top four firms; the WCDP industry had 19 plants owned by the top four firms. The industry market share of these 32 plants varied from 6.8 percent to 0.08 percent of their relevant markets.* *
zzz.
A Test of the Plant Scale and MPP Explanations Concentration
of Market
A more direct test of the combined effects of plant scale and MPP is formulated using our divergence measure and several alternative measures of plant size to explain differences in the amount of concentration observed among the industries. Ordinary least squares regression is used to estimate the following equation: Hfi = a + blSi + b2DMi where Hfi is the Herfindahl sure of average plant
+ ui
(1)
index for the ith industry,
size for the ith industry,
Si is a mea-
and DMi is our
measure of divergence for the ith industry. For the purposes of this analysis, the basic unit is the four-digit industry; 13 observations are used in the analysis. The results of the estimations are shown in Table 3 .* 3
22 Blair found evidence ducts, soybean oil. and computer and turbines and photographic moderate divergence. 23
between false
“extreme” industries, equipment.
or “wide” divergence in the gypsum proand “moderate” divergence in steam engines Our results conform with his definition of
A potential problem with this formulation is that a spurious correlation DM and Hf could be present if He is unrelated to Hf. This would create the
impression
same variable. Meyer
of
problem
that In fact,
Hf
and DM
are correlated
He and Hf have
is not relevant
here.
a positive
because correlation
they
are transformations of 0.68 and the classic
of the Kuh
10
TABLE Concentration
Industry’
ES1 ATC PC1 FMCD EM1 MCI OIL SMI SAS DES OG PES WCDP
l IdentitP
Ratios and Divergence in the Instruments
Market Share of Top Companies 4 12
16.03 42.80 24.90 32.57 34.58 18.85 32.91 24.29 32.73 41.77 35.90 55.90 47.80
29.44 68.28 49.30 68.92 50.82 30.01 52.09 45.29 49.00 63.62 51.76 70.63 67.22 .--
1
Market of Top 4
12.41 21.82 22.21 27.79 20.10 16.00 22.84 13.44 15.79 29.13 24.22 39.54 21.82
of Industries
ES1 - Engineering & Scientific Instruments ATC - Automatic Temperature Controls PC1 - Process Control Instruments FMCD - Fluid Meters and Counting Devices EM1 - Electric Measuring Instruments MCI - MeamringKonnol Instruments N.E.C. OIL - Optical Instruments & Lenses SMI - SurgicaI & Medical Instruments SAS - SurgicaI Appliances & Supplies DES - DentaI Equipment & Supplies OG - Opthaimic Goods PES - Photographic Equipment & Supplies WCDP - Watches, Clocks, Devices & Parts
Measures Industries
Share Plants 12
22.67 40.52 45.07 59.68 35.29 29.96 40.34 26.52 33.03 48.45 36.66 54.78 47.37
for Corporations
Divergence 4 12
Total Sales ($ Mills)
6.77 27.76 4.23 9.24 15.53 3.05 11.75 18.77 15.97 15.17 15.10 15.85 19.85
2,539.2 1,324.l 1,755.4 543.6 2.960.1 1.351.2 L275.7 2.316.2 3,280.2 944.0 1.331.5 10,663.4 1552.2
3.62 20.98 2.69 4.78 14.49 2.85 10.07 10.85 16.94 12.64 11.68 16.36 25.98
11
TABLE Herfindahl
Industry
ES1 ATC PC1 FMCD EM1 MCI OIL SMI SAS DES OG PES WCDP
*
2
Ratios and the Divergence Measure for the Scientific Instruments Industry Establishments
Firms
He
Hf
.0091 .0133 .0233 .0382 .0192 .0117 .0236 .0214 .0236 .0323 .0240 .0484 .0257
*See Table 1 for Industry
Titles
.0125 .07 34 .0278 .0481 .0398 .0152 .0464 .0363 .0569 .0570 .0447 .0964 .0792
Divergence DM = Hf/He
1.37 3.01 1.19 1.26 2.06 1.30 2.00 1.70 2.41 1.75 1.86 1.99 3.08
12
Plant Scale. The differences in plant size are dramatic in the four-digit SIC 38 industry group. Even within the largest firms, mean plant size per firm is misleading. A multiplant firm may operate quite different sized establishments. For example, one company in SIC 3811 operated eight establishments. The largest was ranked tenth in the industry (market share of 1.18 percent). The smallest was in the middle of the size distribution (market share of 0.12 percent). While it is true that the largest firms are the most likely to have multiplant operations, their plants differ in size and are not necessarily the largest in the industry.24 Moreover, there is not a strong correlation across industries in the average size of the plants owned by the top firms. In light of these facts, it is prudent to utilize several measures of plant size in the analysis. The first is average plant size in millions of dollars, measured by the mean size of the largest four plants and the mean size of the largest twelve plants.25 The second is the mean market share of the largest four plants and the mean market share of the largest twelve plants. This measure is the traditional one for capturing minimum efficient scale, i.e., plant output relative to the total market.26 The third measure is relative scale of plant, defined by the ratio of the mean market share of the four largest plants to the mean market share of plants in each four-digit industry.
