l. Introduction
A companion paper to this one (Flath , 2009) estimates Cobb-Douglas production functions for 70 Japanese manufacturing industries, 1961-1990, and from these estimates constructs annual time series for industry price-cost margins.  Here, I explore the temporal relation between these price-cost margins and the annual time series of Herfindahl index of concentration in each industry.  Under the simple homogenous product Cournot model, industry price-cost margin is proportionate to Herfindahl, and the constant of proportionality is the reciprocal of elasticity of demand facing the industry.  If, on the other hand, each industry comprises a collection of price- setting and product differentiated firms –i.e is monopolistically competitive, or equivalently, in a Bertrand pricing equilibrium– then the industry price-cost margin is a weighted average of the reciprocal demand elasticities facing each firm.  A non-nested test based on Vuong (1989), comparing these two specifications for each of the 70 industries, at the ten percent significance level, favors the homogeneous product Cournot specification for ten industries and the product differentiated Bertrand specification for 44 of industries.  Further comparisons of each of these specifications with the hybrid specification that nests both of them lead to the conclusion that the simple Cournot specification is the most likely for five of the industries, the simple Bertrand specification is the most likely for 35 of them, and the hybrid specification is the most likely for 30. An earlier study of price-cost margins in Japanese manufacturing industries was performed by Ariga, Ohkusa and Nishimura (1999).  Their study focused on manufacturing firms rather than industries and demonstrated a positive but weak association between price cost margins and market shares, which is broadly consistent with my findings.
2. Price-cost margins
The price-cost margins from the companion paper to this one (Flath, 2009) are constructed from estimates of Cobb-Douglas production functions for 70 industries at the four-digit s.i.c. level. For each industry,  annual observations of output are constructed by deflating value of shipments by the annual average wholesale price index for the corresponding product.  The required matching of industries from the Census of Manufacturers (Ministry of International Trade and Industry, serial; and METI, url) with the product categories of the Wholesale Price Index (Bank of Japan, serial) limits the sample to a relatively small set of industries, but ones for which the output measure is accurate.  The appendix describes the data sources in more detail. In Flath (2009) I estimated an equation on the pooled annual time-series, cross-section of 70 industries at the four-digit s.i.c. level,  1961-1990.  The  regression equation is the following:
where the error term follows a first-order autoregressive (AR1) process:
Here Q it represents value of shipments by industry i in year t divided by average monthly wholesale price index for the corresponding product during the same year.  The labor input is L 41 defined as the number of workers employed in the industry i in year t.  And K it is the book value of the fixed tangible assets of the industry i at the beginning of year t.    This specification imposes constant returns to scale and allows for implicit deflation of book value of capital stock. Essentially, this means that the deflated capital stock series e A K it is measured in pan-industry efficiency units.  Any economy-wide technological advances or improvements in labor quality are reflected in the deflator e^t , leaving only industry-specific technological advances to the residual error term vit. From the estimates of these Cobb-Douglas production functions for each industry I constructed time series for the price-cost margins of each industry.  For details, refer to the paper (Flath, 2009).   In brief,  the method of construction follows the logic of Hall (1988).  The labor coefficients from the Cobb-Douglas production functions measure labor's share in total cost for each industry.  Price-cost margins are computed as the percentage by which value added minus total cost exceeds value of shipments  (where total cost is the wage bill divided by the Cobb- Douglas labor coefficient).  After dropping from the sample the four industries for which average price-cost margin was negative, the remaining average price-cost margins range from Glass Bulbs for Use in Cathode Ray Tubes at 1.2 percent to Sheet Glass at 45.4 percent.  The average price-cost margin across the 70 industries is 12.56 percent, with standard deviation 8.53%. The sample industries vary in concentration.  The average Herfindahl indices range from Sake at 0.005 to Pianos at 0.460.  The average Herfindahl index across the 70 industries is 0.155 with standard deviation 0.124. The object of the current paper is to consider how the annual time series for industry price- cost margins interact with Herfindahl indices of industrial concentration.  The question I address is for which, if any, of the industries do price-cost margin and Herfindahl index move together as the homogenous product Cournot model predicts?
3.  Herfindahl indices and price-cost margins
The Cournot model of a homogenous product oligopoly implies a precise relation between industry-level price-cost margin and Herfindahl index of concentration defined on shares of output.  Specifically, the industry price-cost margin equals the Herfindahl index divided by elasticity of market demand.  This has been well-known for many years.  See for example Cowling and Waterson (1976), or Tirole (1988), pp. 222-3.  Let us call this relationship between price-cost margin and Herfindal index "Model 1–Cournot".  The relationship follows directly from the fact that the price-cost margin of firm f in homogenous-product Cournot industry equilibrium equals its market share divided by the elasticity of market demand:
Here, p r is the firm's price, c r its marginal cost and s r its market share (that is share of industry sales revenue s t = p t q / ∑ p t q t ).  The industry price-cost margin m is, in general, a weighted average of the firms' price-cost margins, with weights equal to market shares:
So in the homogeneous-product Cournot equilibrium, industry price-cost margin equals the summation of squared market shares, or Herfindahl index, divided by elasticity of market demand:
I observe Herfindahl indices H n annually for each of the 70 industries, drawn from the Japan Fair Trade Commission data archives (JFTC ,1974, 1975;JFTC url;  Senou ,1983).  For each industry i, I regress these on the price-cost margin series m it as described by:
(6)

