size of firm, oligopoly, and research: a comment

Size of Firm, Oligopoly, and Research: A CommentAuthor(s): F. M. SchererSource: The Canadian Journal of Economics and Political Science / Revue canadienned'Economique et de Science politique, Vol. 31, No. 2 (May, 1965), pp. 256-266Published by: Wiley on behalf of Canadian Economics AssociationStable URL: http://www.jstor.org/stable/140068 .

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NOTES

SIZE OF FIRM, OLIGOPOLY, AND RESEARCH: A COMMENT'

F. M. SCHERER Princeton University

In the February 1964 issue of this JOURNAL, Professor D. Hamberg, in a statistical analysis covering 340 large firms, found little support for the hypothesis that the intensity of 1960 research and development employment increased with firm size.' I should like to call attention to some problems which affect the analysis and the conclusions.

Hamberg's procedure first of all raises philosophical questions related to the blossoming field of statistical decision theory. He estimated regressions of the forn:

(1) Yi aXibei,

or in logarithmic form,

(2) logYi-loga+b logXi+ei,

where Yi is R&D employment of the ith firm, Xi is some firm size variable, and Ei is an error term. If the exponent b of equation (1) is greater than 1.0, research intensity presumably increases with firm size, while if b is less than 1.0, it decreases with firm size. Eight of the eleven major (two-digit) industries listed in his Table VI had b's greater than 1.0 when employment was the firm size variable; seven when a figure for assets was the size variable. However, only two of these passed a statistical significance test at the .05 level. Hamberg therefore concluded that there is solid evidence suggesting increasing research intensity with increasing size only for two industries.

This conclusion rests upon the choice of the .05 rule, which, like the caste system, depends mainly upon tradition for justification. The .05 rule manifests the agnostic's outlook on life; it means that one is willing to risk being wrong only five times in 100 in admitting the existence of some postulated pheno- menon. But what about the risk of wrongly denying that size does make a difference in research intensity? The .05 rule implies a much higher risk of this second type, and to a policy-maker concerned with economic growth, this risk of overlooking a potentially important stimulant may be the one to mini- mize. Such a policy-maker might seriously consider accepting b coefficients for the chemicals, electrical equipment, motor vehicle, and machinery industries

*The research underlying this paper was supported by a grant from the Inter-University Committee on the Microeconomics of Technological Change, sponsored in turn by the Ford Foundation. Use was also made of computer facilities supported in part by National Science Foundation grant NSF-GP579. I am indebted to Mrs. Noah Meltz for help in collecting data. 1"Size of Firm, Oligopoly, and Research: The Evidence," this JOURNAL, Feb. 1964, 62-75.

XXXI, no. 2, May/mai, 1965



Notes 257

as "best estimate" evidence of a favourable role for firm size, even though they pass significance tests only at the .10, .20, or .30 levels. The case for accepting more "Type I" risk is strengthened by the fact that Hamberg employed virtually all available observations within the population of large firms with which he was concerned, at least for the year 1960. And when we take into account evidence from prior years, Hamberg's results receive still more support. Wor- ley's findings in applying equation (1) to a more limited sample of 1955 R&D employment data match Hamberg's for each of the seven industries with comparable definitions.2

Thus, if the over-all approach pursued by Worley and Hamberg were valid, I should be very much inclined to go out and beat the drum for corporate bigness. But therein lies the second rub. The samples drawn by Worley and Hamberg were neither random nor exhaustive. Hamberg in particular was prevented from exhausting all observations for the 500 largest US industrial corporations partly because some industries embraced too few listed firms, but also because data on R&D employment were not available for all the firms. In connection with a study of inventive activity within the 500 largest US corporations I ran into the same problem. My inventive output variable was the number of patents issued to the firms in 1959, and because it takes four years on the average for a patent application to work its way through corporate channels and the US Patent Office, I was also concerned with research and development manpower inputs for 1955. R&D employment figures were listed in the National Research Council's 1955 survey for only 352 of the 448 firms comprising my basic sample.3 Some of the 96 absentee firms presumably failed to enumerate their R&D staffs for reasons of secrecy, and some perhaps because they did not know how many researchers they employed. But it was quite evident that many firms reported no R&D personnel because they employed none. Of the 96 unlisted firms, 41 per cent obtained no patents in 1959 and 70 per cent obtained four or fewer patents. (The mean number of patents per firm was 36.7.) Alternatively, among the 83 firms out of 448 with no patents, nearly half were also not listed in the National Research Council's census.