24 Substantial concentration exists within the top four plants. For example. in SIC 3811 the largest four plants are fourteen times larger than the average size plant for the industry with a mean market share of 5.5 percent. The plants included in our measures of the mean share and size of the top four and top twelve plants are not always owned by the top four or twelve firms
plants
25 These measures are used to capture the influence of the technologically in the SIC 38 industry group on industry-wide concentration. 26Nelson.
op. cit.,
p. 62.
largest
13
TABLE The
Impact
3
of Scale and Diversification
on Concentration
Hf=a+blS+bDM+u Alternative of Scale
Measures ’
a
bl
b2
R2
1.
Mean Size of Top Plants ($000)
Four
-.OlO
.00004 ~.~l)
.026 wm
.75
2.
Mean Size of Top Plants ($000)
Twelve
-.OlO
.OOOl (.00003)
.026 mw
.74
3.
Mean Market Share of Top Four Plants
-.050
. a77 C.112)
.026 f.003)
.91
4.
Mean Market Share of Top Twelve Plants
-.051
1.531 (.339)
.025 mw
30
5.
Relative Mean Market Share of Top Four Plants*
-. 023
.OOl (.ooOS)
.029 f.007)
.58
*Mean plant sizes are measured in thousands of dollars. Mean market shares are percents of national market. All coefficients are significant at the one percent level or better unless otherwise noted. Numbers in parentheses are standard errors of the coefficient.
14
Estimation of Equation. The findings in Table 3 suggestthat both plant scale and MPP are significant determinants of concentration in the SIC 38 industry. These results are robust with respect to the alternative equation specifications. Note that the variables are all significant at the one percent or better level and each carries the expected sign. The five forms of the equation explain between 58 percent and 91 percent of the variation in concentration. The strong and stable performance of the DM measure is interesting becauseit indicates the importance of MPP for industry concentration. With a mean of Hf = 0.0487 and a mean DM = 1.921, if the DM were reduced to one, the level of concentration as measured by the Herfindahl index would be halved in most of the Scientific Instruments industries. This would reduce concentration in the industry group considerably. Plant scale of the largest establishments also has a consistent and signiftcant impact on the level of concentration. The mean market sharesof the top four and top twelve plants have a greater explanatory effect than the other scalevariables. If the mean plant scale for the top four plants (5.5 percent of the market) or the top twelve plants (3.3 percent of the market) were to double, the Herfindahl index would increaseby 0.1. Since most of the plants in each of these industries produce less than one-half of one percent of total industry output, increased market concentration through the construction of plants similar to the top four or twelve plants is technologically possible. Our findings conform to earlier studies in the sensethat we find that multiplant firms contribute to industry concentration. However, our data also suggestthat large-scaleproduction is an important source of the concentration currently observed in the Scientific Instruments industry. Taken in total, these results suggest that in at least one technologically based industry both scale, when measured by size of operating plants, and MPP are
15
major factors which four-digit industries. ZV.
