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Journal of Economic LiteratureVol. XXXV (March 1997), pp. 40–59

Sutton: Gibrat’s Legacy

Gibrat’s Legacy

JOHN SUTTONLondon School of Economics

The support of the Leverhulme Trust and the Economic and Social Research Council is grate-fully acknowledged. I would also like to thank Alison Hole, Reinout Koopmans, Volker Nocke,Michael Raith, and three anonymous referees for their helpful comments.

I. Background

ONE OF THE MOST important strandsin the literature on market struc-

ture begins with Robert Gibrat’sInégalités Économiques, published inParis in 1931. Gibrat’s book presented thefirst formal model of the dynamics of firmsize and industry structure, and its lengthysubtitle confidently announced a “newlaw”: the Law of Proportional Effect.

Gibrat traced the origins of his think-ing to the work of Jacobus Kapteyn, anastronomer who had become interestedin the widespread appearance of skewdistributions in various settings, espe-cially in biology. Kapteyn’s approach wasto assume that underlying such distri-butions was a simple Gaussian process: alarge number of small additive influ-ences, operating independently of eachother, would generate a normally distri-buted variate z (the “Law of Laplace” inKapteyn’s book). An observed skew dis-tribution of some variate x could bemodeled by positing that some underly-ing function of x was normally distri-buted (Kapteyn and M. J. van Uven1916). In his book, Gibrat postulated the“simplest” such process, suggesting thatthe logarithm of x developed in such afashion. This amounts to saying that theexpected value of the increment to a

firm’s size in each period is proportionalto the current size of the firm.1

The simplest way of presenting the ar-gument, following Joseph Steindl (1965),runs as follows. Denote the size of thefirm at time t by xt and let the a randomvariable εt denote the proportionate rateof growth between period (t − 1) and pe-riod t, so that

xt − xt−1 = εtxt−1

whence

xt = (1 + εt)xt−1 = x0(1 + ε1)(1 + ε2). . .(1 + εt).

If we choose a “short” time period, thenwe can regard εt as being “small,” justify-ing the approximation log(1 + εt) ~− εt.Taking logs, we thus obtain

log xt ~− log x0 + ε1 + ε2 + . . . + εt.

By assuming the increments εt to be in-dependent variates with mean m andvariance σ2, we have that as t → ∞, so theterm log x0 will be small compared to logxt, that the distribution of log xt is ap-proximated by a normal distribution withmean mt and variance σ2t. In other

1 “Size” can be measured in a number of ways,and these arguments have been variously appliedto measures of annual sales, of current employ-ment, and of total assets. Though we might inprinciple expect systematic differences betweenthe several measures, such differences have notbeen a focus of interest in the literature.

40

words, the limiting distribution of xt islognormal.2

Gibrat first applied this to incomedistributions, and then to plant (estab-lishment) sizes in manufacturing. Thegoodness of fit which he obtained wasstriking. (An example is shown in Figure1.) Gibrat presented a broad range ofdata of the size distribution of estab-lishments. This data permitted compari-sons across time (1896–1921), and be-tween broad sectors of the nationaleconomy (agriculture, commerce), re-gional sectors (industrial establishments

in Alsace-Lorraine), and some very nar-rowly defined industries (electrochemi-cals and explosives; metallurgy).3 Gibrat’saim was to convince his readers that thiswas a statistical regularity sufficientlysharp to provide a basis for seriousmathematical modeling. In this he suc-ceeded, albeit with a very long lag. Mi-chael Kalecki’s 1945 article4 describesGibrat’s book as a “great achievement,”but as Gibrat had noted, the collectionand analysis of large data sets in this areainvolved a heavy burden of work. It wasnot until the 1950s and 60s that the ap-parent regularity of the size distributionbecame the focus of sustained empiricaleffort. By that time, a second researchliterature had emerged whose motivationlay in a different, but equally salient fea-ture of market structure.

This new “cross-sectional” literaturewas motivated by the observation thatmarket structure varied in a systematicway from one industry to another, in amanner that seemed to be related to a

2 More formal versions of this argument weredeveloped in the 1950s and 60s (see below). Sev-eral of these early models combined a propor-tional growth hypothesis on firm size x with a con-stant population of firms (no entry or exit). Oneimmediate implication of this is that the varianceof the (lognormal) distribution increases over time(see footnote 7 below).

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log (x-1)

Figure 1. Gibrat’s Data for French Manufacturing Establishments in 1920 and 1921

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z

192

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3 Gibrat also examined the cyclical behavior ofthe size distribution. He found, interestingly, thatwhen an industry expanded, firm numbers roseslowly in comparison with output, most of thegrowth being captured by incumbents; but whenoutput fell, firm numbers fell sharply, as (mostlysmall) firms disappeared. The cyclical behavior ofplant expansion/contraction versus entry/exit hasbeen explored in the recent literature by Tito Bo-eri and Ulrich Cramer (1992) and by Steven Davisand John Haltiwanger (1992).

4 Kalecki (1945) made a number of prescient obser-vations. First, he noted that the Law of ProportionateGrowth (applied to a fixed population of firms) impliedthat the variance of the distribution would increaseindefinitely, a feature which seemed “unrealistic” rela-tive to (many) economic processes. He examined a num-ber of modified processes, including one in which theexpected rate of growth increased less than proportion-ately, leading to a lognormal distribution with constantvariance. More interestingly, he allowed that unspecified“economic” factors would drive the process, and exam-ined the robustness of the law to various constraints onthe process. Finally, he re-examined the empirical per-formance of the prediction of “lognormality” for U.K.data on establishment size (where it worked “fairly well”)and income distributions (where a modified distributionwhich converged to the lognormal for large x fittedreasonably well).

The horizontal axis shows log (x - 1), where x isa size class, measured by employment, and thevertical axis shows z, calculated from observedvalues of R(z), the number of establishmentsof size z or greater, according to the formula

R(z) = 1

√π ∫ e−z2

z

∞ dz (Gibrat 1931, p. 53 and p.

276). If the distribution of x is lognormal, the ob-servations will lie in a straight line.

Sutton: Gibrat’s Legacy 41

number of industry characteristics, suchas scale-economies, the role played byadvertising, or the influence of R&D.The fact that the ranking of industries bysome measure of concentration ap-peared broadly similar from one countryto another lent weight to the notion thatmarket structure was influenced by somebasic “industry characteristics” (Joe Bain1966; Frederic Pryor 1972; Louis Phlips1971).

During the past 15 years, this “cross-sectional” literature has been reformu-lated using game-theoretic models.While these models have proved to beextremely versatile in rationalizing ob-served outcomes, it is less easy to pindown what the theories exclude, and soto pinpoint the content of these models.This is now widely seen as a crucial issuefor game-theoretic formulations of thecross-section literature. (For a compan-ion review of the cross-sectional litera-ture, see Sutton 1997.)

