How Much Does Industry Matter? TORIo Richard P Rumelt Strategic Management Journal, Vol 12, No. 3(Mar, 1991), 167-185 Stable url: http://linksjstor.org/sici?sici=0143-2095%28199103%0291293a3%03c167%03ahmdim%3e2.0.c0%03b2-v Strategic Management Journal is currently published by John wiley sons Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.htmlJstOr'sTermsandConditionsofUseprovidesinpartthatunlessyou have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://wwwjstor.org/journals/jwiley.html Each copy of any part of a jSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission jStOR is an independent not-for-profit organization dedicated to creating and preserving a digital archive of scholarly journals. For more information regarding JSTOR, please contact support@jstor. org http://wwwjstor.org Wed nov204:10:19200
Strategic Management Journal, Vol. 12, 167-185(1991) HOW MUCH DOES INDUSTRY MATTER? RICHARD P RUMELT Anderson Graduate School of Management, University of California, Los Angeles, This study partitions the total variance in rate of return ar TC Line of Business reporting units into industry factors(whatever their nature) tors, factors assoc with the corporate parent, and business-specific factors Schmalensee (1985 reported that industry factors were the strongest, corporate and market share effects being extremely weak, this study distinguishes between stable and fiuctuating effects and reaches markedly different conclusions. The data reveal negligible corporate effects, small stable industry effects, and very large stable business-unit effects. These results imply that the mose portant sources of economic rents are business-specific; industry membership is a much less important source and corporate parentage is quite unimportant Because competition acts to direct resources the total variance of rates of return on assets in towards uses offering the highest returns, persist- the 1975 LB data into industry, corporate, and ently unequal returns mark the presence of either market-share components. He reported that:(1) natural or contrived impediments to resource corporate effects did not exist;(2) market-share flows. The study of such impediments is a effects accounted for a negligible fraction of the principal concern of industrial organization eco- variance in business-unit rates of return; ( 3) nomics and the dominant unit of analysis in industry effects accounted for 20 percent of the that field has been the industry. The implicit variance in business-unit returns; (4) industry sumption has been that the most important effects accounted for at least 75 percent of the arket imperfections arise out of the collective variance in industry returns. He concluded circumstances and behavior of firms. However, " the finding that industry effects are important the field of business strategy offers a contrary supports the classical focus on industry-level view: it holds that the most important impedi- analysis as against the revisionist tendency to ments are not the common property of collections downplay industry differences"(1985: 349) of firms, but arise instead from the unique Schmalensee's study was innovative and techni endowments and actions of individual corpo- cally sophisticated. Nevertheless, there are diffi- rations or business-units. If this is true. the ulties with it traceable to the use of a single industry may not be the most useful unit of year of data. In this article I perform a new analysis. Consequently, there should be consider variance co nents analysis of the FTC LB able interest in the relative sizes of inter-industry data that corrects this weakness. I analyze the nd intra- industry dispersions in long-term profit four years(1974-1977)of data available and Despite these arguments for this issue's sali- ence, surprisingly little work addressed it until 'Industry and ffects are (unobserved)com Schmalensee's(1985 )estimation of the variance moenmbesrsh returns that are associate omponents of profit rates in the FTC Line of industry return'is the calculated average return of the Business(LB)data. Schmalensee decomposed business-units in that industry 0143-2095/91/030167-190950 Received 16 February 1990 c 1991 by John Wiley Sons, Ltd Revised 28 December /990
168 R. P. Rumelt include components for overall bu cycle profitability is unrelated to ffects, stable and transient industry effects, as effects. While industry differences matter, they well as stable and transient business-unit effects. 