It seems almost certain that if Hamberg had been able to get data for every firm in his initial sample, he would have found a substantial number of zero values in his 1960 R&D employment vector. But in computing the linearized regression of Y _ aXb, how does one take the logarithm of Y = 0?

This is no picayune point. Like Hamberg, I was interested in whether the inventive activity of manufacturing corporations increased more or less than proportionately with size. Unlike him, I took as my basic measure of inventive activity the number of patents received, rather than R&D employment, partly because patent data are available for virtually all corporations. The b exponent test of equation (1) is an elegant and hence attractive one. As mentioned, however, 83 of the 448 firms in my sample received no patents in 1959. Still, 2J. S. Worley, "Industrial Research and the New Competition," Journal of Political Eco- nomy, April 1961, 183-6. 3US National Academy of Sciences, National Research Council, Industrial Research Labora- tories of the United States, 10th ed., 1956. The 11th edition of this publication was the source of Hamberg's R&D data.



258 F. M. SCHERER

to see what would happen, three alternative conventions were tried. First, all firms with zero patents were deleted from the sample. Second, it was assumed that zero patents really meant one patent. Third, it was assumed that zero patents really meant one-half patent. In the logarithmic regression of 365 or 448 patent observations on three different scale variables, the resulting values of b were as in Table I. For all three scale variables, whether one infers on a best-estimate basis that inventive output increases more or less than proportionately with size depends almost entirely on the arbitrary convention adopted to deal with zero values!

TABLE I

Assets Sales Employment

Zeros deleted .795 .814 .920 Zero = 1.0 .925 .987 1.059 Zero = 0.5 1.014 1.062 1.158

The same problem has inevitably crept into Hamberg's analysis, given the evidence that most firms listing no R&D personnel in fact did little or no formal R&D. The form in which the National Research Council census of R&D employment is presented forced him to accept the deletion convention, which penalizes the case for bigness most. But it is impossible to say how great the penalty is, since any convention for handling zero values in a logarithmic analysis is necessarily arbitrary. The only conclusion possible is that the equation (1) approach is invalid whenever zero values exist in the relevant population.

With patent data this dilemma can be avoided completely by using non- linear regression equations which permit zero values; with R&D employment data the deletion bias is difficult to escape. There are also other advantages to be gained from fitting non-logarithmic equations, as we shall see in a moment.

First, however, a further methodological point must be pondered. The above table of b values shows that one's conclusion regarding the influence of firm size may also depend upon tlhe choice of a size variable. With patents, as with R&D employment, the greatest increases in intensity show up when employment is taken as the scale variable, while intensity increases least as a function of assets. Hamberg offered the reader a choice between assets and employment, but it would be preferable to identify the variable most suitable in terms of economic theory.

Ideally, we should also know why the results come out differently when different variables are used before making such a choice. Unfortunately, the truth is stubborn. I have three hunches, but two cannot be verified. One involves a statistical property. In the standard Markoff least squares regression model it is assumed that the independent variates are fixed; e.g., not subject to measurement errors. If there are errors in the Xi's of equation (2), the regression estimate of b will be biased toward zero-in this case downward. The greater the variance of the errors relative to the variance of log Xi, the



Notes 259

greater the bias will be.4 Now is it possible that the scale measurement errors relevant to a research intensity analysis are greatest for assets, second greatest for sales, and least for employment? Asset errors could intrude because of variations in accounting practices and acquisition price levels, while sales and (to a lesser degree) employment errors might be due to short-run demand fluctuations not affecting R&D or its output. Yet it is impossible to know defi- nitely whether such a hierarchy of errors actually exists. Even disregarding the measurement problem, one must first know what kind of error is relevant to the model, and this presupposes a theory identifying the optimal scale variable.

y

PI SIZE A,E FIGURE 1

My other two hunches concern the structure of American industry. First, the largest firms tend to be more capital-intensive and less employee-intensive than smaller firms. In my sample, the top-ranked 20 firms accounted for 40.0 per cent of the assets of all 448 firms, 38.1 per cent of the sales, and 34.9 per cent of the employees when separate rankings were prepared for each scale variable. The effects of this structural condition can be shown with a simplified illustration. Assume that the best-fitting regression of inventive activity Y on assets A is linear-e.g., line HOJ in Figure 1. Now suppose we introduce employment E as an alternative scale variable. Let point 0 be the locus of both the inventive output and the two scale variables' means. Because large firms are less employee-intensive than capital-intensive, the employment value for a representative giant firm will lie relatively closer to the centre of gravity 0 than will the asset value. Since inventive output Y is constant for that firm, the firm's Y E combination will lie at a point like K, to the left of point J represent- ing the YA combination. This shift bends the employment regression line upward from its centre of gravity 0, giving the non-linear relationship HOK. Other things being equal, the employment regression HOK will then have a higher b coefficient than the assets regression when equation (1) is fitted. Naturally, other things do not remain equal. Y-E observations for the smallest, 4See J. Johnston, Econometric Methods (New York, 1963), 148-50.