It is, however, the parallel revival ofinterest in the older Growth-of-Firms lit-erature during the past decade which isthe focus of interest in what follows.This revival had its roots, not in theory,but in new empirical findings which be-gan to appear during the mid-80s. Thedevelopment of the literature since thenhas involved a continual interplay be-tween theoretical modeling and empiri-cal evidence, and a shift of focus interms of the empirical regularities whichseem to be of primary interest to re-searchers. At the same time, there hasbeen a heavy emphasis on discarding theolder type of purely “stochastic” models infavor of introducing stochastic elementsinto standard “maximizing” models.

The new “maximizing” models have fo-cused on various specific settings whichdiffer in the assumptions made on thenature of the technology, the informa-tion available to firms, and the descrip-tion of the product market. Among the

earliest studies was that of Lennart Hjal-marsson (1974), which examined the sizedistribution of plants in a homogeneous-goods industry, in the presence of in-creasing returns to scale at plant level.5

The model of Boyan Jovanovic (1982)also assumed a homogeneous-goods in-dustry, but introduced a learning mecha-nism which gradually revealed firm-specific efficiency differences as the in-dustry evolved (see Section III below).Reinhard Selten (1983) considered amodel in which firms incurred fixed out-lays in enhancing consumers’ willing-ness-to-pay for their respective products,which were then sold in a series of (sub-)markets of varying sizes.6

One theme which emerges from thesedevelopments echoes the lesson learntfrom the recent game-theoretic litera-ture: reasonable “maximizing” models canbe designed in many ways, and their im-plications will depend on a wide range ofindustry characteristics, some of whichwill be very difficult to identify, or con-trol for in empirical studies. In particu-lar, there is no obvious rationale for pos-iting any general relationship between afirm’s size and its expected growth rate,nor is there any reason to expect the sizedistribution of firms to take any particu-lar form for the general run of indus-tries. Most authors now claim only thatthe distribution will be “skew,” but donot specify the extent of skewness, or theparticular form which the size distri-

5 In a later paper, Hjalmarsson (1976) reportssome tests of his model for two Swedish industries(particle board and cement) for which the assump-tions made on product homogeneity and on plants’cost structure are reasonable.

6 Another important series of models, following Rich-ard Nelson and Sidney Winter (1982) avoids strict maxi-mizing assumptions in favor of weaker rationality re-quirements. This literature raises some fundamentalquestions as to the appropriateness of making strongrationality and informational assumptions on agents whoface continuing technological change. A review of thisliterature, which lies beyond the scope of the presentpaper, will be found in Wesley Cohen and Richard Levin(1989).

42 Journal of Economic Literature, Vol. XXXV (March 1997)

bution might take. Meanwhile, empiricalinvestigations from the 1960s onwardshave thrown doubt on whether any singleform of size distribution can be regardedas “usual” or “typical” for the general runof industries; wide differences in theform of the size distribution occur be-tween one industry and another (RichardSchmalensee 1989, p. 994).

These developments in the Growth-of-Firms literature are very much remi-niscent of what we have seen happeningrecently in the game-theoretic formula-tions of the cross-sectional literature.The lessons that might be drawn fromthis are explored in Section IV below.

II. The Early Literature

During the 1950s and 60s, a substan-tial class of models appeared which com-bined “Gibrat’s Law” with a range of an-cillary assumptions. (For a review ofthese models, see Steindl’s 1968 over-view and his monograph of 1965.).Meanwhile, a growing empirical litera-ture, associated with Peter Hart and Sig-bert Prais in the U.K. and with HerbertSimon and his co-authors in the U.S.,had a major influence within IndustrialOrganization.7

The generation of “stochastic growth”models developed in this period culmi-nated in the volume based on the papersof Simon and his co-authors (Yuji Ijiriand Simon 1977), following which therewas relatively little interest in the fieldfor a decade. The model used by Simonand his co-authors modified Gibrat’smodel by incorporating an entry processaccording to which firm numbers roseover time as the industry grew. Thisavoided the implication that the varianceof the size distribution increased withoutlimit. The Simon model provides a usefulpoint of departure in assessing the laterliterature. It assumes a framework inwhich the market consists of a sequenceof independent opportunities, each ofsize unity, which arise over time. Thebest way to think of this is to imagine anumber of isolated “island” markets,each big enough to support exactly oneplant. As each opportunity arises, thereis some probability p that it will be takenup by a new entrant. With probability (1− p) it will be taken up by one of thosefirms already in the market (“activefirms”). The size of any (active) firm ismeasured by the number of opportuni-ties it has already taken up. There aretwo assumptions:

(i) Gibrat’s Law: the probability thatthe next opportunity is taken up byany particular active firm is pro-portional to the current size of thefirm.

(ii) Entry: the probability that the nextopportunity is taken up by a newentrant is constant over time.

Assumption (ii) is rather arbitrary,though it may be a reasonable empiricalapproximation. Simon regarded it merelyas providing a useful benchmark, andpresented various robustness tests show-ing that “reasonable” departures fromthe assumed constancy of p would haveonly a modest effect on the predictions

7 The Hart-Prais model, like that of Gibrat, im-plied that variance grew over time. Prais (1976)proposed this as a mechanism to explain the rateof increase in the share of the top 100 firms inU.K. industry. By measuring the variance in theyear-to-year proportional growth rate, Prais couldpredict (ex post) a trend rate of growth for theshare of the top 100 firms for 1909–1970. Whilethe predicted trend fitted the observations quitewell, Prais’ interpretation of this result was chal-lenged. The stochastic growth model does not dis-tinguish between “internal growth” and growthachieved by way of acquisitions (or mergers).Leslie Hannah and John Kay (1977) claimed thatmost of the observed increase in concentrationwas due to mergers and acquisitions, rather thaninternal growth, and that once the effect of merg-ers and acquisitions were netted out, internalgrowth alone could not account for the degree ofincrease in concentration. See, however, the com-ments on this issue in Prais (1976) and the laterassessment of Hannah and Kay (1981).


of the model. The predictions are drivencrucially by Assumption (i) (Gibrat’s Law).What this leads to is a skew distributionof the Yule type, and Simon presentedvarious empirical studies for large firms inthe U.S. which suggested that it provideda good approximation to the size distri-bution of large manufacturing firms.

The goodness of fit of the size distri-bution provides only indirect evidencefor Gibrat’s Law. A second strand of theliterature of the 1950s and 60s focusedon the direct investigation of Gibrat’sLaw, by looking at the relation betweenfirm size and growth over successiveyears in a panel of firms. While variousstudies of this kind cast doubt on theidea that proportional growth rates wereindependent of firm size, no clear alter-native characterization emerged.8 Sum-marizing the literature in 1980, FredericScherer remarked on the wide disparitybetween different studies, but tenta-tively concluded that assuming growthrates uncorrelated with initial firm size“is not a bad first approximation,” atleast for the U.S. On the other hand,most studies agreed that the standarddeviation of growth rates rose less thanproportionally with firm size (see Hart1962; Stephen Hymer and PeterPashigian 1962; Ajit Singh and GeoffreyWhittington 1968, 1975; and Scherer1980, p. 148). This observation raises thequestion of whether the pattern of re-siduals in certain fitted relationshipsmight exhibit heteroscedasticity; see Sec-tion III.

