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Aggregation and studies of industrial profitability
161
Economics Letters 10 (1982) 161-165 North-Holland Publishing Company
AGGREGATION PROFITABILITY Stephen Michigan
David
AND STUDIES *
MARTIN State University,
East Lansing. MI 48824, USA
J. RAVENSCRAFT
Federal Trade Commision, Received
OF INDUSTRIAL
5 November
Washington,
DC, USA
1981
This letter shows that studies of profitability at the industry level cannot between the impact of market concentration and the impact of market share.
discriminate
Empirical studies of the impact of market concentration on industrial profitability generally find a positive relationship [Weiss (1974)]. The conventional interpretation of these results is that ‘ . . . concentration facilitates tacit or explicit collusion’ [Weiss (1974, p. 232)]. It is also generally accepted that market share will have an impact on firm profitability which is independent of the effect of market concentration [Gale (1972), Shepherd (1972)]. We show in this letter that if this independent impact of market share on firm profitability holds, then the conventional interpretation of industry-level profitability studies does not follow, since industry level results cannot distinguish the impact of market share from the impact of market concentration. * The representations and conclusions presented herein are those of the authors and have not been adopted in whole or in part by the Federal Trade Commission or its Bureau of Economics. The Assistant Director of the Bureau of Economics for Financial Statistics has certified that he has reviewed and approved the disclosure avoidance procedures used by the staff of the Line of Business Program to ensure that the data included in this paper do not identify individual company line of business data.
01651765/82/0000-0000/$02.75
0 1982 North-Holland
162
S. Martin, D.J. Ravenscraft
/ Aggregation
and rndustrial profitability
Suppose there is a linear relationship between market concentration, and firm profitability: v,JS,,
= (Y+ ,&VS,, + yHERF, +
firm
.. .
The rate of profit (r,,) on sales (S,,) of firm i in industry by the market share of firm i in industry j, MS, = 4,/S,
HER?
market
share,
(1)
j is explained
(2)
3
by the Herfindahl
studies
index of market
= 2 (MS,,)‘,
concentration, (3)
and by other factors which we omit from explicit consideration here [see Martin (1979) or Martin (1981) Ravenscraft (1981)]. Eq. (1) may be aggregated from the division of the firm level to the industry level by multiplying both sides of the equation by MS,, and summing over all firms in the industry; the result is r,,‘S,=a+(p+y)HER~+
... .
(4)
It follows that if eq. (1) represents an accurate model of the impact of market share and market concentration on the profitability of the divisions of firms, then industry-level studies of profitability cannot distinguish between market concentration effects (the coefficient y) and firm specific market share effects (the coefficient p). The most that can be estimated is the industry-level combination of the two effects. The industry average rate of profit on sales corresponds to what is probably the most common measure of industrial profitability in crosssection studies, the price-cost margin [Collins and Preston (1969)]; it can also be computed from Internal Revenue Service data. Studies of industrial profitability are generally robust to the use of alternative measures of profitability [Martin (1979)]. Measuring profitability in different ways will not avoid the problem identified here. In view of the high correlation between alternative measures of market concentration, the conclusion that industry-level studies of profitability can at most estimate the combined impact of market concentration and market share may be extended to studies which measure market con-
S. Martin, D.J. Ravenscraft
/ Aggregation
and industrial profitability
studies
/ 163
centration by seller concentration ratios. This is confirmed by Ravenscraft (1980), using a Monte Carlo approach. He shows that if the true measure of market concentration is the four-firm seller concentration ratio instead of the Herfindahl index, industry level studies still provide a biased estimate of market concentration effects. As noted by Gale (1972, p. 413), market share may represent either market power at the firm level or the realization of economies of scale. The latter interpretation is emphasized by Demsetz (1973). If this scaleeconomy interpretation is valid, then the use of proxies for scale economies, such as minimum efficient scale or the cost disadvantage ratio [Caves et al. (1975)] in industry-level studies will reduce but not eliminate the bias in the estimation of market concentration effects [Ravenscraft (1980)]. Our argument may be extended to allow for relationships which are more complex than eq. (1). Gale (1972) concludes that the impact of market share on profitability depends on the interaction of market share with concentration. This may be modeled by including in eq. (1) a term which is the product of market share and the Herfindahl index. Upon aggregation to the industry level, such a variable is transformed into the square of the Herfindahl index. It follows that an estimated quadratic effect of market concentration on profitability at the industry level may reflect the interaction of market share and market concentration. Eq. (1) assumes that the correct specification of the market concentration effect is as a continuous variable. If the correct specification of the market concentration effect at the disaggregate level is a dummy variable keyed on some critical concentration level, then our aggregation argument implies that the correct specification of an industry-level profitability equation includes both the Herfindahl index (by aggregation from market shares) and the dummy variable. Such sharp differences in functional form may be sufficient to mitigate the confounding of market share and concentration effects [Ravenscraft (1980)]. The force of the aggregation argument is not restricted to the analysis of profitability. Our argument shows that an industry-level study of advertising intensity (advertising per dollar of sales) can only estimate the combined impact of market share and market concentration. A quadratic impact of market concentration on advertising intensity at the industry level [Greer (1971)] may simply reflect an interaction between market share and market concentration at the disaggregate level.