260 F. M. SCHERER

most labour-intensive firms will lie to the right of the analogous YA observations, e.g., at point L in Figure 1. This H-to-L shift might be sufficient to offset the J-to-K shift, leaving the YE relationship LOK linear when plotted on arithmetic co-ordinates, as in Figure 1. But even if these linearity-preserving shifts occur, the counterclockwise rotation from HOJ with assets to LOK with employment necessarily causes an increase in the estimated b coefficient when equation (2) is fitted on logarithmic co-ordinates. This is so because functions linear on arithmetic grids are linear on logarithmic grids only when their intercepts in the arithmetic case equal zero. Thus, the differences observed in b coefficients are undoubtedly due in part to differences in the concentration of assets as opposed to employment, although I have not found a way to estimate the magnitude of the effect.

My other structural hypothesis implicates electrical industry companies, which play an especially biasing role in analyses of research intensity for the members of all industries combined. The electrical industry accounted for a disproportionate 31 per cent of both 1955 R&D employment and 1959 patents in my sample, and (next to the combined textiles and apparel group) it had the most employees per billion dollars of sales among 14 industry groups. Due to an interaction of these special characteristics, electrical industry firms pulled the over-all estimate of b upward more forcibly with employment as the scale variable than with assets. The disparity in b estimates between the asset and employment regressions shrank from .125 with all non-zero patent observations included (as in the first row of Table I) to .084 when electrical industry observations were deleted.5

Assuming that these complex structural relationships are influencing the research intensity estimates, can we ascribe a causal role to them? If, for example, the high employment intensity of the electrical industry favours invention-perhaps because labour-saving inventions are easier to make than capital-saving inventions6 -a case could be argued on theoretical grounds for adopting employment as the preferred scale variable. But this is probably a spurious lead, since a survey showed that only about 3 per cent of patented inventions in the electrical industry involved production processes, the other 97 per cent being in the new product category.7 The structural argument for choosing assets in fact seems stronger, for the percentage of industry patents concerned with production processes is inversely correlated with employees per billion dollars of sales among eight two-digit industries on which comparable data were available, with a rank correlation coefficient of -.83. Still more generally, the relative amount of research and development stimulated by factor-saving considerations is small. Surveys cited by Gustafson disclosed that

5An even more violent change occurred in the correlation coefficients. In patenting, as in R&D employment, the highest correlations for the observations of all industries together were obtained with employment as the scale variable. But when the electrical industry firm observations were deleted, assets turned out to be more strongly correlated with patenting than employment. This was true when the variables were correlated in their natural form as well as when logarithms were taken. 6Cf. H. J. Habakkuk, American and British Technology in the Nineteenth Century (Cam- hridge, 1962), 163. 7F. M. Scherer, S. E. Herzstein, et al., Patents and the Corporation (rev. ed., Boston, 1959), 114.



Notes 261

less than one-fourth of US industrial research was directed toward cost-saving.8 In a random sample of 129 industrial patents issued in 1959, I found the pro- portion of process inventions to be 29 per cent. A larger but non-random survey indicated that only 13.5 per cent of industrial patents covered internally-used processes, as opposed to products.9 Clearly, the bulk of American industrial R&D is directed toward new products, and it is therefore not apt to be much affected by intra-industry factor intensities.

In view of this, it appears preferable on theoretical grounds to choose a scale variable neutral in terms of factor proportions. Value added would be most suitable, but the data are seldom available for individual firms. Sales data are the closest substitutes. They have two additional advantages. First, they yield b exponent estimates intermediate between those with assets and employment, and thus compromise the possible extremes. More compellingly, sales appears to be the principal scale variable taken into account by company decision- makers in setting R&D budgets.10 For these reasons, the following estimates are based upon sales rather than assets or employment. It must be recognized that if a better case could be made for the alternatives, somewhat less increase in R&D intensity with increasing size would be shown with assets, and somewhat more with employment.