The contribution of Edwin Mansfield

(1962) is of particular interest. Mans-field’s study was based on samples of“practically all” firms in three specific in-dustries (steel, petroleum, tires) over anumber of different time periods (gener-ating ten samples in all). The authorpointed out that “Gibrat’s Law” may beinterpreted in different ways, dependingon the way we treat firms “disappearing”from the sample (whether by “exit” orotherwise). Does the law relate to allfirms, with the proportional growth rateof disappearing firms set at minus one?Or does it propose that the proportionalrate of growth conditional on survival isindependent of firm size?9

Mansfield’s results rejected the firstversion of the hypothesis in seven of histen samples, while the second versionfailed in four of his ten samples. Whilethis led Mansfield to conclude that “Gi-brat’s Law does not seem to hold up verywell empirically,” it nevertheless leftopen the possibility that Gibrat’s Lawmight still be true in yet another form.Consider the distribution of growth ratesof firms that would have resulted if nonehad left the industry. Interpret Gibrat’sLaw as saying that this distribution is in-dependent of firm size. Then it is possi-ble that the measured growth-size rela-tions could still exhibit the qualitativefeatures observed in Mansfield’s data;this depends upon the growth rates thatwould have been achieved by exitingfirms. Now suppose that small firmswith low growth rates are more likelyto exit. Then the proportional rateof growth, conditional on survival, willbe smaller for large firms. Whether anappeal to this “sample censoring” effectcould rescue some underlying versionof Gibrat’s Law was one of the mainquestions posed in the literature of the1980s.

8 While smaller firms are found to grow fasterthan large firms in most recent studies (see Sec-tion III below, and also Manmohan Kumar 1985;Zoltan Acs and David Audretsch 1990), some ear-lier studies reported the reverse tendency (JohnSamuels 1965; Prais 1976). This latter tendency inpart reflects the greater role played by growththrough acquisition among larger firms. (Modifiedversions of Gibrat’s Law, are described in PatrickMcCloughan 1995.)

9 Mansfield also noted a further distinction,made by Simon, which postulated that the lawheld only above some minimal size of firm.


III. The New Literature

The new literature which developed inthe 1980s had two main themes. Thefirst lay in a concern with econometricissues, and here a major focus lay indealing with the problems of sample cen-soring, the specification of an appropri-ate functional relationship, and the prob-lem of heteroscedasticity.10 A centralquestion was whether a “failure” of(some version of) Gibrat’s Law could beattributed to any of these effects. Thesecond major theme in the literature layin a dissatisfaction with the models ofthe 1950s and 60s. It seems to have beenwidely felt that these models might fitwell, but were “only stochastic.” The aimwas to move instead to a program of in-troducing stochastic elements into con-ventional maximizing models.11

The problems of measurement wereaddressed in three influential contribu-tions, which led to a common view onsome basic statistical regularities. Bron-wyn Hall’s (1987) paper was based, like

much of the earlier work, on a sample oflarge firms (1778 publicly traded manu-facturing firms). Her focus of interest layin directly tackling several econometricissues, including those noted above, andin particular the problem posed by sam-ple selection bias. The studies of DavidEvans (1987a, 1987b) and of TimothyDunne, Mark Roberts, and Larry Samu-elson (1988, 1989) both covered thefull range of firm sizes and ages. Evans’work was based on a large dataset forU.S. manufacturing industry, con-structed by the U.S. Small Business Ad-ministration using information collectedby Dun and Bradstreet for its credit re-ports. That of Dunne, Roberts, and Sam-uelson related to plants rather thanfirms, and was based on a compilation ofthe individual plant-level data collectedin five successive U.S. Censuses ofManufactures (1963–82). Apart from theeconometric issues noted above, a majorfocus of interest in both this study andEvans’ lay in unravelling the roles playedby firm age and firm size as determi-nants of growth.

The focus of interest in all these stud-ies lies in estimating

(a) the probability of survival of a firm,conditional on its age, size, andother characteristics, and

(b) the probability distribution describ-ing the firm’s growth rate conditionalon survival, and its dependency onage, size, and other characteristics.

Before turning to results, it is worthpausing to note an important differencein method between the studies of Halland of Evans and that of Dunne,Roberts, and Samuelson. This will re-quire some notation.

Following Dunne, Roberts, and Sam-uelson, we distinguish three distri-butions: let the random variable g′ de-

10 The particular problems of sample censoringis important in itself, apart from any implicationswhich it has for the size-distribution literature. Toanalyse the effect of an economic policy on firms,some allowance must be made for the impact onthose firms who “disappear from the sample”when they exit the industry. Because these “disap-pearing” firms may include a disproportionatenumber of those firms most adversely affected bythe policy, it is particularly important to “correct”for this effect.

11 This goal is a reasonable one, but the underlyingworry that the earlier models are “not maximizing mod-els” is misplaced. It is easy to interpret the Simon modelas a maximizing model by simply regarding each marketopportunity as being “independent.” It consists, say, ofthe opportunity to open up a new production plant onan isolated island, whose population is sufficient to sup-port only one plant. A maximizing model will decree thatone firm enters, and will be silent on the selectionmechanism that chooses the lucky firm from amongpotential entrants. What is striking about the “stochasticgrowth models” is not their lack of “optimizing agents,”but their reliance on Gibrat’s Law. If we recast thesemodels as simple maximizing models within a marketconsisting of independent opportunities, then thereseems to be no reason to posit this particular relationshipbetween firm size and growth.


note a proportional growth rate, and let xdenote a vector of characteristics de-scribing a firm or plant (size, age, etc.).Let j(g′|x) denote the probability densityfunction for g′ for a firm or plant with agiven set of characteristics (“the distri-bution of potential growth rates”).

The density j(g′|x) is not observable,for some firms will exit, and these willnot be a random cross-section of firms.What can be measured directly is thedensity of growth rates conditional onsurvival, labeled h(g|x) where g denotesthe actual proportional growth rate, andthe density of measured growth rates, la-beled f(g|x), in which all exiting firms areassigned the growth rate −1.12

In the studies of Hall, and of Evans,the technique used is to apply a standardsample selection model (for example,Takeshi Amemiya 1984), in which agrowth equation and a (profit) survivalequation are estimated jointly usingmaximum likelihood. This allows theconditional mean of the distribution ofpotential growth rates j(g′|x) to be esti-mated. The effect of x (size and age) onthe means of f(g|x) and h(g|x) can thenbe examined. In both studies, it wasfound that the tendency for proportionalgrowth rates to decrease with firm sizesurvives these corrections for sample se-lection effects.