2 are clearly not all that matters. If this intra- Like Schmalensee, I find that corporate effects industry variance is due to transient disequilib are negligible. However, I draw dramatically rium phenomena, then the 'classical focus on different conclusions about the importance of industry'would still be a contender; although it industry effects, the existence and importance of explains only 8 percent of the variance, it would business-level effects, and the validity of industry- be the only stable pattern in the data. But, if a level analysis large portion of the intra-industry variance is due The me raightforward ble differeng analysis is to start with what Schmalensee's results industries, then the 'classical focus on industry' left undecided. The first major incertitude is that, may be misplaced although 20 perce usiness-unit returns explained by industry effects, we do not know In this study, I find that the majority of this industry effects rather than to transient phena a how much of this 20 percent is due to sta residual variance is due to stable long-term diferences among business-units rather than ena. For example, in 1975 the return on assets to transient phenomena. Using Schmalensee's of the passenger automobile industry was 6.9 sample, I find that stable business-unit effects percent and that of the corn wet milling industry account for 46 percent of t e variance. Indeed was 35 percent. But this difference was far from the stable business-unit effects are six times able: in the following year the industries more important than stable industry effects in virtually reversed positions, auto's return rising explaining the dispersion of returns. Busines to 22. 1 percent and corn wet millings return units differ from one another within industries falling to 11.5 percent (Federal Trade Con a great deal more than industries differ from mission, 1975, 1976). The presence of industry one another specific fluctuations like these adds to the variance in industry returns observed in any one year. The conceptual conclusions are straightfor Thus, Schmalensee's snapshot estimate of the ward. The classical focus on industry analysis variance of industry effects' is the variance is mistaken because these industries are too among stable industry effects plus the variance heterogeneous to support classical theory. It of annual fluctuations. But the classical focus'is is also mistaken because the most important surely on the stable differences among industries, impediments to the equilibration of long-term ather than on random year-to-year variations in rates of return are not associated with industry, those differences but with the unique endowments, positions, and strategies of individual businesses My analysis of the FtC lb data shows that The empirical warning is equally striking. Most stable industry effects account for only 8 of the observed differences among industry percent of the variance in business-unit returns. returns have nothing to do with long-term Furthermore, only about 40 percent of the industry effects; they are due to the random dispersion in industry returns is due to stable distribution of especially high and low-performing business-units across industries. As will be shown an FtC industry return must be at least 15.21 The second incertitude concerns the variance not percentage points above the mean to warrant a explained by industry effects. Schmalensee noted conclusion(95 percent confidence)that the true (p.350)it ortant to recognize that stable industry effect is positive. Fewer than 80 percent of the variance in business-unit in forty industry returns are high enough to pass 2'Stable'industry effects are the(unobserved )time-invariant BACKGROUND (unobserved) time-invariant components or eets are the Most industrial organization research on business returns that are not due to industry or corporate membership. corporate, and industry profitability tests prop
How Much Does Industry Matter? 169 ositions about the causes of differential perform- Most prior work touching on the issue of locus ance. The primary tradition made industry the has done so tangentially, rough measures of intra- unit of analysis and sought a link between industry di dispersions in return being me industry concentration(and entry barriers) and in passing within a study on a different topic industry profitability (usually measured with Stigler, for example, studying the convergence pooled data).3A second tradition focused on of profit rates over time, used the relative inter-firm differences in performance, seeking proportions of positive-profit and loss corpo explanation first in terms of firm size and later rations to construct rough estimates of intra- in terms of market share. 4 The early reaction industry variances in the rate of return by IRS against the mainline tradition viewed the concen- size class(his estimates unavoidably confound tration-profitability correlation as an artifact inter-period and inter-firm variances). He induced by the deeper share-profitability link. remarked in passing(1963: 48)that these values ly, the stochastic and efficiency views explain were much larger than inter-industry variances both firm profitability and market-share, and thus but drew no implications, Fisher and Hall (1969) concentration, in terms of exogenous differential measured the long-term(1950-1964)dispersion firm efficiencies. 