II

To reassess the relationship between firm size and research and development employment, two kinds of regressions with quadratic and cubic terms were estimated, using 1955 data rather than the 1960 data analysed by Hamberg." First was the simple form:

(3) RD = c+d1Sj +d2S2+?d3S13+ei,

where RDQ is the ith firm's 1955 research and development employment, Si its 1955 sales, and ei an error term. The estimates afforded by such an equation tend to be most strongly influenced and indeed to some extent biased by obser-

8"Research and Development, New Products, and Productivity Change," American Eco- nomic Review, May 1962, 179. 9Scherer, Herzstein, et al., Patents and the Corporation. 1OCf. US National Science Foundation, Science and Engineering in American Industry (1956), 46-7; and Edwin Mansfield, "Industrial Research and Development Expenditures," Journal of Political Economy, Aug. 1964, 319-32. 11Although Hamberg used 1960 data, the base year 1955 is accepted here for two reasons. One is a practical one: I had data for that year only in usable form. But in addition, 1955 data give a better picture of private R&D incentives, since in that year the US federal government supported only (?) 47 per cent of all R&D performed by industry, compared to 58 per cent in 1960. See US National Science Foundation, Reviews of Data on Research and Development, April 1962, p. 2.

National Science Foundation expenditures survey data provide some insight into the possibility of structural changes in the period separating our data. Between 1955 and 1960 total R&D expenditure intensity, and perhaps therefore employment intensity, increased more for firms with more than 5,000 employees tlhan it did for smaller firms. But this was due almost entirely to an increase in the concentration of govemment R&D contract expenditures. See National Science Foundation, Research and Development in Industry: 1961, 39-45.



262 F. M. SCHERER

vations for the largest firms.'2 This is not completely undesirable, since large firms account for the lion's share of national output and presumably have the resources to support at least a comparable share of R&D activity. Still, to suppress the influence of corporate giants and give greater weight to relatively small firms, a logarithmic transformation of the sales variable (but not the R&D variable) was also taken:13

(4) RD1 = g + h, log Si + h2 (log Si)2 + h3 (logS4)3 + ui.

Let us consider first the relationship between R&D employment and sales for all industries combined-that is, with 352 observations. The results are most easily interpreted graphically (Figure 2), and so the equations are banished to an appendix.'4 The non-logarithmic equation (solid line) is rather violently non-linear, showing a declining rate of increase in R&D employment almost up to a local minimum at sales of $7 billion, after which pronounced increasing returns take over. This regression is very much influenced by a few extreme observations. In particular, giants like the Ford Motor Company (with 259 R&D employees in 1955) and US Steel (with 985) pull the curve to its minimum, while General Motors (with 13,340 R&D personnel) is solely respon- sible for the upswing.15 These large-firm influences are muffled by the logarithmic equation (dotted line), whose scale precludes visual identification of a very slight convex curvature between sales of $300 million and $700 million. This is followed by a steadily diminishing rate of increase in R&D employment for the larger firms. If the exceptional case of General Motors is excluded, the general picture is one of R&D employment increasing less than proportionately with sales among the corporate giants.

Research intensity, as the term was used by Hamberg, is found in Figure 2

120n the other hand, regressions of this fonn are biased in a less serious way by errors in measuring the scale variable, as discussed earlier. The greater such errors are, the more the evidence of either increasing or decreasing intensity will be obscured, since the non-linear coefficients will be biased towards zero. With the logarithmic approach of equation (2), the bias is consistently in the direction of showing decreasing intensity. 13See Edwin Mansfield, "Size of Firm, Market Structure, and Innovation," Journal of Poli- tical Economy, Dec. 1963, 565-7. It should be noted that both of the industry-by-industry analyses undertaken by Hamberg-a rank correlation of R&D employment per thousand employees with scale and the equation (1) test discussed earlier-give maximum relative weight to the smaller firms. The rank correlation approach, for example, implies that the difference of 128,000 employees between US Steel and Bethlehem Steel is equivalent to the difference of 200 employees between Lukens Steel and Granite City Steel. If, as I con- clude, research intensity increases with firm size for small but not for large firms, the emphasis on small firms in Hamberg's equation (1) tests could explain the predominance of b coefficients exceeding 1.0. In this respect it should also be noted that among the 448 firms in my full sample, the 73 firms with sales exceeding $500 million accounted for 63 per cent of the 1955 sales of all the sampled firms. This concentration of research-supporting potential is good reason for placing statistical emphasis on the behaviour of the largest firms. 14AJl coefficients in these two equations were statistically significant at the .05 level or higher. 15The great contrast between General Motors and Ford is clearly not due to an imbalance of defence orders, since General Motors' defence sales were only about three times Ford's in 1955. It seems to have two main grounds: the greater diversification of General Motors into such dynamic fields as electronics, and the tradition of technical conservatism inherited by Ford from the last years of the senior Henry Ford's reign. Financial and styling reforms came much more quickly during the administration of Henry Ford II than did changes in research and development policy.