The approach taken by Dunne,Roberts, and Samuelson is different.Taking advantage of the huge size of theCensus data set, the authors groupedplants into cells corresponding to succes-sive intervals of size, and of age. Consis-tent estimates of the parameters of thedistribution of growth rates for all plantsf(g|x), and the distribution for nonfailing

plants h(g|x) could be obtained, subjectto the assumption that the plants withineach cell are homogeneous up to a ran-dom disturbance with zero mean andconstant variance (which might be “cell-dependent”). This technique does not al-low identification of the parameters ofj(g′|x); on the other hand, it avoids theneed for any distributional assumptions,or for assumptions on the functionalform of the growth/size/age relation. Italso avoids the difficulties faced in otherstudies of separating out sample selec-tion effects from heteroscedasticity andfrom any nonlinear effects of explanatoryvariables.

The studies of Evans and of Dunne,Roberts, and Samuelson both permit aninvestigation of age as well as size ef-fects. Both studies suggest two statisticalregularities:

1. Size and Growth: (a) the probabil-ity of survival increases with firm (orplant) size. (b) the proportional rate ofgrowth of a firm (or plant) conditional onsurvival is decreasing in size.

2. The Life Cycle: For any given sizeof firm (or plant), the proportional rateof growth is smaller according as thefirm (or plant) is older, but its probabil-ity of survival is greater.

What these results indicate is thatthere are two effects at work in the size-growth relationship: larger firms (plants)have lower growth rates, but are morelikely to survive. The combined effect ofboth these tendencies can be summa-rized by taking a cohort of firms in somesize interval, and comparing the totaloutput of these firms at the beginning ofthe sample period with the total outputof the surviving firms at the end. Thisprocedure is used to define the “net”growth rate for firms of a given sizeclass. The data presented by Dunne,Roberts, and Samuelson allowed a dis-tinction to be made between plantsowned by single-plant firms and those

12 The relation between h and f is particularlysimple in one model considered by Dunne,Roberts, and Samuelson. In this model, all firmswith a growth rate below some critical value g*exit. The density h(g/x) is f(g/x) except with zeroprobability attached to the growth rate −1.


owned by multi-plant firms. For singleplant firms, the reduction in plant fail-ure rates with size and age was in-adequate to offset the tendency forlarger and older surviving plants togrow more slowly: the net growth ratefalls with plant size and age. The oppo-site was true of plants owned bymultiplant firms. For this group, thenet growth rate of plants tended toincrease with size and age: the fall inplant failure rate with size and ageoutweighed the tendency for growthrates to fall with size and age amongsurviving plants.

These findings prompted new interestin theoretical models of firm growth. Anobvious candidate model was the re-cently published “learning” model ofJovanovic (1982). In the Jovanovicmodel, a sequence of firms enters themarket. Each firm has some level of“efficiency” (its unit cost of production),but it does not know what its relativeefficiency is prior to entering. Over time,the profits it achieves provide informa-tion on its relative efficiency. Moreefficient firms grow and survive. Lessefficient firms “learn” of their rela-tive inefficiency, and (some) choose toexit.

This model provides a qualitative de-scription of a process of excess entry fol-lowed by some exit, and this was theaspect of the model which made it at-tractive as a vehicle for discussing thenew empirical results. As to the size dis-tribution of firms, the model said little:it would depend inter alia on unob-servables, such as the initial distributionof “efficiency levels.” This theme wouldbe echoed throughout the next series oftheoretical models.

This new interest in age-growth rela-tions led in turn to a renewed interest inmodeling the life cycle of the industryitself, and the evolution of market struc-ture over time.13 An important impetus

to the discussion came with the publica-tion of the first of a series of papers bySteven Klepper and his co-authors,based on data assembled from entries intrade journals, regarding the evolution offirm numbers over time for a wide rangeof narrowly defined product markets(Klepper and Elizabeth Graddy 1990;Klepper and Kenneth Simons 1993). Thefeature of the data which these authorsemphasize constitutes a third statisticalregularity which has been influential inshaping the recent literature:

3. Shakeout: It is frequently observedthat the number of producers tends firstto rise to a peak, and later falls to somelower level.

The extent and timing of this“shakeout” varies very widely acrossproduct markets. In some cases, it comesearly in the life of the product, and isvery sharp. An example of such a caseis shown in Figure 2, which is takenfrom Jovanovic and Glenn MacDonald(1994).

Two types of model have been postu-lated in response to this observation. Thefirst is due to Jovanovic and MacDonald,who begin by stating that Klepper’s dataon shakeout can not be accounted for byappealing to the “Learning” model ofJovanovic (1982). Instead, the authorspostulate a model in which early entrants

13 The life cycle of the industry had been a focusof interest since the 1960s, see for example, Ray-mond Vernon (1966). As the focus of interest inthe literature has shifted back to industry “life cy-cle” effects, less attention has been paid to firmage/survival effects. These effects, however, re-ceive considerable attention in the literature onthe sociology of organizations. Glenn Carroll(1983) for example, lists 32 studies on groups oforganizations of various kinds. Many of these stud-ies investigate the firm-specific factors associatedwith individual failures. A recurring theme is thatmany failures reflect a bad initial judgment ofmarket opportunities, managerial incompetence,or simply the fact that the entrant set up a busi-ness which had only modest prospects of survival,as an alternative to entering the labor market,where opportunities were poor.


employ a common technology which af-ter some time is superseded by a newtechnology. The new technology offerslow unit costs, but at a higher level ofoutput per firm (scale economies). Thetransition to the new technology involvesa shakeout of first generation firms, andthe survival of a smaller number of firmswho now employ the new large-scaletechnology. By calibrating the modelagainst the data for the U.S. tire indus-try, the authors can simulate successfullythe number of firms, and the movementof stock prices over time.

Another candidate model is developedin Klepper (1993). This model combinesa stochastic growth process for firms,who enter by developing some new vari-ant (“product innovation”), with the ideathat each firm may spend some fixedcosts to lower its unit cost of production(“process innovation”). Assuming someinertia in sales, and some imperfection incapital markets, those firms whose cur-rent sales are larger find it profitable todevote more fixed costs to process inno-

vation (because the fixed costs incurredare spread over a larger volume of sales).As the larger firms cut their unit pro-duction costs, some smaller firms are nolonger viable, and these exit, generat-ing the “shakeout.” This process is verysimilar to the “escalation” process thathas been studied in the recent game-theoretic literature; see Sutton (1991,chs. 3 and 8).

IV. The Size DistributionReconsidered: A Bounds Approach

The new generation of models de-scribed in the preceding section, and inSection V below, differ from the olderstochastic growth models in that the“random growth” process has been re-placed by one in which firms that differin various attributes make differentprofit maximizing choices. The modelsremain stochastic but the source of ran-domness has either been pushed back-ward, into a description of firms’ “intrin-sic efficiency differences,” or forwardinto random outcomes emanating fromR&D programs.