6 in rates of return about industry averages in In contrast to economics, business strategy order to obtain a measure of risk that could be research began with the presumption of hetero- regressed against industry profitability. Although geneity within industries and has only recently they did not remark the fact, they obtained come to grips with the question of how differences estimates that were approximately double their in efficiency are sustained in the face of compe- reported standard deviation in inter-industry rates tition. Thus. the earliest case research informed of return by the ' concept focused on the different McEnally (1976), in an analysis of results roaches ompetition adopted by firms obtained by Conrad and Plotkin(1968) within the same industry. As the field matured, that industries with larger average return tend attention turned towards developing quantitative also to have larger dispersions in long-term inter- measures of this diversity' and, more recently, firm rates of return. His figures"show inter-firm o its explanation in economic terms variances that are two to five times as large as Each of these streams of work presumes inter-industry variances different causal mechanisms and employs differ- As part re-examination of the ent units of analysis. Claims about whether profit- concentration-profitability relationship, Gort and persion reflects collusion, share-based Singamsetti (1976) were apparently the first to market power, or difficult-to-imitate resources explicitly ask whether or not 'the profit rates of are coupled with claims that the more aggregate firms cluster around industry means. Assigning phenomena are spurious or counter-claims that firms to 3-digit and 4-digit industries, they found less aggregate phenomena are noise. My intention to their surprise that the data failed to support here is to suppress concern with causal mechan- the hypothesis that industries have different isms and focus instead on the question of locus. characteristic levels of profitability. Furthermore Put differently, my concern here is with the they noted that the proportion of the total existence and relative importance of time, corpo- variance explained by industry was low rate, industry, and business-unit effects, however (approximately 11 percent, adjusted), did not generated,on the total dispersion of reported increase as they moved from 3-digit to 4-digit rates of return industry definitions, and did not increase as the sample was restricted to more specialized firm See Weiss'( 1974)survey of this line of work ad and See Demsetz(1973)and Mancke(1974), as well as Lippi Plotkin computed intra-industry variances and Rumelt(1982). directly from deviations about industry averages. Because hey are not based on true Hatten and Schendel (1977) provided early contribution their results may overestimate intra-industry variances and see McGee and Thomas(1986)for a review of the strategic produce substantially upwards biased estimates of inter- dustry variances (although the latter was not of direct K See Teece(1982), Rumelt(1984)and Wernerfelt(1984) interest to them or to McEnally)
170 R. P Rumelt In an unpublished working paper I performed a sample of 217 large U. K firms, they measured a variance components analysis of corporate how much of firms' profitability movements over returns using 20 years of Compustat data(Rumelt, time were unique, how much were related to 1982). Although problems of industry definition other firms' movements, and how much were and firm diversification prevented definitive related to common industry movements. Nearly results, here again the intra-industry effect one-half of the companies in their sample dominated the inter-industry effect: the measured exhibited no common industry-wide response to intra-industry variance in long-term firm effects dynamic factors was three to ten times as large as the variance Hansen and Wernerfelt (1989) studied the due to industry-specific effects relative importance of Schmalensee's(1985)study was the first pub- zational factors in explaining inter-firm differences is the direct ancestor of the work presented he aa in profit rates. They found that industry explained lished work aimed squarely at these issues an Looking at the 1975 FTC LB data, Schmalensee that organizational characteristics were roughly estimated the following random-effects model: o twice as important rk=μ+ax1+βk+nS/k+∈ DATA where rik is the rate of return of corporation k's tivity in industry i, Sik is the corresponding Because the impetus for this study comes from market share, a, and Bk are industry and the existence of the unique FTC LB data corporate effects respectively, and Eik is a and because the statistical work performed is disturbance. Schmalensee used regression to fundamentally descriptive rather than hypothesis conclude that corporate effects were non-existent testing, I break with convention and discuss the Bk=0), and variance components estimation data before introducing the model to show that industry effects were significant and Data on the operations of large U. S. corpo substantial (o>0), and that share effects were rations are available from a variety of sources significant but not substantial(m >0 and o> However, there is only one source of disaggregate 2a3) data on the profits of corporations by industry- Kessides (1987) re-analyzed Schmalensee's the FTCs Line of Business Program. The FTC data, excluding corporations active in less than collected data on the domestic operations of three industries. He found statistically significant large corporations in each of 261 4-digit FTC corporate effects in