Notes 263

11,000/

10,000/

9,o00

8,000s

7,000

6, * ... -0-- ./

6,000

3),000

1,000 s

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 30.0 11V3 12.0

1955 SAE (BILONS)

FIGURE 2. Regressions for all industries combined.

by the slope of a straight line drawn through the origin to a point on the fitted curves. It can readily be seen that both functions show research intensity reaching its maximum (a point of tangency between the straight line and the fitted curve) at sales levels below $500 million.16 At higher sales levels the tendency is toward declining intensity with increased sales, at least until the General Motors effect takes hold.

A picture similar to the aggregated analysis, but with more diversity, emerges when individual two-digit industry groups are examined. Graphs for six fairly homogeneous industries on which 20 or more observations were available are presented in Figure 3.17 The equations are again relegated to the appendix. Most of the coefficients are not statistically significant by conven- tional standards, in large measure because the linear, squared, and cubed sales variables are highly collinear, with intercorrelation coefficients running between .90 and .99. Therefore the results can only be viewed as best estimates of the -6See also Mansfield, "Size of Firm, Market Structure, and Innovation," who uses a similar methodology and reaches similar conclusions in his analysis of important innovations in four industries. Precise location of the scale conducive to maximum research intensity by this method is hazardous, since estimates for the smallest firms may be biased by small errors in the R&D function's intercept term estimate. The intercept estimates are subject to error not only because of random disturbances and curve-fitting problems, but also because no 1955 sales observations under $55 million were included in my sample. 17No attempt is made here to analyse eight other industry groups defined in connection with my study of corporate patenting. In most of these cases there were too few observations for a meaningful non-linear analysis. The aircraft industry is also excluded because private incentives have so little to do with a contractor's military R&D employment.



264 F. M. SCIERER

7,000,

500 6,000

400 i 5,000

~300

3,000 200 l FOOD AND TOBACCO

2.,000

100 / 1,000 CHEMICALS

.5 1.0 1.5 2.0 2.5 .5 1.0 1.5 2.0

1.955 SALES 1955 SALS (BILLIONS) (BILLIONS)

5,000 1C000

(34,00 800

3,OO ) 600

2,000) 400

1,000 PTOLU 200A

PRIMRY METALS

1.0 2.0 3.0 4.0 5.0 6.0 7.0 1.0 2.0 3.0 4.0 5.0 1955 SAILS (BILLIONS) 1955 SAULS (BILLIONS)

800 8,000

| 700 E' 7,000 co co,

600 /6,000.

500 *-... 5,000

400 '* 4,000 *ELCTRICAL

300 7 3,000

200- / MACHINERY 2,000

100 1,000

.25 .50 .D5 1.0) 15 .5 1.0 1.5 2.0 2.5 3.0

1955 SAIES (BILLIONS) 1955 S.-.LL3 (3sLLIONS)

FIGURE 3

structural pattern in 1955, along lines suggested in the opening pa,iragraphs of this comment.

In nearly every case the equations with logarithmic sales terms in Figure 3 imply that research intensity increases (usually slightly) with size aimlong tlle smallest and medium-sized firms. Declines tend to set in between sales of $200



Notes 265

million and $600 million, except that in the chemicals industry there are indi- cations of either increasing or constant intensity out to the largest firm (duPont) .18 Both the untransformed and the logarithmic equations show research intensity declining with size among larger firms in the non-chemical groups. However, in the primary metals industry the untransformed equation is pulled back into a stage of increasing intensity by US Steel-a leader in its own field, but a laggard compared to firms in more dynamic industries.