Implications
explain
the variation
in concentration
across
of the Analysis
The SIC 38 industry group provides a good example of the market situation in a high-technology industry. This industry employs a large percentage of scientists and engineers, has had a large post-war growth, and has experienced relatively large capital outlays over the past few decades. Its products are marketed nationwide and, for the most part, are relatively inexpensive to ship relative to market value. They are also highly specialized and have been subject during the last few years to the microprocessor revolution. The evolution of the structure of these industries occurred in the post-Robber Baron era when anti-trust constraints on industry limited the use of predatory behavior for shaping industry structure. Viewed in such a context, the analysis presented in this paper is enlightening to the problems faced in formulating policy regarding the maintenance of competitive market structures. Technological change, to the extent that it has an impact on the plant structure of these industries, has a definite and measurable impact on the level of current concentration, The current levels of concentration in these industries could increase dramatically if large numbers of small single plant firms were to go out of business and be replaced by large scale plants. At the same time, the presence of multiplant firms is closely associated with the prevailing level of industry concentration. The observed divergence of firm production from plant scale, using a sample of the largest firms, indicates that multiplant market advantages are significant. It seems clear that substantial market concentration based on multiplant economies is present in the group, particularly in the Photographic, Dental, Watch, and Temperature Control industries.
16
The knowledge that concentration is traceable to both technical plant economies and multiplant economies is not an argument in support of the status quo. Economic theory, at least as it relates to the relative of scale versus decentralization, remains too primitive to provide meaningful insights into the effects of a policy designed to decentralize ownership. Social policy toward this industry must be built around the knowledge that a policy of either increased or decreased concentration must be based on more intensive analysis of the industry than can be obtained by aggregate methodologies of the type described in this paper.
PRODUCTION AS CONCENTRATION P. Tuckman’
Over a decadeago, Stigler concluded that classicaltheory had nothing to say about relative firm size.’ A more recent survey of the literature concluded that “neoclassical theory has no full explanation of why firms grow at all nor why it is that the typical pattern of the growth rate of firms seems to lead inexorably towards persistently increasing business concentration.“3 A consequenceis that empirical researchershave tended to concentrate solely on the number and relative size of firms in an industry to measure market concentration and market power. In Stigler’s words, “the number of firms completely describes the industry structure . . . “4 The purpose of this paper is to suggestthat Stigler’s assumption is inadequate due to the importance of multiplant production (MPP), that analysis of industrial structure can be improved by the addition of a measure of plant as well as firm concentration, and that a model incorporating a measure of plant/establishment divergence and of plant scale can explain a significant amount of the concentration
in industries.
1
The authors are, respectively, Associate Professor and Distinguished Economics at Memphis State University. They would like to thank Don research assistance and Barbara Tuckman and Donald Norman for their ments.
1968),
‘George p. 33.
Invisible
3Robin Marris and Dennis Mueller, ‘The Corporation, Hand,” Journal of Economic Litmahwe, March 1980, 4
Stiglcr,
J. StigIer,
op. cit.
The Orgari~tion
of Industy
(Homewood:
Professor of Green for his helpful com-
Richard
Competition, p. 33.
D. Irwin,
and
the
2
The paper is divided into three parts. Part I reviews the work that has been done on scale economies and on multiplant production. Part II proposes a measure of divergencethat can be used to examine the impact of multiplant production (MPP) economies on concentration in an industry. Part III provides an empirical analysis of the effects of plant scale and multiplant production on concentration in the SIC 38 four-digit industries. 1.
The Economies from Plant Scale and Multiplant
Operation
Traditional price theory explains concentration within an industry largely by the presenceof scale economies. The sources of these economies differ among industries. In automobiles they result from the specialization of labor and capital, in petroleum and chemicals from the more than proportional physical gains which occur from processingliquids in large quantities, in computing and other service-intenseindustries from what Robinson calls “the economies of massed reserves,” and in aircraft production from falling unit costs due to the so-called learning curve.’ Because these economies are usually realized intra-plant, they alone are not sufficient to provide a satisfactory explanation of the development of MPP. Inter-plant scale economies result from the centralization of management services,researchand development, warehousing,distribution, and product advertising. Additional economies are attainable if specialized plants are each used to produce part of a full product line. Economic arguments other than economies of scale have been employed to explain the growth of MPP, including the advantagesof size in capital accumulation and accessto financial
‘E. University
A. G. Robinson, The of Chicago Press, 1968),
Structure
pp.26-27.