the restricted sample, suggest- manufacturing industry categories. Information ng that inclusion of the less-diversified corpo- on a total of 588 different corporations was rations had lowered the power of Schmalensee's collected for the years 1974-1977; because of late test. In a related vein, Wernerfelt and Montgom- additions, deletions, acquisitions, and mergers ery(1988)estimated a model patterned after the number of corporations reporting in any one Schmalensee's, replacing return on assets with year ranged from 432 to 471. The average Tobin,s q and replacing the numerous corporate corporation reported on about 8 business-units dummy variables with a single continuous meas- Schmalensee's sample was constructed by ure of ' focus'(the inverse of diversification). starting with Ravenscraft's(1983)data-set of They found industry effects and share effects of 3186 stable and meaningful business-units-those about the same magnitudes as Schmalensee which were not in miscellaneous categories and found, and also found a small. bl all, but statistically which were neither newly created nor terminated significant, positive association between corporate during the 1974-1976 period. He then dropped focus and performance business-units in 16 FTC industries judged to Cubbin and Geroski (1987) attacked the be primarily residual classifications, dropped question of the relative strength of industry and business-units with sales less than 1 percent of firm effects with a different methodology. Using 1975 FTC industry total sales, and excluded one I I have altered his notation to preserve consistency within sets were used his research labeled A and B Sample a was constructed by
How Much Does Industry Matter? 171 starting with Schmalensee's sample of 1775 systematic biases in reported returns, the esti- business-units from the 1975 file and appending mated variance components will reflect these data on the same business-units from the 1974, facts and, therefore, help in estimating their 1976, and 1977 files. After this expansion, one importance business-unit was judged to have unreliable asset measures(in 1976-77)and was dropped. Eight other observations were eliminated because assets A VARIANCE COMPONENTS MODEL yere reported as zero. Sample a then contained 6932 observations provided by 457 corporations In discussing the heterogeneity within industries on 1774 business-units operating in a total of 242 the term firm has an ambiguity that easily lead 4-digit FTC industries to confusion. In economics a 'firm'is usually an Sample B was constructed by adding to Sample autonomous competitive unit within an industry, A the 1070'small business-units which had failed but the term is also often used to indicate a legal Schmalensee's size criterion. After adjoining the entity: a ' company'or corporation,. Because units,34 were excluded due to (apparent) and because most large corporations are substan- measurement problems: negative or zero assets, tially diversified, legal or corporate 'firms'are sales-to-assets ratios over 30, and extreme year- at best, amalgams of individual theoretical to-year variations in assets that were unconnected competitive units. Confusion can arise if one o changes in sales. Sample B then contained author uses the term firm effects'to indicate 10, 866 observations provided by 463 corporations intra-industry dispersion among theoretical on 2810 business-units operating in a total of 242 firms', and another author uses the same term 4-digit FTC industries to denote differences among corporations which The rate of return was taken to be the ratio are not explained by their patterns of industry of profit before interest and taxes to total assets, activities expressed as a percentage. In sample a the To reduce the ambiguity in what follows I average return was 13.92 and the sample variance avoid the term 'firm. Instead, I use the term was 279.35. In sample B, the average and business-unit to denote that portion of a com sample variance of return were 13 17 and 410. 73 pany's operations which are wholly contained expective within a single industry. 12 I use the term The FtC defined operating income as total corporation to denote a legal company which evenues(including transfers from other units) owns and operates one or more business-units less cost of goods sold, less selling, advertising, Thus, both industries and corporations are and general and administrative expenses. Both considered to be sets of business-units expenses and assets were further divided into In this regard, note that Schmalensee(1985) traceable,and untraceable,components, the used the term firm-effects'to denote what I call traceable component being directly attributable corporate effects. Thus, his first proposition to the line of business and the untraceable firm effects do not exist'(p. 349)refers to what component being allocated by the reporting are here termed corporate effects. Consequently firm among lines of business using reasonable as he noted, finding insignificant corporate effects procedures. In 1975, 15.8 percent of the to does not rule out the presence of substantial expenses and 13.6 percent of total assets of the