III

Several conclusions applicable at least to the year 1955 emerge from my analysis. First, the relationship between research and development employment and firm size commonly has at least one point of inflection and may in some cases not even be monotonic. Equation (1) fitted by Hamberg and Worley, while elegant, is unable to detect such structural features.19 Second, there is some indication that R&D employment intensity increases with size among firms with sales of less than roughly $500 million. An even more pronounced increase might be observed if zero observations could be included, since the firms among Fo-tune's 500 which presumably maintained no formal R&D organiza- tions were clustered in the sales range under $200 million.20 Finally, declining research intensity appears to be the dominant tendency among firms with sales greater than $500 million in 1955. One must, however, recognize important exceptions. The chemicals industry as a whole and the giant leaders of the automobile and steel industries displayed intensity increasing with sales.21

These findings, which agree closely with the results of my corporate patenting analysis and Mansfield's studies of major innovations and R&D spending, provide a perspective of the corporate research world somewhat at odds with Hamberg's statistical results. It is of course conceivable that the differences between my detailed findings and Hamberg's are due to changes in the structure of R&D employment over the five-year period separating our data. But recognizing the similarity between Hamberg's estimates for 1960 and those obtained by WNorley for 1955 with the same methods, I suspect that methodology lies nearer the heart of the problem. My results do, however, support the policy concltusion drawn by Hamberg: that gigantic scale is far from an essen- tial condition for vigorous industrial research and development activity, and that bigness may indeed be a stifling factor. 18M\ansfield also found the chemicals industry to be the only one with increasing intensitv in his analysis of R&D spending in five industries. "Industrial Research and Development Expenditures," 334. 19Becausc of its inflectionless character equation (1) also does not fit the 1955 R&D employment data as well as equations (3) and (4). The standard errors of estimate with all 352 available observations wvere 1,081 (employees) with equation (1), 999 with equation (4), and 927 with equiation (3). The differences between (1) and (3) are significant at the 1 per cent point in an F-ratio test. 20A11 of the 67 firms not listed in the 1955 National Research Cotuncil survey and which received four or fewer patents in 1959 had 1955 sales of less than $400 million. Thirty- seven of them had sales of less than $100 million, and 17 sales between $100 million and $199 million. 21Some hypotheses concerning these exceptions are presented in my paper, "Firm Size, Market Structure, Opportunity, and the Output of Patented Inventions," American Eco- nomic Review (forthcoming).



266 F. M. SCHERER

Appendix / Regression equations: 352 firms combined and six industries*

Industry R2 N

All combined RD =-.1 + 2.21 S - .49 S2 + .032 S3 .51 352 (.20) (.07) (.004)

RD = - 9.8 + 13.51 log S - 6.27 (log S)2 + 1.00 (log S)3 .43 352 (6.58) (2.51) (.31)

Food RD =-.04 + .54 S-.067 S2 - .041 S2 .67 55 (.20) (.243) (.075)

RD = 6.47-8.01 log S + 3.18 (log S) - .40 (log S)' .54 55 (3.40) (1.36) (.18)

Chemicalsf RD = .07 + 1.98 S + .40 S2 + .18 S2 .94 37 (.98) (1.52) (.57)

RD = -42.0 + 58.24 log S-26.76 (log S)2 + 4.12 (log S)' .94 37 (13.46) (5.56) (.75)

Petroleum RD =-.06 +.73 S + .19 S2 - .033 S3 .83 21 (.78) (.48) (.055)

RD = 6.7-6.57 log S + 1.72 (log S)2 _ .056 (log S)3 .83 21 (11.75) (4.27) (.507)

Primary metals RD = - .01 + .47 S - .27 s2 + .053 S3 .65 39 (.16) (.14) (.026)

RD = - 2.8 + 3.77 log S - 1.67 (log S)2 + .252 (log S)3 .60 39 (3.30) (1.28) (.161)

Machinery RD = .00 + .81 S + 1.56 s2 _ 1.78 S3 .33 .34 (1.72) (4.36) (2.61)

RD = 11.4-15.91 log S + 7.24 (log S)' - 1.05 (log S) .30 34 (18.06) (7.61) (1.05)

Electrical RD = .03 + 4.89 S + .46 s' - .40 S3 .84 31 (2.01) (1.94) (.45)

RD = 22.4 -26.37 log S + 9.33 (log S)2 _ .83 (log S)3 .81 31 (39.13) (15.54) (2.01)

'In the untransformed equations, 1955 sales are scaled in billions of dollars. In the logarithmic equations, sales are scaled in millions of dollars. fIncludes SIC 281 (industrial inorganic chemicals), 282 (industrial organic chemicals), and 283 (drugs and medicines) only.



size of firm, oligopoly, and research: a comment

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