where  e1 t is a stochastic error term. In accordance with the theory I impose a zero intercept. An alternative formulation (call it ''Model 2–Bertrand'') is that each firm is in effect an independent monopoly, and the industry price-cost margin is simply a weighted average of the reciprocal demand elasticities  facing each firm, the weights corresponding to market shares.  If the demand elasticities facing each firm are similar to one another, then the industry price-cost margin is the reciprocal of that demand elasticity and this remains true even as the market shares of firms vary in response to innovation and changing input prices.  Under this framework, for each industry i, we have:
(7)

Yet a third specification nests the two previous ones:
(8)

It is possible to construct an example that supports the Hybrid specification.  Suppose that firms in an industry are selling both to loyal customers who either buy from their one favorite firm or not at all, and to less loyal customers who only buy from the firm with the lowest price.  Each firm may have its own loyal customers.  If the firms are price discriminating, charging higher prices to loyal customers, while acting as Cournot oligopolists in selling to the price conscious customers, it can lead to Model 3. It is a kind of hybrid of Bertrand and Cournot.  In particular, if the fraction λ of each firm's own sales that are to loyal customers is the same fraction for all the firms, and the firms are price discriminating as just suggested, then the price-cost margin of firm f is
where ξ t is the demand elasticity of the loyal customers and ξ is the market demand elasticity in the Cournot segment.  The industry price-cost margin is
This is one motivation for the Model 3. For each of the 70 industries in the sample, I next construct specification tests for pairwise comparisons among the models, and from these statistics construct an overall likelihood for each specification for each industry.
4.  Specification Tests
4.1. Nonnested alternatives: 1–Cournot versus 2–Bertrand I estimated both the 1–Cournot and 2–Bertrand regressions for each industry using maximum likelihood, here equivalent to OLS, and also computed the value of log likelihood function for each.  (Note that log likelihood = -n/2 ln(2πSSE/n) -n/2 ).  These results are represented in Appendix Table A1. The two alternative specifications here are non-nested. Accordingly I draw on the work of Vuong (1989) who proposed a likelihood ratio test statistic for model selection among non-nested alternatives.  The Vuong statistic is a normalization of the likelihood ratio that is asymptotically distributed as a standard normal variate under reasonable conditions. Specifically, denote the value of the log likelihood for a single observation by
The value of log likelihood function for a regression specification is the sum of L 4 over all observations i. The Vuong statistic for comparing two alternative non-nested specifications (1–Cournot and 2–Bertrand) is with obvious notation defined as follows.
These Vuong statistics and log likelihoods of the alternate specifications are reported in Appendix Table A2.  In  only 19 of the industries did the likelihood function favor Cournot over Bertrand.  In only ten of these did the data clearly distinguish between the two specifications (i.e. at the ten percent significance level), based on the Vuong statistic.  The ten industries are: BICYCLES JUTE YARN MANMADE-GRAPHITE ELECTRODES ORDINARY STEEL PIPES AND TUBES RECORDS STORAGE BATTERIES SUGAR SYNTHETIC RUBBER THERMOS BOTTLES WHEAT FLOUR There were far more industries, 44 in all, in which the likelihood ratio strongly favored the Bertrand specification over the Cournot one (again, at the ten percent significance level).  That leaves 16 industries for which the Vuong test fails to distinguish between the 1–Cournot and 2–Bertrand specifications, at the ten percent significance level.
4.2. Nested alternatives: 3–Hybrid versus 1–Cournot, or 2–Bertrand
The 3–Hybrid specification nests 1–Cournot and 2–Bertrand.  Specification tests between Hybrid and Cournot, and between Hybrid and Bertrand, are based on the t-statistics for the intercept and slope coefficients in linear regression of price-cost margin on Herfindahl index (the Hybrid specification).   These estimates are reported in Appendix Table A3.  The statistical test between the Cournot and Hybrid specification is the p-value for the null hypothesis that the intercept in the Hybrid specification is greater than zero.  This p-value is the area under the t- distribution, to the right of the t-statistic, for estimated intercept in the Hybrid specification.  It represents the likelihood that the intercept is positive and so the Hybrid specification is superior to the Cournot specification in which the intercept is zero. Similarly, the statistical test between the Bertrand and Hybrid specification is the p-value for the null hypothesis that the slope in the Hybrid specification is greater than zero.  This p-value represents the likelihood that the slope is positive and so the Hybrid specification is superior to the Bertrand specification in which the slope is zero. The results are these.  At the ten percent significance level, the Cournot specification was better than  Hybrid for only one of the industries CAST IRON PIPES AND TUBES.  One other industry RECORDS just missed at the ten percent significance level.  For 38 of the industries, the Hybrid specification was better than Cournot, at the ten percent significance level.   For 17 of the industries, the Bertrand specification is better than the Hybrid at the ten percent significance level, and for 15 of the industries the Hybrid specification is better.