intra-industry effects. However, unless more than average business-unit were allocated one year of data are analyzed, intra-industry A number of scholars have advanced arguments effects pool with the error and cannot be detected that accounting rates of return are systematically Taking the unit of analysis to be the business biased measures of true internal rates of return II unit assume that each business -unit is observed Whatever the merits of this position, the purpose over time and is classified according to its industry of this study is to partition the variance in reported business-unit rates of return. If different 12 It is FTC LB researchers to refe industry practices or corporate policies do induce to a business-unit as an 'LB, I avoid this usage because Line of Businessrefers to an industry group rather than to In particular, see Fisher and McGowan(1983 an individual business-unit within a larger firm
172 R. P Rumelt membership and its corporate ownership. Let rikt nesses. Comparing all industry effects to market denote the rate of return reported in time period share effects may unfairly load the dice in favor t by the business-unit owned by corporation k of industry. Consequently, in this study I extend ind active in industry i. A particular business- Schmalensee's argument to the business-unit and unit is labeled ik, highlighting the fact that it is rather than give special attention to market simultaneously a member of an industry and a share, I measure the importance of all stable corporation. Working with this notation, I posit industry effects, and all stable business-uni the following descriptive model Were this a fixed-effects model, the r=队+α;+k+Y+8+中k+E;(2) assumption would be that the Eikt are disturbances, drawn independently from a distri- where the a are industry effects (i= 1 bution with mean zero and unknown variance la), the pk are corporate effects (k=1,.., IB), 02. In this model I make the additional assumption the y, are year effects(t Ly), the &it that all of the other effects, like the error term, are industry-year interaction effects (s distinct are realizations of random processes with zero it combinations), and the ik are business-unit means and constant, but unknown, variances effects(o distinct ik combinations). The eikt are 0,0B, ox, o, and oZ dom disturbances (one for each of the N Note that this random effects assumption does observations). Each corporation is only active in not mean that the various effects are inconstant a few industries, so lo lalg. Because a few Instead, for example, each business-unit effect ik dustries may not be observed over all years, Is is seen as having been independently generated by Laly. The model takes the assignment of a random process with variance o2, and, having business-units to corporations and industries as once been set, remaining fixed thereafter. given and is essentially descriptive, In particular, The random-effects assumption says nothing it offers no causal or structural explanation for about why effects differ from one an profitability differences across industries, years, effects may differ from one another in either corporations, or business-units--it simply posits fixed-effects or random effects models. The real the existence of differences in return associated substance of the random-effects assumption with these categories that the differences among effects, whatever their There are two key differences between this source, are,, not having been controlled model and Schmalensee's. First, the terms Y, and or contrived by the research design, and are Bit have been added to deal with year-to-year independent of other effects. That is, the effects variations in overall returns and year-to-year in the data represent a random sample of the variations in industry-specific returns. Second, effects in the population. Independence implies In this regard, it is useful to recall Schmalensee's example, is of no help in predicting the valuce the market-share term has been replaced by ik. that knowing the value of a particular persuasive reasons for turning to a nominal of other business-unit effects or the values of any measure of industry. He argued (1985: 343) industry, corporate, or year effects. An important that conventional market-level variables (e. g, exception to this assumption, involving an associ concentration) are very imperfect measures of ation between industry and corporate effects, is the theoretical constructs (perceived inter- discussed below dependence) they are supposed to represent. Readers familiar with fixed-effects regression Therefore, the fact that these variables perform models may be concerned that the effects posited poorly, relative to market-share, in cross-sectional in this model are not estimable. Such a concern regressions may not mean that industry,is is well placed-the individual effects cannot unimportant. Hence, Schmalensee sought to be estimated. Furthermore, regression methods measure the importance of all industry effects, cannot deliver unambiguous estimates of the using nominal industry categories, and compare relative importance of classes of effects. However it to the importance of market-share. But, just the statistical problem is not to estimate the as concentration is an imperfect measure of thousands of effects, but to estimate the six industry structure, so market-share is an imperfect variances. Despite the nesting in the model, the measure of resource heterogeneity among busi- variance components are estimable. Note that it