These recent developments, howeverdesirable in themselves, have shifted at-tention away from one feature of theolder stochastic models which may becrucial to a full understanding of marketstructure. This feature relates to the no-tion that the market consists of a se-quence of isolated “opportunities,” eachstrategically independent of the others.This appears to many readers, schooledin the importance of strategic interac-tions, as a rather odd and unattractivefeature of these models. Yet this featurecaptures, albeit in a crude and extremeway, one important aspect of real markets.

Any industry will contain clusters ofproducts or plants that compete closely.But an industry, as conventionally de-fined in official statistics, will usuallycontain more than one such cluster, in

1905 1915 1925 1935 1945 1955 1965 1975Year

300

250

200

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0Num

bers

of F

irm

s

Figure 2. Firm Numbers in the U.S. Tire Industry

Source: The figure is a modified version of Figure 1 of Jovanovic and MacDonald (1994), which is based on data collected by Michael Gort and Klepper (1982).


the sense that it will be possible to iden-tify pairs, or sets, of products that do notcompete directly. In other words, mostconventionally defined industries exhibitboth some strategic interdependencewithin submarkets, and some degree ofindependence across submarkets.

While a great deal of attention hasbeen devoted in recent years to theanalysis of strategic interactions, the roleof independence effects has received lit-tle attention. The question posed here isthis: is it possible that some minimal de-gree of skewness in the size distributioncould arise simply as a result of “inde-pendence effects” per se? In order to ad-dress this question, it is natural to beginby thinking about the extreme case inwhich there are no demand side (strate-gic) interactions at all. The obvious wayto do this abstract from strategic interac-tions is to think of a “market” which con-sists of many independent submarkets,each of which is large enough to accom-modate exactly one entrant.14 This bringsus to the setting of the Simon model.

It is worth noting that a conventionalgame-theoretic analysis of this situationis uninformative, in that it merely tells usthat there are many pure-strategy Nashequilibria. These will include one inwhich the same firm enters each submar-ket, another in which a different firm en-ters each submarket, and so on.

But if we introduce the notion thateach of a number of active firms hassome probability of being “selected” ineach submarket, then it may turn outthat certain kinds of outcomes, thoughpossible, are “unlikely.” Instead of im-posing Gibrat’s Law (which says that theprobability of capturing the next oppor-tunity increases proportionately with thefirm’s current size), suppose instead thatthe relation between firm size and the

probability of capturing the next oppor-tunity can take any form that satisfies thefollowing constraint:

Condition 1: The probability that thenext market opportunity is filled byany currently active firm is nonde-creasing in the size of that firm.

Consider two businesses of differentsizes. Condition 1 is violated if thesmaller business is more likely to take upthe next market opportunity than is thelarger one. This might happen, for exam-ple, if the incremental profit realizedfrom the new investment was smaller forthe larger firm. This supposed disadvan-tage to the larger firm could deriveeither from the cost side or through“strategic effects” on the demand side.Here, we abstract from demand sideconsiderations, and focus on the costside. A larger business may enjoy an ad-vantage through economies of scope inoffering several products, or in operatingmany plants. On the other hand, a tradi-tional argument suggests that it will notsuffer any cost disadvantage; for, if an in-tegrated business of larger size hadhigher unit costs, then it should be possi-ble to split the business into completelyindependent and separately managedunits under single ownership, so that anysuch disadvantage is eliminated. This isthe standard “replication” argument fornon-diminishing returns, and it is a veryappealing one. It suggests that Condition1 might be a reasonable hypothesis forthe artificial setting where firms face asequence of “independent opportuni-ties.” This in itself is of little empiricalinterest, however, because the generalrun of industries will be characterized bya combination of strategic interactionswithin certain submarkets, and some de-gree of independence across submarkets.To see why Condition 1 might be ofinterest, we need to inquire how thepresence of strategic interactions among

14 In other words, the firm’s profit function isadditively separable into a number of contribu-tions, one for each submarket.


firms might lead to a violation of thiscondition. The game-theoretic literaturehas afforded us a rich menu of examplesin which the larger firm suffers a disad-vantage in the sense that the profit perproduct (or plant, or unit capacity) is de-creasing in the number of products (orplants, or units of capacity) operated bythe firm. This effect has a simple intui-tive interpretation: if the multi-productor multi-plant firm expands output orcuts price in order to improve the profitof one of its plants, it generates a nega-tive externality for the other plants. Inmaximizing its total profit, the firm seeksto “internalize” this externality. Thisleads to higher prices and lower profitson each product or plant.

Nonetheless, empirical evidence onsize-profitability relationships acrossbusinesses of different sizes within an in-dustry suggests that the rate of return(profit) is nondecreasing in the size ofthe business. This suggests that firmsmay have some way of circumventingsuch strategic disadvantages where theyarise. This will be the case whenevermarket opportunities are dispersed eithergeographically or in some space of “prod-uct attributes.” If a firm that owned anumber of closely clustered plants wereto earn lower profit per plant, then thatfirm could simply expand by opening asequence of plants in dispersed loca-tions, thereby avoiding the strategic dis-advantage. In this case, Condition 1 maystill hold as an approximation, when thenumber of submarkets is large.

In Sutton (1995) the Simon model de-scribed in Section II is modified by re-placing Gibrat’s Law (assumption (i)) byCondition 1, while retaining Simon’s(“benchmark”) assumption (ii) whichposits a constant rate of entry as Condi-tion 2. It is claimed that this modifiedmodel provides a good empirical descrip-tion of the least unequal distribution thatwe are likely to find at the 4- or 5-digit

SIC level. This claim is advanced in anumber of steps, as follows:

(i) In the modified Simon model, thesize distribution tends to a limiting dis-tribution whose Lorenz curve is nocloser to the diagonal than a certainreference curve, which serves as a“benchmark case.” (In what follows,we describe how Condition 1 leads tothis result.)(ii) This result continues to hold goodin a more general model, in whichthere are many identical independentsubmarkets. No restriction is placedon the nature of strategic interactions,or outcomes, within each submarket.It is assumed, however, that there areno strategic links across submarkets.(It is allowed that economies of scopemay or may not exist across submar-kets. If such economies are present,large firms enjoy an advantage, andthis is consistent with Condition 1).(iii) It is claimed that this more gen-eral model can reasonably be appliedto the broad run of industries at the 4-and 5-digit SIC level.15 At this level ofaggregation, markets tend to containlarge numbers of more or less inde-pendent submarkets.(iv) It is noted that this relationshipmay break down if we define marketsso narrowly that all products andplants interact strategically. This al-lows the present interpretation to betested by looking at a large geographi-cal market for a physically homogene-ous product, that contains many localsubmarkets.The stochastic process describing firm

growth is as follows: we begin at time 1with a single firm of size 1. In each sub-

15 Strictly, to those industries in which neitheradvertising nor R&D are important. If advertisingor R&D are important, strategic interdependenceacross submarkets is certainly present. However,this strategic effect runs in favor of large firms, asopposed to small, so it does not lead to any viola-tion of Condition 1.


sequent period, a new unit opportunity istaken up. With probability p, it is takenby a new entrant. With probability 1 − p,it is taken up by one of the Nt firms thatare already active. It can be shown thatthe least skew limiting distribution con-sistent with Condition 1 is attained inthe special case where each of these Ntactive firms has an equal probability (1 −p)/Nt of capturing the opportunity.