of
Competitive
Industry
(Chicago:
3
markets, pooling of risk, effects of patent laws, and the role of distributional economies. These arguments can be compelling in the analysis of individual cases,but they do not provide a general extension of price theory to the caseof MPP. On the empirical side, long run economies of scale have long been recognized as a potential source of profits.6 Moreover, the research of Saving, Weiss, Scherer et al and others provides estimates of the percentages of market share provided by the minimum optimum scale of plant (MOS). ’ Severalrecent studies of MOS have emphasized the difficulties present in its conceptual origin, its estimation, and its relationship to concentration.8 A technical link between MOS and concentration remains largely undiscovered. Bain’s classic study of the 1974 market shareof 20 industries raisesthe question of whether scaleeconomies are sufficiently important to explain the concentration existing in that year. He concludes that the existence of large scale economies relative to the whole market is “left in doubt by this investigation.“’ To date this conclusion has not been refuted. The recent massive study by Scherer et al reinforces the findings of Bain’s analysis. 6 See Matshal Hall and Leonard Weiss, “Firm Size and Profitability,” Review Economics and Statistics, August 1967, pp. 319-331 and J. M. Samuels and D. J. Smyth, “Profits. Variability of Profits, and Finn Size,” Economica, May 1968, pp. 127-139.
of
‘T. R. Saving, “Estimation of Optimum Size of Plant by Survivor Technique,” Quarsady Journal of Economics~ November 1961, pp. 569407. Leonatd Weiss, “The SutvivaI Technique and the Extent of Suboptimal Capacity,” Journal of Political Economy, June 1964, pp. 246-261. F. M. Scbetet, Alan Bechenstein, Erich Kaufet, and R. D. Murphy, Tbe Economics of Multi-Hant Operation: An IntemationcJ Comparisons Study (Cambridge: Hatvatd University Rest., 1975). 8 Peter
F. Coty, “A Technique for Obtaining Improved Estimates of Scale, ” Rev&w of Economics and Statistics, Febtuaty 1981. pp. “Minimum Efficient Size and Seller Concenttation: An Empirical Journal of Industrial Economkx, Match 1980, pp. 287-307. Bela Gold, Perspectives on Size, Scale, and Returns,” Tbe Journal of Economic Litemturr, 1981, pp. 5-33. Optimal Davies,
Twenty 38-39.
9Joe S. Bain, ManufacNting
” Economies Industties,”
of ScaIe,
Concentration,
Am&can
Economic
and Condition
Review, Match
Minimum 96-106. S. Problem,” “Changing Match
of Entty in 1954. pp.
4
The role of MPP in facilitating concentration has also been explored. Nelson, for example, examines concentration in the manufacturing industries and finds that several industries have substantial numbers of multiproduct firms.’ ’ Similarly, Blair finds a substantial number of industries in which a divergence exists between the number of firms and the number of plans.’ ’ More recently Scherer et al and Miller have examined the effects of minimum efficient scale on multiplant operation.’ 2 Scherer also deals briefly with the effects of MPP on concentration in his textbook. These studies provide an interesting insight into the importance of MPP in industry; they do not consider the direct relationship between MPP, MOS, and industrial concentration. The evidence suggeststhat MPP is related to concentration. For example, Nelson’s study of 83 four-digit industries finds that the leading four firms own more than one plant in 79 of these industries; they own more than three plants in half.’ 3 Nelson also reports a negative correlation between the ratio of the average plant size of the top four firms to the industry averageand the four firm concentration ratio. His work supports the view that MPP, rather than large plant size, is responsiblefor market concentration .
Statar
10 Ralph L. (New Haven:
vitch,
“John 1972),
Nelson, Concentration Yzlc University Press,
M. BIG, Economic pp. 102-113.
in Manufacturing 1963).