How Much Does Industry Matter? 173 is the assumption that the underlying effects are do not rapidly fade away; Mueller(1977, 1985) realizations of random processes that allows a and Jacobson(1988)have found them to be measure of their relative importance. Were they extraordinarily persistent. This consideration, and d to be 'fixed one could test for statistical the fact that the ftc lb dat ata only 4 significance, but there would be no reliable way years, leads to modeling the business-unit effects of assessing importance. It is only by estimating as fixed. If this assumption is incorrect, and the the variances of effects that relative importance business-unit effects decay over time, then the an be assessed estimated residuals will display positive autocor- The a, represent all persistent industry-specific relation. Such a finding would signal the need impacts on observed rates of return. Differences for a more complex autoregressive model. As among the a, reflect differing competitive will be seen, no such autocorrelation was found behavior, conditions of entry, rates of growth, in the data studied here demand-capacity conditions, differing levels of The Y, represent year-to-year fluctuations risk, differing asset utilization rates, differing macroeconomic conditions that influence all accounting practices, and any other industry- business-units equally. The 8i represent industry specific impacts on the rate of return. The specific year-to-year fluctuations in return fundamentally descriptive model used here offers Finally, there is an Eikt associated with each o hypotheses as to the nature of these industry observation. Although these effects have been ifferences-the a, represent their total collective named 'error, they may equally well be though of as year-to-year variations that are specific to c. Corporate effects Bk should arise from differ- each business-unit ences in the quality of monitoring and control, In an important exception to the independence differences in resource sharing and other types assumption, Schmalensee 1985: 344)argued that of synergy, and differences in accounting policy. corporations which are more skillful at operating Total corporate returns will, of course, also be businesses might also be more skilled at having affected by the industry memberships of their identified and entered more profitable industries onstituent businesses. However, the unit of thereby inducing a dependence between the analysis here is the business-unit, not the corpo. values of B and a observed across business-units Incorporating this presumption, and maintainin The ik represent persistent differences among elsewhere the assumption of independence, the business-unit returns other than those due to total variance o? of returns may be decomposed Idustry and corporate membership. That is, they into these variance-covariance components are due to the presence of business-specific skills resources, reputations, learning, patents, and 0=02+02+02+02+02+02+ 2CaB(3) other intangible contributions to stable differences fron. returns. Such differences where CaB is the covariance between a; and pki nay also arise from persistent errors in the given that corporation k is active in industry i allocation of costs or assets among a corporation's (i.e., E(a Bk)= CaB if business-unit ik exists rate do ot wide or industry-wide biases in accounting will appear as corporate or industry effects. )The Section on Empirical Results presents the results ESTIMATION METHODS of allocation errors Are the differences among business-unit returns As did Schmalensee(1985: 348), I rely on Searle's within industries simply disequilibrium phenom-(1971: ch. 9-11) treatment of the theory and ena? Until recently, rates of return were thought practice of variance component estimation. The to converge fairly rapidly to 'normal' levels. basic method draws on the fact that any quadratic Consequently, the idea of business-unit effects form in observations is a linear combination of had little currency. If they surfaced empirically, the variance components. To see this, let they were treated as an autocorrelation problem. the vector of N observed returns, let r However, researchers using more disaggregate and let V= var(r). From(2) it should be clear data have discovered that abnormal profit rates that every element of r is k and that each