164
S. Martin, D.J. Ravenscraft
/ Aggregation
and industrial profitability
studies
Empirical tests We report here results obtained using data for the year 1975, collected by the Line of Business Program of the Federal Trade Commission. The LB Program surveys 475 diversified firms. Each firm reports separately on its operations in different industries, following an industrial classification which is between the 3- and 4-digit SIC levels. By combining LB data with industry-level data from familiar sources, we can examine profitability at the LB level and avoid the aggregation problem outlined above. Martin (1981) estimates a structural equation explaining LB profitability as part of a simultaneous system. Profitability is measured as sales less traceable expenses, as a percentage of sales. Common costs of the firm are not allocated to the LB level. Market share figures combine reported LB sales and industry sales figures from the 1975 Annual Survey of Manufactures. An approximate Herfindahl index of Schmalensee (1977) is used as a measure of market concentration. An additional 37 explanatory variables control for differences across firms and industries. For a sample of 2297 LBs, the estimated effects of market share and market concentration are PCM75 = 10.6796MS75 (3.1034)
-40.2362HERF72 (5.7408)
+ ...
(5)
(asymptotic f-statistics in parentheses). Although the estimated impact of market share is positive, as expected, the market concentration index has a negative impact on profitability. The implied industry-level combined effect, the sum of the two coefficients, is negative, which contrasts with most industry-level studies. These results are robust to variations in specification. In particular, Ravenscraft (1981) obtains qualitatively similar results. He defines profitability so that common costs of the firm are allocated to the LB level. He measures market concentration by the four-firm seller concentration ratio, not the approximate Herfindahl index. He allows for interaction effects, and employs an alternative set of additional explanatory variables. The estimated effect of the market concentration variable remains significantly negative. However, the negative effect of concentration on profitability is smaller than market share’s positive effect. The combined effect of market share and market concentration on profitability implied by the Ravenscraft estimates is thus positive.
S. Martrn, D.J. Ravenscraft
/ Aggregation
and industrial profitability
studies
‘165
These results suggest that there is no general positive linear impact of market concentration of profitability, for manufacturing industries, which is independent of market share, at least for the mid-1970s. Gale and Branch (1982) have also reached this conclusion, using a distinct data base. Further research is needed, however, to fully understand the reasons behind the significantly negative impact of market concentration in the LB regressions.
References Caves, Richard E., Javad Khalilzadeh-Shirazi and Michael E. Porter, 1975, Scale economies in statistical analyses of market power, Review of Economics and Statistics 57, 133- 140. Collins, Norman R. and Lee E. Preston, 1969, Price-cost margins and industry structure, Review of Economics and Statistics 5 1, 27 l-286. Demsetz, Harold, 1973, Industry structure, market rivalry, and public policy, Journal of Law and Economics 16, l-9. Gale, Bradley T., 1972, Market share and rate of return, Review of Economics and Statistics 54, 412-423. Gale, Bradley T. and Ben S. Branch, 1982, Concentration versus market share: Which determines performance and why does it matter, Antitrust Bulletin, forthcoming. Greer, Douglas F., 1971, Advertising and market concentration, Southern Economic Journal 38, 19-32. Martin, Stephen, 1979, Entry barriers, concentration, and profits, Southern Economic Journal 46, 471-488. Martin, Stephen, 1981, Market, firm, and economic performance: An empirical analysis, Line of Business Program (Federal Trade Commission). Ravenscraft, David J., 1980, Price-raising and cost-reducing effects in profit-concentration studies: A Monte Carlo simulation analysis, Ph.D. dissertation (Northwestern University, Evanston, IL). Ravenscraft, David J., 1981, Structure-performance relationships at the Line of Business and industry level, Line of Business Program (Federal Trade Commission). Schmalensee, Richard, 1977, Using the H-index of concentration with published data, Review of Economics and Statistics 59, 186-193. Shepherd, William G., 1972, The elements of market structure, Review of Economics and Statistics 54, 25-37. Weiss, Leonard W., 1974, The concentration-profits relationship and antitrust, in: Harvey J. Golds&mid, H. Michael Mann and J. Fred Weston, eds., Industrial concentration: The new learning (Litte Brown, Boston, MA) 184-245.