Concenmtion
(New
York:
12P. M. Schcrcr, et zl., op. cit. See also Edwzrd hl. Miller, of Plant,” Sovtbem Econmic Journal, April 1978, pp. 861-872. 13N&on,
op.
cit.,
pp. 62-77.
Indurtties
of
tbe
Hzrcourt,
Brzce,
“Size
of Finn
United
Jovzno-
znd Size
5
Further support is found in Blair’s work which uses 1967 Census data to analyze plant size and finds the highest productivity levels in plants in the middle size range.’ 4 Blair also finds that large plants (measured by number of employees) are declining in importance through time, a conclusion also reached by Shepherd in an independent study.’ ’ If MPP is a major source of market concentration, then Stigler’s belief that the number of firms “describes” the industry is an oversimplification; students of market concentration must also consider the divergence between the number of plants and the number of firms in explaining industrial concentration. Moreover, if MPP is a major source of concentration, industry studies should reveal a large number of plants owned by a limited number of firms in concentrated industries. Alternatively, if scale economies are the sole source of concentration, the industry should be characterized by a few large firms and the number of plants should not diverge sharply from the number of firms. It is important to distinguish the sources of concentration in industry. If scale economies are responsible for concentration, the implication is that technology, rather than collusion, is responsible. In this context anti-trust or other “corrective” actions may not be optimal from society’s point of view since the break-up of large firms will result in higher average costs of production. This increases product prices and in the face of foreign competition puts domestic industry at a competitive disadvantage. Alternatively, if ownership economies are the source of MPP, existing theory provides little guidance concerning the effects of successful anti-trust actions.
14 15
Blair,
op. cit.,
pg. 98.
William C. Shepherd, “What Does mies of Scale?” Soutbem Economic Journal,
the Survivor July 1967,
Technique pp. 113-122.
Show
about
Econo-
6
ZZ. Divergence Measures, MPP, and Concentration
Ratios
A number of indices are currently used to measure concentration; measures of divergence are usually based on some variant of these. Most frequently employed is the concentration ratio which measures the market share of the top firms in an industry (usually the leading 4, 8, or 12). Blair uses the percentage point difference between the shares held by the eight largest plants and those held by the eight largest companies to capture divergence.r 6 A problem with his measure is that it limits analysis of concentration in an industry to the top firms and ignores what is happening among smaller firms.’ 7 Likewise, Nelson uses the ratio of the difference in the number of firms and establishments to the number of firms in an industry. This measure works best if firms and plants are assumed to have equal sized market shares since it assigns equal importance to each firm.’ ’ The Herfindahl index, a second measure of concentration is computed from the sum of the squared market shares of each firm in an industry. ’ 9 Since the market share of a firm must always be equal to or exceed the market share of a plant, the ratio of the Herfindahl index for the firms in an industry to the Herfindahl index for plants must be equal to one (if the number and size of firms and plants is equal) or exceed one. This measure of divergence, referred to as DM, is more complete than Blair’s and more accurate than Nelson’s.
16Blair’s by an analysis
choice of the
of measure was apparently determined by data availability, not type of concentration measure best able to capture divergence.
17William Boyes and David Smyth, Economics, September 1979, pp. 289-302. 18 Nelson,
op. cit.,
p. 62.
19Stigler,
op. cit.,
p. 33.