Let Nt denote the total number offirms in the market at time t. The distri-bution of Nt is simply a binomial distri-bution with mean 1 + p(t − 1).

Let ni,t denote the number of firms ofsize i at time t, for i = 1, 2, 3 . . . Webegin by calculating the expected valueof nt, conditional on Nt. Our focus of in-terest lies in the behavior of E(ni,t|Nt)evaluated at Nt = 1 + p(t − 1), in the limitwhere t → ∞. It can be shown that:

Limt − ∞

E

ni,t

1 + p(t − 1) = p(1 − p)i−1

so that the size distribution takes theform of a geometric distribution. Forempirical purposes, it is useful to ap-proximate this by the corresponding ex-ponential distribution. Subject to this ap-proximation, it can be shown that thefraction of opportunities accounted forby the k largest firms satisfies

Ck ≥ kN

γk − ln

kN

.

(1)

Here Ck is the k-firm (asset) concen-tration ratio, N is the number of firms inthe industry, and γk is a constant. Fork = 1, γk is Euler’s constant (~−0.577),and γk increases with k and converges to1 as k → ∞. (A table of values of γk isgiven in Sutton 1995.)

We can illustrate this inequality bydrawing a Lorenz curve, i.e., a relationbetween the fraction of (top ranking)firms k/N represented in the k-firm con-centration ratio and their share of indus-

try assets, Ck. The theory says that thesepoints will lie above the reference curveobtained by expressing (1) as an equality.

Hence we obtain a quantitative predic-tion on a lower bound to concentration.16

This lower bound is independent of theentry rate (the proportion of opportuni-ties captured by new entrants). The rateof entry, as noted earlier, is assumed tobe constant over time, following Simon’ssecond (“benchmark”) assumption. It isshown that the result is fairly robust toempirically reasonable relaxations of thisassumption. It is unaffected by a numberof empirically reasonable changes in themodel, such as allowing opportunities tovary in size, and is invariant to differenttime patterns of industry growth. In par-ticular, it is invariant to a process ofshakeout which removes a random sub-set of plants or firms.

The model does, however, rest on theassumption that the industry grows overtime, possibly reaching some limitingsize. It might in principle be violated inan industry which declined over time;the above assumption on size-growth re-lations says nothing about this.

This lower bound appears to fit wellto data for various countries and timeperiods. An example is shown in Figure3, which shows observed values of the 5-firm concentration ratio for all U.K.product markets in 1977.17 Similarbounds for the U.S. and Germany are re-ported in Sutton (1995). The comparisonbetween these two cases is interesting, inthat the “clouds” of points for the two

16 The model does not provide any confidenceinterval around this bound. The model uses onlyan inequality constraint on the size-growth rela-tion, and no statistical structure is placed on thedistribution of the residuals (Ck − Ck) where Ck isdefined by writing (1) as an equality.

17 This is the lowest level of aggregation at which U.K.statistics are available, and corresponds to a level inter-mediate between the U.S. 4-digit and 5-digit levels.Statistics at this level have not been published for morerecent years. Only sales concentration ratios, rather thanasset concentration ratios, are reported.


countries are very different, reflecting thefact that concentration in the U.S. tendsto be higher, for a given number of firms.In spite of the wide divergence in averageexperience, however, the lower bound toboth “clouds” remains close to the refer-ence curve given by the inequality (1).

This remark provides some motivationfor the view that, in spite of the apparentimportance of “unobservables” in drivingwide differences in “average” outcomes,there may be a bound to outcomes whichis relatively sharp. What makes such abound interesting is the fact that muchof the skewness we observe in “typical”industries may be a reflection of the op-eration of independence effects per se,with greater skewness in some industriesemanating in part from additional mech-anisms such as the operation of scopeeconomies across otherwise independentsubmarkets. If this is so, then the searchfor some “average” or “typical” shape tothe size distribution may not be wise.

This conclusion is very much in line withthe growing pessimism among boththeoretical and empirical researchers asto the reasonableness of postulatingsome “typical” form for the size distri-bution.

V. Turbulence

The characterization offered by thetime series models described above hasbeen one of convergence towards somesteady state of the industry, in whichconcentration levels and firm numberswill eventually become static. Empiricalevidence on entry and exit patterns, how-ever, emphasizes that continuing entryand exit occur over the entire life of theindustry. Much empirical work on entryand exit patterns has suggested a fourthstatistical regularity that some authorssee as particularly noteworthy:

4. Turbulence: Across different indus-tries, there is a positive correlation be-tween gross entry rates, and gross exitrates, i.e., the “churning” of the popula-tion of firms is greater in some industriesthan others. However, most of this entryand exit has relatively little effect on thelargest firms in the industry.18

Within any one country, quite a strongcorrelation usually exists between entryand exit rates by industry. Paul Geroski(1991), for example, reports a correlationcoefficient of 0.796 for a sample of 95industries in the U.K. in 1987. The mostcomprehensive data on this issue comesfrom a compilation of country studies ed-ited by Geroski and Joachim Schwalbach(1991). The cross-country comparisonsafforded by this study indicate that thereis at least a weak correspondence be-tween the ranking of industries by turbu-

100

80

60

40

20

00.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

5/N

C/5

(Sal

es)

Figure 3. Five-firm Sales Concentration Ratios for U.K. Product Markets, 1977The limiting Lorenz curve (1) for γk = γ5 = 0.90 is shown as the solid curve. Each point corresponds to a different industry, the horizontal coordinate being 5/N where N is the number of firms, and the vertical coordinate shows the 5-firm sales concentration ratio.

18 The volatility of market shares among largefirms has been less widely studied. An importantearly study was that of Richard Caves and M. E.Porter (1977), which used the PIMS data-set. Seealso the recent study by Steven Davies et al.(1991). See also Davis and Haltiwanger (1992).


lence in different countries. This is im-portant, in that it suggests that there maybe some systematic, industry-specific,determinants of turbulence levels.19

These results have prompted interestin the determinants of turbulence (de-fined as the sum of gross entry and grossexit rates) across different industries. Atleast three types of influence are likelyto be involved,

(a) underlying fluctuations in the pat-tern of demand across product varie-ties or plant locations;(b) the displacement of existing tech-nologies (modes of production) by al-ternatives; and(c) the displacement of existing prod-ucts by new and superior substitutes.Of these, the first factor may be of pri-

mary importance, but while it is easy tomodel, it is very difficult to measure it orto control for its influence empirically.The second and third factors pose moreinteresting questions in terms of model-ing. Some new models have been devel-oped recently, but these have not yet ledto empirically tested claims regardingthe influence of industry characteristicson the degree of turbulence.