4.3  Likelihoods of each of the three specifications
From the three pairwise tests among the different specifications, I now construct  likelihoods of each specification, using Bayes' rule.  Here I make the natural assumption that the likelihood of Cournot versus Hybrid is uninformative regarding the likelihood of Cournot versus Bertrand. And the likelihood of Bertrand versus Hybrid is uninformative regarding the likelihood of Cournot versus Bertrand.  Then the likelihood of the Cournot specification is its likelihood versus Bertrand, times its likelihood versus Hybrid.  Similarly, the likelihood of the Bertrand specification is its likelihood versus Cournot, times its likelihood versus Hybrid.  The likelihood of the Hybrid specification equals one minus the likelihoods of Cournot and Bertrand. Here is the reasoning.  Models "1", "2" and "3" are mutually exclusive.   Denote the probability that model 1 is the true one by P(1).   Let A=not 1, B=not 2 and C=not 3.  Denote by P(C|B)=P(1|B) the conditional probability of C, given B.  Thus, P(B|C) is the likelihood of Model 1 versus Model 2 based on the Vuong test, and P(C|B) is the likelihood of Model 1 versus Model 3 based on the t-test that the intercept is positive in the Model 3 specification.  P(B(1) = 1, by definition.  Bayes' rule is (13) P(C|B) =  P(B|C) P(C) / P(B), or (14) P(1|B) =  P(B|1) P(1) / P(B) =  P(1) / P(B). Thus (15) P(C|B) = P(1|B) =  P(1) / P(B). I assume that P(C|B) is uninformative regarding P(B|C), meaning that (16) P(B|C) = P(B) , or, in words, the posterior probability of B conditional on C, equals the prior probability of B. But then, from equation (15), we have that (17) P(B|C) P(C|B) = P(1) . By similar logic, I assume that (18) P(A|C) = P(A) and deduce that
(19)
P(A|C) P(C|A) = P(2) .
The likelihoods of each model, computed in the way just described, are reported in Table 1. 1–Cournot is the most likely for five of the industries, 2–Bertrand is the most likely for 35 of the industries, and the 3–Hybrid specification is the most likely for 30 of the industries.  The five for which Cournot is the most likely are: CAST IRON PIPES AND TUBES JUTE YARN RECORDS SUGAR THERMOS BOTTLES. If we consider only the 18 industries for which the likelihood of one specification was at least 90 percent, then there were 11 for which Bertrand was preferred, seven for which Hybrid was preferred, and none for which Cournot was preferred.  RECORDS just misses with 89 percent likelihood of Cournot.  A summary of the results for all the specification is in  Table 2. Some statistics describing the five industries  for which the simple Cournot specification was the most likely are shown in Table 3.  And comparable statistics for the eleven industries with likelihood of Bertrand specification greater than 90 percent and the seven with likelihood of Hybrid specification greater than 90 percent are in Table 4 and Table 5. The statistics in these tables include reciprocals of estimated coefficients for preferred specifications, average Herfindahl index, average price-cost margin, and elasticity of output with respect to labor from the estimated Cobb-Douglas production functions.   None of the differences in average among the Cournot, Bertrand and Hybrid groups, for Herfindahl, price-cost margin and labor elasticity, are statistically significant, based on a t-test.  The reciprocals of estimated coefficients for the Cournot and Bertrand specifications represent implied elasticities of market demand.  This elasticity of demand ranges from 0.4 to 3.0 for the five putative Cournot industries and from 2.2 to 50.0 for the eleven Bertrand industries.  The Bertrand industries generally face more elastic demand than the Cournot industries.  The reciprocals of intercept and slope for the Hybrid industries represent weighted elasticities of demand, the weights being the reciprocals of fraction of sales to loyal customers and others.  Because we cannot infer these weights the estimates are not easy to characterize. The homogenous product Cournot model is a good starting point for thinking about many topics in industrial organization.  The reasons are many. The model is simple yet elegant, in that it represents the unique Nash solution to a well-defined game.  It can be manipulated easily and comports with common sense notions of the way prices, profits and market shares might respond to mergers, technological advance, entry, and exit.  But as industrial organization specialists turn toward econometric analysis, the simple Cournot model is a lot less useful.  