I1The Optimal
Concentration
Ratio,”
Applied
7
The Data. In framing our analysis toward the future rather than the past, we have chosen to analyze a high technology industry group which has exhibited growth and change in the last decade. The SIC 38 industry group (Scientific Instruments) provides a good example of the market situation in a high-technology industry. This group has 13 four-digit industries, including Engineering and Scientific Instruments (ESI), Automatic Temperature Controls (ATC), Process Control Instruments (PCI), Fluid Meters and Counting Devices (FMCD), Electrical Measuring Instruments (EMI), Measuring and Control Instruments Not Elsewhere Classified (MCI), Optical Instruments and Lenses (OIL), Surgical and Medical Instruments (SMI), Surgical Appliances and Supplies (SAS), Dental Equipment and Supplies (DES), Opthalmic Goods (OG), Photographic Equipment and Supplies (PES), and Watches, Clocks, Devices and Parts (WCDP). Our analysis utilizes data from the population of firms and establishments maintained by Economic Information Systems, a New York firm, as of December 1978. This source includes all firms and plants in the U.S. with more than 25 employees.*’ In the SIC 38 industry group are 3,550 plants and 2,932 firms. The use of population rather than sample data eliminates problems of sample bias and permits more accurate Herfindahl calculations. Blair’s measure of divergence is calculated in Table 1 which also shows the four and twelve firm and plant concentration ratios for each industry. The figures suggest substantial variation in the degree of measured concentration among the industries.
20 Since the it is a comprehensive group.
EIS
data bank provides relatively complete population coverage, data base for measuring concentration in the SIC 38 industry
For example, the Photographic Equipment and Supplies industry is heavily concentrated (55.9), while the Engineering and Scientific Instruments industry is relatively unconcentrated (16.0) at the four-firm level. Note, too, that divergence exists in virtually all of the industries with the largest measuredlevel in the most concentrated industries. The weakness of Blair’s divergence measure is evidenced in Table 1, its susceptibility to variation based on the number of firms and plants used in the calculation. For example, in two industries (PES and WCDP) divergence narrows when the top twelve firms/establishments, rather than the top four, are examined. Our divergence measure, DM, is shown in Table 2, together with the Herfindahl indexes for the firms and plants in each industry. Like Blair’s measure, it suggestssubstantial variation in the degreeof concentration among industries. However, rank ordering the numbers produced by each measure shows that they differ in their ordering of the industries according to divergence.*’ The Spearman rank-order correlation between our measure and the Blair four-firm/plant ratio is 0.91; between our measure and the Blair twelve-firm/plant ratio the correlation is 0.80. Note that the correlation is extremely sensitive to the number of firms included in the Blair measure.We favor elimination of this problem by the use of the Herfindahl ratio. In no industry does our divergence measure equal one. Virtually all of the high technology industries have more than one plant per firm, and in severalthe number of plants owned by the firms with the largest market sharesis considerable.For example,
with
*‘Note that in our measure the greatest divergence occurs in the WCDP ATC a close second, while the least occurs in the PC1 industry.
industry
9
at the end of 1978 the ES1 industry had 13 plants owned by the top four firms; the WCDP industry had 19 plants owned by the top four firms. The industry market share of these 32 plants varied from 6.8 percent to 0.08 percent of their relevant markets.* *
zzz.
A Test of the Plant Scale and MPP Explanations Concentration
of Market
A more direct test of the combined effects of plant scale and MPP is formulated using our divergence measure and several alternative measures of plant size to explain differences in the amount of concentration observed among the industries. Ordinary least squares regression is used to estimate the following equation: Hfi = a + blSi + b2DMi where Hfi is the Herfindahl sure of average plant
+ ui
(1)
index for the ith industry,
size for the ith industry,
Si is a mea-
and DMi is our
measure of divergence for the ith industry. For the purposes of this analysis, the basic unit is the four-digit industry; 13 observations are used in the analysis. The results of the estimations are shown in Table 3 .* 3
22 Blair found evidence ducts, soybean oil. and computer and turbines and photographic moderate divergence. 23
between false
“extreme” industries, equipment.
or “wide” divergence in the gypsum proand “moderate” divergence in steam engines Our results conform with his definition of
A potential problem with this formulation is that a spurious correlation DM and Hf could be present if He is unrelated to Hf. This would create the
impression
same variable. Meyer
of
problem
that In fact,
Hf
and DM
are correlated
He and Hf have
is not relevant
here.