174 R. P Rumelt element of V is a linear combination of the seven It is also useful to treat the problem as one known variances and co ariances. A theorem of analysis of variance using dummy variable by Searle ( 1971: 54)establishes that for any regression methods. Standard analysis of variance symmetric matrix Q provides statistical tests for the presence of some of the effects, provides residuals that can be E(rQr)=rQr+ tr(Qv) examined for autocorrelation and generates an efficient estimator of a2 that can be compared (normality is not required). Consequently, defin- to that obtained by the variance components method. The primary challenge in performing analysis of variance for the model is the problem,s o=[u2oZopoyogo3o2CaBI size: estimating the model with sample B amounts we have to performing a regression with 3533 independent (dummy) variables! By recasting the problem in E(rQr)=ho, terms of least-squares, it was possible to develop the fit of Estimation proceeds by equating the expected criterion is met. The program, ITROVA, iace %L where h is a vector of constants a set of coefficients until the least values of quadratic forms to their sample values in Appendix 2 and solving for the unknown variance com ponents. 3 To be specific, consider q different quadratic forms generated by Qi,(=1 A variance components demonstration g), where there are q unknown variances and Few economists or business strategy researchers covariances. Corresponding to each quadratic are familiar with variance components models or form, there is a calculated, or sample' value he methods for their estimation This subsection demonstrates estimation of a simplified version Working with(2), I omit the terms for and an expected value corporate effects, the year effects, and the industry-year effects, giving E(rQr)=ho. Now assemble the z into a column vector z and assemble the row-vectors h; into a matrix H. This model has a simple nested structure. There Then the system of equations(4)can be written are industry effects a;, business-unit effects i within industries, and errors Eik, in the obs of each business-unit return over time, yrvation Estimates of the unknown variances and unbiased estimates of the variance-covariance 0202, and o2 can be obtained by working with components are obtained as any set of three independent quadratic forms To aid intuition, and to help establish the link E(o)=H-Z between the unknown variance components and (6) observed variances, I shall work with the sample Details on the eight quadratic forms used in this variances among industry returns, among busi study and on the symbolic form of H are given ness-unit returns, and among all observations in Appendix 1 I if corporation k has a business-unit in industry i in year t, and 0 otherwise, I adopt the notation that a 'dot available in a number of commercial statistic As will be seen in the next section, omitting the year and a pro corporate effects should have no material impact on the plexity studied in this paper the assumed covariance between the industry and corporate estimated value of a? and will also distort the estimates of
How Much Does Industry matte presents summation over the subscript normally Developing the corresponding expression for in that position. For example, nik. is the total Ey? and substituting into(9) gives number of observations of business-unit ik, and the total number of observations w= n Define the average return yi of industry i as the arithmetic average of all observations in Es2=02+ industry i. Thus, yi= r./n;.., and, using(7) That is, the observed average industry return is the sum of u, the industry effect a; and weighted averages of the business-unit effects and errors variance components and describes the precise ithin th to compute yi for each of the 242 industries an to then calculate the sample variance sy among A and equating the expected and computed these industry returns. The result is sa=61.90. values of sy gives How good an estimate is this of o2? Examining (8), it should be clear upon refection that overestimates o2. The variance among industry E=2+0.1950+0.050302=6190.(1) returns will be oa plus terms in o, and o2. That is, industry returns vary from one another because That is, the observed variance in industry returns of industry effects and because of the random is expected to be the true variance in industry impact of business-unit effects and errors on effects plus (approximately) one-fifth of the ed industry returns. To develop an variance in business-unit effects, plus Esx in terms of variance com-(approximately) one-twentieth of the error vari ponents, first note that ance Next consider fik=rik/nik, the average return 52=2iyi-y.a (9) of business-unit ik. The varia s of busine unit returns(sample A)is 1 7.49. Using steps parallel to those taken above, this sample variance ow conside The independence assump- can be equated to its expected value tions assure he expectations of cross- products are zero(e.g, E(a, dik)=0), and that within families of effects, expectations of products E=0.95802+o+0.25902=18749.(12) E(a, a )=0 if i=j, and 0 otherwise. Squaring That is, the variance among business-unit returns (8)and taking the expectation, yields is expected to be the true variance among business-unit effects, plus(approximately) the variance in industry effects, plus(approximately) one-fourth the error variance Finally the same method can be used to obtain for Es2. the expected total observed ariance in returns I5 E∑y=la2+l2 E2=0.99502+0.999%+2=279.35.(13) Is Note that Es2*o?+oi+o? because s is calculated u the sample average rather than the true p