For example, the Berry, Levinson, and Pakes (BLP) approach to intra-industry demand estimation presumes Bertrand pricing.  With the wide application of the BLP technique over the last few years, the presumption seems to have settled in that the typical industry actually is best regarded as one in which price-setting firms face differentiated demand.  The simple, homogenous product Cournot model, so useful for algebraic explorations, is not in fact empirically apt. Or is it? If the simple Cournot model did represent an actual industry very well, how would we know that? And how rare are such industries? In fact, are there any such industries? This paper has taken a modest step toward answering these questions.  And the answer is that homogenous product Cournot industries may exist but are rare. This paper explored a panel data set matching establishment-based production statistics from Japan's Census of Manufacturers with wholesale price indices from the Bank of Japan, and Herfindahl indices from the Japan Fair Trade Commission.  The data include annual observations over the period 1961-1978 for 70 industries at the four-digit s.i.c. level.  I estimated Cobb- Douglas production functions and used these to construct annual time series for price-cost margins in each industry. Industry price-cost margins in only 7 percent of the industries varied with temporal changes in Herfindahl index as the simple Cournot model would predict.  Far more of the industries, 50 percent of them,  exhibited stable price-cost margins as industrial concentration fluctuated, as the product differentiated Bertrand model might predict.  The remaining industries were a hybrid of Cournot and Bertrand.  From this sample, the modal Japanese manufacturing industry is a product differentiated Bertrand industry in which the seven or so major firms each face a demand with elasticity of ten or greater. I have constructed a panel data set by merging 1961-1990 calender year observations from three different sources for the intersecting subset of four-digit s.i.c. industries, of which there were 70. From Japan’s Census of Manufacturers – Report by Industries , listed in the references under the author MITI, we draw value-added, value of shipments, employment, wages, and book value of fixed tangible assets.  The book value of tangible assets is observed for establishments employing ten or more. All other items are for establishments employing four or more.  The book value of tangible assets is observed at the beginning of the calender year.  These data and continuation of like data through 2002,  are available for downloading from the website of the Ministry of Economy, Trade and Industry (METI) here: http://www.meti.go.jp/statistics/kougyou/arc/index.html From two published sources and a website we compile observations of Herfindahl index of industrial concentration of production.  The two published sources are JFTC (1975) and Senou (1983).  These data are collected by the Japan  Fair Trade Commission in fulfillment of its charge under the antimonopoly law .  The two sources comprise overlapping time-series, respectively: (1960-1972) and (1971-1980). The series are continued (1975-2002) in data posted on the website of the Japan Fair Trade Commission from which I was able to extend my data through 1990: http://www.jftc.go.jp/ruiseki/ruisekidate.htm , The FTC observations on Herfindahl indices, both from the published sources and the web site, represent the summation of squared shares of industry production for nearly 500 industries. These data are,  in principle,  shares of physical units produced, not shares of revenues.    But apparently for many of the industries a production index is used in lieu of physical units. Finally I collect the monthly observations of wholesale price index series for each commodity, from the Bank of Japan for 1962-1990.  Monthly data from 1985 on are available in electronic format from the website of the BOJ here: http://www.boj.or.jp/en/type/stat/dlong/index.htm Earlier data were drawn from the BOJ serial Price Indices Annual.  From these sources I converted linked series to common 1980 base year units and calculated calender year averages for each. The three sets of data correspond to imperfectly matched industries.  I was able to identify an overlapping subset of 74 industries with observations from all three sources (corresponding to the four-digit s.i.c. level in the Census of Manufacturers ).  In the current study I dropped the four of these for which average price-cost margin was negative, leaving 70 industries in all.   This is a relatively small subset of any of the three sources.  For example there are about 450 industries for which the JFTC reports Herfindahl indices and more than a thousand commodities for which the BOJ tracks wholesale price indices.  And Japan's  Census of Manufacturers identifies around 700 four-digit s.i.c. industries. Appendix Table A1.  Regression analysis of average industry price-cost margin: Cournot versus Bertrand m, = β 1 H, + e1, , Model 2–Bertrand: m t = β o + e2 , t=1,..., T t=1,..., T.
13