Economics Letters 10 (1982) 161-165 North-Holland Publishing Company
AGGREGATION PROFITABILITY Stephen Michigan
David
AND STUDIES *
MARTIN State University,
East Lansing. MI 48824, USA
J. RAVENSCRAFT
Federal Trade Commision, Received
OF INDUSTRIAL
5 November
Washington,
DC, USA
1981
This letter shows that studies of profitability at the industry level cannot between the impact of market concentration and the impact of market share.
discriminate
Empirical studies of the impact of market concentration on industrial profitability generally find a positive relationship [Weiss (1974)]. The conventional interpretation of these results is that ‘ . . . concentration facilitates tacit or explicit collusion’ [Weiss (1974, p. 232)]. It is also generally accepted that market share will have an impact on firm profitability which is independent of the effect of market concentration [Gale (1972), Shepherd (1972)]. We show in this letter that if this independent impact of market share on firm profitability holds, then the conventional interpretation of industry-level profitability studies does not follow, since industry level results cannot distinguish the impact of market share from the impact of market concentration. * The representations and conclusions presented herein are those of the authors and have not been adopted in whole or in part by the Federal Trade Commission or its Bureau of Economics. The Assistant Director of the Bureau of Economics for Financial Statistics has certified that he has reviewed and approved the disclosure avoidance procedures used by the staff of the Line of Business Program to ensure that the data included in this paper do not identify individual company line of business data.
01651765/82/0000-0000/$02.75
0 1982 North-Holland
162
S. Martin, D.J. Ravenscraft
/ Aggregation
and rndustrial profitability
Suppose there is a linear relationship between market concentration, and firm profitability: v,JS,,
= (Y+ ,&VS,, + yHERF, +
firm
.. .
The rate of profit (r,,) on sales (S,,) of firm i in industry by the market share of firm i in industry j, MS, = 4,/S,
HER?
market
share,
(1)
j is explained
(2)
3
by the Herfindahl
studies
index of market
= 2 (MS,,)‘,
concentration, (3)
and by other factors which we omit from explicit consideration here [see Martin (1979) or Martin (1981) Ravenscraft (1981)]. Eq. (1) may be aggregated from the division of the firm level to the industry level by multiplying both sides of the equation by MS,, and summing over all firms in the industry; the result is r,,‘S,=a+(p+y)HER~+
... .
(4)
It follows that if eq. (1) represents an accurate model of the impact of market share and market concentration on the profitability of the divisions of firms, then industry-level studies of profitability cannot distinguish between market concentration effects (the coefficient y) and firm specific market share effects (the coefficient p). The most that can be estimated is the industry-level combination of the two effects. The industry average rate of profit on sales corresponds to what is probably the most common measure of industrial profitability in crosssection studies, the price-cost margin [Collins and Preston (1969)]; it can also be computed from Internal Revenue Service data. Studies of industrial profitability are generally robust to the use of alternative measures of profitability [Martin (1979)]. Measuring profitability in different ways will not avoid the problem identified here. In view of the high correlation between alternative measures of market concentration, the conclusion that industry-level studies of profitability can at most estimate the combined impact of market concentration and market share may be extended to studies which measure market con-
S. Martin, D.J. Ravenscraft
/ Aggregation
and industrial profitability
studies
/ 163
centration by seller concentration ratios. This is confirmed by Ravenscraft (1980), using a Monte Carlo approach. He shows that if the true measure of market concentration is the four-firm seller concentration ratio instead of the Herfindahl index, industry level studies still provide a biased estimate of market concentration effects. As noted by Gale (1972, p. 413), market share may represent either market power at the firm level or the realization of economies of scale. The latter interpretation is emphasized by Demsetz (1973). If this scaleeconomy interpretation is valid, then the use of proxies for scale economies, such as minimum efficient scale or the cost disadvantage ratio [Caves et al. (1975)] in industry-level studies will reduce but not eliminate the bias in the estimation of market concentration effects [Ravenscraft (1980)]. Our argument may be extended to allow for relationships which are more complex than eq. (1). Gale (1972) concludes that the impact of market share on profitability depends on the interaction of market share with concentration. This may be modeled by including in eq. (1) a term which is the product of market share and the Herfindahl index. Upon aggregation to the industry level, such a variable is transformed into the square of the Herfindahl index. It follows that an estimated quadratic effect of market concentration on profitability at the industry level may reflect the interaction of market share and market concentration. Eq. (1) assumes that the correct specification of the market concentration effect is as a continuous variable. If the correct specification of the market concentration effect at the disaggregate level is a dummy variable keyed on some critical concentration level, then our aggregation argument implies that the correct specification of an industry-level profitability equation includes both the Herfindahl index (by aggregation from market shares) and the dummy variable. Such sharp differences in functional form may be sufficient to mitigate the confounding of market share and concentration effects [Ravenscraft (1980)]. The force of the aggregation argument is not restricted to the analysis of profitability. Our argument shows that an industry-level study of advertising intensity (advertising per dollar of sales) can only estimate the combined impact of market share and market concentration. A quadratic impact of market concentration on advertising intensity at the industry level [Greer (1971)] may simply reflect an interaction between market share and market concentration at the disaggregate level.