a positive
because correlation
they
are transformations of 0.68 and the classic
of the Kuh
10
TABLE Concentration
Industry’
ES1 ATC PC1 FMCD EM1 MCI OIL SMI SAS DES OG PES WCDP
l IdentitP
Ratios and Divergence in the Instruments
Market Share of Top Companies 4 12
16.03 42.80 24.90 32.57 34.58 18.85 32.91 24.29 32.73 41.77 35.90 55.90 47.80
29.44 68.28 49.30 68.92 50.82 30.01 52.09 45.29 49.00 63.62 51.76 70.63 67.22 .--
1
Market of Top 4
12.41 21.82 22.21 27.79 20.10 16.00 22.84 13.44 15.79 29.13 24.22 39.54 21.82
of Industries
ES1 - Engineering & Scientific Instruments ATC - Automatic Temperature Controls PC1 - Process Control Instruments FMCD - Fluid Meters and Counting Devices EM1 - Electric Measuring Instruments MCI - MeamringKonnol Instruments N.E.C. OIL - Optical Instruments & Lenses SMI - SurgicaI & Medical Instruments SAS - SurgicaI Appliances & Supplies DES - DentaI Equipment & Supplies OG - Opthaimic Goods PES - Photographic Equipment & Supplies WCDP - Watches, Clocks, Devices & Parts
Measures Industries
Share Plants 12
22.67 40.52 45.07 59.68 35.29 29.96 40.34 26.52 33.03 48.45 36.66 54.78 47.37
for Corporations
Divergence 4 12
Total Sales ($ Mills)
6.77 27.76 4.23 9.24 15.53 3.05 11.75 18.77 15.97 15.17 15.10 15.85 19.85
2,539.2 1,324.l 1,755.4 543.6 2.960.1 1.351.2 L275.7 2.316.2 3,280.2 944.0 1.331.5 10,663.4 1552.2
3.62 20.98 2.69 4.78 14.49 2.85 10.07 10.85 16.94 12.64 11.68 16.36 25.98
11
TABLE Herfindahl
Industry
ES1 ATC PC1 FMCD EM1 MCI OIL SMI SAS DES OG PES WCDP
*
2
Ratios and the Divergence Measure for the Scientific Instruments Industry Establishments
Firms
He
Hf
.0091 .0133 .0233 .0382 .0192 .0117 .0236 .0214 .0236 .0323 .0240 .0484 .0257
*See Table 1 for Industry
Titles
.0125 .07 34 .0278 .0481 .0398 .0152 .0464 .0363 .0569 .0570 .0447 .0964 .0792
Divergence DM = Hf/He
1.37 3.01 1.19 1.26 2.06 1.30 2.00 1.70 2.41 1.75 1.86 1.99 3.08
12
Plant Scale. The differences in plant size are dramatic in the four-digit SIC 38 industry group. Even within the largest firms, mean plant size per firm is misleading. A multiplant firm may operate quite different sized establishments. For example, one company in SIC 3811 operated eight establishments. The largest was ranked tenth in the industry (market share of 1.18 percent). The smallest was in the middle of the size distribution (market share of 0.12 percent). While it is true that the largest firms are the most likely to have multiplant operations, their plants differ in size and are not necessarily the largest in the industry.24 Moreover, there is not a strong correlation across industries in the average size of the plants owned by the top firms. In light of these facts, it is prudent to utilize several measures of plant size in the analysis. The first is average plant size in millions of dollars, measured by the mean size of the largest four plants and the mean size of the largest twelve plants.25 The second is the mean market share of the largest four plants and the mean market share of the largest twelve plants. This measure is the traditional one for capturing minimum efficient scale, i.e., plant output relative to the total market.26 The third measure is relative scale of plant, defined by the ratio of the mean market share of the four largest plants to the mean market share of plants in each four-digit industry.
24 Substantial concentration exists within the top four plants. For example. in SIC 3811 the largest four plants are fourteen times larger than the average size plant for the industry with a mean market share of 5.5 percent. The plants included in our measures of the mean share and size of the top four and top twelve plants are not always owned by the top four or twelve firms
plants
25 These measures are used to capture the influence of the technologically in the SIC 38 industry group on industry-wide concentration. 26Nelson.
op. cit.,
p. 62.
largest
13
TABLE The
Impact
3
of Scale and Diversification
on Concentration
Hf=a+blS+bDM+u Alternative of Scale
Measures ’
a
bl
b2
R2
1.