The second factor (displacement ofproduction technologies) has been mod-eled by Lambson (1991), who considersan industry facing exogenous shocks torelative factor prices, which occur at in-frequent intervals. Firms incur sunkcosts in building a plant using a giventechnology, and when factor priceschange, an entrant—knowing that factorprices shift rarely—may find it profitableto enter the industry and displace incum-bents. In this kind of model, the level ofsunk costs incurred by firms will influ-ence entry and exit rates, conditional onthe volatility of industry demand.

The third factor listed above relates tothe idea that (some) exit may be inducedby entry, as new and superior productvarieties displace existing products. Thisis the basic idea discussed in the verticalproduct differentiation literature. Thekey theoretical question is why the oldvarieties cannot continue to retain apositive market share at some price,given that their costs of product develop-ment are sunk. Such varieties would in-deed continue to survive in a “horizon-tal” product differentiation model, butthis is not necessarily true in a “verti-cal” product differentiation model (JeanJaskold-Gabszewicz and Jacques Thisse1980; Avner Shaked and Sutton 1983).

This contribution to turbulence hasbeen explored most fully by RichardEricson and Ariel Pakes (1995). In theEricson-Pakes model, equilibrium ischaracterized as the stationary state of astochastic process, in which the fortunesof individual firms rise and fall overtime. Each firm’s current state is in-dexed by a number which can be thoughtof as the relative quality of the product itoffers. The vector of qualities maps intoa vector of profits earned in the currentperiod. Between one period and thenext, each firm’s quality will either staythe same, or rise by one unit. The firmchooses a level of R&D spending in each

19 A major focus of interest in this literature hasbeen on the way in which fluctuations in industryprofits induce changes in the rate of entry andexit. Various authors have estimated net entryequations, following Dale Orr (1974), but the ex-planatory power of such regressions has been poor(see the review of results set out in Geroski’s 1991monograph, and the comments of Roger Clarke1993). A new attack on this problem has beenemerging recently, following the work of AvinashDixit and Robert Pindyck (1994) on investmentunder uncertainty. Here, the focus is on analysingthe different thresholds associated with entry deci-sions, which involve sunk costs, and decisions toexit (see the review by Glenn Hubbard 1994 andthe comments in Eugene Lambson 1991 below).Another strand in this literature looks at the dif-ferent experience of different types of entrant,distinguishing between de novo entrants and entryinto new markets by diversifying firms. The lattertype of entrant tends to have a larger initial size,grow more rapidly, and have a lower rate of exit(see Geroski 1991, pp. 31ff. for an overview ofstudies on this question).


period, and the more it spends, thehigher is the probability that its quality“jumps.”

The model also assumes an upwarddrift in factor prices, or in the quality ofsome rival good, so that “standing still”in terms of market share and profits re-quires that the firm achieve a steady rateof quality improvement over time. Theauthors characterize a (Markov perfectNash) equilibrium in this setting inwhich each firm, taking as given the cur-rent distribution of qualities and marketparameters (factor prices), decides on anoptimal level of R&D spending. The re-sult is a steady state distribution of thevector of relative qualities. In this steadystate, firms’ optimal actions will reflecttheir relative position in the quality spec-trum. Firms with intermediate qualitylevels will spend on R&D in each period.Those with high levels may stop spend-ing (“coasting”). Those with low levelsmay exit the industry. The distribution ofrelative qualities at any time is itself sto-chastic; and just as certain configurationsmay be reached at which some firms exit(their market share drops to zero), so toothere will be configurations at which newentry occurs.

The strength of the Ericson-Pakesmodel lies in the fact that it offers ananalysis of turbulence as a steady statephenomenon within a game-theoreticsetting. The authors’ aim of setting up asgeneral a framework as possible carriesthe cost that few restrictions can beplaced on the pattern of equilibrium out-comes. The authors have, however, de-veloped a simulation package for generaluse, and this is already proving a usefulresearch tool (Pakes and Paul McGuire1994; Pakes, Gautam Gowrisankaran,and McGuire 1993).20

These models developed by Pakes andhis co-authors raise an interesting ques-tion as to the link between turbulence(entry and exit rates) and market sharevolatility among leading firms. In the sto-chastic growth models discussed earlier,the setting is one in which the size of themarket grows, at least up to some limit-ing size, and the size distribution offirms converges to some limiting distri-bution. The entry and growth of newfirms leads to market share volatility, inthe sense that new firms might displaceold ones as market leaders within thatdistribution. However, the probabilitythat the market leader at any point is arelatively recent entrant is small. Thesefeatures seem to accord well with theempirical observations on entry and tur-bulence noted earlier.

In the Ericson-Pakes model, on theother hand, the focus in the numericalsimulations reported to date has been ona small number of firms (fewer thanten), operating in a steady state environ-ment where the degree of turbulence ismagnified by way of stochastic returns toR&D outlays. Here, if numbers aresmall, the whole size distribution mayswing widely over time. While thereseems to be little evidence for wideswings at the 4- or 5-digit SIC level, itwould be interesting to examine whethersuch swings are common in more nar-rowly defined markets where firm num-bers are small.

VI. Decline and Exit

The literature discussed so far hasbeen concerned with the growth of anindustry to some steady state; in this sec-tion we turn to the final phase of indus-

20 One obvious question relates to industry-specific factors influencing turbulence. The Pakes-Ericson model deals with the particular setting ofan R&D-intensive industry where market share

fluctuations are driven by the stochastic returns toR&D. It may be that broadening the scope of themodel, by exploring different environments, maylead to testable predictions on the industry-specific determinants of turbulence.


trial decline. Is the process of industrialdecline associated with any systematicchanges in market structure? As the in-dustry declines, firm numbers tend tofall and reported concentration ratiosshow a weak tendency to rise. The lattertendency is in part, at least, a simpleconsequence of exit. A question that hasattracted some interest lately relates tothe way in which the size distribution ofsurviving firms evolves: is there, for ex-ample, a tendency for the largest firms inthe industry to converge in size, i.e., dothe bigger firms shrink proportionallyfaster, so that the firm size distributionbecomes “less skew”?

Though this question has attractedsome interest, there is little systematicevidence at the cross-industry level. Oneway of checking this is to look at the ra-tio of, say, the 4-firm sales concentrationratio with the 8- or 20-firm concentrationratio. Figure 4 shows some scatter dia-grams of the ratio of C4 to C8 at twowidely separated dates for the set of 4-digit U.S. manufacturing industries thathave experienced a large (> 40%) fall in

firm numbers. The scatter shown in thefigure does not suggest any tendency forthe sizes of the top four firms and sizes ofthe next four firms to converge as the in-dustry declines. (A similar pattern holdswhen we look at the ratio of C4 to C20.)