1 4

Appendix Table A2.  Vuong Statistic for Test between Model 1–Cournot and Model 2–Bertrand Model 1–Cournot:
Model 2–Bertrand : m, = βρ + e2, , t=1,..., T.

17

18

Appendix Table A3.  Regression analysis of average industry price-cost margin: m, =  β o  + β i H,  + e3, , t=1,..., T.

21

22

23
Ariga, Kenn; Ohkusa, Yasushi and Nishimura, Kiyohiko G. (1999). "Determinants of Individual-Firm Markup in Japan: Market Concentration, Market Share, and FTC Regulations", Journal of the Japanese and International Economies, Vol. 13, Issue 4 (December), pp. 424-450 Bank of Japan (Serial). Price Indexes Annual. Nihon ginkou toukeikyoku, Serial [1970-2002]. http://www.boj.or.jp/en/type/stat/dlong/index.htm Cowling, Keith and Michael Waterson.  (1976).  "Price-Cost Margins and Market Structure", Economica, Vol. 43 (August), pp. 267-274. Flath, David.  (2009).  "Industrial Concentration, Price-cost Margins, and Innovation," Institue of Social and Economic Research (Osaka University), Discussion Paper no. 739. Hall, Robert E. (1988).  “The Relation between Price and Marginal Cost in U.S. Industry,” Journal of Political Economy, vol. 96, no. 5 (Oct.), pp. 921-947. JFTC [kousei torihiki iinki jimu kyoku hen (Japan Fair Trade Commission, executive office, ed.)] (1974). Dokusen kin konkai shiryou shuu IV (Antitrust meeting data set), oukurasho insatsu kyoku seizou. JFTC [kousei torihiki iinki jimu kyoku hen (Japan fair trade commission, executive office, ed.) ] (1975). Shuuyou sangyou ni okeru ruiseki seisan shucchuudo to haafindaaru shisuu no suii (shouwa 35 nen - 47 nen) (Cumulative concentration and Herfindahl index measures of industrial concentration in major industries, 1960-1972), zaidan houjin kousei torihiki kyoukai. JFTC: http://www.jftc.go.jp/ruiseki/ruisekidate.htm , METI : http://www.meti.go.jp/statistics/kougyou/arc/index.html Ministry of International Trade and Industry (Serial). Kougyou toukei hyou (Census of Manufacturers – Report by Industries). Senou, Akira  (1983).  Gendai nihon no sangyou shucchuu (Industrial concentration in contemporary Japan), nihon keizai shinbunsha, 1983. Tirole, Jean  (1988).  The Theory of Industrial Organization, MIT Press. Vuong, Quang H.  (1989) "Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses", Econometrica, vol. 57, no. 2 (March), pp. 307-333.
Table 2. Results of Specification Tests. Numbers of industries in each category at ten-percent statistical significance.
preferred specification:
0
7
52 Numbers of industries in each category; most likely specification, regardless of statistical signifcance.
slope > 0 preferred specification:
p-value for  Likelihoods Hybrid
S
Table 3.  Five industries for which Cournot specification was the most likely. Table 4.  Eleven industries for which likelihood of Bertrand specification was at least 90 percent.
Table 5.  Seven industries for which likelihood of Hybrid specification was at least 90 percent.