164
S. Martin, D.J. Ravenscraft
/ Aggregation
and industrial profitability
studies
Empirical tests We report here results obtained using data for the year 1975, collected by the Line of Business Program of the Federal Trade Commission. The LB Program surveys 475 diversified firms. Each firm reports separately on its operations in different industries, following an industrial classification which is between the 3- and 4-digit SIC levels. By combining LB data with industry-level data from familiar sources, we can examine profitability at the LB level and avoid the aggregation problem outlined above. Martin (1981) estimates a structural equation explaining LB profitability as part of a simultaneous system. Profitability is measured as sales less traceable expenses, as a percentage of sales. Common costs of the firm are not allocated to the LB level. Market share figures combine reported LB sales and industry sales figures from the 1975 Annual Survey of Manufactures. An approximate Herfindahl index of Schmalensee (1977) is used as a measure of market concentration. An additional 37 explanatory variables control for differences across firms and industries. For a sample of 2297 LBs, the estimated effects of market share and market concentration are PCM75 = 10.6796MS75 (3.1034)
-40.2362HERF72 (5.7408)
+ ...
(5)
(asymptotic f-statistics in parentheses). Although the estimated impact of market share is positive, as expected, the market concentration index has a negative impact on profitability. The implied industry-level combined effect, the sum of the two coefficients, is negative, which contrasts with most industry-level studies. These results are robust to variations in specification. In particular, Ravenscraft (1981) obtains qualitatively similar results. He defines profitability so that common costs of the firm are allocated to the LB level. He measures market concentration by the four-firm seller concentration ratio, not the approximate Herfindahl index. He allows for interaction effects, and employs an alternative set of additional explanatory variables. The estimated effect of the market concentration variable remains significantly negative. However, the negative effect of concentration on profitability is smaller than market share’s positive effect. The combined effect of market share and market concentration on profitability implied by the Ravenscraft estimates is thus positive.
S. Martrn, D.J. Ravenscraft
/ Aggregation
and industrial profitability
studies
‘165
These results suggest that there is no general positive linear impact of market concentration of profitability, for manufacturing industries, which is independent of market share, at least for the mid-1970s. Gale and Branch (1982) have also reached this conclusion, using a distinct data base. Further research is needed, however, to fully understand the reasons behind the significantly negative impact of market concentration in the LB regressions.
References Caves, Richard E., Javad Khalilzadeh-Shirazi and Michael E. Porter, 1975, Scale economies in statistical analyses of market power, Review of Economics and Statistics 57, 133- 140. Collins, Norman R. and Lee E. Preston, 1969, Price-cost margins and industry structure, Review of Economics and Statistics 5 1, 27 l-286. Demsetz, Harold, 1973, Industry structure, market rivalry, and public policy, Journal of Law and Economics 16, l-9. Gale, Bradley T., 1972, Market share and rate of return, Review of Economics and Statistics 54, 412-423. Gale, Bradley T. and Ben S. Branch, 1982, Concentration versus market share: Which determines performance and why does it matter, Antitrust Bulletin, forthcoming. Greer, Douglas F., 1971, Advertising and market concentration, Southern Economic Journal 38, 19-32. Martin, Stephen, 1979, Entry barriers, concentration, and profits, Southern Economic Journal 46, 471-488. Martin, Stephen, 1981, Market, firm, and economic performance: An empirical analysis, Line of Business Program (Federal Trade Commission). Ravenscraft, David J., 1980, Price-raising and cost-reducing effects in profit-concentration studies: A Monte Carlo simulation analysis, Ph.D. dissertation (Northwestern University, Evanston, IL). Ravenscraft, David J., 1981, Structure-performance relationships at the Line of Business and industry level, Line of Business Program (Federal Trade Commission). Schmalensee, Richard, 1977, Using the H-index of concentration with published data, Review of Economics and Statistics 59, 186-193. Shepherd, William G., 1972, The elements of market structure, Review of Economics and Statistics 54, 25-37. Weiss, Leonard W., 1974, The concentration-profits relationship and antitrust, in: Harvey J. Golds&mid, H. Michael Mann and J. Fred Weston, eds., Industrial concentration: The new learning (Litte Brown, Boston, MA) 184-245.