At the theoretical level, there does notseem to be any general argument thatsuggests either a convergence or a diver-gence in the sizes of the largest firms. Arich variety of potential influences areavailable, and reasonable models can beconstructed which lead to either out-come. Under these circumstances, it isnatural to turn to a narrower domain,and to ask whether there are any types ofindustry for which some prediction ispossible.

Pankaj Ghemawat and Barry Nalebuff(1990) consider a homogeneous goodsindustry with a particular kind of coststructure: unit costs are constant up tofull capacity, and fixed costs are propor-tionate to plant capacity (as opposed tocurrent output). Capacity can be re-duced irreversibly in a continuous man-ner over time. The authors analyze agame in which firms reduce capacity asdemand declines. They show that, alongthe equilibrium path of the game, thelargest firm sheds capacity until it isequal in size to its nearest rival; thenboth these shrink together until they hitthe size of the next largest, and soon.21,22 The authors present some strik-

1

0.8

0.6

0.4

0.2

00 0.2 0.4 0.6 0.8

C4 / C8 (67)

C4

/ C

8 (8

7)

Figure 4. The ratio of the 4-firm sales concentration ratio to the 8-firm sales concentration ratio in 1987 (vertical axis) and 1967 (horizontal axis), for all 4-digit U.S. Manufacturing industries that experienced a fall in firm numbers exceeding 40 percent. If the sizes of the top four firms and the sizes of the next four firms converge over time, the scatter of points will lie below the diagonal.

21 The intuition for this result is as follows: pricein each period is determined by equating supply(total output Q) with demand; and the market de-mand schedule Pt(Q) is falling over time. Eachfirm i produces to full capacity in each period, andits marginal revenue equals Qi Pt′ (Q) + Pt(Q),where its output Qi equals its current capacity.This expression is decreasing in Qi. Therefore, it isthe larger firm that has the greater incentive towithdraw a unit of capacity as market demand de-clines.

22 John Londregan (1990) showed that the “size ef-fect” also held in a model where re-entry was possible,and Stanley Reynolds (1988) showed that it held good inthe presence of cost differences, so long as these werenot too large. On the other hand, if the model of Ghe-


ing evidence on the pattern of plant clo-sures in the U.S. soda-ash industry, anindustry for which these assumptions onproduct homogeneity and cost conditionsare reasonable. The observed pattern ofplant closure conforms closely to theprediction that large firms close plantsfirst. A number of later studies havelooked at industries for which the as-sumptions of the Ghemawat-Nalebuffmodel are reasonable. Marvin Lieber-man (1990) looked at a large sample ofproduct markets in the chemicals sector.Controlling for plant size, Liebermanfound that large multiplant firms tendedto close individual plants ahead of theirsmaller rivals. For plants in the U.S.steel industry, however, Mary Deily(1991) found that the primary determi-nants of plant closure seem to have beena set of factors underlying plant profit-ability. Firms first disinvested in theleast profitable plants, and then closedthem. Controlling for plant and firmcharacteristics, the influence of size ran(weakly) in the opposite direction to thatpredicted by the theory. An earlier studyby Deily (1985), however, looks in detailat the pattern of disinvestment and plantclosure by the largest firms in this indus-try, and this suggests a less clear pattern(Deily 1991, p. 262).

Moving beyond the special setting towhich the Ghemawat-Nalebuff modelapplies, a number of recent studies havefocused attention on the fact that the

menu of relevant factors may run far be-yond those normally included in the sim-ple game-theoretic models. In looking atthe U.K. steel casings industry, CharlesBaden-Fuller (1989) found that many ofthe closing plants were not the leastprofitable ones. Rather, firms that werediversified and financially strong weremore likely to close plants. The author’sanalysis of managers’ views suggestedthat, in these firms, there were fewer in-ternal conflicts between owners, debtholders, and managers.23

A similar theme emerges in the workof Martha Schary (1991) who appealsto a richer discussion of the determi-nants of exit, distinguishing betweenthree routes by which firms “disap-peared” (bankruptcy, voluntary liqui-dation, or merger). Schary’s paper exam-ines the process of exit in the U.S. cottontextile industry, using a model in whichfirms make a series of decisions, con-sidering each exit route in turn, in a pre-determined order. She finds that it ispossible to reject a simple “thresholdprofitability” model against this morecomplex schema. While it is probablyfair to say that the specific results ob-tained may be sensitive to the main-tained assumptions on the decision-mak-ing sequence, this study nonethelesssuggests that a richer type of model maybe called for in this area.

VII. Summary and Conclusions

The development of the literatureover the past decade has been heavily in-fluenced by a concern with a small num-ber of statistical regularities (labeled 1–4above). The aim has not, however, beento achieve some level of descriptive real-ism by finding a model consistent with

mawat and Nalebuff is modified by disallowing continu-ous shrinkage so that multiplant firms of varying size taketurns in making discrete choices on the closure of (indi-visible) plants, Michael Whinston (1988) shows that thetendency for large firms to close down plants first is lesssharp, in that multiple equilibria now appear in themodel, and it can happen along the equilibrium path thata smaller firm closes a plant ahead of a larger rival.Finally, Ingemar Dierickx, Carmen Matutes, andDamien Neven (1991) show that if decline is driven, notby a shrinkage in the consumer base, but by a diminutionin consumers’ willingness-to-pay, then the “size” predic-tion may no longer hold.

23 It was pointed out by Jeremy Bulow and JohnShoven (1978) that consideration of such decisionmaking processes “within” the firm, (especially be-tween equity and debt holders) might be crucial tounderstanding decisions on bankruptcy.


this or any other set of statistical regu-larities. Rather, the role played by theseregularities has been to stimulate inter-est in the possibility that there may besome systematic economic mechanismsat work. The emphasis in modeling hasbeen on trying to capture features thatare relevant to the working of some pos-tulated mechanism, and to see whetherthe model can lead to further predictionsor explanations.

One theme suggested above is that aproper understanding of the evolution ofstructure may require an analysis notonly of such economic mechanisms, butalso of the role played by purely statisti-cal (independence) effects, and that acomplete theory will need to find an ap-propriate way of combining these twostrands. This can be done in two ways.The current trend is towards buildingstrategic interactions into models of thegrowth of firms. Along this route thesame indeterminacy problem is encoun-tered which is familiar throughout thegame theory literature. An alternativeway forward is to begin by tackling theindeterminacy problem by turning to aBounds approach, as outlined in SectionIV above, with a view to isolating therole played by independence effects perse. This approach may prove easier to in-tegrate within a more general game-theoretic analysis which encompassessstrategic interactions.

The evolution of market structure is acomplex phenomenon and the quest forany single model that encompasses allthe statistical regularities observed isprobably not an appropriate goal. Yetthere remain phenomena which may wellbe worth encompassing in a more gen-eral theory than is currently available,and which are still poorly understood.Most notable among these are questionsof the industry-specific determinants offirm turnover (turbulence) and the vola-tility of market shares. Another such area

is that of the pattern of exit in decliningindustries. Nothwithstanding recent pro-gress on these topics, many importantquestions still remain open.

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