Mean Size of Top Plants ($000)
Four
-.OlO
.00004 ~.~l)
.026 wm
.75
2.
Mean Size of Top Plants ($000)
Twelve
-.OlO
.OOOl (.00003)
.026 mw
.74
3.
Mean Market Share of Top Four Plants
-.050
. a77 C.112)
.026 f.003)
.91
4.
Mean Market Share of Top Twelve Plants
-.051
1.531 (.339)
.025 mw
30
5.
Relative Mean Market Share of Top Four Plants*
-. 023
.OOl (.ooOS)
.029 f.007)
.58
*Mean plant sizes are measured in thousands of dollars. Mean market shares are percents of national market. All coefficients are significant at the one percent level or better unless otherwise noted. Numbers in parentheses are standard errors of the coefficient.
14
Estimation of Equation. The findings in Table 3 suggestthat both plant scale and MPP are significant determinants of concentration in the SIC 38 industry. These results are robust with respect to the alternative equation specifications. Note that the variables are all significant at the one percent or better level and each carries the expected sign. The five forms of the equation explain between 58 percent and 91 percent of the variation in concentration. The strong and stable performance of the DM measure is interesting becauseit indicates the importance of MPP for industry concentration. With a mean of Hf = 0.0487 and a mean DM = 1.921, if the DM were reduced to one, the level of concentration as measured by the Herfindahl index would be halved in most of the Scientific Instruments industries. This would reduce concentration in the industry group considerably. Plant scale of the largest establishments also has a consistent and signiftcant impact on the level of concentration. The mean market sharesof the top four and top twelve plants have a greater explanatory effect than the other scalevariables. If the mean plant scale for the top four plants (5.5 percent of the market) or the top twelve plants (3.3 percent of the market) were to double, the Herfindahl index would increaseby 0.1. Since most of the plants in each of these industries produce less than one-half of one percent of total industry output, increased market concentration through the construction of plants similar to the top four or twelve plants is technologically possible. Our findings conform to earlier studies in the sensethat we find that multiplant firms contribute to industry concentration. However, our data also suggestthat large-scaleproduction is an important source of the concentration currently observed in the Scientific Instruments industry. Taken in total, these results suggest that in at least one technologically based industry both scale, when measured by size of operating plants, and MPP are
15
major factors which four-digit industries. ZV.
Implications
explain
the variation
in concentration
across
of the Analysis
The SIC 38 industry group provides a good example of the market situation in a high-technology industry. This industry employs a large percentage of scientists and engineers, has had a large post-war growth, and has experienced relatively large capital outlays over the past few decades. Its products are marketed nationwide and, for the most part, are relatively inexpensive to ship relative to market value. They are also highly specialized and have been subject during the last few years to the microprocessor revolution. The evolution of the structure of these industries occurred in the post-Robber Baron era when anti-trust constraints on industry limited the use of predatory behavior for shaping industry structure. Viewed in such a context, the analysis presented in this paper is enlightening to the problems faced in formulating policy regarding the maintenance of competitive market structures. Technological change, to the extent that it has an impact on the plant structure of these industries, has a definite and measurable impact on the level of current concentration, The current levels of concentration in these industries could increase dramatically if large numbers of small single plant firms were to go out of business and be replaced by large scale plants. At the same time, the presence of multiplant firms is closely associated with the prevailing level of industry concentration. The observed divergence of firm production from plant scale, using a sample of the largest firms, indicates that multiplant market advantages are significant. It seems clear that substantial market concentration based on multiplant economies is present in the group, particularly in the Photographic, Dental, Watch, and Temperature Control industries.
16
The knowledge that concentration is traceable to both technical plant economies and multiplant economies is not an argument in support of the status quo. Economic theory, at least as it relates to the relative of scale versus decentralization, remains too primitive to provide meaningful insights into the effects of a policy designed to decentralize ownership. Social policy toward this industry must be built around the knowledge that a policy of either increased or decreased concentration must be based on more intensive analysis of the industry than can be obtained by aggregate methodologies of the type described in this paper.